GUNASEKARAN S. y MEHMET M. [2003] CHEESE RHEOLOGY AND TEXTURE.pdf

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Cheese Rheolog yand Texture

Sundaram GunasekaranM. Mehmet Ak

© 2003 by CRC Press LLC

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Dedication

To:

My parents, Raga Palanisamy Sundaram and Kamala Sundaram, for inspiring me to always strive for excellence.

My wife, Sujatha, and children, Suvai and Suman,for their love, support, and patience.

— SG

My father, Haci Ak, and mother, Zeynep Ak,for giving me the opportunities they never had.

My wife, Nese, who continuously supported my efforts and patiently endured the time I spent working on this book.My daughter, Asli, and my son, Efe, who cheered me up

in times the situation looked hopeless.

— MMA


ForewordTwo complex scientific areas, cheese and rheology, create an exponential increasein complexity when combined. This text makes a significant contribution to anunderstanding of this complexity. It underscores limitations and considerations inevaluating and conducting research on cheese rheology, points out some importantgaps in our understanding of cheese rheology, and thoroughly reviews methods,theories, and applications of rheology in general and specifically for cheese.Rheologists will gain a better understanding of the physicochemical properties ofcheese, and cheese researchers will be exposed to the wide range of rheologicalmethods and the theoretical bases of those methods. Both groups should realizethe need for collaborative research after exposure to the individual complexities ofcheese and rheology.

The diversity of observations, and seemingly contradictory observations, on thephysical and chemical properties of cheese that appear in this text should not besurprising since many of the observations were made before instruments wereimproved and were specifically adapted to deal with unique properties of cheeses.Also, confusion resulted from: cheese scientists who used techniques inadequateto definitively measure physical properties of cheese; rheologists who chose testsamples of cheese that did not possess comparable chemical properties except forthe property to be measured; and inadequately defining the chemical properties ofcheese. The authors have discussed unique characteristics of cheese that rheologistsshould be cognizant of in designing experiments. Comments on merits and deficien-cies of wide range of rheological test methods as applied to cheese should assistcheese scientists in appropriately using the procedures. The chronology of cheeserheology research outlined in this book is encouraging as evidenced by the increasein collaborative research groups or research groups with better understanding ofboth research areas.

The physicochemical properties of cheese have always been an important com-ponent in assessing cheese quality and value. The assessment was usually done bysensory evaluation, which was quite adequate because cheese was generally con-sumed in its “original” state. Development of heat-processed cheese products in theearly 1900s prompted some research on the physical properties of cheese, primarilyby modifying chemical properties, however, only limited research was done onrheological properties. The last several decades have greatly changed the forms anduses of cheese in the market place. Cheese has to be sliced or shredded by high-speed cutting devices; the melt and flow properties of cheeses have to be morecarefully controlled; flavor intensities and flavor profiles have to be modified withoutadversely affecting physical properties of cheese; and cheese products must possessadequate stability, often under wide ranges of environments. This myriad of desiredproperties greatly increases the need for procedures to independently control specificproperties and the need for adequate methods to measure the properties specifically


being controlled. The authors of this book have facilitated attainment of these goalsby their thorough review of the present status of cheese rheology research and byproviding guidance for further research efforts.

Norman F. OlsonDepartment of Food Science and Center for Dairy Research

University of Wisconsin-Madison


PrefaceRheology of cheese has been studied since the early 1950s. In fact, “Cheese Rheology”is the name of a chapter in the 1958 FAO Report*. Since then, many advances havetaken place both in cheese technology and rheology. As cheese became an importantpart of the diet in many parts of world, the cheese industry responded by manufac-turing new types of cheeses with varying textures to suit varied needs and to promotecheese use both as a table cheese and as an ingredient food. This flurry of newcheeses and applications and cheesemaking technologies has also brought about anacute need to characterize the rheological and textural attributes of cheeses to ensuretheir high quality. Thus, for food rheologists and food scientists, cheese is amongthe most popular subjects of study.

In this book, we have attempted to summarize the vast literature available oncheese rheology and texture. Needless to say, the sheer volume of informationavailable and the complexity of both cheese and rheology made this a particularlydifficult task. Our goal was to bring together many of the dispersed publishedinformation on cheese rheology and texture in one book to serve as a comprehensivereference source. A unique aspect of this book is that it contains detailed descriptionsof several methods to study rheology of foods in general and cheese in particular.This is to provide the interested readers the necessary basic information on manytechniques reported in the literature which often do not have adequate explanation.

Chapter 1 provides an overview of cheesemaking technology. Fundamentalrheological test methods are described in much detail in Chapter 2. This chapterwill facilitate the readers to gain a deeper understanding of the various rheologicaltest methods. The uniaxial testing, one of the most widely used classes of rheologicaland texture testing methods, is the focus of Chapter 3. The fracture mechanics arean extension of the uniaxial test methods. These are discussed in Chapter 4. InChapter 5, linear viscoelastic methods are described. This is now among the mostpopular rheological test performed on cheeses, and is also known as dynamic testing.Both the theory and applications are discussed in a manner benefiting those whoare already familiar and those who are new to the subject. Chapter 6 focuses onnonlinear viscoelasticity of cheeses. This subject has not received much attentiondue to the lack of available instrumentation and the complexity of data analysis.This chapter will be more useful to those familiar with rheological analysis than tothe casual reader. The discussion on cheese texture in Chapter 7 is limited tomechanical texture of cheese, as it is more in line with rheological measurements.Cheese meltability and stretchability, two of the most important properties of cheeseused in prepared foods, are the topics of Chapters 8 and 9. The emphasis in thesechapters is on measurement methods. The effects of various factors on cheesefunctional properties are addressed in Chapter 10.

* Kosikowski, F.V. and G. Mocquot. 1958. Advances in Cheese Technology, FAO Studies No. 38. Foodand Agriculture Organization of the United Nations. Rome, Italy.


Acknowledgments

We would like to acknowledge many individuals who have contributed directly orindirectly toward making this book a reality. First and foremost, we would like toexpress gratitude to Professor Norman F. Olson, who was instrumental in helpingus to initiate our first project on cheese rheology in 1989, when S.G. was a newassistant professor and M.M.A. was a graduate research assistant. Since then, withhis expert knowledge and friendly personality, Professor Olson has been a sourceof great support. Thanks are also due to Dr. Mark Johnson, Dr. Rusty Bishop, JohnJaeggi, and other past and current staff at the Wisconsin Center for Dairy Research.These people are invaluable resources for cheese research. This book draws frommuch of the research performed in S.G.’s laboratory. As such, the efforts of manygraduate students and post-doctoral research associates are deeply appreciated. Theyinclude: Chyung Ay, James Colby, Kexiang Ding, Chang Hwang, Sun Young Kim,Sanghoon Ko, Gul Konuklar, Meng-I Kuo, Laura Marschoun, Kasiviswanathan Muth-ukumarappan, Hongxu Ni, Ramesh Subramanian, Salman Tariq, Deepa Venkatesan,Ya-Chun Wang, and Chenxu Yu. Thanks are also due to S.G.’s colleagues, ProfessorsA. Jeffrey Giacomin and Daniel Klingenberg at the Rheology Research Center,University of Wisconsin-Madison, and Professor Karsten B. Qvist of KVL, Den-mark. Thanks to Hallie Kirschner for typing parts of the manuscript. The financialsupport of Wisconsin Milk Marketing Board and Dairy Management Inc. for manyof S.G.’s projects is also deeply appreciated.

M.M.A. wishes to thank each member of his family for their full support andpatience during the writing of this book. He expresses appreciation to the following:Suat Yasa and Murat Yasa of Aromsa Limited Company, for their interest in the book;friends Elsie and Warren Sveum, Sarah and Alvaro Quinones, Mar Garcimartin-Akgul, and Arzu and Yann LeBellour for their constant encouragement; and formerstudents Filiz Lokumcu and Metin Yavuz for their valuable assistance in gatheringsome of the publications.

Sundaram GunasekaranM. Mehmet Ak


Table of Contents

Chapter 1 Cheesemaking — An Overview

Cheese TypesCheesemaking

Milk PretreatmentCoagulationSyneresisShaping and SaltingRipeningProcess Cheese

References

Chapter 2 Fundamental Rheological Methods

Definition of RheologyBasic Concepts

StrainStressStrain Rate

Fundamental MethodsUniaxial CompressionUniaxial TensionBending Test

Specimen with a Rectangular Cross-SectionSpecimen with a Circular Cross-Section

Torsion TestVane MethodStress-Relaxation Test

Analysis of Relaxation BehaviorCreep Test

Analysis of Creep BehaviorShear Rheometry

Sliding-Plates GeometryConcentric-Cylinders GeometryCone-and-Plate GeometryParallel-Plate GeometryCapillary Rheometry

Extensional RheometryLubricated Squeezing FlowEquations for Different Fluids in Lubricating Squeezing Flow

References


Chapter 3 Uniaxial Testing of Cheese

Uniaxial Compression MeasurementsStructure and Composition EffectsStress-Relaxation MeasurementsTorsion MeasurementsTension MeasurementsCreep MeasurementsBending MeasurementsVane MeasurementsShear MeasurementsLubricated Squeezing Flow MeasurementsReferences

Chapter 4 Fracture Properties of Cheese

Fracture MechanicsBrittle FractureGriffith CriterionDetermination of KI

Fracture Tests on CheeseNotch Tests

Cutting, Slicing, and ShreddingCutting with Wire and BladeEye/Slit Formation and GrowthReferences

Chapter 5 Linear Viscoelasticity of Cheese

Mathematical Relations in Linear ViscoelasticityTypes of SAOS Measurements

Strain (or Stress) SweepFrequency SweepTemperature SweepTime Sweep

Time–Temperature SuperpositionApplication of SAOS in Cheese Rheology

Linear Viscoelastic Region of CheesesCheddar CheeseGouda CheeseMozzarella CheeseMozzarella: Time–Temperature Superposition ExampleFeta CheeseImitation CheeseQuarg CheeseProcessed Cheese

Cox–Merz RuleReferences


Chapter 6 Nonlinear Viscoelasticity of Cheese

Pipkin DiagramSliding Plate RheometerLarge Amplitude Oscillatory Shear FlowSpectral AnalysisDiscrete Fourier TransformDetermining Material PropertiesAmplitude SpectrumStress–Shear Rate LoopsEffect of Wall SlipConstitutive Model for CheeseRelaxation Modulus Obtained from SAOSRelaxation Modulus Conforming to LAOSReferences

Chapter 7 Cheese Texture

Texture Development in CheeseCheese Manufacturing Factors that Affect TextureTextural Changes during Storage

Measurement of TextureTexture Profile AnalysisTPA Testing of Cheese

Uniaxial Tests for Cheese Texture MeasurementCompression TestWedge Fracture Test

Torsion Test and Vane RheometryTexture Map

Dynamic TestsEmpirical Tests

CrumblinessCone PenetrometerStringiness

References

Chapter 8 Measuring Cheese Melt and Flow Properties

MeltabilityEmpirical TestsObjective Tests

Steady Shear ViscometryCapillary RheometrySqueeze-Flow RheometryUW MeltmeterViscoelasticity Index for Cheese MeltabilityDynamic Shear RheometryHelical Viscometry


Cheese Melt Profile MeasurementUW Melt ProfilerDetermination of Melt Profile Parameters

Graphical MethodModeling Melt Profile

Constant Temperature TestTransient Temperature Test

Conduction HeatingReferences

Chapter 9 Measuring Cheese Stretchability

Empirical MethodsInstrumented MethodsVertical ElongationHorizontal ExtensionCompression TestsHelical ViscometryFiber-Spinning TechniqueThe Weissenberg EffectReferences

Chapter 10 Factors Affecting Functional Properties of Cheese

Properties of MilkCheesemaking Procedures

Addition of Starter Culture and CoagulantsCurd HandlingCooking, Stretching, and Cooling

Cheese CompositionMoisture ContentFat ContentSalt ContentpH

Post-Manufacturing ProcessesAging/RipeningFreezing and Frozen StorageHeat ProcessingOther Factors

References

Cheesemaking —An Overview

Cheese is one of the first and most popular manufactured food products. Whatperhaps started out as an accidental curdling of milk has been further refined intocheesemaking. Over several thousand years, cheesemaking has advanced from anart to near science. Cheese varieties have proliferated to suit varied conditions andrequirements, especially during the last decade or so. It is estimated that more than2000 varieties exist (Olson, 1995), and the list may still be growing. Cheese is nowan important part of foods consumed in many countries (Table 1.1). In a recentsurvey, after spices, cheese was named the top ingredient that makes cooks feel morecreative (Doeff, 1994). Several cheeses satisfy varied requirements in order to beused as suitable ingredients in various dishes from baby foods to baked products(Table 1.2). Battistotti et al. (1984) described the history of cheese and cheesemakingin much detail. This chapter provides a broad overview of cheesemaking. For furtherdetails, readers are referred to many recent books on the subject (Scott et al., 1998;Spreer, 1998; Law, 1999; Walstra et al., 1999; Fox et al., 2000).

CHEESE TYPES

Today’s wide array of cheeses may be classified according to the country of origin,manufacturing process, or some end-use property. Classifying cheeses based onmanufacturing and maturation processes by Olson (1979) produces a succinct list.A classification based on firmness and the maturation agent used produces a longerlist but may be more relevant if textural and rheological properties are important(Figure 1.1). A classification based on the distinctive manufacturing process involvedis also useful to understand the effect of the process on the cheese texture (Table 1.3).Other classifications of cheeses, e.g., according to milk source, overall appearance(color, size, shape), chemical analysis, etc., are also possible. Davis (1965) recog-nized the difficulty in classifying cheeses and attempted to group them based on thenature and extent of chemical breakdown during ripening or according to flavor.Such a classification is still not available. Fox (1993) proposed that the products ofproteolysis could be most useful for classification. One of the main difficulties whenusing classification schemes is that differences exist in the moisture range allowedwithin various categories published in the literature (Banks, 1998). Davis (1965)assigned some empirical texture/rheological parameter values to the terms from veryhard to soft (Table 1.4). The United States Code of Federal Regulations (CFR, 1998)stipulates certain standards of identity for cheeses classified according to theirconsistency, as listed in Table 1.5. The typical composition of milk and several cheesevarieties is given in Table 1.6. In the United States, the cheese market is dominated(almost equally) by Cheddar and Mozzarella cheeses. They comprise about two-thirds of the total cheese production over the past several years (Figure 1.2).

1


TABLE 1.1Consumption of Cheese in Selected Countries

Country

Consumption per Capita (kg)

1995 2000

a

North America

Canada

Mexico

United States

10.86

1.47

12.26

10.76

1.61

13.75South America

Argentina

Brazil

Venezuela

10.35

2.82

3.48

11.06

2.72

2.76Western Europe

Denmark

France

Germany

Ireland

Italy

Netherlands

Spain

Sweden

Switzerland

United Kingdom

16.84

21.51

11.90

5.54

18.66

14.68

5.46

16.14

14.28

8.75

16.22

22.49

12.50

6.70

20.38

14.97

6.25

16.12

14.31

9.88Central Europe

Poland 2.90 3.87Balkans

Romania 4.05 4.26Eastern Europe

Russia

Ukraine

2.03

1.26

1.41

0.79North Africa

Egypt 5.27 5.83Southern Asia

Japan

South Korea

1.46

0.27

1.77

0.70Oceania

Australia

New Zealand

8.25

8.17

11.10

8.48

a

Preliminary

Source:

After International Dairy Federation (www.dairyinfo.gc.ca/).


http://www.dairyinfo.gc.ca/

TABLE 1.2 Typical Requirements of Cheese as a Food Ingredient

Requirement Examples of Food ApplicationsExamples of Cheese or

Cheese-based Ingredient

Crumbles when rubbed Mixed saladsSoup

Feta, Cheshire, StiltonStilton

Sliceability Filled cheese rolls (finger foods)Sandwiches (filled, open, toasted)Cheese slices in burgersCheese slices on crackers

Swiss-type, Gouda, EdamSwiss-type, Cheddar, MozzarellaCheddarCheddar

Shreddability Consumer packs of sliced cheesePizza pie (frozen/fresh baked)Pasta dishes (lasagna, macaroni and cheese)

Swiss-type, Cheddar, MozzarellaMozzarella, Provolone, Cheddar, analog pizza cheese, Monterey

Cheddar, Romano, ProvoloneFlows freely when shaken Cheese sprinklings (on lasagna)

Snack coating (e.g., popcorn)Dry soup/sauce mixes

Grated Parmesan and RomanoCheese powdersCheese powders, enzyme-modified cheese

Flowability when blended with other raw materials

Fresh cheese desserts Quark, Fomage frias, Cream cheese

Ability to “cream” or to form a paste when sheared

CheesecakeTiramisuHomemade desserts

Cream cheese, RicottaMascarponeCream cheese

Nutritional value Baby foods Dried cheeses, esp. rennet-curd varieties (high in calcium)

Meltability upon grilling or baking

All cooked dishes (including sauces, fondues, pizza pie)

Mozzarella, Cheddar, Raclette,Swiss, Romano, analog pizza cheese, PCPs

a

Flowability upon grilling or baking

Most cooked dishes (e.g., pizza pie, cheese slices on burgers)

Chicken cordon-bleu

Mozzarella, Cheddar, Swiss, Romano, analog pizza cheese

PCPs, Cream cheeseFlow resistance upon deep-frying

Deep-fried breaded cheese sticksDeep-fried burgers with cheese inserts

Fried cheese dishes

PCPs, analog pizza cheese,custom-made

Mozzarella or string cheesePCPs, analog pizza cheesePaneer, acid-coagulated Queso Blanco

Stretchability when baked or grilled

Pizza pie Mozzarella, Kashkaval, young Cheddar, analog pizza cheese

Chewiness when baked or grilled

Pizza pie Halloumi, Mozzarella, Provolone,Kashkaval, young Cheddar

Limited oiling-off when baked or grilled

Pizza pie Mozzarella, Kashkaval

Limited browning when baked or grilled

Macaroni and cheeseLasagnaPizza pie

Cheddar, RomanoCheddar, Romano, ParmesanMozzarella, analog pizza cheese


CHEESEMAKING

Though there are numerous cheese varieties, the manufacturing processes of mostof them share several common steps. Variations at one or more steps during manu-facture produce cheeses of different textures and flavors. The essential steps incheesemaking and some variations for a few types of cheeses are schematicallyillustrated in Figure 1.3. These steps are as follows.

M

ILK

P

RETREATMENT

Milk used for cheesemaking is normally standardized and heat treated. In somecases, milk is homogenized. An acid-producing starter culture is then added.

The standardization of milk has become necessary to ensure that milk obtainedfrom several producers or dairies is of a “standard” composition and conditionthroughout the year. This is critical in cheesemaking because the legal standards ofvarious cheeses specify certain fat-to-protein ratios. The fat-to-protein ratio is deter-mined mainly by the fat-to-casein ratio in the milk (Fox et al., 2000) which can bemodified by removing fat or by adding cream or skim milk or skim milk powder,etc. It is also common to add color (annatto or carotene) and calcium (in the formof CaCl

2

) to the milk and to adjust milk pH to a desired level, known as preacidi-fication. Adding calcium speeds up coagulation or reduces the amount of rennetneeded and produces a firmer gel.

Heat treatment of milk is primarily intended to destroy the harmful microbialpopulation and enzymes in raw milk to assure product safety and quality. Pasteuri-zation is the most commonly used heat treatment (72°C with 15 s holding time). It

Viscosity SoupsSaucesCheesecake

Cheese powders, PCPsCheese powders, Cheddar, Blue cheese, PCPs

Cream cheeseFlavor Most cheese dishes, soups

Baked productsSnack coatingsDressingsBaby foodReady-made meals

Cheddar, Romano, Swiss-type, Parmesan

Cheese powders, enzyme-modified cheese

Cheese powdersCheese powdersDried cheeseCheese powders

a

Pasteurized process cheese products.

Source:

After Fox et al., 2000. With permission.

TABLE 1.2 (continued)Typical Requirements of Cheese as a Food Ingredient

Requirement Examples of Food ApplicationsExamples of Cheese or

Cheese-based Ingredient


not only destroys most of the bacteria present, including lactic-acid bacteria, butalso inactivates many enzymes. A gentle heat treatment, known as thermization(60 to 65°C with 15 to 30 s holding time) may also be used advantageously beforeor after pasteurization (Spreer, 1998). However, many cheeses are still producedfrom raw milk, especially in Europe (Fox et al., 2000). If the cheeses are made fromunpasteurized milk, they must be cured for at least 60 days at not less than 1.7°C(35°F), and the label should indicate the manufacturing date or state “held for morethan 60 days.” (NDC, 2000).

In traditional cheesemaking, the acid produced by microorganisms present inraw milk lowers the milk pH to a level sufficient for subsequent coagulation. How-ever, if the milk undergoes a heat treatment, selected cultures of lactic-acid bacteria

FIGURE 1.1

Natural cheeses classified according to the maturation agent used and firmness.(After Vedamuthu and Washam, 1983; Fox et al., 2000.)

TYPES OF NATURALCHEESES

Acid CoagulatedConcentrated(from Whey)

Surface Ripened

Enzyme Coagulated

Mould RipenedInternal Bacteria

Ripened

Internal Mould

Semi-softBlue

DanabluGorgonzolaRoquefort

HardStilton

Surface Mould

SoftBrie

CamembertCoulommiersCarre de l’Est

Very HardAsiagoGrana

ParmesanParmigiano

RomanoSabrinzSardo

SoftSalt-cured/

PickledDomiati

Feta

Semi-soft

CaerphillyMahon

Monterey Jack

Pasta filataMozzarellaProvolone

Caciocavallo

HardCaciocavallo

CheddarCheshire

ColbyGraviera

RasCheese with eyes

EdamEmmental (Swiss)

GoudaGruyere

MaasdamSamsoe

GjetostMyost

Primost

SoftCottageCreamQuark

Queso BlancoBaker’s

NeufchatelRicotta (Acid and heatcoagulated from whey)

Semi-softBrick

Bel PaeseHavarti

LimburgerMunster

OkaPort du Salut

St. PaulinTrappistTaleggioTilsiter

SoftLiderkranz


TABLE 1.3Classification of Cheeses by the Distinctive Manufacturing Process Involved

DistinctiveProcess Involved Characteristics Example Cheeses

Curd particles matted together Close texture, firm body CheddarCurd particles kept separate Slightly open texture Colby, Monterey JackBacteria-ripened throughout interior

Gas holes or eyes with eyeformation throughout cheese

Swiss (large eyes), Edam or Gouda (small eyes)

Prolonged curing period Granular texture; brittle body Parmesan, RomanoPasta filata Plastic curd; stringy texture Mozzarella, ProvoloneMold-ripened throughout interior

Visible veins of mold (blue-green or white); piquant, spicy flavor

Blue, Gorgonzola, Roquefort

Surface-ripened mainly by bacteria and yeasts

Surface growth; soft, smooth, waxy body; mild to robust flavor

Brick, Limburger

Surface-ripened mainly by mold Edible crust; soft, creamy interior; pungent flavor

Brie, Camembert

Curd coagulated mainly by acid Delicate soft curd Cottage, Cream, Neufchatel

Source:

After NDC, 2000. With permission.

TABLE 1.4Empirical Texture/Rheological Parameter Values Used in Cheese Classification

Cheese Type Moisture (%)

Logarithmic Scale Values

Viscosity Factor Elasticity Factor Springiness Factor

Very Hard < 25 > 9 > 6.3 > 2.3Hard 25–36 8–9 5.8–6.3 2–2.3Semihard 36–40 7.4–8 < 5.8 1.8–2Soft > 40 < 7.4 < 5.8 < 1.8

Source:

After Davis, 1965.

TABLE 1.5United States Federal Standards for the Maximum Moisture and Minimum Milk Fat for Classes of Cheese Designated by Consistency

ConsistencyMaximum moisture

content (%)Minimum milk fat

in solids (%)

Hard grating 34 32Hard 39 50Semisoft 50 (>39) 50Semisoft part skim 50 45 (<50)Soft Not specified 50

Source:

After CFR, 1998.


TABLE 1.6Typical Composition (% by Weight) of Milk and Some Cheese Varieties

Type and Cheese Moisture Protein TotalFat

TotalCarbohydrate

Fat in DryMatter Ash Calcium Phosphorus Salt pH

a

Milk

CowGoatSheepBuffalo

87.387.780.782.8

3.42.94.54.8

3.74.57.47.5

4.84.14.84.8

29.136.638.341.7

0.70.81.00.8

0.12———

————

0.900.951.100.85

6.7————

Acid Coagulated

Dry curd cottageCreamed cottageQuarkCreamNeufchatel

79.879.072.053.762.2

17.312.518.07.510.0

0.424.58.034.923.4

1.82.73.02.72.9

2.121.428.575.462.0

0.71.4—1.21.5

0.030.060.030.080.07

0.100.130.350.100.13

nil1.00—

0.730.75

5.05.04.54.64.6

Heat-Acid Coagulated

ChhanaQueso Blanca, acidRicotta from 3%-fat milkRicotone from whey and milk

53.055.072.282.5

17.019.711.211.3

25.020.412.70.5

2.03.03.01.5

53.244.845.72.9

————

————

————

—3.00<0.5<0.5

—5.45.95.8

Unripened-Rennet Coagulated

Queso Blanco-rennetQueso de FrierItalian fresh cheese

52.052.449.0

23.023.028.0

20.019.516.0

———

42.041.031.4

————

———

———

2.503.00nil

5.85.86.5


TABLE 1.6 (continued)Typical Composition (% by Weight) of Milk and Some Cheese Varieties

Type and Cheese Moisture Protein TotalFat

TotalCarbohydrate

Fat in DryMatter Ash Calcium Phosphorus Salt pH

a

Soft Ripened High Acid

CamembertFetaBlueGorgonzola

51.855.242.036.0

19.814.221.026.0

24.321.329.032.0

0.5—2.3—

50.347.550.050.0

3.75.25.15.0

0.390.490.53—

0.350.340.39—

2.10—

3.50—

6.94.46.5——

Semihard Washed

ColbyGoudaEdamFontinaHavarti-DanishMunster

40.041.541.442.843.541.8

25.025.025.024.224.723.4

31.027.427.825.526.530.0

2.02.21.4——1.1

51.746.947.644.646.951.6

3.43.94.23.32.83.7

0.680.700.73——

0.72

0.460.550.54——

0.47

0.650.820.961.202.201.80

5.35.85.75.65.96.2

Hard Cheese Low Temperature

CheddarManchego, SpainProvoloneMozzarella

36.737.940.954.1

24.928.125.619.4

33.126.926.621.6

1.3—2.12.2

52.445.245.147.1

3.93.64.72.6

0.72—

0.760.52

0.51—

0.500.37

1.801.502.201.00

5.55.85.45.3

Hard Cheese High Temperature

ParmesanRomanoSwissKaflatyri, Greece

29.230.937.234.2

35.731.828.424.8

25.826.927.428.3

3.23.63.4—

36.539.043.7—

6.06.73.54.7

1.181.060.96—

0.690.760.60—

3.003.001.20—

5.45.45.65.2

a

pH at time of retailing.

Source:

After Hill, 1995; Fox et al., 2000.


must be added. The type of bacteria added depends on the cheese type and cheese-making protocol used. These bacteria break down the milk sugar, lactose. Lacticacid produced during this process lowers the pH. An alternative to adding starterculture is to acidify the milk directly by adding lactic acid or hydrochloric acid orgluconic acid-

δ

-lactone, an acidogen. Though this direct acidification allows bettercontrol, starter culture remains active in the cheese during ripening, months aftercheese manufacture, and contributes to cheese flavor. Therefore, direct acidificationis used primarily when manufacturing cheese varieties for which texture is moreimportant than flavor, e.g., cottage cheese, quark, Mozzarella, etc. (Fox et al., 2000).

Walstra and Jenness (1984) reported an increase in cheese yield when usingpasteurized milk. This is due to casein–whey protein interaction and greater moistureretention. One disadvantage of pasteurization, however, is that aged cheeses developtheir flavors more slowly and to a lesser extent than cheeses made with raw milk(Kristoffersen, 1985). This has led many cheesemakers to use milk heated to 60 to68.5°C for 15 s or less instead of pasteurized milk (Johnson, 1998).

C

OAGULATION

Since pretreating milk is a fairly recent practice relative to the history of cheese-making, many consider coagulation as the first and most important step in cheese-making. Coagulation is the step during which milk undergoes a profound physicaland rheological change, that is gelation. Milk gel is formed by aggregation of milkprotein, the caseins. This can be accomplished by:

1. The action of a proteolytic enzyme2. Lowering the pH below the isoelectric point of protein (~ 4.6)3. Heating to about 90ºC at a pH of about 5.2 (i.e., higher than the isoelectric point)

FIGURE 1.2

United States total (excludes cottage cheese) and Cheddar and Mozzarellacheese production trends. (After Annual Summary of Dairy Market Statistics of years 1997through 2001. Agricultural Marketing Service, USDA. Mozzarella data from University ofWisconsin Dairy Marketing Web site: www.aae.wisc.edu/future.)


http://www.aae.wisc.edu/future/

Among these, enzymatic coagulation is the most popular. Acid coagulation viafood-grade acidulants is used to manufacture quark, cottage, and cream cheeses.Heat coagulation is used for Ricotta and Queso Blanco cheeses (Johnson and Law,1999; Fox et al., 2000).

Enzymatic coagulation is accomplished by enzymes from animal (e.g., calfrennet, porcine pepsin), plant (e.g., Cynara Cardunculus from Cardom, Circium and

FIGURE 1.3

Major steps in cheesemaking (actual steps and/or conditions for a particularcheese may vary). (After Scott et al., 1998; Fox et al., 2000.)

Pasta Filata Cheese(e.g., Mozzarella)

Pretreatment(Standardization, Homogenization, Heat treatment, Starter addition)

Coagulation(Rennet /Coagulant addition)

Syneresis(Cutting, Stirring, Scalding/cooking, Whey removal)

Milk

Hard Cheese(e.g., Cheddar)

Soft Cheese(e.g., Camembert)

Semi Hard Cheese(e.g., Gouda)

Moulding

Brining

Storage

Turning

Packing

Hot waterWashing

Pressing &Moulding

Brine Salting

Waxing &Wrapping

Cheddaring

Milling

Dry Salting

Ripening

Heating &Stretching

Moulding

Brine Salting


Carlina Spp. from thistle), or microbial (e.g.,

Endothia parasitica

,

Rhizomucor miehei

)origin. Enzymatic coagulation consists of two phases. During the first or primaryphase, the hydrophilic hairy structure, stabilized by steric hindrance, of

κ

-casein iscleaved off at Phe105-Met106 bond. The secondary or clotting phase is initiated as85 to 90% of the

κ

-casein is cleaved and results in the aggregation of the alteredprotein micelles. The

κ

-casein loses its ability to stabilize the remainder of thecaseinate complex. The result is soluble glycomacropeptides (residues 106–169),and hydrophobic, para-

κ

-casein (residues 1–105). As the protein micelles continueto aggregate, a loose network forms, entrapping fat globules, water, and water-solublematerials. The para-

κ

-casein left on the micelle is still connected to

α

- and

β

-casein,but it is highly hydrophobic and basic, leading to destabilization of the micelle.

Gel formation by association of the modified micelles in the secondary phaseis highly dependent on the milk’s temperature and calcium content. The coagulationrate is also highly dependent on the concentration and activity of the enzyme solution.Increases in both of these factors shorten coagulation time and increase firmness.Although it is not clear how the micelles aggregate, there are two hypotheses. Oneis that hydrophobic bonding occurs between the para-

κ

-casein. The other is thatcalcium and calcium phosphate bonding occurs in

α

- and

β

-caseins.Other factors that affect aggregation are casein concentration and milk pH. The

aggregation rate is proportional to the square of casein concentration (Lomholt and Qvist,1999). As discussed previously, the effect of renneting action strongly depends on milkpH. Each milk-clotting enzyme has an optimum pH at which it is most active. Extremesin acid or base also denature the enzymes but not as irreversibly as high temperatures.Lowering the pH leads to a decrease in coagulation time mainly due to increasedenzyme activity, but rate of aggregation is also affected (Lomholt and Qvist, 1999).

The aggregation of casein micelles forms strands of casein particles of aboutthree particles wide and 10 particles long, alternated by some thicker nodes ofparticles (Walstra et al., 1999). After this, the aggregates grow more compact (Baueret al., 1995). The time when aggregates become visible is known as the flocculationtime or rennet coagulation time (RCT). When the flocs grow to occupy the entirevolume, the gel is said to have been formed. The gel network is very irregular, withmany pores several micrometers in width (Walstra et al., 1999). Aggregation ofcasein micelles into chains, then into strands and clusters, and eventually into anamorphous mass has been observed by microscopic evaluation in both acid- andenzyme-coagulated systems (Kimber et al., 1974; Glaser et al., 1980).

From a rheological standpoint, casein aggregation and gel formation representan increase in viscosity and gel modulus, respectively. The viscosity increase inrenneted milk, however, is observed after an initial lag time (~ 60% RCT) duringwhich the viscosity may actually decrease slightly due to a decrease in voluminosityof the casein micelles following the release of macropeptides (Fox et al., 2000). Afterthis, the viscosity increases exponentially up to the onset of gelation (i.e., 100% RCT).The viscosity increase and the concomitant change in physical properties have beenused to identify the RCT (Kopelman and Cogan, 1976; Ay and Gunasekaran, 1994;Fox and McSweeney, 1998; Konuklar and Gunasekaran, 2002).

The modulus of the gel increases markedly at gelation time. In fact, gelationtime is defined as the time at which the gel modulus increases rapidly. The initial


increase in modulus is due to the increase in number of contacts between micelles.Subsequently, the strengthening of intermicellar bonds translates into increased gelmodulus (Walstra et al., 1999). It has been premised that the increase in gel firmnessis due to the increase in the number of bonds with time (Lomholt and Qvist, 1999).This premise was based on the observation that, though the modulus continues toincrease, the phase angle stays relatively constant, i.e., the nature of the bonds doesnot change (Dejmek, 1987; Lopez et al., 1998). Figure 1.4 shows a typical plotdepicting changes in viscoelastic moduli and the phase angle of the coagulating milkgel system. As more micelles aggregate, they may fuse together and strengthen thebonds (Lomholt and Qvist, 1999). The modulus continues to increase for severalhours after gelation time, signifying gel firming. The microstructure of the gel hasbeen observed to become coarser with larger pores and thicker strands (Lomholtand Qvist, 1999). Carlson et al. (1987) presented a detailed analysis of all aspectsof milk coagulation kinetics in a four-part series of papers.

S

YNERESIS

Due to its porous nature, the coagulum has the propensity to contract and expelentrapped liquid. This is known as syneresis, an important step in concentratingthe milk. To a great extent, the success of the remaining cheesemaking steps dependson satisfactorily draining the whey. Also, most of the lactose, a substrate forpostproduction microbial activity, is lost in the whey, which helps to prevent some

FIGURE 1.4

Changes in storage (G

′

) and loss (G

″

) moduli and phase angle (

δ

) of therennetted milk during coagulation. The gel point is identified at G

′

–G

″

crossover which occursat

δ

= 45°. (After Uludogan, 1999.)

10–4

10–3

10–2

10–1

100

101

102

G′,

G′′

(Pa)

350030002500200015001000500

Time (s)

80

70

60

50

40

30

20

δ(°)gel point

G′ G′′δ


adverse effects (Scott et al., 1998). In an undisturbed gel, however, syneresis occursvery slowly. Therefore, during cheesemaking, syneresis is accelerated by cuttingthe coagulum into small cubes, which increases the surface area and reduces thedistance for the diffusion process to facilitate whey removal. Syneresis can also beenhanced by decreasing the pH or increasing the temperature of the coagulum(Walstra et al., 1999).

Cutting the coagulum to facilitate faster whey removal must be timed precisely.If the coagulum is cut too soon, some milk solids leave the curd along with whey.Whey normally carries water-soluble components including lactose, whey proteins,salts, peptides, and other nonprotein nitrogenous substances (Scott et al., 1998). If itis cut too late, more water gets trapped in the matrix, resulting in high-moisturecheese. Therefore, cheesemakers have been striving for many years to identify thecorrect curd-cutting time. Since the coagulum firmness continues to increaseuneventfully over several hours, it is hard to determine an optimal curd-cutting time.Many instrumented and so-called objective curd-cutting-time predictions have beenmade (Hori, 1985; Payne et al., 1993; Gunasekaran and Ay, 1996; O’Callahan et al.,1999). Some commercial units are available based on some of these techniques (Foxand McSweeney, 1998; O’Callahan et al., 1999). However, there is still no universalprocedure to identify optimal curd-cutting time. Most large factories apply a set timeschedule, depending on the cheese type, to cut the curd after adding the rennet. Inmany smaller cheesemaking facilities, cutting time is still determined by the sub-jective judgment of the cheesemaker. Recently, Konuklar and Gunasekaran (2002)reported a novel rheological technique for identifying the curd-cutting time. Theyobserved that the viscosity versus time curves during coagulation under continuoussteady shear exhibit several abrupt peaks. The first peak over 40 kPa.s coincideswith cutting time determined by an experienced cheesemaker during Cheddar, Swiss,and Gouda cheesemaking (Figure 1.5.)

Syneresis is the process that a cheesemaker can use to closely control themoisture content of the cheese and hence the microbial and enzymatic activity inthe cheese, which affects ripening, stability, and quality of the cheese (Fox et al., 2000).Therefore, it is specific to a particular cheese type or cheese family. Walstra et al.(1999) listed the following factors as affecting syneresis: firmness of gel at cutting;surface area of the curd; any applied pressure; acidity; temperature; composition ofthe milk; and other variables. Pearse and Mackinlay (1989) discussed the mechanismand biochemical aspects of syneresis.

Stirring exerts pressure, causing curd particles to collide, and facilitates theircompression for a short time. Stirring also keeps the curd from settling in the vat.For Cheddar- and Swiss-type cheeses, the cut coagulum is not stirred immediatelyafter cutting. The curd–whey mixture is cooked (at about 40ºC for Cheddar-typeand 50ºC for Swiss-type) and vigorously agitated during cooking. For soft cheeses,the curd is ladled and hooped which allows whey to drain without stirring. Cookingthe curd, also known as scalding, enhances syneresis by facilitating contraction ofthe protein matrix. Heating further enhances acid production by the starter organisms.Lowering pH, combined with increased temperature, not only helps to expel morewhey but also affects the dissolution of calcium phosphate, and thus has majorimplications for characteristics of the cheese (Johnson and Law, 1999). The scalding


step can be used to distinguish four major groups of cheese — excluding soft cheeses,some of which may be scalded (Scott et al., 1998):

1. Textured cheeses such as Cheddar or Cheshire2. Pasta filata types or kneaded cheeses3. Cheeses untextured in the vat (e.g., Edam and Gouda) and those which

acquire texture later (e.g., Tilsiter and Emmental)4. Blue-veined cheeses

FIGURE 1.5

Viscosity (

η

) of coagulating milk system vs. time after rennetting measuredunder a continuous steady shear stress of 0.2 Pa. The first viscosity peak over 40 kPa.scoincided with the cutting point (CTP) determined manually during (a) Cheddar; (b) Swiss;and (c) Gouda cheesemaking. (After Konuklar and Gunasekaran, 2002. With permission.)


To manufacture some cheeses (e.g., Edam, Gouda, or Havarti), the curd is washedby adding water to the curd–whey mixture. This accomplishes two things:

1. It adjusts the pH of the cheese independently of its moisture content byremoving lactose and other solubles from the curd.

2. It enhances whey removal by adding hot water to raise the curd tempera-ture, as is the case during direct heating.

It should be noted that using hot water to stretch pasta filata cheeses (e.g.,Mozzarella, Provolone, etc.) is not considered as washing (Scott et al., 1998).

S

HAPING

AND

S

ALTING

When the curd is at the desired moisture content and pH, it is separated from thewhey. The curd particles are subsequently shaped into some form and salted(primarily by NaCl), not necessarily in that order. These steps, though common formost cheeses, are performed very differently, depending on the cheese type. AsJohnson and Law (1999) stated, the manner in which cheese curd and whey areseparated can affect texture as well as color and flavor.

When manufacturing hard cheeses such as Cheddar, the curd–whey slurry ispumped into a vat with a perforated bottom for whey removal. The curd is “cheddared”for about 90 min. Cheddaring is the process in which curd particles are allowed tofuse or “mat” together. The mats are then cut into slabs and stacked on top of eachother. Physical properties and pH of the curd at this stage affect curd fusion andappearance of the finished cheese (Olson, 1995). When the desired pH has beenreached, the slabs are milled into small pieces. At this stage, the curd may be sprayedwith warm water and stirred for further whey removal. Salt is sprinkled on at a levelof about 2 to 3% which expels additional whey. The salted curd is then hooped inmolds and pressed overnight.

Manufacturing steps for Mozzarella and other pasta filata cheeses differ mark-edly after the milling stage described above. The milled curd is “kneaded,” i.e.,heated and stretched in warm water (about 60 to 70°C) using an open-channel,single-screw or twin-screw extruder/auger. This transforms the curd into a cohe-sive, viscoelastic mass. Due to the conveying action of the auger, the curd massgets stretched into a continuous stream of molten material. This stretching step isunique to Mozzarella manufacturing. It imparts the characteristic oriented micro-structure and related textural attributes of these cheeses (Oberg et al., 1993; Akand Gunasekaran, 1997). The molten cheese is then placed into molds and cooled.When the cheese is cool enough to keep its shape, the mold is removed and thecheese is salted by dropping it in a nearly saturated brine solution (about 25%salt) at 1 to 4°C. The cold brine temperature cools the cheese further. In fact,much of the total cooling of Mozzarella occurs during brining (Nilson, 1968).Brine salting is a slow process, taking several days for uniform salt distributionwithin a cheese block. It should be noted that, concomitant with salt intake, thecheese loses moisture. The salt and moisture gradients in a cheese during saltingare opposite of each other (Turhan and Gunasekaran, 1998; Walstra et al., 1999;


Fox et al., 2000). Though brine salting is the traditional method, salting of Moz-zarella can also be done by adding salt directly to the curd just before stretching,during stretching, or between stretching and molding. This direct salting reducesthe subsequent brining time.

Another major variation is surface salting. Salt is rubbed directly on the cheesesurface (e.g., Romano and Gorgonzola). This is repeated for several days so the saltdiffuses throughout. In many other cheeses, surface salting and brining are used incombination (e.g., Gruyere and Emmental).

Regardless of the method used, salting is a vital step in cheesemaking becauseunsalted cheese is virtually tasteless (Olson, 1995). Salt also plays a major role inthe texture, flavor, and microbial quality of cheese (Kindstedt et al., 1992; Paulsonet al., 1998; Fox et al., 2000). Salt inhibits the growth of certain bacteria, whichare harmful to the cheese and cause spoilage, especially on the surface. It furtherassists in dissolving the casein and in rind formation, as well as in slowing downenzyme activity. Salt concentration in cheese varies greatly from less than 1% inEmmental to 7 to 8% in Domiati (Fox and McSweeney, 1998). The salt contentmay also vary considerably within a cheese block due to the slow diffusion of salt.Thus, there is more water and less salt at the center of a cheese block comparedto at the surface (Prentice, 1993). This unevenness in the salt (and water) distributionalso leads to variation in the rheological properties of the cheese within the block(Visser, 1991).

As already noted, hard and semihard cheeses are shaped by applying externalpressure. Pressing expels whey and facilitates faster curd fusion into an integral massof a desired shape with a rind. Though simple enough, pressing is perhaps the leastunderstood step in cheesemaking (Scott et al., 1998). The time, pressure, and effi-ciency of pressing are related to the condition of the curd at pressing time and thedecrease in pH during pressing (Johnson and Law, 1999). Sometimes pressing isdone in conjunction with vacuum to force out any entrapped air.

The complex nature of the interrelationships among many of the cheesemakingparameters makes controlling cheese properties very hard. Tables 1.7a to 1.7d presenthow various cheesemaking and technological factors affect cheese quality. This setof four tables was prepared in 1961 for the Danish Samso cheese (Birkkjaer et al.,1961), but the information it contained is generally valid for other hard/semihardcheeses (e.g., Gouda).

R

IPENING

Ripening is the natural process of microbial and biochemical reactions that occursin a cheese after its manufacture and during storage. Ripening gives different cheesestheir unique flavors, textures, and appearances. Except for some soft cheeses (e.g.,cottage cheese, cream cheese, quark, etc.), almost all cheeses are held under con-trolled conditions to develop distinct attributes. Ripening essentially results from theaction of microorganisms present within the curd mass and on its surface. Ripeningis also influenced by residual enzymes present in the cheese curd. Cheeses areripened over a range of time from several days (e.g., Mozzarella) to more than ayear (e.g., Cheddar).


Fox et al. (2000) list the following ripening agents in cheese:

1. Coagulant — chymosin or other suitable proteinase2. Milk — some indigenous enzymes contained in milk, e.g., plasmin3. Starter culture — host of enzymes released upon cell death and lysis4. Secondary microflora — microflora that perform some specific secondary

function (e.g., propionic acid, bacteria, and yeasts and molds)5. Exogenous enzymes — proteinases, peptidases, and lipases added by

cheesemakers to accelerate ripening

TABLE 1.7A Effect of Cheesemaking Parameters on Cheese Quality (Prepared forDanish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a Harder Cheese and Their Primary and Secondary Effects

Factor No. Efficiency

a

Modifications Primary Effect Secondary Effect

b

1 Use fresh milk or pasteurize at approx. 70ºC (158ºF)

Slightly improves whey expulsion

Cheese becomes slightly less acid. Ca content increases slightly

2 + Reduce or omit addition of water to the milk

Improves whey expulsion

Cheese becomes more acidic. Ca content increases

3

c

+ Add CaCl

2

to the milk

Improves whey expulsion Ca content increases. Adding more than40 g/100 kg milk (0.68 oz/110 lbs milk)may give an off flavor

4 + Increase amount of culture/starter or prolong pre-ripening period of the milk

Slightly improves whey expulsion from the curd

Cheese becomes more acidic. Ca content decreases. Too much culture/starter or too long a preripening makes cheese sour, short, and flaky

5

c

(+) Lower renneting temperature

At the same cooking temperature, whey drain in the vat increases slightly due to a greater rise in temperature. If no cooking occurs, whey is reduced, and cheese becomes softer

A renneting temperaturethat is too low results in weak curd and thus a bigger loss in the whey.Ca content decreases

6

c

+ Cut curd into smaller cubes

Improves whey expulsion Very fine cutting may result in a bigger loss in whey. Many of the “grains” may retain some of the whey during molding/pressing, so cheese may be softer


8 + Reduce or omit addition of water during cooking

Improves whey expulsion of curd, esp. by reducing relatively large additions of water

Cheese becomes sour and may eventually become too firm in the curd and thus will often break.Ca content increases

9 +++ Increase cooking temperature

Increases whey expulsion in the vat

Cheese becomes less acidic and tougher At high temperatures, esp. above 40ºC (105ºF); cheese may develop an off flavor

10 +++ Avoid a temperature drop during final stirring

Increases whey expulsion in the vat and during pressing

Cheese becomes less acidic. Ca content increases

12 ++ Reduce or omit salt addition to whey during final stirring

Cheese “grains” swell less and thus retain less whey

Cheese becomes less acidic. Ca content increases. Brine salting may be prolonged to get adequate salt content

13

c

+++++

d

Leave cheese at cooking temperature in water or whey after pressing in the vat

Cheese liberates a relatively large quantity of whey before rind is closed

Ca content decreases considerably

14 ++ Increase temperature in pressing room

Increases amount of whey draining during pressing

Cheese becomes slightly less acidic. If it is not cooled longer, the risk of cracked rind and gas from coliforms may increase

15

c

+ Prolong pressing time (possibly until the next morning)

Increases amount of whey draining during pressing

You might see adhesion, especially when using cotton cloths and a relatively high pressing temperature. Counteract this by using nylon cloths and cooling during last part of pressing

a

+ Represents relative efficiency, the higher the better. (+) means that the effect depends on other conditions.

b

Shaded effects reduce acidity; bold-faced effects increase acidity.

c

Factor numbers 3, 5, 6, 13, and 15 show modifications that influence either acidity or firmness but notboth. All other factors influence both.

d

An extraordinary change in technique, 3 hours at 38ºC.

Source:

After Birkkjaer et al., 1961. With permission.

TABLE 1.7A (continued)Effect of Cheesemaking Parameters on Cheese Quality (Prepared forDanish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a Harder Cheese and Their Primary and Secondary Effects


a


b


TABLE 1.7B Effect of Cheesemaking Parameters on Cheese Quality (Prepared forDanish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a Softer Cheese and Their Primary and Secondary Effects


a


b

1 Pasteurize at 65ºC (150ºF) or above 75ºC (166ºF), esp. above 80ºC (175ºF)

Slightly reduces whey expulsion (above 80ºC [175ºF] somewhat)

Cheese becomes (above 80ºC [175ºF] somewhat) more acidic. Ca content decreases. High pasteurization temperatures often lead to weak eye formation

2 + Add water to the milk

Reduces whey expulsion Cheese becomes less acidic. Ca content increases

3

c

+ Reduce or omit addition of CaCl

2

to the milk

Reduces whey expulsion Ca content decreases

4 + Reduce amount of culture/starter or shorten or omit preripening period of the milk

Slightly reduces whey expulsion

Cheese becomes less acidic. Ca content decreases. Not enough culture/starter or a pre-ripening that is too short may produce a tough cheese with an off flavor

5

c

(+) Raise renneting temperature

At the same cooking temperature, whey expulsion in the vat is slightly reduced due to a smaller rise in temperature. If no cooking occurs, whey expulsion increases and cheese is firmer

A renneting temperature that is too high will cause cutting problems since the coagulum will be too firm during cutting. Ca content increases slightly

6

c

+ Cut curd into bigger cubes

Reduces whey expulsion Big curd cubes can be easily stirred into smaller pieces, causing greater whey drain than intended and greater loss in the whey. Many “grains” may retain some whey when cheese is molded so cheese becomes softer than intended

8 + Add more water during cooking

Reduces whey expulsion, esp. when relatively large amounts of water are added

Cheese becomes less acidic. Ca content decreases. If you add more than 20% of the quantity of milk, cheese often develops an off flavor


9 +++ Lower cooking temperature

Reduces whey expulsion Cheese becomes more acidic. Cheese which is already acidic may crack easily

10 +++ Cool curd cubes for about 15 min before final stirring ends

Reduces whey expulsion in the vat and during pressing

Cooling without water leads to acidic cheese. Cooling with water leads to small or no change in acidity, depending on amount of water. Ca content decreases

12 ++ Add more salt to whey during final stirring

Curd cubes swell more and retain more whey

Cheese becomes more acidic. Ca content decreases. Shorten brine salting so cheese is not too salty. Heavy salting in the vat may restrain fermentation, producing cheese with high pH

13c +++++d Reduce pressing temperature or drain the whey faster

Rind closes earlier, slowing whey expulsion

Ca content increases

14 ++ Lower temperature in pressing room

Reduces whey expulsion during pressing

Moderate cooling yields more acidic cheese. Cooling too soon retards fermenting and gives high pH cheese. Cooling after or during last part of pressing, if long enough, slows rind cracking and coliform production

15c + Use low pressure to start or shorten pressing time

Less whey is pressed out of the cheese

Low pressure and short pressing time may causebad rind closing, fermenting in rind (cracked rind) and open texture

a + Represents relative efficiency, the higher the better. (+) means that the effect depends on other conditions.b Shaded effects reduce acidity; bold-faced effects increase acidity. Shaded and bold-faced effects may resultin more or less acidity.c Factor numbers 3, 5, 6, 13, and 15 show modifications that influence either acidity or firmness but notboth. All other factors influence both.d An extraordinary change in technique, three hours at 38ºC.

Source: After Birkkjaer et al., 1961. With permission.

TABLE 1.7B (continued)Effect of Cheesemaking Parameters on Cheese Quality (Prepared forDanish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a Softer Cheese and Their Primary and Secondary Effects

Factor No. Efficiencya Modifications Primary Effect Secondary Effectb


TABLE 1.7C Effect of Cheesemaking Parameters on Cheese Quality (Prepared forDanish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a Less Acidic Cheese and Their Primary and Secondary Effects


1 + Use raw milk or pasteurize at approx. 70ºC (158ºF)

Slightly improves whey expulsion

Cheese becomes slightly firmer. Ca content increases slightly

2 ++ Add water to the milk Reduces whey expulsion Cheese becomes softer. Ca content decreases

4 ++ Reduce amount of culture/starter, or shorten preripening period of the milk

Less acidification Cheese becomes a little softer. Ca content increases. Not enough culture/starter and a weak preripening produces a tough cheese with an off flavor

7c ++ Start cooking earlier by shortening prestirring or intermediate stirring, and prolong final stirring correspondingly

Development of lactic-acid bacteria is restrained and whey is expelled

Ca content increases

8 +++ Add more water during cooking

Greater diffusion of sugar and Ca from curd cubes to the whey

Adding more than 20% water may produce a cheese with an off flavor. Increasing the water added produces cheese with a higher water content and lower Ca content

9 ++++++ Raise cooking temperature

Development of lactic-acid bacteria in the vat is slowed. Whey is expelled earlier

Cheese becomes firmerand tougher. At high temperatures, especially above 40ºC (105ºF), cheese develops an off flavor

10 ++ Avoid a drop in temperature during final stirring

Development of lactic-acid bacteria is slowed

Cheese becomes firmer. Ca content increases

11c + Prolong the time for final stirring so total stirring time is longer

Acidity is slightly changed because development of lactic-acid bacteria is slowed. But because curd cubes are kept in the whey longer, more Ca is discharged

Cheese consistency becomes more supple (flexible), so cheese is easier to cut


Various methods of influencing cheese ripening are summarized in Table 1.8.The primary factors in this process are (Scott et al., 1998):

1. Storage temperature and humidity, humidity being less important forcheeses hermetically packed (e.g., with a wax coating).

2. Chemical composition of the curd — fat content, level of amino acids,fatty acids, and other by-products of enzymatic action.

3. Residual microflora of the curd — primarily from the starter culture. Thecheesemaker can do little to influence it except in the case of blue-veinedor surface-ripened cheeses.

Temperature and humidity are factors that cheesemakers can control duringripening. In general, higher temperatures increase the microbial growth rate andother biochemical reactions occurring in the curd. Thus, cheeses matured at differenttemperatures can have different flavor profiles. Accordingly, proper control of storagetemperature is essential. Variety-specific storage temperature control protocols have

12 Reduce or omit addition of salt to whey during final stirring

Curd cubes swell less and thus retain less whey

Cheese becomes firmer. Ca content increases. Brine salting should be prolonged to get an adequate salt content

14 + Cool cheese early, or carry through pressing at high temperature 40ºC (105ºF)

Development of lactic-acid bacteria is slowed

Cooling results in a softer cheese. Cooling too early may result in high pH cheese. High pressing temperature makes a firmer cheese, and the danger of a cracked rind and fermentation is increased if it is not cooled after pressing

a + Represents relative efficiency, the higher the better.b Shaded effects result in softer cheese; bold-faced effects result in firmer cheese. Shaded and bold-facedeffects may result in softer or firmer cheese.c Factor numbers 7 and 11 show modifications that influence either acidity or firmness but not both. Allother factors influence both.


TABLE 1.7C (continued)Effect of Cheesemaking Parameters on Cheese Quality (Prepared forDanish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a Less Acidic Cheese and Their Primary and Secondary Effects



TABLE 1.7D Effect of Cheesemaking Parameters on Cheese Quality (Prepared forDanish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a More Acidic Cheese and Their Primary and Secondary Effects


1 + Pasteurize at 65ºC (150ºF) or above 75ºC (166ºF), esp. above 80ºC (175ºF)

Slightly reduces whey expulsion (above 80ºC [175ºF] somewhat)

Cheese becomes slightly softer (above 80ºC [175ºF] somewhat). Ca content decreases slightly

2 ++ Reduce or omit addition of water to the milk

Improves whey expulsion from the curd

Cheese becomes a little firmer. Ca content increases

4 ++ Increase amount of culture/starter or prolong preripening of the milk

Increases acid production Cheese becomes a little firmer. Ca content decreases. Too much culture/starter and too strong preripening causes cheese to be sour, short, and flaky

7c ++ Cook longer by prolonging prestirring or intermediate stirring, and shorten final stirring correspondingly

Lactic-acid bacteria have better growth conditions in the vat. Whey expulsion occurs later

Ca content decreases. A long intermediate stirring time increases the loss in the whey because curd is easily stirred into pieces

8 +++ Reduce or omit addition of water during cooking

Less diffusion of sugar and Ca from curd cubes to the whey

Cheese retains more Ca and less water. It may become too acidic and stiff and break. Cheese becomes softer. Cheese which is already acidic may crack

9 ++++++ Lower cooking temperature

Lactic-acid bacteria have better growth conditions in the vat. Whey expulsion occurs later

Cheese becomes softer.Ca content decreases

10 ++ Cool curd cubes for about 15 min before end of stirring. A small amount of water is optional

Lactic-acid bacteria have better growth conditions

A short stirring time produces a tough cheese. Cut surface often gets horny and greasy after storage

11c + Shorten the time of final stirring so total stirring time is shorter

Acidity is changed slightly because development of lactic-acid bacteria is improved. But because curd cubes are kept in the whey for a shorter time, less Ca is discharged

Cheese becomes softer.Ca content decreases. Brine salting should be shortened so cheese is not too salty


been developed to optimize cheese quality. For example, Swiss-type Emmental isheld at a low temperature initially (10 to 15°C) to facilitate the growth of lactic-acidbacteria. Later, the temperature is increased (20 to 24°C) so that propionic bacteriacan grow. These are essential for the characteristic Emmental flavor and “eyes.” Forblue-veined cheeses (e.g., Gorgonzola, Roquefort, Stilton), warm-temperature stor-age is followed by low-temperature storage (Scott et al., 1998). Prevailing relativehumidity during storage (80 to 85%) helps to control the moisture content of cheesesnot covered with moisture barriers such as a wax coating. The moisture equilibriumin the cheese changes due to reactions occurring that require or release water.Increase in moisture content during storage affects the solute concentration andmicrobial growth rate. In general, higher moisture content promotes more vigorousgrowth of microorganisms than does lower moisture content. In addition to tempera-ture and moisture, other factors such as curd pH, inhibitory substances (e.g.,antibodies and salts), and oxidation–reduction potential affect the microbial popu-lation in the cheese (Scott et al., 1998; Fox et al., 2000). The enzymes relevant formaturation in most hard cheeses are active in the pH range of 4.9 to 5.5, and in softcheeses from pH 5.3 to 6.0 (Scott et al., 1998).

Protein, fat, and lactose are hydrolyzed (i.e., proteolysis, lypolysis, and glycoly-sis, respectively) to varying extents during cheese ripening. Among these, proteolysisof casein is the most important. Proteolysis of α- and β-casein occurs due to any

12 Increase amount of salt added to the whey during final stirring

Curd cubes swell more and thus retain more whey

Too heavy salting in the vat restrains acidification, which may produce a high-pH cheese

14 + Take care that cheese temperature during pressing stays near the optimum temperature of the bacteria

Lactic-acid bacteria have better growth conditions during pressing. Pressing at high temperatures, or cooling too early to low temperatures in the curd, restrains acidification

Since rind fermentation can be prevented rather effectively by cooling, cheese should be cooled after pressing or during the last part of pressing,if this is long enough

a + Represents relative efficiency, the higher the better.b Shaded effects result in softer cheese; bold-faced effects result in firmer cheese.c Factor numbers 7 and 11 show modifications that influence either acidity or firmness but not both. All otherfactors influence both.


TABLE 1.7D (continued)Effect of Cheesemaking Parameters on Cheese Quality (Prepared forDanish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a More Acidic Cheese and Their Primary and Secondary Effects



residual rennet from what was added for coagulation, natural proteases, and proteasesand polypeptidases from starter or adventitious bacteria (Scott et al., 1998). This isessential for cheese flavor development. Fat contains lipophilic flavor compounds,which develop or are released by microbial or enzymatic action through oxidation,decarboxylation, and eventually reduction of decarboxyl compounds. Glycolysis isalso initiated by adding a starter culture and reaches its peak in the milk during thepreripening stage. Here lactic acid, acetic acid, and CO2 are produced. In somecheeses, citrate is also metabolized into citric acid.

Proteolysis is also mainly responsible for changes in the body and texture ofcheeses. The breakdown of proteins first involves the conversion of casein fractionsinto large peptides. These peptides are later broken down to lower molecularweight products. The primary proteolysis in ripening has been defined as thechanges in caseins, which can be detected by polyacrylamide gel electrophoresis.The products of secondary proteolysis include the peptides and amino acids thatare soluble in the aqueous phase of the cheese. In mature Cheddar, approximatelyone-third of the protein has been broken down to forms that are soluble at pH 4.6(Banks, 1998).

TABLE 1.8Methods of Influencing Cheese Ripening and Their Advantages and Disadvantages

Method of Influence Advantages Disadvantages

Increased storage temperature Easy to performNo aspects determined by law

No specific effectRisk of destroying bacteria

Increased inoculation level in starter culture

Natural enzyme balanceNo aspects determined by law

Influences pH and consistency

Addition of EnzymesProteases/peptidasesLipases, animal, and microbial

Relative low costSpecific effect

Few usable enzymesRisk of over-ripeningAspects determined by lawUse of whey

Special CulturesLactobacillus/pediococciBrevibacterium linesMoldPropionic-acid bacteria

Naturally balancedNo aspects determined by law

Opposite effect on pH and consistency

Different taste profile

Modified Starter CulturesCold/warm treatedLysozyme treatedNonacidic producing

Natural enzyme balanceEasy to conform to

Technologically complex

Source: After Kristensen, 1999. With permission.


PROCESS CHEESE

Process cheese is manufactured from one or more of the natural cheeses describedthus far. The basic premise is to stabilize the proteins that are normally affectedalready during one or more of the cheesemaking steps (Shimp, 1985). This isaccomplished by heating and mixing cheeses with some emulsifying salts. Thecareful selection of cheeses, emulsifying salts, and processing factors allows makingprocess cheeses of varied textures suitable for many end uses.

The primary reasons for manufacturing process cheese are (Spreer, 1998):

1. Long shelf life due to heat treatment and hot filling2. Wide variety due to a multitude of ingredients and composition3. Efficient utilization due to spreadable consistency and small portions4. Upgrading of defective rennet cheese products if the defects limit the shelf

life but the products are still edible

The basic steps in the manufacture of process cheese are selecting and blendingraw materials, heat processing, and forming and packaging. The raw materialsinclude the natural cheeses, emulsifying salts, and other ingredients. Using theappropriate cheeses in the blend is very critical to obtain the desired texture andflavor. The emulsifying salts, primarily phosphates and citrates, are selected for theirability to disperse and increase hydration of the cheese proteins, which createssmoothness and fat emulsification (Olson, 1995). Other ingredients vary, from dairyand nondairy products such as skim milk powder, whey protein concentrate, spicesand vegetables, and muscle food ingredients, etc. In general, good quality rawmaterials ensure good quality process cheese.

Process cheeses can be grouped into three major categories based on compositionand consistency: process cheese block, process cheese food, and process cheesespread. The selection of type of heat processing and raw materials for each are doneaccordingly. A fourth group, process cheese analog based on vegetable fat-caseinblend, is also manufactured. Specific manufacturing steps, ingredient selection, etc.,are detailed in Caric and Kalab (1993). The manufacturing conditions for sliceableand spreadable process cheese are summarized in Table 1.9.

The heat-processing step converts the raw material into a homogeneous product.Heating is performed under atmospheric pressure or vacuum at 85 to 95°C or underpressure at 105 to 120°C. Temperatures under 90°C are desirable to avoid a browningreaction when the raw materials are high in lactose. During heating, the mix iscontinuously stirred at 60 to 140 rpm. The process duration varies from 4 to 8 minfor processed cheese blocks to 8 to 15 min for processed cheese spread (Caric andKalab, 1993).

After heat processing, the melt is conveyed to filling machines where it is moldedinto different shapes or put into containers. It can also be spread on conveyor beltsand sliced. The cheese is then cooled. Cooling is performed fairly slowly (10–12 h)for process cheese blocks and very quickly (15–30 min) for process cheese spreadto facilitate softening of the product.


REFERENCES

Ak, M.M. and S. Gunasekaran. 1997. Anisotropy in tensile properties of Mozzarella cheese.Journal of Food Science 62(5):1031–1033.

Ay, C. and S. Gunasekaran. 1994. An ultrasonic attenuation measurement for estimating milkcoagulation time. Transactions of the ASAE 37(3):857–862.

Banks, J.M. 1998. Cheese. In The Technology of Dairy Products, Ed. R. Early, 81–122.London, U.K.: Blackie Academic and Professional.

Battistotti, B. et al. 1984. Cheese: A Guide to the World of Cheese and Cheesemaking. NewYork: Facts on File Publications.

Bauer, R. et al. 1995. The structure of casein aggregates during renneting studied by indirectFourier transformation and inverse Laplace transformation of static and dynamiclight-scattering data, respectively. Journal of Chemical Physics 103:2725–2737.

Birkkjaer, H.E. et al. 1961. The influence of the cheesemaking technique upon the quality ofcheese. Report No. 128, Danish Government Research Institute for Dairy Industry,Hillerod, Denmark. (Translated from Danish and reprinted with permission in theDairy Pipeline, 1998, Center for Dairy Research, University of Wisconsin-Madison,Madison, WI, 53706, U.S.A.)

TABLE 1.9Manufacturing Conditions for Sliceable and Spreadable Process Cheese

Condition

Process Cheese Type

Sliceable Spreadable

Average age of the raw material Fresh to half-mature;mostly fresh

Combination of fresh, half-mature,and over-ripe

Relative casein contentstructure

75–90%, mostly long 60–75%, short to long

Melting salt Structure: not creamy Emulsifier: high molecular Polyphosphate, etc.

Structure: creamyEmulsifier: lower or medium molecularPolyphosphate, etc.

Water, how added 10–25%, all at once 20–45%, in portions

Temperature 80–85ºC (176–185ºF) 85–98ºC/150ºC (185–208ºF/302ºF)

Time for melting, stirring 4–8 min, slow 8–15 min, fast

pH 5.4–5.6 5.7–5.9

Process cheese 0–2% 5–20%

Whole milk powder or whey powder 0 5–10%

Homogenization None Desirable

Packaging (filling) 5–15 min

Cooling Slow (10–20 h) at room temperature

Fast (15–30 min) in freezing conditions (cool air)

Treatment Very careful Intensive (powerful)

Source: After Kristensen, 1999. With permission.


Caric, M. and M. Kalab. 1993. Processed cheese products. In Cheese: Chemistry, Physicsand Microbiology, Vol. 2, Major Cheese Groups, 2nd ed., Ed. P.F. Fox, 467–505.New York: Chapman and Hall.

Carlson, A., C.G. Hill, Jr., and N.F. Olson. 1987. Kinetics of milk coagulation: I-IV. Biotech-nology and Bioengineering 29(4):582–589, 590–600, 601–611, 612–624.

CFR, 1998. Cheeses and Related Cheese Products. Code of Federal Regulations, Title 21,Part 33, pp 294–346. United States Department of Health and Human Services, Foodand Drug Administration, Washington.

Davis, J.G. 1965. Cheese, Vol. 1, Basic Technology. London: Churchill Livingstone.Dejmek, P. 1987. Dynamic rheology of rennet curd. Journal of Dairy Science 70:1325–1330.Doeff, G. 1994. Cheese in the U.S.A. Dairy Foods Sept., p. D.Fox, P.F. 1993. Cheese: an overview. In Cheese: Chemistry, Physics and Microbiology, Vol. 1,

General Aspects, Ed. P.F. Fox, 1–32. London: Chapman and Hall.Fox, P.F. et al. 2000. Fundamentals of Cheese Science. Gaithersburg, MD: Aspen Publishers, Inc.Fox, P.F. and P.L.H. McSweeney. 1998. Dairy Chemistry and Biochemistry. London: Blackie

Academic and Professional.Glaser, J., P.A. Carroad, and W.L. Dunkley. 1980. Electron microscopic studies of casein

micelles and curd microstructure in cottage cheese. Journal of Dairy Science63:37–48.

Gunasekaran, S. and C. Ay. 1996. Milk coagulation cut-time determination using ultrasonics.Journal of Food Process Engineering 19(3):331–342.

Hill, A.R. 1995. Chemical species in cheeses and their origin in milk components. In Chemi-stry of Structure-Function Relationships in Cheese, Eds. E.L. Malin and M.H. Tunick,43–58. New York: Plenum Press.

Hori, T. 1985. Objective measurements of the process of curd formation during rennettreatment of milks by hot wire method. Journal of Food Science 50:911–917.

Johnson, M.E. 1998. Part II — Cheese chemistry. In Fundamentals of Dairy Chemistry,Ed. N.P. Wong, 634–654. New York: Van Nostrand Reinhard Co.

Johnson, M. and B.A. Law. 1999. The origins, development and basic operations of cheese-making technology. In Technology of Cheesemaking, Ed. B.A. Law, 1–32. Sheffield,England: Sheffield Academic Press Ltd.

Kimber, A.M. et al. 1974. Electron microscope studies of the development of structure inCheddar cheese. Journal of Dairy Research 41:389–396.

Kindstedt, P.S., L.J. Kiely, and J.A. Gilmore. 1992. Variation in composition and functional prop-erties within brine-salted Mozzarella cheese. Journal of Dairy Science 75:2913–2921.

Konuklar, G. and S. Gunasekaran. 2002. Rennet-induced milk coagulation by continuoussteady shear stress. Journal of Colloid and Interface Science (in press).

Kopelman, I.J. and U. Cogan. 1976. Determination of clotting power of milk clotting enzymes.Journal of Dairy Science 59(2):196–199.

Kristensen, J.M.B. 1999. Cheese Technology — A Northern European Approach. Aarhus,Denmark: International Dairy Books.

Kristoffersen, T. 1985. Development of flavor in cheese. Milchwissenschaft 40:197–199.Law, B.A. (ed.) 1999. Technology of Cheesemaking. Boca Raton, FL: Sheffield Academic

Press.Lomholt, S.B. and K.B. Qvist. 1999. The formation of cheese curd. In Technology of Cheese-

making, Ed. B.A. Law. Sheffield, England: Sheffield Academic Press Ltd.Lopez, M.B., S.B. Lomholt, and Q.B. Qvist. 1998. Rheological properties and cutting time

of rennet gels: effect of pH and enzyme concentration. International Dairy Journal8:289–293.


NDC. 2000. Newer Knowledge of Dairy Foods/Cheese. National Dairy Council(www.nationaldairycouncil.org). Managed by Dairy Management Inc., Rosemont, IL.

Nilson, K.M. 1968. Some practical problems and their solutions in the manufacture ofMozzarella cheese. In Proc. 5th Annual Marschall Italian Cheese Seminar, 1–7.Madison, WI.

Oberg, C.J., W.R. McManus, and D.J. McMahon. 1993. Microstructure of Mozzarella cheeseduring manufacture. Food Structure 12:251–258.

O’Callaghan, D.J., C.P. O’Donnell, and F.A. Payne. 1999. A comparison of on-line techniquesfor determination of curd setting time using cheese milks under different rates ofcoagulation. Journal of Food Engineering 41(1):43–54.

Olson, N.F. 1979. Cheese. In Microbial Technology II, Eds. H.J. Peppler and D. Perlman,39–77. New York: Academic Press.

Olson, N.F. 1995. Cheese. In Biotechnology, Vol. 9, Eds. H.-J. Rehm and G. Reed, 355–384.Weinheim, Germany: Verlag Chemie.

Paulson, B.M., D.J. McMahon, and C.J. Oberg. 1998. Influence of sodium chloride onappearance, functionality and protein arrangements in non-fat Mozzarella cheese.Journal of Dairy Science 81:2053–2064.

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Pearse, M.J. and A.G. Mackinlay. 1989. Biochemical aspects of syneresis: A review. Journalof Dairy Science 72:1401–1407.

Prentice, J.H. 1993. Cheese rheology. In Cheese: Chemistry, Physics & Microbiology, Vol. 1,General Aspects, Ed. P.F. Fox, 303–340. Elsevier Applied Science, London.

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Visser, J. 1991. Factors affecting the rheological and fracture properties of hard and semihardcheese. Bulletin of the International Dairy Federation No. 268, 49–61, IDF, Brussels,Belgium.

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http://www.nationaldairycouncil.org/

Fundamental Rheological Methods

Fundamental rheological methods are performed under well-defined and controlledconditions. Though some assumptions about the materials and test methods may bemade, calculations of material properties are based on well-defined rheological terms(e.g., strain, stress). Moreover, material properties determined by fundamental methodsare independent of the apparatus used for measurements, which allows comparison ofdata from different research groups (Mitchell, 1984; Shoemaker et al., 1987; Tunickand Nolan, 1992; Tunick, 2000). These fundamental methods help researchers studycheese properties and effects of many manufacturing factors, and eventually developcheeses with desired and consistent textural and rheological properties. Few reviewshave been published on the fundamental rheological methods employed in cheeseresearch (van Vliet, 1991a; Konstance and Holsinger, 1992; Luyten et al., 1992).

DEFINITION OF RHEOLOGY

The term

rheology

was coined by Professor E.C. Bingham to represent a new branchof mechanics concerned with

the study of deformation and flow of matter

(Reiner,1964). This definition was accepted at the inaugural meeting of the Society ofRheology (then, the American Society of Rheology) in 1929. Although significantrheology research has been performed prior to this date, the progress in the field ofrheology seems to have greatly accelerated after its inception in 1929 as a separatediscipline (Doraiswamy, 2002). Rheology is now a well-recognized field with manyapplications in different industries. Professionals from various disciplines (e.g.,physicists, chemists, biologists, engineers, mathematicians) are interested in thetheoretical and practical aspects of rheology.

As stated in the definition, rheology aims at measuring those properties ofmaterials that control their deformation and flow behavior when subjected toexternal forces. Thus, rheology is mainly concerned with the relationship betweenstrain, stress, and time. When subjected to external forces, solids (or truly elasticmaterials) will deform, whereas liquids (or truly viscous materials) will flow.However, contemporary rheology is more interested in the behavior of real mate-rials with properties intermediate between those of ideal solids and ideal liquids(Doraiswamy, 2002). These industrially important materials are called viscoelasticmaterials, which include almost all real materials.

BASIC CONCEPTS

Rheology deals with the relationship between three variables: strain, stress, and time.Strain and stress are related to deformation and force, respectively. Strain accounts

2


for the size effect on material deformation due to difference in length (or height) ofspecimens, whereas stress accounts for the size effect on applied force due todifference in cross-sectional area of specimens. Using strain and stress, rheologistsare able to obtain true material properties independent of the sample size andgeometry, and compare test results for samples of different sizes and geometries.Many rheological terms are defined and described by van Vliet (1991b).

S

TRAIN

When a material is subjected to an external force, individual points of the body willmove relative to one another causing a change in the size and shape of the material.The

deformation

is the measure of such a change in size and shape. Deformation,however, is not uniquely related to force as illustrated in the following example.Two specimens (

A

and

B

), made of the same material and having identical shapeand size, are subjected to the same axial force,

F

, applied

perpendicular

to thematerial surfaces (Figure 2.1). This will result in the same amount of extension

FIGURE 2.1

Effect of test specimen length on force–extension relationship. (After Hall, 1968).

FF

FF

Before deformation

After deformation A

A

Before deformation

After deformation B

B

BABefore deformation Before deformation

After deformation After deformation BA

F F

L

L

∆L/2

∆L/2

∆L ∆L

∆L/2

∆L/2

Deformation = ∆L

Total deformation = 2∆L

Deformation = ∆L

Lo

Lo

2 L

2 Lo


(or deformation), denoted by

∆

L

. Let us now imagine that we join the two specimensend to end and again apply the same axial force

F

. Since each specimen willexperience the same axial force as they did when stretched separately, they eachwill extend to the same amount as before (i.e.,

∆

L

) giving a total extension of 2

∆

L

.However, when we divide the total extension 2

∆

L

by the total original length 2

L

o

,the resulting quantity has the same numerical value as when the specimens werestretched separately (i.e.,

∆

L

/

L

o

). This way, we arrive at a quantity that is independentof original specimen length (or height) and is referred to as

strain

. Thus, strain is aquantitative measure of the intensity of deformation.

When the deformation is divided by the initial length of a specimen, as illustratedabove, the resulting strain is known as the

engineering strain

(or

nominal strain,Cauchy strain

). The average engineering axial strain is then given by:

(2.1)

This expression defines the tensile engineering strain (+) when

L

(current lengthor height) is greater than

L

o

(original length or height), or compressive engineeringstrain (-) when

L

is smaller than

L

o

. Both of these strains are known as

normalstrains

or

axial strains

.There is also another kind of strain, the

shear strain

, which exists when theforce is applied

parallel

to the material surfaces. This is depicted in Figure 2.2. Ashear strain is defined as the change in angle between two lines originally at rightangles in the undeformed state, that is,

γ

≡

θ

(Fletcher, 1985). The angle

θ

may bedifficult to measure. Hence, the average shear strain (

γ

) is obtained by dividing thedeformation,

δ

, by sample height,

h

:

(2.2)

FIGURE 2.2

Simple shear deformation. When the deformation is uniform, shear strain isindependent of size of element taken. Thus, shear strain

γ

= (

∆δ

/

∆

h) = (

δ

/h).

ε = ±−

= ±L L

L

L

Lo

o o

∆

γ δ δ θ= = =∆∆h h

tan

h

θ

δ

F

∆δ

∆h


It is assumed that the strain is uniform and each small element of the materialis subjected to the same local deformation, and that is also equal to the overall strain.Hence, we can write (

∆δ

/

∆

h) = (

δ

/

h

). In writing Equation (2.2), it is also assumedthat the deformation,

δ

, is small.From the definition of strain it is evident that both normal strain and shear strain

are dimensionless quantities. Sometimes, normal strain is expressed in units of, forinstance,

mm

/

mm

or as a

percentage

, and shear strain in

radian

.The utility of engineering strain is limited to very small deformations (typically

< 1% in tension), and the meaning becomes distorted when

L

becomes appreciablylarger than

L

o

during the test (and also in fluid flows). The following two casesdemonstrate why engineering strain is not appropriate for large deformations.

First, we consider a tensile test where the specimen is stretched from

L

o

to 2

L

o

.According to Equation (2.1), the engineering strain is equal to 1 (i.e.,

ε

= 1). However,let us now consider that the test is done in two steps, such that the specimen is firststretched from

L

o

to 1.4

L

o

and then from 1.4

L

o

to 2

L

o

. In the first step, the engineeringstrain is calculated to be

ε

1

= 0.4, whereas in the second step it is

ε

2

= 0.43. Whenwe add these two strains we obtain

ε

=

ε

1

+

ε

2

= 0.83, which is less than the expectedvalue of 1.

Second, when engineering strain is equal to 1 in a tensile experiment, it means

L

= 2

L

o

, that is 100% extension. On the other hand, an engineering strain of 1 incompression gives an awkward result as:

(2.3)

This yields

L

= 0, which is physically impossible.There are a number of ways to measure strain when the deformations are large.

For up to about 25% deformation all measures of strain yield similar stress–strainrelationships in an ideal compression (Peleg, 1984). However, when deformationsinvolved are large, the stress–strain relationships differ depending on how strain (andstress) is measured. In food rheology, the so-called

Hencky strain

(or

true strain,natural strain

) is most commonly used when large deformations are involved.Hencky strain is a better measure of strain than engineering strain because deforma-tions are referenced to the current specimen length (or height) rather than to theinitial specimen length.

Using Hencky strain can eliminate the problems associated with engineeringstrain such as the ones encountered in the two illustrative examples above. Let usconsider that a uniaxial extension experiment is performed in many small steps fromthe initial specimen length

L

o

to the final length

L

. In each step, one can define anincremental engineering strain (

∆ε

) as follows:

(2.4)

where,

∆

L

i

is the differential increase in the length during the i

th

step and

L

i

isthe length of specimen at the beginning of that step. The total strain is obtained bysumming all the incremental strains from

L

o

to

L

, thus:

ε = − =−

1L L

Lo

o

∆∆

ε =L

Li

i


(2.5)

This is known as Hencky strain,

ε

H

. If we reconsider the two examples givenearlier, we see that Hencky strain is additive. That is:

(2.6)

Furthermore, when

ε

H

= –1, this means that

L

= 0.37

L

o

, which is a meaningfulresult.

Both relations, Equations (2.1) and (2.5), represent average quantities and validonly when strain is uniform all along

L

as illustrated in Figure 2.3. Whenever thereis necking in the gage length in a tensile specimen, or bulging in a compressivespecimen (Figure 2.4), these strain calculations become inaccurate or invalid.

It can be shown that, engineering strain (

ε

) and Hencky strain (

ε

H

) are related as:

(2.7)

Equation (2.7) is valid for both in tension and compression as long as themagnitude of

ε

is used with appropriate sign (i.e., plus (+) for tension and minus(–) for compression). We should point out that Hencky strain is larger in compressionand smaller in tension than the corresponding engineering strain. The differencebetween Hencky strain and engineering strain steadily increases with deformation(Figure 2.5). Hencky strain is approximately equal to engineering strain up to about

FIGURE 2.3

Description of uniform deformation along a tensile test piece. For uniform strain:

∆

L/L =

∆

A/A =

∆

B/B =

∆

C/C =

∆D/D.

εHi

i L

L

o

L

L

dL

L

L

Lo

= = =

∑ ∫∆

ln

ε

ε ε ε

H totalo

o

H H Ho

o

o

o

L

L

L

L

L

L

, ln ln

ln.

ln.

ln . ln ln . ln

=

= [ ]

= + =

+

= [ ] + [ ] − [ ] = [ ]

22

1 4 2

1 41 4 2 1 4 22

and,

1

ε ε ε ε εH = +( ) = − +ln ...1

2 3

2 3

A B C DF F

L

C + ∆C D + ∆DB + ∆BA + ∆A

L + ∆L

After deformation

Before deformation


5% deformation, but the difference increases so that, for instance, ε = –0.25 (25%compressive strain) corresponds to nearly εH = –0.29 (about 16% difference).

The use of Hencky strain is also convenient when considering the constant-volumeassumption, which is frequently used in the calculation of true stress (see below).For this assumption Hencky strain yields:

(2.8)

where, the subscripts x, y, and z for εH refer to the three orthogonal directionsof strain in a volume element.

FIGURE 2.4 Necking in tension and bulging in frictional compression.

FIGURE 2.5 Comparison of engineering strain (ε) and Hencky strain (εH) of a specimen intension (Note: in tension εH < ε; in compression εH > ε).

Necking

Gage length

TENSION

COMPRESSION

Bulging

F

F F

0

0.05

0.1

0.15

0.2

0.25

0 5 10 15 20

Deformation (%)

Str

ain

Engineering

Hencky

ε ε εH x H y H z, , ,+ + = 0


STRESS

Stress is defined as force per unit area over which the force is applied. Thus, the unitof stress in SI system is Pa ( = N/m2). The concept of stress is developed to eliminatethe artificial effect of sample size on the material properties. Let us consider twocylindrical specimens of same material but different diameters subjected to an axialforce, F (Figure 2.6). We will measure different deformations although specimens aremade of the same material. The reason is that although the force is the same on bothspecimens the intensity of the force, or force per unit area, is higher for the thinnerspecimen. Therefore, stress, instead of force, is a parameter that includes the effect ofspecimen dimensions and can be used to evaluate the mechanical response of a material.

Two types of stress can act on a surface: normal stress and shear stress. Normalstress acts perpendicular to the surface whereas shear stress acts parallel to thesurface (Figure 2.7). Normal stress is further classified as tensile and compressivedepending on the directions of force and unit normal vector of the surface. In tensionthese two vectors are in the same direction (angle 0°) while in compression they arein opposite directions (angle 180°).

In simple shear the force is applied tangentially to the surface as shown inFigure 2.8. The solid lines indicate the original shape of the element. The deforma-tion of the element is such that there is a change in the shape but not in the volumeof the element. The tangential force divided by the area (of the x–y plane) it actson gives the shear stress, denoted by σxy = τ:

(2.9)

In fact, stress and strain at a point in a material are tensorial quantities havingnine components as shown in Figure 2.9.

FIGURE 2.6 Effect of cross-sectional area of test piece on force–deformation relationship.

FF

Thicker specimen Thinner specimen

L0 L0

∆L1 ∆L2

∆L1 < ∆L2

dD

τ =F

At


FIGURE 2.7 Normal (tension and compression) and shear stresses acting on a surface andthe unit normal vector.

FIGURE 2.8 A cubic element undergoing simple shear due to tangential force, Ft.

Tension:

n

F

Compression:

n

F

Shear:

n

Ft

Tangential force, Ft

Normal force, F

Unit normal vector, n

Area, A

A

x

z

y

A

q q

h

d

Ft

Surface area


When stress calculation is based on the initial cross-sectional area of a specimenit is known as engineering stress, σ:

(2.10)

Since the cross-sectional area of a test piece is changing continuously during alarge deformation test, the engineering stress may not precisely represent the stateof stress in the material. Thus, stress calculation based on the current cross-sectionalarea, known as true stress, σt is used more commonly:

(2.11)

The true stress and engineering stress are related to each other by the followingexpression:

(2.12)

Here, exp(εH) = 1 + εH + εH2 /2!… Therefore, for small strains the true and

engineering stresses are essentially the same (i.e., σt .σ). Equation (2.12) is valid

FIGURE 2.9 General state of stress acting on a cubic element (all stresses have positivesense). The corresponding strains are also indicated.

x

y

z

σxx; εxx

σxy; εxy

σyx; εyx

σyy; εyy

σyz; εyz

σzy; εzy

σzz; εzz

σzx; εzxσxz; εxz

σ ≡ F

Ao

σ t

F

A≡

σ σ ε σ εt H= + = ⋅( ) exp( )1


for both in tension and compression as long as the magnitude of ε is used withappropriate sign (i.e., plus (+) for tension and minus (–) for compression). We shouldpoint out that true stress is smaller in compression and larger in tension than thecorresponding engineering stress.

After defining strain and stress, it is useful to demonstrate with an example why itis better to use stress–strain relations rather than force–deformation relations. For this,let us consider force–deformation graphs of three cylindrical specimens of the samematerial but different dimensions undergoing a tensile deformation (Figure 2.10A)(Riley et al., 1995). At first sight we cannot guess that all three curves describe thesame material behavior. In the next figure (Figure 2.10B) the same data are replottedas stress vs. deformation. Here, we see that two of the previous graphs overlay, butthe third one still appears to be different. Finally, we plot the data as the stress vs.strain (Figure 2.10C) to see that all three previously separate curves in fact form asingle graph. This example illustrates that stress and strain are better parameters touse in evaluating and classifying the response of materials to applied forces.

STRAIN RATE

The third important rheological variable, “time,” is introduced in the measurementof strain rate. The concept of strain rate is necessary to describe flow behavior ofmaterials. In flow situations, since the strain will attain very large values withincreasing time, it is preferred to discuss material behavior in terms of stress–strainrate rather than stress–strain. The strain rate is simply the time derivative of strain.For instance, strain rate in compression, and strain rate in simple shear, are given by:

(2.13)

and

(2.14)

where, Vz = axial velocity and Vx = velocity of the moving plate.

FUNDAMENTAL METHODS

UNIAXIAL COMPRESSION

Uniaxial compression is the most popular test for determining rheological propertiesof foods, including cheese. This test is popular probably because it is easy to executeand there is no need for sample gripping (Luyten et al., 1992).

Nearly all compression tests on cheese are done using one of the versatile instru-ments commonly referred to as Universal Testing Machine (UTM) (Figure 2.11). TheUTM provides precise control of deformation while accurately measuring force.

ε HzdL L

dt L

dL

dt

V

L= ( ) = =1

γ δ= =1h

d

dt

V

hx


FIGURE 2.10 Diagrams for accounting the height and cross-sectional area effects of threespecimens (No. 1, No. 2, and No. 3) of same material but different dimensions. No. 1: area= 10 mm2, length = 30 mm; No. 2: area = 10 mm2, length = 60 mm; No. 3: area = 20 mm2,length = 30 mm. (After Riley et al., 1995.)

A

0

1

2

3

4

5

6

7

8

9

0 0.05 0.1 0.15

For

ce (

kN)

No: 1

No: 2

No: 3

B

0

100

200

300

400

500

0 0.05 0.1 0.15

Str

ess

(MP

a)

No: 1

No: 2

No: 3

C

0

100

200

300

400

500

0 0.1 0.2 0.3 0.4 0.5

Strain (%)

Str

ess

(MP

a)

No: 1

No: 2

No: 3

Deformation (mm)

Deformation (mm)


UTMs can be used to conduct compression as well as tension, bending, and sheartests. A number of companies (Table 2.1) are making computer-controlled UTMswith many useful features for operating the machine and acquiring, storing, analyzing,and reporting of the data. The UTMs are designed for various materials such asmetals, concrete, ceramics, papers, polymers, and foods.

FIGURE 2.11 Schematic view of a universal testing machine (UTM).

TABLE 2.1Some Major Manufacturers of Universal Testing Machines (UTMs)

Company Web Site

ATS Applied Test Systems http://www.atspa.comInstron http://www.instron.comLloyd Instruments http://www.lloyd-instruments.co.ukM&L Testing http://mltest.comMTS http://www.mts.comShimadzu http://www.shimadzu.comStable Micro Systems http://www.stablemicrosystems.comTinius Olsen http://www.tiniusolsen.comThwing-Albert http://www.thwingalbert.comUnited Testing Systems http://www.tensiletest.comZwick http://www.zwick.com

Specimen

Load cell

Movingcrosshead


http://www.atspa.com

http://www.instron.com/index.asp

http://www.lloyd-instruments.co.uk

http://www.mltest.com/index.shtml

http://www.mts.com

http://www.shimadzu.com

http://www.stablemicrosystems.com

http://www.tiniusolsen.com

http://www.thwingalbert.com

http://www.tensiletest.com

http://www.zwick.com

A typical arrangement for a compression test is shown in Figure 2.12. In this test,a specimen of known shape and size is placed between two parallel rigid plates of aUTM, and often the upper plate is moved downward at a constant (crosshead) speed(i.e., constant deformation rate) while recording the force as a function of time. Theresulting force–time data pairs are converted into corresponding stress and strainvalues from which other rheological quantities such as Young’s modulus or modulusof elasticity can be calculated (Figure 2.13). A higher value of modulus of elasticity

FIGURE 2.12 Schematic drawing of uniaxial compression test with and without frictional effects.

FIGURE 2.13 Linear elastic constants to be obtained from stress–strain curve.

BEFORE COMPRESSION

Cheese specimen

AFTER COMPRESSION AFTER COMPRESSION

F

F: ForceVz: Deformation rate

Upper Platen(moving)

Lower Platen(stationary)

With friction(inhomogeneousdeformation)

Without friction(homogeneousdeformation)

Vz

Strain

Str

ess

mat

eria

l A

mat

erial

B

Elastic limit for A

Slope A > Slope B(A is stiffer than B)

proportionallimit for B

Elastic limit for B

proportionallimit for A

Slope givesYoung’s modulus


corresponds to a higher material stiffness, as shown schematically in Figure 2.13 formaterials A and B. It is important to note that since Young’s modulus is calculatedfrom the initial part of the stress–strain data the test piece must have perfectly flatand parallel ends for accurate determination of this property (Figure 2.14). For highlynonlinear stress–strain curves, the Young’s modulus is sometimes expressed as the5% strain secant modulus (Charalambides et al., 1995).

Since food materials are viscoelastic and the stress–strain curve is nonlinear,the existence of a true elastic limit, as seen in Hookean solids, is questionable.Therefore, to maintain the purity of the term modulus of elasticity, representingrigidity or stiffness of a material, Mohsenin and Mittal (1977) proposed the term“modulus of deformability” to be used when dealing with stress–strain curves offood materials.

The point at which the linearity between stress and strain ceases to exist iscalled the proportional limit (Figure 2.13). Said differently, the Hooke’s law isapplicable only up to the proportional limit of the material. On the other hand, theelastic limit is the greatest stress, which a material is capable of sustaining withoutany permanent strain remaining upon release of the stress (ASTM, 1995). Thus, ifa stress is applied to a specimen and then removed, the specimen will return to itsoriginal shape and size as long as the stress did not exceed the elastic limit. Ingeneral, the elastic limit is greater than the proportional limit, but for some materialsthey are difficult to distinguish.

In addition to the proportional limit and elastic limit, several other significantparameters, particularly for engineering materials, can be determined from thestress–strain curves such as yield point or yield strength, ultimate strength, resilience,toughness, etc. Each of these parameters is described in Table 2.2 and its calculationillustrated in Figures 2.15–2.18.

In uniaxial compression tests on cheese, mostly cylindrical specimens arepreferred, except few cases where cubic samples are used. It must be noted thatsharp corners in cubic samples are prone to stress concentrations. The tools to

FIGURE 2.14 Effect of shape of test piece on the force–deformation diagram. The “tail” at thebeginning of the curve on right is due to specimen ends not being parallel. (After Bourne, 1982.)

For

ce

DeformationF

orce

Deformation

Specimenwith

parallelends

Specimen withends not parallel

Tail


TABLE 2.2 Description of Some Commonly Encountered Terms in Analysis of Stress–Strain Curves of Engineering Materials

Parameter Description

Young’s modulus ormodulus of elasticity

It is a measure of material’s resistance to axial deformation. It represents the stiffness of the material to an applied load. The larger the stiffness, the higher the force or stress needed to cause a given deformation or strain. Its value is calculated as the slope of the stress–strain curve in the linear section. In shear loading it is called Rigidity Modulus. See Figure 2.13.

Tangent modulus It is defined as the slope of a line drawn tangent to the stress–strain curve at a particular stress (or strain) level. Thus, the tangent modulus can have different values according to the point at which it is calculated. When this point falls within the linear part of the stress–strain curve, the tangent modulus is equal to the Young’s modulus. In general, the tangent modulus describes the stiffness of a material in the plastic region. See Figure 2.15.

Secant modulus It is the slope of a line connecting the origin of the stress–strain curve and any point (e.g., 5% strain) on the curve. It is therefore true that the secant modulus takes different values depending upon the strain at which it is evaluated. The secant modulus also describes the stiffness of a material in the inelastic region of the stress–strain diagram. See Figure 2.15.

Proportional limit It is the highest stress at which stress is directly proportional to strain. Hooke’s law applies up to the proportional limit. The proportional limit also marks the start of nonlinearity in the stress–strain curve. See Figure 2.13.

Elastic limit It is the maximum stress the material can sustain without any measurable permanent strain remaining upon the full release of load. Thus, the material will return to its original shape/size when the stress is removed. To determine the elastic limit, one conducts a cumbersome incremental loading–unloading test procedure until a permanent (or plastic) deformation is detected. See Figure 2.13.

Yield point/yield strength

A small increase in stress above the elastic limit results in a relatively large increase in strain. The specimen is permanently deformed even if the load is reduced to zero. The stress that causes this yielding is termed the yield stress or yield strength. Some materials exhibit a distinct yield point, but many others do not have a well-defined yield point. Therefore, it is common practice to define a yield strength using a procedure called the offset method. In this method, most commonly a 0.2% strain offset is applied. For that, a line parallel to the initial straight-line portion of the stress–strain curve is drawn starting from point 0.002 (or 0.2%) on the strain axis. The point where this line intersects the stress–strain curve is taken as the yield strength. The 0.2% strain offset is arbitrarily chosen and it can be different. Note that the offset method requires a linear portion in the stress–strain curve. For materials showing no linear portion it is practical to define the yield strength as the stress to produce a certain strain (e.g., 0.5%). See Figure 2.16.

Ultimate strength It is the highest stress reached in the stress–strain curve before fracture. The important point is that the ultimate strength is based on the original cross-sectional area of the test piece. If the specimen develops necking (e.g., ductile materials), then the engineering stress will decrease with further increase in strain, but the true stress will continue to increase until fracture. See Figure 2.16.

Resilience It is the amount of energy absorbed by a material in the elastic range. Its value is obtained from the area under the stress–strain curve up to the elastic limit of a material. Materials with a high-yield stress and a low modulus of elasticity will have good resilience. See Figure 2.17.

Toughness (or modulus of toughness)

It is the amount of energy absorbed by a material until fracture (or the amount of work per unit volume). Its value is equal to the total area under the stress–stain diagram. The larger the area, the tougher the material. See Figure 2.17.


Brittle material It is a material that fractures before undergoing little or no plastic deformation. See Figure 2.18.

Ductile material It is a material that exhibits yield point and undergoes significant plastic deformation before failure. The usual measures of ductility are the engineering strain at fracture and the reduction of area (particularly for tension) at fracture. See Figure 2.18.

FIGURE 2.15 Different ways of obtaining modulus from stress–strain relationship.

FIGURE 2.16 Schematic illustration of yield strength, ultimate strength, and fracture stresson the stress–strain curve.

TABLE 2.2 (continued)Description of Some Commonly Encountered Terms in Analysis of Stress–Strain Curves of Engineering Materials

Parameter Description

Strain

Str

ess

5%

Slope = Young’s modulus

8%

Slope = Tangent modulus at selectedlocation (e.g., at 8% strain)

Slope = Secant modulus at selectedlocation (e.g., at 5% strain)

Str

ess

Strain0.2%

Ultimatestrength

FracturestressOffset (e.g., 0.2%)

yield strength


prepare cylindrical cheese specimens typically include a cork borer and a wire cutter(Figure 2.19). The cork borer is useful for cutting out uniform cylinders of certaindiameter from a cheese block, and the wire cutter is good to obtain a certain height(or length) from the cheese cylinders.

The success of a compression test depends largely on the quality and accuracyof the test specimen. It is therefore important that the samples maintain true cylin-drical shape with perfect parallel end faces. This is easier said than done, especiallywhen preparing cylindrical cheese specimens. Van Vliet and Peleg (1991) made anumber of recommendations to ensure proper sample preparation and, consequently,correct experimental data. They state that after boring or cutting an elastic materialthe shape and dimensions of the resulting test piece are different from that of theborer or cutter used to produce it. A similar concern is expressed in ASTM Standard

FIGURE 2.17 Description of modulus of resilience (A) and modulus of toughness (B).

Str

ess

Strain

Fracture

Str

ess

Strain

Fracture

A

B

Modulus oftoughness

Modulus ofresilience

Proportionallimit


(1996) for sample preparation in compression testing of rubber, where the suggestionis to use a cutting tool (Figure 2.20) that is larger in diameter than the specimen toallow for cutting pressure. This hollow cutting tool is rotated in a drill press andlubricated with soapy water to obtain a smooth-cut surface.

Luyten (1988) used a similar borer shown in Figure 2.21 for cutting cylindricalspecimens of Gouda cheese without compression and erosion at the sides of thespecimens. This borer has an inner diameter slightly larger than the diameter of thecutting part. Cheese boring or cutting should be carried out as slowly as possible.Other recommendations for proper cheese sample preparation are listed in Table 2.3.

A wide range of test conditions has been used in uniaxial compression of cheese(Ak and Gunasekaran, 1992). A brief list of experimental conditions is presented inTable 2.4. Since most food products are viscoelastic, and therefore strain-rate sensi-tive, they can produce significantly different responses according to the crossheadspeeds involved. For instance, it is shown that White Stilton cheese is firmer or lessfirm than Gouda cheese depending on the compression speed and the degree ofcompression (Shama and Sherman, 1973). It is considered crucial to know the condi-tions prevailing (e.g., strain rates) during sensory evaluation in order to select theoptimum conditions for instrumental measurements (Sherman, 1975; Voisey, 1975).Bourne (1977) remarked that the rate of compression of solid foods in the mouthvaries widely with many factors such as variations in chewing speeds from person toperson, length of stroke of the jaws, type of food, etc. It is reported that the maximumrate of jaw movement during chewing ranges from 15 mm/s to 30 mm/s, with maleschewing at a faster rate than females (Langley and Marshall, 1993). We shall note,as an exception, that for UF-Feta cheese it is not necessary to run uniaxial compressiontesting at the chewing rate to get a good correlation with sensory evaluation, providedthat the crosshead speed is greater than 50 mm/min (Wium et al., 1997).

FIGURE 2.18 Schematic drawing of stress–strain curves for brittle and ductile materials.

Brittle material

Ductile material

FractureS

tres

s

Strain


Obviously, accurate control of test temperature is extremely important as physi-cal properties of cheeses (and foods in general) are greatly affected by temperaturechanges. It is equally important to make sure that the specimen and the platens aremaintained at the same temperature during a compression test.

The choice of specimen dimensions requires special care. Buckling may occurif the aspect ratio (ratio of sample length or height, L to its diameter, D) is relativelylarge (e.g., L/D > 2). On the other hand, if L/D ratio is small (e.g., L/D < 1) the testresults may be greatly affected by the specimen end conditions (e.g., friction effects).For instance, Chu and Peleg (1985) examined apparent deformability modulus,(determined as the engineering stress divided by engineering strain at 20% defor-mation) and failure conditions (i.e., failure stress and failure strain) of potato, bolognasausage, and process American cheese as a function of height-to-diameter ratio inthe range 0.12 ≤ L/D ≤ 1.00. The flat (i.e., lower L/D ratio) specimens exhibitedhigher apparent deformability modulus (i.e., higher stiffness). This is particularly

FIGURE 2.19 Tools that can be used for sample preparation for compression testing ofcheese. A: a cork-borer machine (from www.hmc-hsi.com, with permission); B: set of corkborers and sharpener (from www.boekelsci.com, with permission); C: table-top wire cheesecutter (from www.ashtongreen.com); D: cheese specimens for compression (after Ak, 1993).


http://www.hmc-hsi.com/

http://www.boekelsci.com/

http://www.ashtongreen.com/

the case when there is considerable friction between the specimen ends and themachine plates (e.g., when plates are coated with emery cloth). For instance, theapparent deformability modulus of the cheese sample with L/D = 0.12 is about 3.5times greater than that for the sample with L/D = 1.0.

Culioli and Sherman (1976) examined the effect of contact surface conditionson force–compression behavior of Gouda cheese at crosshead speeds of 2.5, 10, and50 cm/min and L/D ratio of 1.0. At any of three crosshead speeds the level of friction

FIGURE 2.20 The ASTM cutting tool for cutting cylindrical compression test specimens.(Per ASTM D638.) (After ASTM, 1996. With permission.)

FIGURE 2.21 Cork borer for cutting cylindrical cheese specimens. (After Luyten, 1988; vanVliet and Peleg, 1991.)

ASTM Cutting Tool

DTOOL

DTOOL = 28.804 mm (+0.000/−0.025)

DSPECIMEN = 28.6 ± 0.1 mmLSPECIMEN = 12.5 ± 0.5 mm

14 mm

14.7 mm

17 to 21 mm

Cheese borer

Cheese block

14-mm diameter Cheese sample


at contact surfaces (i.e., with emery paper or with oil) exerted no influence on theforce–compression behavior until 40% compression. At fracture point the force waslower when an emery paper was used at the interface than when the specimen endswere lubricated with oil. However, when the true stress is plotted against percentcompression, the stress was greater when an emery paper was used at the interfacethan when the specimen ends were lubricated with oil. On the other hand, Luyten et al.(1992) found no clear effect of using emery paper or oil at the specimen–machineinterface on the fracture stress of Gouda cheese. Moreover, they recalculatedstress–strain curves from the data of Culioli and Sherman for emery paper and oil,and found no difference between them.

The effect of aspect ratio on the fracture stress of young Gouda cheese is depictedin Figure 2.22. In this figure, data for different friction conditions (i.e., normal plates,lubricated, and emery paper) are pooled together since no clear effect of friction onthe fracture stress is reported (Luyten et al., 1992). It is seen that the fracture stressof this cheese shows a tendency to become constant beyond the L/D ratio of 1.5.

Although the uniaxial compression test appears simple in principle and practice(e.g., no need to grip the sample), the data analysis is complicated by the effect offriction between the specimen and the testing machine platens. Friction influencesnot only the magnitude of the force for compression but also the appearance of thecompressed specimens (Culioli and Sherman, 1976). Barreling due to friction(Figure 2.12) is an indication of nonhomogeneous deformation. During compressionthe cheese specimen is to move relative to the platens and thus the force requiredto achieve a certain level of compression depends also on the friction. Therefore,stresses in the presence of friction (i.e., shear-plus compression) are always greaterthan in the absence of friction (i.e., shear-free compression).

The common practice of reducing the friction is to lubricate the sample–plateninterfaces with low-viscosity oil. It has been shown that type of lubricating oil canhave a significant impact on the measurements (Charalambides et al., 1995). Analternative way of accounting for friction is to bond the sample to the platens usingadhesives such as cyanoacrylate (Casiraghi et al., 1985). Charalambides et al. (2001)described a method based on the Cooke and Larke procedure to account for friction.

TABLE 2.3Recommendations for Cheese Sample Preparation for Uniaxial Compression Tests

If it exists, remove hard rind of cheesePrepare specimens when they are cold (refrigeration temperature)Take sample from the same location in a cheese (e.g., center) and in the same directionTake samples from locations that are sufficiently away from each other since fracture may occur in the

cheese loaf during previous samplingCut specimens as slowly as possible, preferably using a motorized borer and cutting toolLubricate all surfaces of the borer with mineral oil to minimize distortion during cutting outUse a tightly stretched, thin wire cutter, lubricated with mineral oilMeasure actual dimensions of each specimen before testingMake sure that the size of specimen is large compared to the size of the heterogeneity

Source: After van Vliet and Peleg, 1991.


TABLE 2.4Experimental Conditions Used in Uniaxial Compression Testing of Cheese

Cheese TypeCrosshead speed

(mm/min)Temperature

(°C)Sample Diameter, D

(mm)Sample Height, L

(mm)Aspect ratio:

L/D Surface Condition Reference

Cheddar 2.5, 6.4, 12.7, 25.4, 50.8, 127

22 19 19, 29 1, 1.53 Mineral oil Ak and Gunasekaran (1992)

Leicester 25, 50, 250,500, 1000

Room,23–26, 30–37

25 25 1 Mineral oil;emery sheet

Vernon-Carter and Sherman (1978)

Brie 33.3 5, 20 15 19.5 1.3 Smooth hydrophobic paper

Molander et al. (1990)

UF-Feta 100, 200, 300, 400 13 15.3 15.3 1 Low-viscosity oil Wium and Qvist (1997)

Immature Cheddar, Cheshire, Leicester

5–1000 0–40 28.5–29.5 30 ~1 Machine plates Dickinson and Goulding (1980)

Mozzarella cheese analogs

20 20 23 20 0.87 Machine plates Yang and Taranto (1982)

Camembert 10 20 13.8 10 0.72 Machine plates Mpagana and Hardy (1986)


Emmentaler 5, 20, 80 15 16.4 17.5 1.07 Paraffin oil Rohm and Lederer (1992)

Gouda 5, 10, 50 20–21 10, 20, 25 (also cubes of 10 and 20 mm)

7.5–35 0.3–3.5 Mineral oil;emery paper

Culioli and Sherman (1976)

Gouda 0.1–500 20 15 20–30 1.33–2 Machine plates Luyten et al. (1991a)Mild Cheddar, Sharp Cheddar, Monterey Jack

10 4 20 7, 10, 13, 20 0.35–1 Machine plates Charalambides et al. (1995)

Process American cheese

5 Room 10–21 2.5–10 0.12–1 Machine plates; emery cloth (No.120)

Chu and Peleg (1985)

Mozzarella, Cheddar, Processed cheese spread

0.5, 5, 50 7, 22 57 20, 30, 40 0.35–0.70 Paraffin oil; bonding with cyanoacrylate; machine plates

Casiraghi et al. (1985)

Gouda 10 20 20 20 1 Paraffin oil Rohm et al. (1997)Gruyere, processed Mozzarella

3.6, 5.8, 7.9,10.8, 14.4

room 20 5, 8, 11, 15, 20 0.25–1 Machine plates; synthetic grease

Charalambides et al. (2001)


According to this procedure, measurements are made on specimens with a constantdiameter and various heights. Then, results are plotted as true stress against 1/H forconstant values of strain. The intercept of the resulting line (i.e., at 1/H = 0) givesthe correction to be applied to the stress for that strain level.

For uniaxial compression, Hencky strain can be written in terms of the deforma-tion rate (or crosshead speed), Vz as below:

(2.15)

where, L = current sample height, Lo = initial sample height, ∆L = deformation(= Vz t), and t = time.

Since L ≤ Lo in uniaxial compression, εH will have a negative value, an appro-priate sign for compressive strains. Most often the right-hand-side of Equation (2.15)is multiplied with –1 to make the resulting strain values positive for common use.

In lubricated compression a cylindrical specimen of radius Ro and height Lo isdeformed into a cylinder of radius R and height L. From the assumption of constant-volume deformation we can obtain radius at any time from the following relation:

(2.16)

The true stress for lubricated compression is calculated from:

(2.17)

where, F(t) = applied force at any time, A(t) = cross-sectional area at any time,Ao = initial cross-sectional area, Lo = initial length.

FIGURE 2.22 Effect of aspect ratio (height-to-diameter ratio) on fracture stress of Goudacheese in compression. (After Luyten et al., 1992.)

0

50

100

150

200

0.0 0.5 1.0 1.5 2.0 2.5

Aspect ratio

Fra

ctur

e st

ress

(kP

a)

εHo

o

o

o z

o

L t

L

L L

L

L V t

L=

=

−

=

−

ln

( )ln ln

∆

R RL

Loo=

1 2/

σ to o

o z

o o

F t

A t

F t L t

A L

F t L V t

A L= = =

−[ ]( )( )

( ) ( ) ( )


In bonded compression, the cross-sectional area in contact with the compressionplatens remains constant, and the stress in bonded compression is given as (Casiraghiet al., 1985):

(2.18)

The stress is then corrected, σBC, for the shape changes using the followingequation:

(2.19)

This corrected stress equation is shown to be effective to bring results in bondedcompression into agreement with those in lubricated compression up to a strain levelof 0.37 for Cheddar, 1.4 for Mozzarella, and 0.8 for processed cheese spread, wherestrain is defined as ∆L/L. This definition of strain is used since it relates directly tothe extent of bulging (i.e., δo). For the bonded sample the relation is given by thefollowing equation (Christianson et al., 1985):

(2.20)

Kamyab et al. (1998) and Charalambides et al. (2001) analyzed the uniaxialcompression test with friction between the sample and the compression platens,which is quantified by the coefficient of friction. They provided a scheme that enablescalculation of true stress–Hencky strain curve from uniaxial compression data influ-enced by friction. The resulting analytical equation in its simpler form is given as:

(2.21)

where, ∀o = initial sample volume (i.e., πRo2Lo), µ = coefficient of friction, and

Do = initial sample diameter. The results from compression tests are analyzed byplotting [FL/∀o] as a function of [Do/Lo] at fixed values of [Lo/L]. The intercept givesthe true stress, σt, and the slope can be used to calculate the coefficient of friction,µ. Thus, using this procedure one can construct true stress–Hencky strain curvesand determine variation of µ with strain.

More parameters, such as the modulus of deformability and fracture energy pervolume or toughness per volume, can be extracted from stress–strain curves fromuniaxial compression. To facilitate parameter calculations, Ak and Gunasekaran(1992) suggested using polynomial expressions to describe the stress–straincurves as:

σπB

o

F t

R= ( )

2

σσ

BCB

oR

L

=+( )1

2

2

2

δo oRL

L= 3

4

∆

F L L

L

D

Lot t

o o

o

∀

= +

σ σ µ

3

3 2/


(2.22)

where, i denotes an index for the coefficients (ai) and a power for the Hencky-strainterm (εΗ

i ). The coefficients (ai) can readily be determined using a curve-fitting procedure.The modulus of deformability, ED, can be obtained from Equation 2.22 using

the following definition:

(2.23)

The coefficient of the first term in Equation 2.22 becomes equal to the modulusof deformability, and this is why it is necessary to apply a constraint so that it hasnon-negative values in curve-fitting procedure. As an alternative approach, we shallmention that Wium et al. (1997) determined the deformability modulus of UF-Fetacheese as the maximum slope in the range 0 ≤ εΗ ≤ 0.05.

The peak strain, εf, which may sometimes correspond to fracture strain, can beestimated by locating the strain at which the slope becomes zero. That is:

(2.24)

The strain that makes the slope zero (or nearly zero with some tolerance) canbe determined using a root-finding procedure with computation software. Once thepeak strain is computed, then its value can be inserted back into Equation 2.22 todetermine the corresponding peak stress, σf , which may sometimes correspond tofracture stress. Of course, in some cases, it may be easier to obtain the fracture stressand fracture strain values directly from the experimental data without using Equation2.24. However, for cases where a distinct peak is not readily discernible, use ofEquation 2.24 is a practical approach. It is important to restate that in compressiontests the fracture usually starts in the interior of the specimen and often before themaximum stress is reached (Luyten et al., 1991a).

One can obtain fracture work per unit volume (W) (or the total energy per unitvolume, or modulus of toughness) from the area under the stress–strain curve(Figure 2.17):

(2.25)

The calculation of fracture work becomes simpler with the substitution ofEquation 2.22 for stress in Equation 2.25. With this approach we can also easily

σ ε ε ε εt H H H i Hi

i

N

a a a a= + + + ==

∑1 22

33

1

...

Ed

daD

t

HH

=

=

→

σε

ε 0

1

d

dat

Hi H

i

i

Nσε

ε= = −

=∑0 1

1

W dt H

f

= ∫ σ εε

0


obtain the work up to any given strain or deformation by simply changing the upperlimit of the integral. For instance, if we insert the proportional limit for the upperlimit of integral the resulting area is termed the modulus of resilience and is thework done per unit volume to reach the proportional limit (Figure 2.17). The modulusof toughness is a measure of the ductility of a material. The larger the modulus oftoughness relative to the modulus of resilience, the more ductile is the material(Fletcher, 1985).

In Figure 2.23 we present a numerical example where the mechanical parametersmentioned above are extracted from the experimental data. As can be seen inFigure 2.23, there are more than one minimum and maximum points in the slopevs. strain curve. It is not clear if these points relate to some structural changes duringthe compression test.

FIGURE 2.23 Example showing extracting various parameters from stress–strain data (symbols)

by fitting a polynomial equation ( ) to the true

stress–Hencky strain curve (line) (A). From the plot of slope vs. Hencky strain (B), the

modulus of deformability (= slope when Hencky strain approaches zero = 214 kPa) and fracturestrain (εH,f = 0.95), and fracture stress (σf = 58 kPa) are calculated at zero slope. Integratingthe true stress–Hencky strain polynomial equation between the limits εH = 0 and εH = 0.95,according to Equation (2.25), yields the value of fracture work or modulus of toughness as35 kJ/m3. (After Ak and Gunasekaran, 1992.)

0

10

20

30

40

50

60

70

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Hencky strain (-)

Tru

e st

ress

(kP

a)

−50

0

50

100

150

200

250

0.00 0.50 1.00 1.50

Hencky strain (-)

Slo

pe (

kPa)

A

B

σ ε ε ε ε ε= − + − +214 695 1342 1158 3552 2 4 5H H H H H

d

d H

σε


Another important rheological parameter is the Poisson’s ratio (Figure 2.24).When a specimen of length Lo is compressed to final length L it experiences aconcomitant increase in diameter from original value of Do to final D. That is, theimposed axial strain brings about a lateral strain. The Poisson’s ratio is the ratio oflateral strain to axial strain as given below:

(2.26a)

or, in terms of Hencky strains, it is given as:

(2.26b)

The negative sign indicates that the lateral dimensions decrease as the axialdimensions increase. It also makes ν a positive number since the lateral and axialstrains are of opposite sign. The Poisson’s ratio is a material property and is basedon the observation that when a material is subjected to an axial force, let us saytension, it will not only elongate but it will also contract laterally (Riley et al., 1995).

FIGURE 2.24 When a material is compressed by ∆L (from original length Lo to final L), itsdiameter increases by ∆D (from original Do to final D). The associated axial and lateral strainsare used to calculate the Poisson’s ratio. (Equations 26a and 26b.)

F

L

D

∆D/2 D0 ∆D/2

∆L

L0

νεε

= − = − = −−−

lateral strain

axial strainlateral

axial

( ) /

( ) /

D D D

L L Lo

o o

0

νεε

= − = −

H lateral

H axial

O

DD

LL

ln

ln0


Equations 26a and 26b are applicable only to homogeneous isotropic materials;that is, materials with the same properties in all directions. It assumes that the lateralexpansion in uniaxial compression and lateral contraction in uniaxial tension isuniform in the radial direction. This may not be the case for some cheeses. Forinstance, Ak and Gunasekaran (1997) demonstrated that the kneading and stretchingof the curd in hot water results in a Mozzarella cheese with anisotropic tensile andcompressive properties. Anisotropy refers to the fact that material behavior is depen-dent on the direction in which stress is applied or on the direction in which samplingis done. As shown in Figure 2.25, the postdeformation appearances of compressedspecimens taken parallel and perpendicular to the fiber orientation are clearlydifferent. Thus, Poisson’s ratio calculations based on the lateral expansion of thesetwo cases would certainly produce different values. For some cheeses, anisotropicmechanical properties may also be of commercial importance. For Gruyère deComté, a Swiss-type hard cheese, it is reported that anisotropic rheological propertiesare important in the formation of eyes and slits (Grappin et al., 1993). The resistanceto wire cutting of Cheddar cheese (4 months old) from different manufacturers isreported to vary with the cutting direction (Ney, 1985).

Although allowable range of Poisson’s ratio is from –1 to 0.5, its value generallyvaries from 0 (totally compressible) to 0.5 (incompressible). For most metals it hasa value between 0.25 and 0.35 (Riley et al., 1995). Rubber has a Poisson’s ratioabout 0.5, making it nearly incompressible. On the other hand, cork has a Poisson’sratio close to zero, which makes it a good bottle stopper. An axially loaded corkwill not show a lateral expansion, thus making its insertion into a bottle easy.

A negative value for Poisson’s ratio has been reported for polymeric and metallicfoam structures (Lakes, 1987; Friis et al., 1988). Regarding cheese, experimental

FIGURE 2.25 Picture of compressed Mozzarella samples taken parallel and perpendicularto the fiber direction. (After Ak, 1993.)


results indicate that the Poisson’s ratios of Cheddar and Gouda cheeses vary between0.40 and 0.45; that is 20% and 10% lower than the theoretical value of 0.5 for incom-pressible materials (Calzada and Peleg, 1978; Luyten et al., 1991b; Rohm et al., 1997).

The Poisson’s ratio is related to the elastic constants such as Young’s modulus(E), shear modulus (G), and bulk modulus (K) by the following formulas (Findleyet al., 1989):

(2.27)

Bulk modulus describes the change in volume in response to hydrostatic pressure(i.e., equal pressures in all directions). From Equation 2.27, for an incompressible(ν = 0.5) linear elastic solid we can compute E = 3G and K = ∞.

UNIAXIAL TENSION

As far as the direction of applied stress is concerned, uniaxial tension is simply theopposite of uniaxial compression. However, a more fundamental difference betweentension and compression tests is in the strain rate. When a specimen is deformed ata constant speed, the strain rate decreases in tension but increases in compression.Various features of different fundamental methods are listed in Table 2.5.

Uniaxial tension tests are considered not suitable for routine measurements sincethey are more difficult to execute due to lengthy sample preparation and difficultyof gripping (Luyten et al., 1992). Specially designed grips are often necessary inorder to eliminate slippage and breakage of sample in the grips. Grip surfaces canbe scored or serrated to enable better holding. It is generally assumed that the gripassembly and the specimen ends are nearly rigid and all of the deformation is takingplace in the gage section of the specimen. A large number of grips are commerciallyavailable for different purposes and materials (Figure 2.26). The existence of manysophisticated grips designed for particular materials is sufficient to show that thetensile test is difficult to perform even for engineering materials. Therefore, it is nota commonly performed test for cheese, particularly at temperatures above meltingpoint of fat in the cheese.

The test specimen used in tensile testing may have either a circular or a rectangu-lar cross-section. The latter shape is more suitable for cheese. The ends of tensilespecimens are generally enlarged to provide extra area for gripping and to preventsample prematurely breaking at the grips. A typical tension specimen described inASTM Standards for plastics is illustrated in Figure 2.27. The specimen must bealigned as perfectly as possible with the direction of stretching so that the long axisof the test specimen will coincide with the direction of the grip assembly.

Strictly speaking, data from only those tests that produce failure in the gagelength should be used to obtain material properties. In practice, specimens may failnear the grips where there is stress concentration. Therefore, a small notch can bemade in the central part of the test piece to ensure the location where the fracturewill start (Luyten, 1988) (Figure 2.28).

E G

KE

V

= +( )

=−( )

2 1

3 1 2

ν


TABLE 2.5 Advantages and Drawbacks of Various Test Methods Used for Cheese

Test Method Test Type Advantages Drawbacks

I. Uniaxialcompression

Constant rate

a) Easy to prepare samples and to perform the test

b) Young’s modulus can be obtained

c) Fracture stress and strain can be obtained

d) Easy to vary deformation rate

e) Small samples with less chance of containing undesired inhomogeneities

a) Difficult to obtain specimens with flatand perfectly parallel ends

b) Friction affects the property calculationsc) The strain rate increases during a test if a

constant crosshead speed is applied (typical of Universal Testing Machines used in food studies)

d) Rheological parameters depend on specimen size as a result of friction, varying strain rate, and the inhomogeneities in the cheese

e) Start of fracture is often inside the test piece and does not correspond to the maximum stress in the stress–strain curve

f) Assumptions of constant volume and perfect cylinder shape during deformation may not hold

g) Test piece undergoes inhomogeneous straining

Lubricated squeeze flow

a) Biaxial extensional viscosity may be determined relatively easily when cheese specimen is compressed between lubricated plates

b) Deformation rate can easily be varied to obtain biaxial extensional viscosity as a function of strain rate

a) Difficult to separate elastic contribution from viscous contribution to material’s response

b) Difficult to completely eliminate frictionc) Equations will not apply unless the

assumption of perfect cylinder shape holds

Constant force

a) Constant force tests (creep tests) can be executed easily for long time scales provided that necessary precautions are taken to avoid physical and chemical changes

b) The Young’s modulus and the compliance can be determined

c) An apparent viscosity can be calculated from the so-called “secondary stage” where the strain rate is nearly constant

d) Relevant to hole (eye) formation in cheese and sagging of cheese under its own mass

a) Stress decreases during the test if the plate diameter is greater than specimen diameter

b) Strain rate varies during the testc) Drawbacks mentioned above for the

constant rate case applies here as well except that related to strain rate


Parameter calculations in uniaxial tension are similar to those given earlier foruniaxial compression. Strain and stress in uniaxial tension can be calculated usingthe following expressions, respectively:

(2.28)

II. Uniaxial tension

Constant rate or force

a) Fundamental rheological and fracture properties can be determined, such as Young’s modulus, fracture stress, fracture strain, toughness

b) Friction effect is not presentc) Fracture initiation and

propagation can be controlled using notched samples

a) It is often difficult to grip the sample, thus requires specially designed grips to hold samples

b) Fracture may occur at the grips, which is avoided using special sample shapes (e.g., dog-bone shape)

c) Test piece must be long compared to other dimensions for deformation to be homogeneous and for reliable stress–strain calculations.

d) Strain rate decreases during a tension testIII. Bending Constant

rate orforce

a) Easy to perform the testb) No need to fix the specimen

to an apparatusc) Fracture can be observed

mostly on the outside (tension side) of the specimen

d) Test imitates closely the sensory evaluation of cheese by graders

a) Test can be used only for cheese of some rigidity and fairly short texture

b) Large test pieces increase the possibility of containing an undesired inhomogeneity

c) Length of samples must be much larger than the other dimensions, which is sometimes not practical

d) Deformation is far from being homogeneous as it varies from a compressive strain to a no strain at neutral axis, and to a tensile strain at the outside

IV. Cutting(wire or wedge)

Constant rate

a) Easy to execute and no need to clamp sample

b) Small test piecec) Useful for determination of

fracture energy of cheesed) Similar to biting food with

teethe) Fracture is in tension

a) Only fracture energy is determined from this test, and other tests are to be carried out to obtain other rheological and fracture properties

b) Additional cracks may be formed due to inhomogeneities in the structure of brittle materials

c) Friction between the wedge and the specimen may contribute to the measured force, which can be reduced by lubricating the wedge

Source: After van Vliet, 1991a; Luyten et al., 1992.

TABLE 2.5 (continued)Advantages and Drawbacks of Various Test Methods Used for Cheese

Test Method Test Type Advantages Drawbacks

ε εHo

o

o

o z

o

L t

L

L L

L

L V t

L=

=

+

=

+

= +( )ln

( )ln ln ln

∆ 1


(2.29)

Here, Lo and L are initial and final gage lengths instead of total specimen lengths.In stress calculation it is assumed that the volume of specimen remains constantduring extension (i.e., A(t) L(t) = Ao Lo). In strain calculation it is assumed that thedeformation as a result of the crosshead movement is taking place in the gage lengthof the specimen. If this assumption is of suspect, one way to obtain strain values is

FIGURE 2.26 Various designs of commercial grips for tensile tests. (From www.itinscale.com/grips.htm; www.dillon.fm/grip.htm#clevis; www.cscforce.com/gripping.htm. With permission.)

σ to o

o z

o o

F t

A t

F t L t

A L

F t L V t

A L= = =

+[ ]( )( )

( ) ( ) ( )


http://www.itinscale.com/grips.htm

http://www.itinscale.com/grips.htm

http://www.cscforce.com/gripping.htm

to draw marker lines on the specimen before testing and take photographs or video-tape of the specimen during the deformation (Figure 2.29). Using the distancebetween the lines one can calculate the real strain values. Of course, more advancedtechniques involving video recording and image analysis would yield quicker andmore accurate results.

There is an alternative technique to measure tensile properties while actuallyperforming the test in compression. This technique is called the diametral compression(also known as the Brazilian test, indirect tension test, or compression splitting test),which is simpler to execute than the uniaxial tension test. It is a well-establishedmethod to measure the tensile strength of brittle materials such as concrete andceramics (Fahad, 1996). Its application to determine the tensile strength of rice grains

FIGURE 2.27 Tensile specimen with recommended dimensions.

FIGURE 2.28 Tensile specimens with notches.

W

G

D

LO

L

WO

R

Sample thicknessDimension Tolerance

WL

WO (min)LO (min)

GDR

7 to 14195729

24650

11576

4 to 71357191655011576

<43.189.539.5363.57.6225.412.7

±0.5±0.5

+6.4 (3.18 for <4)No max±0.25

±5±1

Recommended tensile specimen dimensions (in mm) for samples of the thickness (mm) listedbelow (after Swallowe, 1999).

Gage length

Notch


has also been reported (Kamst et al., 1999). The diametral compression test is basedon the fact that tensile stresses develop when a circular disc is compressed betweentwo diametrically opposite faces (Fahad, 1996).

For a specimen in the form of a right-circular cylinder of diameter D andthickness t undergoing diametral compression (Figure 2.30) the tensile strength valueσΤ is calculated from:

(2.30)

where, F is the applied force. This equation is derived for a Hookean solid forwhich the stress is proportional to the strain. Equation 2.30 is strictly valid forsamples with a thickness-to-diameter ratio of 0.25 ≤ t/D ≤ 0.5 (Newton et al., 2000).

FIGURE 2.29 Pictures of a deforming cheese specimen at different times in the uniaxialhorizontal extension experiment. (After Ak, 1993.)

σπT

F

D t= 2


BENDING TEST

In sensory evaluation of cheese the panelist takes the ends of a cheese plug by theforefingers and thumbs of both hands and bends the plug slowly into a semicircleto observe when the sample breaks, as well as the nature of the break. This sensoryevaluation sort of mimics the bending test. The bending test can be readily practicedwith a rubber eraser or with a piece of string cheese. The major advantage of thebending test is that there is no need to fix the specimen to the measuring instrument.In this respect the bending test is easy to conduct, especially for brittle and otherhard-to-grip materials. Typically, a cylindrical or rectangular cross-section sampleis laid horizontally on a support with two (blunt or rounded) supporting edges, andthe sample is pushed down at the center of the specimen (Figure 2.31) by meansof a blunt (or rounded) plunger attached to the crosshead of a UTM. There arethree points at which the material comes in contact with the test device. Thus, thistest is also known as the three-point-bending test. The part of the sample on theside of the plunger experiences compressive stress (and compressive strain), andthe opposite side experiences tensile stress (and tensile strain). The plane of tran-sition from compressive to tensile stress (and strain) is known as the neutral axis.Fracture can often be observed on the side of the sample experiencing tensile stress(and strain).

For a proper bending test, the test piece must have a large ratio of length todiameter or thickness, which is hard to obtain with cheese (van Vliet, 1991a).According to Luyten (1988), for Gouda cheese, this ratio should be 3.33 or greater

FIGURE 2.30 Schematic drawing of diametral compression test (F = compressive force;R = sample radius; t = sample thickness; σT = tensile stress developed in the material).

R

F

t

σT


in order to obtain reproducible results. Large specimen size implies higher proba-bility of presence of inhomogeneities in the specimen (see Table 4.1 for variouspossible inhomogeneities in cheese). Luyten (1988) further noted that the bendingtest is good for mature and acid cheese with low fracture strain (i.e., short consis-tency), but not suitable for young cheese with high fracture strain where the testpiece can slide from the supports before it fractures. For soft and deformablematerials, penetration of the plunger used for bending complicates the situation asit introduces a significant compressive stress (Luyten, 1988). It can generally bestated that the bending test is most suitable for studying brittle materials.

The equation for a linear elastic solid giving the bending stress can generallybe expressed in the following form:

(2.31)

where, M is the bending moment, c the vertical distance between the neutralaxis and the point at which the stress is sought, and I the area moment of the cross-section of the beam. The maximum deformation occurs at the center of the beamwhere the load is applied. We can write the following relations for stress and strain.

Specimen with a Rectangular Cross-Section

Maximum stress is given by:

(2.32)

where, F is the applied force, L the span or the distance between supports, b thewidth of test piece, and h the height or thickness of test piece.

FIGURE 2.31 Schematic drawing of three-point bending test.

Neutral axis

F

Plunger

L

-Front view-

compression

tension

neutral

-Side view-

F/2 F/2

h (height or thickness)

b (width)

σ = M cI

σmax = ± 32 2

b F L

h


The corresponding strain at the base of the beam is given by:

(2.33)

where, ∆y is the (maximum) deflection at the center of the beam. We note thatfor the test piece with rectangular cross-section the maximum compressive stress(Equation 2.32 with negative sign) occurs at the top of the beam, whereas themaximum tensile (Equation 2.32 with positive sign) stress occurs at the bottom ofthe beam. The inherent assumption is that the elastic moduli of the material are thesame in tension and compression.

Specimen with a Circular Cross-Section

Maximum stress is given by:

(2.34)

The corresponding strain is given by:

(2.35)

All of the equations given for bending are valid only for small strains and linearelastic materials (Luyten, 1988).

TORSION TEST

Torsion test is applied by twisting a specimen about its longitudinal axis. Specimensused in torsion tests are usually circular in cross-section (Figure 2.32). The test piececan be fixed to the apparatus by gluing; for instance, by using cyanoacrylate adhesive.The torsion test produces pure shear, and hence does not change the specimenvolume. Therefore, it is ideally suited for materials that may exude some of theircontents (e.g., moisture, fat, etc.) under applied force.

For a homogeneous and isotropic material exhibiting linearly elastic behavior(i.e., Hooke’s law applicable, τ = Gγ) the equations to calculate stress and strain aregiven below.

Maximum shear stress at the surface of test piece:

(2.36)

ε = 62

h y

L

∆

σπmax = 8

3

F L

D

ε = 62

D y

L

∆

τπmax

max=2

3

T

R


Maximum shear strain at the surface of test piece:

(2.37)

where, Tmax is the torque on the surface, R the radius of the specimen, θ the totalangle of twist in radians, and L the length of the specimen. The equations given aboveapply to solid, circular materials. Montejano et al. (1983) used capstan-shaped (i.e.,narrow mid-section and enlarged ends) specimens to minimize undesirable stressconcentrations at the locations where the twisting moments are applied (Figure 2.33).Since the diameter of the specimen is not uniform, a geometric correction factor, K,is to be applied to Equations 2.36 and 2.37 for calculating shear stress and shearstrain (Hamann, 1983). The maximum shear stress is given by:

(2.38)

where, Rmin, is the specimen minimum radius, K the constant depending on thesample geometry. K is given by (Lanier, 2000):

(2.39)

FIGURE 2.32 Schematic drawing of torsion test (L = specimen length; R = specimen radius;T = torque applied during test; θ = angle of twist; γ = shear strain).

γ

T

L

θ

rR

τ

r

γ

R

γ θmax = R

L

τπmax

max

min

= KT

R

23

K

R

R

R

R

c

c

=

+ +

+ +

3 1 1

4 1 2 1

1 2 2

1 2

min

/

min

/


and the maximum shear strain is obtained from:

(2.40)

Q is given by:

(2.41)

where, z varies from 0 (center of the groove) to zo (boundary of the groove andend section). For instance, Montejano et al. (1983) used cylindrical gel specimenswith L = 28.7 mm, zo = 6.4 mm, D = 18.6 mm, Rmin = 5 mm, and Rc = 9.4 mm.Using these numerical values and Equations 2.39 and 2.41 we find that K = 1.08and Q = 8.32 × 106 m–3.

VANE METHOD

The vane geometry has been developed to eliminate slip effects frequently observedin yield stress measurements with the rotational viscometers (Barnes and Nguyen,2001). It is simple but effective means of directly measuring the yield stress (Barnesand Nguyen, 2001; Nguyen and Boger, 1983; Nguyen and Boger, 1985). In a recentreview, Barnes and Nguyen (2001) discuss the utility of the vane technique inmeasuring various rheological quantities such as (a) modulus of linear elastic solidsand viscosity of Newtonian liquids; (b) yield stress; and (c) flow-curves of non-Newtonian fluids. In food rheology, the vane geometry is primarily used for directmeasurement of yield stress (Table 2.6).

FIGURE 2.33 Schematic drawing of a capstan-shaped test piece for torsion test (D = specimendiameter at ends; Rmin minimum radius at the specimen center, Rc = radius of curvature; T = torqueapplied during test). (After Montejano et al., 1983.)

RcRmin

T

T

D

γ θπmax

min

= 23

K

R Q

Qdz

R R R zc c

zo

=+( ) − −( )[ ]∫4

2 2 1 2 4

0π

min

/


TABLE 2.6 Experimental Conditions in Food-Related Studies Using the Vane Method

Test MaterialPropertyMeasured

Vane Spindle

Instrument UsedNumber of

Blades

Thicknessof Blades

(mm)

RotationalSpeed(rpm) References

Diameter(mm)

Height(mm)

Frozen ice cream Yield stress 18 38 Lab-made 4 0.1 1 Briggs et al., 1996Spreadable foods Yield stress 10 20

2836

BrookfieldHBTDV-I &5X HBTDV-I

4 0.80 0.5Daubert et al., 1998

Stirred yogurt Equilibrium stress 45 67.5 PhysicaRheolab MC100

4 NAa NA Geraghty and Butler, 1999

Set yogurt Yield stress 35 40–60 Haake VT 550 6 NA NA Dimonte et al., 1998Processed cheese analogs

Yield stress 6 5.5 BrookfieldHBTDV-I

4 NA NA Mleko and Foegeding, 2000

Processed and natural cheese

Fracture stress and equilibrium stress

6–10 15–20 Haake VT 550 4 NA 0.028–5 Truong and Daubert, 2001

Cream cheese Yield stress and strain

10b 2025b

35

Haake VT 5504 0.7 0.5

Breidinger and Steffe, 2001

Protein foams Yield stress 10 20242832

BrookfieldDV-I 25xLVTDV 4 NA 0.3

Pernell et al., 2000


Molten chocolate

Yield stress 152025

405570

Brabender Rheotron 4 0.55

0.0640.1200.224

Wilson et al., 1993

Food dispersions Yield stress 40 (CRc mode)21 (CSd mode)

60 (CR mode)30 (CS mode)

Haake RV2Deer Rheometer III

6 (CR mode)4 (CS mode)

NANA

0.4 Yoo et al., 1995

a NA = Not Availableb Recommended dimensionsc CR = Controlled rate moded CS = Controlled stress mode

TABLE 2.6 (continued)Experimental Conditions in Food-Related Studies Using the Vane Method

Test MaterialPropertyMeasured

Vane Spindle

Instrument UsedNumber of

Blades

Thicknessof Blades

(mm)

RotationalSpeed(rpm) References

Diameter(mm)

Height(mm)


Although the existence of a yield stress as a physical reality has been debated inthe literature (Barnes, 1999), the utility of this rheological parameter is recognized infood processing (Campanella and Peleg, 1987a; Steffe, 1996). Contributing to thediscussion on yield stress, Schurz (1992) mentioned the critical role of this parameterin polymer processing and suggested the use of the term apparent yield stress as aresolution of the debate. Astarita (1990) stated that whether yield stress is or is not anengineering reality depends on the problem in consideration. Thus, from a processingpoint of view, the concept of yield stress is useful as long as the Deborah number (i.e.,the ratio of a material’s characteristic relaxation time to the characteristic process time)is large (Zhu et al., 2001).

Many reasons can be advanced to support usefulness of the concept of yieldstress in food rheology. For instance, (a) for the short time scales encountered infood processing, consumption, and handling activities, a viscoplastic or elastoplasticmaterial may demonstrate solid-like behavior (i.e., not flowing within the timeavailable under a given stress); (b) rheological equations with a yield-stress term(e.g., Bingham, Casson, Herschel-Bulkley models) are successfully used in modelingbehavior of several foods; (c) yield stress is considered a key parameter for qualitycontrol and evaluation of many products (e.g., ketchup, cream cheese, mayonnaise,various spreads) (Steffe, 1996). These commercially important products are formu-lated to display yield stress.

The vane geometry is similar to the concentric cylinder system, except that theinner cylinder (i.e., the bob) is replaced by a vane spindle. The vane spindle is simplyan attachment adapted to fit an existing rotational rheometer or viscometer (e.g.,Brookefield viscometer) (Nijman and Chakrabarti, 1997). A vane consists of a number(2 to 8) of thin blades arranged at equal angles around a slender central shaft.A schematic drawing of a typical four-bladed vane rotor is presented in Figure 2.34.Several examples and dimensions of vane rotors used are listed in Table 2.6.

The key assumptions in vane rheometry are that the shearing stress is uniformover the virtual cylindrical surface described by the outer edges of the blades, thematerial trapped between the blades of the vane is rotating as a rigid body, and thereare no secondary flows between the blades (Barnes and Nguyen, 2001). Theseassumptions are valid if the vane consists of four or more blades and rotates at lowspeeds. There are experimental results on various nonfood and food systems suchas shaving cream (Zhang et al., 1998), oil-in-water emulsions (Yoshimura et al.,1987), and applesauce (Qiu and Rao, 1988), as well as simulation data (Yan andJames, 1997) to support validity of assumptions under stated conditions.

In addition to eliminating the wall slip, the vane geometry offers other advantagesover conventional rotational techniques (e.g., concentric cylinder): the sample prepa-ration is simple and gentle, which enables measurements on weak materials insertingthe vane spindle into the sample causing little disturbance to the material structure.This is important, particularly when working with thixotropic systems and delicatestructures such as foams (Zhang et al., 1998). Multi-phase systems (e.g., suspensions,emulsions) have a tendency to form a low-viscosity, particle-depleted layer adjacentto the shearing surfaces of the traditional viscometer geometries. The velocity gradi-ent in the low-viscosity layer at a fixed shear stress is larger than that in the bulkmaterial, which then results in apparent slip. However, the vane geometry avoids


the wall-slip problem by using the test material contained between the vane bladesas the virtual shearing surface. In a way, the vane acts like a solid cylinder (i.e.,bob) without the wall-slip complications. It is also worth noting that the slip at theouter cylindrical boundary can be eliminated by inserting a slender gauze basketinside the outer cylinder (Barnes and Nguyen, 2001) or lining the inner wall withaluminum foil (Yoshimura et al., 1987).

Another advantage of the vane method is that original product containers canbe used as sample holders while measuring with the vane spindle. There is no needfor a narrow gap (in contrast to concentric cylinder geometry), and the vane is lesssusceptible to artifacts arising from the presence of large particles. Breidinger andSteffe (2001) recommend the vane dimensions of 10 mm in length by 25 mm indiameter after considering the size of most commercial cream-cheese containers andmaximum torque capacity of rotational viscometers.

Nguyen and Boger (1983) studied the effect of rotational speed on the yieldstress of bauxite residue suspensions (red mud) over a range of speeds from 0.1 rpmto 256 rpm. Their results, replotted in Figure 2.35, indicate a practically constantyield stress between 0.1 rpm to 8 rpm, followed by a rising yield stress with

FIGURE 2.34 The vane rotor with four blades (H = vane height; D = vane diameter; Ω =angular velocity).

H

D

Ω

D

H


increasing rotational speed. However, Nguyen and Boger (1983) used the lowestavailable speed of 0.1 rpm to minimize any unforeseen errors. As noticed inTable 2.6, in studies on foods, the vane is often rotated at a constant speed less than1 rpm. There is experimental evidence indicating the effect of rotational speed onthe yield stress values of molten chocolates and food dispersions (Wilson et al.,1993; Qiu and Rao, 1988) and TiO2 suspensions (Liddell and Boger, 1996). Highvane speeds, particularly in low-viscosity liquids, are risky since secondary flowsmay develop between the blades (Barnes, 1999).

A typical torque-time response for a material having a yield stress is illustratedin Figure 2.36. The initial elastic region is followed by a slightly curved part beforereaching the peak torque. After a distinct maximum torque, a decline (rapid or

FIGURE 2.35 Effect of vane rotational speed on yield stress of red mud. Vane geometry:H/D = 1.923. (After Nguyen and Boger, 1983.)

FIGURE 2.36 Typical torque-time response from the vane in a rate-controlled mode. Maximumtorque (Tmax) occurs after a certain time (tmax) of rotation of the vane.

0

100

200

300

400

0.1 1 10 100 1000

Rotational speed (rpm)

Yie

ld s

tres

s (P

a)T

orqu

e

Tmax

Timetmax


gradual depending upon conditions) is observed towards an equilibrium torque value.In general, the peak torque is the only parameter derived from these curves tocompute the yield stress. The peak torque is, of course, readily and unequivocallydetermined in comparison to other points of possible interest (e.g., departure fromlinearity, equilibrium level).

When the vane blades are entirely immersed in a sample, as shown in Figure 2.37a,the following equation is used to calculate the yield stress (τy) from the measuredmaximum torque and vane dimensions:

(2.42)

where Tmax is the maximum torque, D the vane diameter, H the vane height.When the top of the vane blades are aligned even with the top surface of the sample(Figure 2.37b), the stress contribution from the material above the vane is eliminated,and Equation 2.42 takes the form:

(2.43)

The following geometrical ratios have been proposed for accurate measurementswith the vane method: H/D < 3.5; DT/D > 2.0; Z1/D > 1.0; Z2/D > 0.5 (Nguyen andBoger, 1985). Here, DT is the diameter of the container, Z1 and Z2 are height of

FIGURE 2.37 Schematic diagram of vane system (diameter, D; height, H, and containerdiameter, DT; Ω = angular velocity) in different positions: (a) immersed in the sample (Z1

and Z2 height of sample above and below the vane, respectively), (b) top surface in level withthe sample.

Z1

Z2

(a) (b)

H

D

Ω Ω

DT

τπy

T

D

H

D=

+

−2 133

1max

τπy

T

D

H

D=

+

−2 163

1max


material above and below the vane, respectively. Typically, the blades are made ofstainless steel with the thickness less than 1 mm.

Recently, a new instrument called “slotted-plate device” has been developed todirectly measure static yield stresses of suspensions (Zhu et al., 2001). The slotted-plate device is reported to be more reliable for evaluating smaller yield stresses andavoids possible secondary flows between the blades and nonuniform stress distribu-tion along a virtual cylindrical surface — the key assumptions in the vane geometry.

The success with the vane method has resulted in new applications and designsof this geometry such as oscillatory testing and texture analysis (Junus and Briggs,2001) and hand-held versions of the vane instrument (Keener et al., 1999).

STRESS-RELAXATION TEST

One of the fundamental tests to study viscoelastic response is stress relaxation. Thistest can be performed in (uniaxial) tension, compression, shear, bending, torsion,etc. When a constant strain is applied to a viscoelastic material isothermally, thestress necessary to maintain that strain is not constant but decreases with time. Hence,the decrease of stress at constant strain is called stress relaxation.

Two kinds of relaxation experiments can be conducted: stress relaxation after asudden step strain, which is often applied to solids; and stress relaxation followinga cessation of steady flow, which is often applied to liquids (Figure 2.38) (Dealy,1995; Ferry, 1980; Whorlow, 1980).

Stress-relaxation response permits rapid characterization of material behavioras shown in Figure 2.39. When a step strain is applied to ideal elastic solid, a finiteand constant stress will be reached. Ideal elastic solids store all the energy chargedduring the straining step and would expend this energy upon removal of stress toreturn to its original size and shape. In a way, ideal elastic solids possess a perfectmemory of the initial state. Thus, the same stress should be kept on the specimen at

FIGURE 2.38 Two types of stress relaxation test: step strain for solids and cessation of steadyflow for liquids.

Time

Stepstrain

Cessation offlow

Str

ain


FIGURE 2.39 Step-strain input (A) and stress relaxation response of ideal elastic material(B), ideal viscous material (C), and viscoelastic material (D). The stress and strain on theviscoelastic material is schematically depicted at different times during the test at the bottom.

1

2

3

4

4321

σ1=0 σ2 σ3 σ4 σ2 > σ3 > σ4

Time

ε0ε0ε0

Str

ess

Str

ess

Str

ess

Str

ain

Constant strain input

Time

Time

Time

Ideal elastic response

Ideal viscous response

Linear viscoelastic response


all times for strain to remain constant. On the other hand, for ideal viscous liquids thestress decays to zero immediately after the cessation of strain application. Ideal viscousliquids do not store any energy and have no memory of the initial state. However,various materials, including foods, are viscoelastic and exhibit an intermediateresponse where stress relaxes at a finite rate characterized by the relaxation time (Peleg,1987). Viscoelastic materials can be considered as materials with “fading memory.”

If a viscoelastic material relaxes to zero stress within a certain period (e.g.,experimental time) it is further characterized as “viscoelastic liquid.” In contrast, aviscoelastic material is considered as “viscoelastic solid” if a finite stress remainsunrelaxed (i.e., residual stress) after a sufficiently long time. With most foods,however, the “sufficiently long time” is on the order of few minutes due to chemical,enzymatic, and physical changes that foods normally experience. The residual stressafter an arbitrary time for test duration (e.g., 10 min) is suggested as a quantitativemeasure of the degree of “solidity” of foods (Peleg, 1987).

The relaxation experiment can be viewed as composed of two steps: the strainingstep and the relaxation step. Ideally, the straining step is instantaneous, but in realityit takes finite time. The time it takes to apply the step strain is called the rise time. Therise time depends upon the capability of the instrument used and the magnitude ofstrain. For instance, if the highest crosshead speed of a UTM machine were1000 mm/min, then it would require 0.09 s to apply 10% deformation on a sample of15 mm height. Since stress relaxation of a viscoelastic material is affected by the historyof deformation, the time taken for the straining step is important (Meissner, 1978).Accurate stress-relaxation tests require the rise time of the applied strain to be short incomparison with the relaxation times to be measured. With the advanced rheometersit is possible to apply a step strain within few seconds or milliseconds (e.g., 20 ms to1000 ms) (Lauger and Huck, 2002). Obviously, for a proper test the applied strain, andconsequently the resulting stress, should be lower than the corresponding fracture value.

Although in nonfood applications stress-relaxation tests can be continued for along time, the test duration for foods is limited (on the order of minutes, e.g., 10 minor less) because degradation of sample may occur before the test is completed as aresult of physical changes (e.g., moisture exchange with environment), microbialactivity, and chemical and biochemical changes (e.g., enzymatic browning in fruits,oxidation in oil-containing foods) (Peleg, 1987).

For a linear viscoelastic material subjected to an instantaneous constant strain(εo),* the initial stress will be proportional to the applied strain and will decreasewith time (Figure 2.40). By linearity it is meant that when the applied strain ismultiplied by any factor (e.g., doubling), the stress it produces also changes by thesame factor (e.g., doubling). The rate of stress decay is quantified by a materialcharacteristic time known as relaxation time, λ. The relaxation time in practice isdefined as the time for stress to decay to about 37% of the initial level. However,single-relaxation time is often insufficient to fully describe the relaxation curve ofmost food materials. A better representation of relaxation curve is possible by usingmore than one relaxation time or, ideally, by using a continuous relaxation-timespectrum (Peleg and Normand, 1983).

* The symbol ε hereafter denotes Hencky strain unless stated otherwise.


For linear viscoelastic materials the stress decay with time t can be described,in tension or compression, by the following equation:

(2.44)

where, the function E(t) is called the relaxation modulus. The relaxation modulusrepresents the change in stress per unit of applied strain and is a material property.For linear elastic solids the E(t) = E, the Young’s modulus. In shear configurationthe corresponding equations are given as:

(2.45)

where, τ(t) is the shear stress, G(t) the shear stress relaxation modulus, and γ o

the applied constant shear strain.

FIGURE 2.40 In actual relaxation test, the strain is applied over a finite time (rise time).The peak stress at the end of the straining stage is the inital stress (σo). Time taken for thestress to decay to 0.37σo during the relaxation stage is the relaxation time, λ .

Relaxation stageStraining stage

Str

ess

Relaxationtime, λ

TimeRise time

0.37σ0

σ0

σ ε

σε

t E t

or

E tt

o

o

( ) = ( )

=

( )( )

τ γ

τγ

( ) ( )

( )( )

t G t

or

G tt

o

o

=

=


Analysis of Relaxation Behavior

Stress relaxation is a basic test providing information on the viscoelastic characterof materials rapidly. Although in principle relaxation test can be done in any con-figuration (i.e., compression, tension, shear, torsion, bending, etc) the most commonone in cheese studies is compression.

To determine linear viscoelastic region of a material in relaxation, a series ofrelaxation curves is obtained by sequentially increasing the applied strain. When theresulting data is replotted in terms of modulus vs. time, the curves within the linearviscoelastic region will overlap. The strain level at which the curve does not overlapindicates that the linear viscoelastic region is exceeded. Alternately, the linear rangeof the isochronal — the plot of stress against strain at a specific time — will indicatethe extent of strain level over which the material response can be considered linear(Ak and Gunasekaran, 2001). The process of obtaining isochronal plots is illustratedin Figure 2.41. The data obtained at two constant strains (ε1 and ε2) are representedin Figures 2.41A and 2.41B. From these, data points (for, e.g., a, b, c, d inFigure 2.41A and 2.41B) are gathered at different times (e.g., t1 and t2). Then thecorresponding σ(t) vs. ε plot is constructed for each of the times at which the stressresponse is measured (Figure 2.41C). The strain value at which the isochronal beginsto deviate from linearity (indicated by dotted line in Figure 2.41C) is the upper limitof the liner viscoelastic region for the material. The hatched region in Figure 2.41Cindicates the nonlinear range of the material studied.

The mechanical model most suitable for quantification of relaxation behaviorof foods and a variety of polymeric materials has traditionally been the generalizedMaxwell model (Figure 2.42) with a discrete number of elements (Peleg andNormand, 1983):

(2.46)

where, Eo is the modulus of the single spring (λ = ∞) in parallel to Maxwellelements in Figure 2.42, t the time, Ei the modulus of each Maxwell element, andλi the relaxation time of each Maxwell element. It must be mentioned that for a trueviscoelastic liquid the first term (i.e., Eo) will be zero and the material will eventuallyrelax completely.

For linear viscoelastic behavior, the relaxation parameters are a function of timeonly. However, for nonlinear viscoelastic behavior, the relaxation parameters willbe a function of time as well as imposed strain and strain history.

An alternative model to describe relaxation and creep curves of viscoelasticsolids is suggested by Peleg (1979, 1980):

(2.47)

σε λ( )

( ) expt

E t E Et

oo i

ii

n

= = + −

=

∑1

t

Y tk k t

( )= +1 2


and

(2.48)

where, σo is the initial stress and σ(t) the decaying stress. This linearizationmakes the calculation of model parameters easy as the slope gives k2 and the interceptgives the k1. As it is also true for the parameters of the generalized Maxwell model,

FIGURE 2.41 Plotting isochronals to determine linear viscoelastic range from stress relax-ation data. (A) relaxation experiment at applied strain ε1; (B) relaxation experiment at appliedstrain ε2; and (C) isochronals plotted using data points a, b, c, and d from A and B at timest1 and t2. (After Ak and Gunasekaran, 2001.)

t

tt

t

ab

dc

t1 t2 t1 t2

ε2

ε1

σ2(t)σ1(t)

d

c

b

a

σ

Linear

Nonlinear

ε1 ε2 ε

σ(t2)

σ(t1)

(a) (b)

(c)

Y tto

o

( )( )

=−σ σσ


the dependency of the constants k1 and k2 on the applied strain is an indication ofnonlinear viscoelasticity related to the structural modifications that occur duringdeformation. Peleg (1980) further stated that 1/k1 represents the initial decay rate,while 1/k2 represents asymptotic level of Y(t) when t→∞.

CREEP TEST

As with stress relaxation, a creep test can be performed in different configurations(i.e., compression, tension, shear, torsion, etc). In an isothermal creep test, a constantstress is applied to the material, and the resultant strain is recorded as a function oftime (Figure 2.43). In an actual test the stress application is not instantaneous butcan be rapid such as by dropping the weight on the specimen.

Analysis of Creep Behavior

In a creep test a constant step-stress is applied to a material and the resultingdeformation or strain is measured as a function of time. The distinction betweenconstant stress and constant force is necessary, especially for highly deformablefoods, because of the progressive change in the cross-sectional area of the specimen.Hence, a constant force (i.e., dead weight) results in a progressively increasing stressin uniaxial tension and decreasing stress in uniaxial compression (Purkayastha et al.,1985). Although in principle creep tests can be done in any configuration (i.e.,compression, tension, shear, torsion, bending, etc.), the most common one in cheesestudies is compression.

For linear materials, the time-dependent compliance, D(t), is given by (Findleyet al., 1989):

(2.49)

where, ε(t) is the tensile or compressive strain. Symbol J(t) is used to representthe shear creep compliance, that is, J(t) = γ (t)/τo, where γ (t) is the shear strain, and

FIGURE 2.42 Generalized Maxwell element for stress relaxation (E0, E2, E3, … En are springstiffnesses; η1, η2, η3, … ηn are dashpot viscosities).

hn

En

h3

E3

h2

E2E1

h1

E0

D t t o( ) ( )≡ ε σ


FIGURE 2.43 Typical creep–recovery test. (A) application of instantaneous and constantstress (σo); (B) strain response of elastic solid and viscous liquid; (C) strain response ofviscoelastic material. The application and removal of load (W) is shown at the bottom atvarious times along the creep–recovery curve for the viscoelastic material.

1 2

W

WW

W

Str

ain

Str

ain

Str

ess

1

Creep

0

0

0

2

3

4

5

Recovery

3 4 5

A

B

C

Linear viscoelastic responset1

t1

t1

Permanentstrain

εi

εo

σo

εi

Viscous liquid response

Elastic solid response

Time

Time

Time

Load removedConstant stress application


τo the applied shear stress. The objective of creep tests is to determine materialproperties D(t) and J(t) from the experimental strain vs. time data (Figure 2.44).

To determine linear viscoelastic region of a material in creep, a series of creepcurves is obtained by sequentially increasing the applied stress (Figure 2.45). Whenthe resulting data is replotted in terms of creep compliance vs. time the curves withinthe linear viscoelastic region will overlap.

A typical creep compliance curve is shown schematically in Figure 2.44. Unlessthe applied force or stress is carefully selected the test terminates with the failureof the specimen, especially in tension. Quantification of creep behavior of foods anda variety of biological and polymeric materials has been traditionally based on the

FIGURE 2.44 Typical creep compliance D(t) vs. time response of a viscoelastic materialcomprises of instantaneous compliance, delayed creep, and steady state flow (of viscosity η).

FIGURE 2.45 Determining linear viscoelastic region by creep tests. A. Creep curves atdifferent stress levels σ1, σ2, and σ3; B. Compliance D(t) vs. time for the corresponding creepcurves overlap within the linear viscoelastic region (σ1 to σ2). Stress level σ3 is outside oflinear viscoelastic region. (After Anon, 2002.)

Instantaneous compliance

Delayed creep

Steady state flow

Creep Curve

Time

D(t)

∑Di

Do

slope = 1/η

σ1

σ2

σ3

Time

Str

ain

σ3

σ3 > σ2 > σ1

σ2 & σ1

Time

Com

plia

nce

, D

(t)

(a) (b)


generalized Kelvin-Voigt model (Figure 2.46) with a discrete number of elements(Purkayastha et al., 1984):

(2.50)

where, Do is the instantaneous compliance (= 1/Eo), t the time, η1 the Newtonianviscosity while 1/η1 being the slope of the linear portion of the creep curve aftersufficiently long time, Di the delayed compliance of each Kelvin-Voigt element(= 1/Ei), and τi the retardation time of each Kelvin-Voigt element. The last term inEquation 2.50 is called the creep function and denoted by ψ(t) (Purkayastha et al.,1984). It must be mentioned that for a true viscoelastic solid material the secondterm (i.e., t/η1) will be zero, and the material will eventually reach an equilibriumcreep compliance. Equation 2.50 also reveals that a typical creep curve is composedof three components, as illustrated in Figure 2.44.

For linear viscoelastic behaviors the creep parameters are a function of timeonly. However, for nonlinear viscoelastic behaviors the creep parameters will be afunction of time as well as imposed stress and stress history.

As for the relaxation case, the Peleg model (Purkayastha et al., 1984) can beused to linearize and represent the creep behavior of foods. For creep data, the Pelegmodel is used to represent the creep function using constants k1″ and k2″ as:

(2.51)

SHEAR RHEOMETRY

Polymer and food-processing applications involve a wide range of shear rates asshown in Figure 2.47. Thus, various rheometry measurements based on differentgeometries are essential and complementary to each other.

FIGURE 2.46 Generalized Voigt-Kelvin element for creep (E0, E2, E3, … En are springstiffnesses; η1, η2, η3, … ηn are dashpot viscosities).

E0η1

E2

η2 η3

E3 En

ηn

εσ η τ( )

( ) expt

D t Dt

Dt

oo i

ii

n

= = + + − −

=

∑1 2

1

ψη

( ) ( ) " "t D t Dt t

k k to= − − =+1 1 2


Rheological measurements based on shear flow are conveniently divided intotwo groups: (a) drag flows in which shear is generated between a moving and afixed solid surface, and (b) pressure-driven flows in which shear is generated by apressure difference over a closed channel (Macosko, 1994). Examples of shear-flowgeometries belonging to the first group include sliding plates, concentric cylinders,parallel disks, and cone and plate. Examples of shear-flow geometries belonging tothe second group include capillary or Poiseuille flow, slit flow, and axial annulusflow. The working equations for some of these measurement techniques are presentedhere. Interested readers are referred to other sources (Collyer and Clegg, 1988;Macosko, 1994; Steffe, 1996) for detailed discussions.

The measurement systems described below can be used to conduct a variety oftests (e.g., steady shear, dynamic, relaxation, creep). In some tests, one system maybe preferred over the others due to the shear-rate range or other advantages it offers.For instance, parallel-plate geometry is often preferred for measuring viscoelasticproperties of solid cheese (e.g., relaxation modulus, creep compliance, dynamicmoduli) since the sample handling is easier and the sensitivity to gap setting is lessas compared to the cone-and-plate geometry.

There are several companies manufacturing highly advanced rheometers andviscometers that will satisfy the measurement needs of researchers. Barnes et al.(1999) summarized the history of commercial viscometry and rheometry. Web sitesof various companies offering rheological instruments are given in Table 2.7 forreaders to have quick access.

SLIDING-PLATES GEOMETRY

The schematic drawing of the sliding-plate geometry is shown in Figure 2.48. Thisrelatively simple arrangement is generally used in defining shear viscosity. The

FIGURE 2.47 Approximate shear rate ranges for different rheometry measurements and thoseinvolved in polymer processing and food processing applications. (After Riande et al., 2000.)

10−3 10−2 10−1 100 101 102 103 104 105

Polymer Processing

Capillary

Elongational

Oscillatory/Vibrational

Rotational

Shear rate (s−1)

Food Processing

10−6


sliding-plate rheometer can be operated in either strain-controlled or stress-controlledmode. The shear strain (γ), shear rate ( ), and shear stress (τ) can be calculated fromthe following equations (Dealy and Wissbrun, 1989; Macosko, 1994):

(2.52)

(2.53)

TABLE 2.7Some Major Manufacturers of Rheometers and Viscometers

Company Web Site

Alpha Technologies http://www.alpha-technologies.com/ATS RheoSystems http://www.atsrheosystems.comBohlin Instruments http://www.bohlin.com/Brookfield http://www.brookfieldengineering.com/Camtel http://www.camtel.co.uk/Dynisco Polymer Test http://www.dynisco.com/GBC Scientific Equipment Pty Ltd. http://www.gbcsci.com/Goettfert Inc. http://www.goettfert.comHaake http://www.thermo.com/Infra Scientific http://www.infra.uk.com/Kaltec Scientific http://www.kaltecsci.com/Paar Physica http://www.physica.de/Porpoise Viscometers http://www.porpoise.co.uk/Pressure Profile Systems, Inc. http://www.pressure-profile.com/Reologica Instruments AB http://www.reologica.se/Research Equipment (London) Ltd. http://www.research-equipment.com/Rheometric Scientific http://www.rheosci.com/TA Instruments http://www.tainst.com/Vilastic Scientific Inc. http://www.vilastic.com/

Source: The Society of Rheology Web site, http://www.rheology.org/sor.

FIGURE 2.48 Description of sliding plate geometry. Application of shear force Fx movesthe top plate by ∆X at a velocity Vx.

sample

Moving plate

Stationary plate

x

y

L

Width of plate = W; Area of plate, A = L.W

Fx,Vx

sampleH

∆X

γ

γ = =∆X

H

V t

Hx

γ =V

Hx


http://www.alpha-technologies.com/main.htm

http://www.atsrheosystems.com

http://www.bohlin.com/

http://www.brookfieldengineering.com/

http://camtel.demonweb.co.uk/

http://www.dynisco.com/

http://www.gbcsci.com/

http://www.goettfert.com

http://www.thermo.com/

http://www.infra.uk.com/

http://www.kaltecsci.com/

http://www.anton-paar.com/ap/apinternet/html/default/CXSN-5PPFLE.en.0

http://www.porpoise.co.uk/

http://www.pressure-profile.com/

http://www.reologica.se/

http://www.research-equipment.com/

http://www.tainst.com/products/rheology.html

http://www.tainst.com/

http://www.vilastic.com/

http://www.rheology.org/sor/

(2.54)

where, L is the plate length, W the plate width, H the sample thickness, ∆X thesliding-plate displacement, Vx the velocity of sliding plate, Fx the shear force, and tthe time.

The shear viscosity is then computed from η = τ / . The assumptions involvedin the sliding-plates geometry include: (a) negligible inertial and edge effects toestablish homogenous, simple shear flow, and (b) L and W are much greater thanH, and H is as small as possible. The principal advantage of the sliding-plategeometry is that it is ideally suited for studying nonlinear viscoelasticity. Therelative advantages and disadvantages of different rheometer geometries for study-ing nonlinear viscoelasticity are listed in Table 6.1. Further discussion on the theoryand application of the sliding-plate rheometer for studying nonlinear viscoelasticityof cheese is presented in Chapter 6.

CONCENTRIC-CYLINDERS GEOMETRY

The schematic views of different concentric-cylinder geometries are shown inFigure 2.49. The concentric-cylinder geometry has long been used in commercialviscometers. The concentric-cylinder system consists of an inner cylinder (called“bob”) positioned inside an outer cylinder (called “cup”). The sample is containedin the annular gap between the “infinitely” long bob and cup. In some cases thecup is rotated at a steady angular velocity while the bob is kept stationary, and inothers, the bob is rotated at a constant angular velocity and the cup is fixed. Theconcentric-cylinder system is typically used with low-viscosity materials andmobile suspensions. The double-gap or double-Couette geometry (Figure 2.49)offers greater sensitivity than the other concentric-cylinder systems at low shearrates and viscosities as a result of its larger surface area.

If sample drying (or skin formation) is likely to be an issue, which is a commonproblem in working with low-fat cheeses, it is better to use a solvent trap with themeasuring system or alternatively a low-viscosity oil can be used as a barrier providedthat the oil used does not interact with the sample to alter the sample properties.

Working equations for shear strain γ, shear strain rate , and shear stress τ aregiven as (Macosko, 1994):

Shear strain:

(2.55)

τ = =F

A

F

L Wx x

γ

γ

γ κ=−

= ≥

=+( )

Ωi

o i

o i

t R

R R

and

RR R

(for narrow gaps; that is

R

Ri

o

0 99

2

. )


Shear strain rate:

FIGURE 2.49 Different concentric-cylinder measurement systems.

Coaxial cylinder with conic base

sample

Bob Cup

Standard concentric cylinder

Mooney cell(recessed bottom cylinder)

Double gap(double Couette)

Wi

a

Lb

L

trapped air

Ri

Ro

z

r

Wi

Wi Wi

L

Lb

˙ ˙ . )γ γκ

κR RR

R Ri oi

o i

i( ) ≅ ( ) =−

=−

>Ω Ω

(for 2

10 992


(2.56)

Shear stress:

(2.57)

where, Ri is the radius of bob, Ro the radius of cylinder, Mi the torque on boband Ωi the angular velocity of bob, L the height of bob.

Other alternative designs that are generally used to minimize end effects or makepossible to account for the end effects are also depicted in Figure 2.49. The shearstress for the coaxial cylinder with conic base is given by:

(2.58)

With the Mooney cell or recessed bob the air is trapped underneath the bob andcontributes practically no torque to the overall response.

As can be seen from Equation (2.56), the shear rate changes across the gap fora wide-gap viscometer. This is a serious concern when using concentric-cylindergeometry with concentrated suspensions. Rotating the bob in a concentrated sus-pension causes particles to migrate away from higher shear-rate regions near thebob to lower shear-rate regions near to the cup (Abbott et al., 1991).

CONE-AND-PLATE GEOMETRY

Sketches of different cone-and-plate (C&P) geometries are shown in Figure 2.50.The C&P system consists of a rotating (stationary) cone and a stationary (rotating)plate with a sample contained between them. The apex of the cone is essentially incontact with the plate. As seen in the following working equations the main advan-tage of using the C&P geometry is that the shear rate is approximately constant (i.e.,independent of radial position) throughout the sample provided that the cone angledoes not exceed a few degrees (e.g., ≤ 4°) (Macosko, 1994). This feature of constantshear rate is the reason why C&P geometry is particularly useful for studying non-Newtonian behavior.

and

Rn

Rn

where

nd M

dR

R R

ii

n oi

n

i

i

o i

˙ ˙

ln

ln

/ /γ

κγ

κκ( ) =

−( ) ( ) =−−( ) < <

= =+

−

2

1

2

1

2

2 2

and

(for 0.5 0.99)

and

Ω Ω

Ω

τπ

RM

R Lii

i

( ) =2 2

τπ π

RM

R L Ri

i

i i

( ) =+

223

2 3


Shear strain:

(2.59)

where φ is the angle of rotation and α the cone angle. It is true that for a smallcone angle tan(α) ≅ α*, for which the shear strain becomes:

(2.60)

It is seen that for a given cone angle the strain is homogeneous and independentof position in the sample.

Shear rate:

(2.61)

For small cone angles the shear rate can be simplified to:

FIGURE 2.50 Different cone-and-plate measurement systems.

* Maclaurin series for tan(α) is given as: tan(α) = α + (α3/3) + (2α5/15) + … where α in radian unit(Thomas and Finney, 1988).

hc

Normal cone-and-plate system

Extended cone-and-plate system

Double cone system

Cone-and-dish system

Rd

R

rR

α

Ω, φθ

sample

Truncated cone-and-plate system

R

Rt

γ φα

=tan

γ φα

=

d

dt

d

dt

γ γ φα α

= = =˙sin sin

1 Ω


(2.62)

where, Ω = specified angular velocity. This equation shows that a uniform shearrate is realized experimentally with cone-and-plate system with small cone angles.According to the calculations of Adams and Lodge, reported in Lodge (1964), theerrors involved in shear rate approximation by Equation 2.62 are 0.02, 0.18, 0.50,and 2% for cone angles of 1°, 3°, 5°, and 10°, respectively, for a material with aconstant viscosity.

Shear stress:

(2.63)

where, M = torque and R = radius of plate. This equation indicates that properloading of the specimen is vital so that a full contact of the cone with the specimenis established since the torque measurement (and, consequently, the stress calcula-tion) depends on R3.

The C&P geometry is typically configured with cones having angles less than4°. The cone angle shall be chosen with care since, for instance, for large coneangles the shear rate across the gap will vary; on the other hand, for the small coneangles there is higher chance for errors due to gap settings. For instance, for a coneangle of 10° the variation in shear rate across the gap is 3%, and the resulting errorin calculated viscosity of Newtonian liquids is 2%. However, since the cone anglestypically used is 4° or less the resulting error is quite small (Dealy, 1982).

The C&P geometry cannot accommodate materials that contain particles sincethe particles can be subjected to grinding action near the tip of the cone. Therefore,quite often the tip of the cone is slightly truncated to allow measurements onparticulate fluids. Cones are often slightly truncated, as shown in Figure 2.50, byremoving the tip of the cone to make them more robust measurement tools. Errorsdue to cone truncation are generally negligible since the radius of truncation Rt ismuch smaller than R. The maximum error in torque associated with truncated conescan be calculated from the following equation:

(2.64)

For instance, if Rt = 0.2R then the maximum theoretical error in torque is 0.8%.Although C&P geometry is very simple and useful there are cases in which it

shall not be preferred: (a) it is not recommended when conducting temperaturesweeps unless the rheometer is equipped with an automatic system for thermalexpansion compensation; and (b) it is not recommended for testing samples withparticulate materials. The particles can jam the cone apex, giving erroneous data.Moreover, cone-and-plate system is not suitable for materials with a high concen-tration of solids, as the solids become expelled from the gap under high shear rates.

γα

= Ω

τπ

= 32 3

M

R

Maximum error = −−

1 100

3 3

3

R R

Rt


In the extended C&P geometry the apex of the cone does not touch the plate,instead there is a finite distance between the apex and the plate, denoted by hc inFigure 2.50. The shear rate for this case is determined from (Powell, 1988):

(2.65)

It is sometimes essential to replace the flat plate with a dish to contain liquidmaterials as seen in Figure 2.50. Truncated and extended cones can also be utilizedwith a dish in place of a flat plate. Furthermore, double cone (or biconical) sensors(Figure 2.50) have been developed and employed for measuring very low viscosityliquids with small sample volume. This geometry eliminates the free surface andvariation of its shape with rotational speed, and minimizes the sample exposureto the environment. On the other hand, it introduces a new type of edge effect(Dealy, 1982).

PARALLEL-PLATE GEOMETRY

A schematic drawing of the parallel-plate geometry is shown in Figure 2.51. Theparallel-plate system consists of a rotating (stationary) upper plate and a stationary(rotating) lower plate separated by the sample to be tested. Although similar in manyways to C&P system, the major difference between the parallel-plate and C&Psystems is that the shear rate in the parallel-plate system is not constant but variesacross the sample. Thus, if the objective is to subject the entire sample to a uniformshear, then the parallel-plate geometry is not appropriate. On the other hand, parallel-plate geometry is not as sensitive to the gap-setting errors as the cone-and-platesystem (Macosko, 1994).

The working equations for the parallel-plate geometry is given as follows:Shear strain:

(2.66)

It is clear that shear strain is not homogeneous and varies with radial position r.Shear rate at the edge (at r = R):

(2.67)

It is seen that the shear rate can be varied in two ways: (a) by changing therotational speed, Ω, and (b) by changing the gap between plates or sample thickness, h.

Shear stress:

(2.68)

˙tan

γαec

c

R

h R=

+ Ω

γ φ= rh

γ R

R

h= Ω

τπ γR

R

M

R

d M

d= +

233

lnln ˙


where, M = torque on the rotating plate. The derivative term in the brackets makesthe shear stress and viscosity calculations in the parallel-plate geometry more involvedand difficult than those in cone-and-plate geometry. The accurate evaluation of thederivative term requires sufficient amount of torque versus edge shear rate data. Fora Newtonian liquid the derivative term is equal to 1.0, and the equation reduces to:

(2.69)

When the lower plate is replaced with a dish to contain the liquid sample therewill be additional torque contribution caused by the increased frictional drag of thedish. Vrentas et al. (1991) presented an analysis of the dish effect (referred to asreservoir effect in their paper) for the flow of a Newtonian fluid in a parallel-platerotational viscometer. According to their results, provided that the ratio of radius of

FIGURE 2.51 Parallel-plate measurement systems.

R

sampleh

h

Rdish

Sample thicknessor gap setting

R

Ω, φ

τπR

M

R= 2

3


dish, Rdish, to radius of upper plate, R, is greater than 1.10, the following equationcan be used to calculate the torque:

(2.70)

The torque, M, from this equation can be used in Equation 2.69 to calculateshear stress τR for a Newtonian fluid.

CAPILLARY RHEOMETRY

Capillary tube rheometry is a well-established technique for studying shear proper-ties of materials. It has been applied to study viscosity of cheese (Smith et al., 1980),butter (Shukla and Rizvi, 1995), and many other food materials (Halliday and Smith,1995; Sharma et al., 1993; White et al., 1993). Capillary viscometers are often usedin laboratories and as an on-line instrument in process industries to measure viscosity(Roberts, 2001).

The capillary rheometer consists of a small tube through which an incompressi-ble fluid is forced to undergo steady axial laminar flow, either by means of animposed pressure or a piston moving at a constant speed (Figure 2.52). The capillaryrheometers can also be designed to have several capillary sections of differentdiameters in series so that non-Newtonian fluids can be characterized in a singlepass of fluid (White et al., 1993).

The quantities normally measured are the volumetric flow rate, Q, and the drivingpressure, Pdriving. When a moving piston generates the flow, the driving pressure isrelated to the piston force (Fpiston) and reservoir radius (Rreservoir) as follows (Dealyand Wissbrun, 1989):

(2.71)

The important assumptions made in the analysis of capillary flow are (Macosko,1994): (a) fully developed, steady, isothermal, laminar flow; and (b) fluid velocityis zero at wall — that is no slip at the wall.

The total pressure drop (∆P) for flow of fluid from a reservoir, through acapillary and out to the ambient pressure consists of two components (Dealy andWissbrun, 1989)*:

(2.72)

where, ∆Pend = excess pressure loss due to the entrance and exit flow (i.e., ∆Pend

= ∆Pentrance + ∆Pexit), and Pambient = ambient pressure. The components of total pressuredrop are schematically illustrated in Figure 2.53.

* Although ∆ means “final-initial,” which makes ∆P a negative value; for convenience we consider theterm ∆P as “Phigher – Plower” to make it a positive quantity.

MM

h

R

measured=+1 1 9.

PF

Rdrivingpiston=

π reservoir2

P P P P Pdriving ambient end capillary− = = +∆ ∆ ∆


FIGURE 2.52 Schematic drawing of a piston-driven capillary rheometer.

W (Dead weight)or

Vz (Constant velocity)

Plunger

Sample

Rr

Reservoir or barrelsection

Capillary sectionR

Q (Volumetric flow rate)

r

z

L


The working equations for capillary rheometry are given as (Macosko, 1994):Wall shear stress:

(2.73)

where, CB (= ∆Pend /(2τw) is the Bagley correction, which takes into account thepressure losses in the entrance and exit of the capillary. The Bagley correction iseither applied to capillary length-to-radius (L/R) term or to the pressure term, aswritten in Equation 2.73 The Bagley correction procedure involves measuring thepressure drop for a number of capillaries having different lengths (thus, differentL/R ratios) at selected values of apparent wall shear rate. It is common practice touse at least three tubes of the same diameter but different lengths. The magnitudesof end corrections are determined from Bagley plots as shown schematically inFigure 2.54.

It may be necessary to apply corrections to the measured volumetric flow rates(Qm) if there is wall slippage. Wall slip is to be suspected when plots of τw vs. apparentshear rate at wall aw, (see below) for capillaries with the same L/R ratio but differentdiameters do not fall on a single curve. In accounting for slip, the slope of [Qm/(πR3τw)]versus [1/R2] is taken as the corrected slip coefficient, βc, and this parameter is usedin the following equation to calculate the corrected volumetric flow rate (Qc):

(2.74)

FIGURE 2.53 The pressure profile in different sections of a capillary rheometer.

∆P

∆Pentrance

∆Pcapillary

∆Pexit

Reservoir section Capillary section

In Out

τwcapillary

B

endP

L R

P

L R C

P P

L R= =

+[ ] =−1

212

12

∆ ∆ ∆ ∆( / ) ( / ) ( / )

γ

Q Q Rc m c w= − β π τ


Apparent or Newtonian shear rate at the wall is given by:

(2.75)

For a non-Newtonian liquid the shear stress at the wall τw is unchanged whilethe shear rate at the wall is calculated from Weissenberg-Rabinowitsch-Mooneyequation (Macosko, 1994):

(2.76)

The term in square brackets is called the Rabinowitsch correction. The slope(dlnQc/dlnPc) is equal to 1.0 for Newtonian fluids, and to (1/n) for power-law fluidswith n being the flow-behavior index. Once shear rate and shear stress are knownat the same location we can then calculate shear viscosity (η = τw/ w) and constructeither the flow curve (τw vs. w) or viscosity curve (η vs. w).

The capillary rheometer can be operated in two modes: (a) controlled volumeor displacement mode, where Q is controlled and ∆P is measured, and (b) controlledpressure mode, where ∆P is controlled and volumetric flow rate (Q) is measured.The first mode can be realized using a Universal Testing Machine with constantcrosshead speeds. The second mode can be realized either by applying a dead weighton the plunger or by using gas pressure to move the plunger.

FIGURE 2.54 Bagley plot for pressure corrections for the end effects. The measured pressuredrop (∆P) for different length-to-radius ratio (L/R) of the pipe is obtained for different wallshear rates ( aw1, aw2, aw3). The correction factors (∆Pend1, ∆Pend2, ∆P end3) are obtained fromthe intercepts.

L/R

∆P

∆Pend3

∆Pend2

∆Pend1

e1e2e3

γaw1.

γaw2.

γaw3.

γ γ γ

γπaw

cQ

R=

43

˙ ˙ln

lnγ γw aw

c

c

d Q

d P= +

34

14

γγ γ


EXTENSIONAL RHEOMETRY

Extensional or elongational rheometry is a relatively new area of active researchwhen compared to shear rheometry, and began to receive increased attention around1970. (Macosko, 1994; Doraiswamy, 2002; Barnes et al., 1989). Its developmentstems from the observation that several industrially important polymer processingoperations such as extrusion, molding, fiber spinning, calendaring, blowing, coating,and foam production involve significant extensional deformation in addition to sheardeformation (Cogswell, 1981; Macosko, 1994; Baird, 1999). Currently, commercialelongational rheometers are available to measure extensional properties of polymermelts (Schulze et al., 2001; Meissner and Hostettler, 1994). Moreover, the filament-stretching rheometer has been developed to measure extensional properties of mobilepolymer solutions (Tirtaatmadja and Sridhar, 1993; Sridhar, 2000).

Extensional flows are more sensitive to variations in molecular structure of apolymeric material, and thus offer a powerful means of polymer characterization(Münstedt et al., 1998). It is possible for polymers to have identical shear flowproperties while exhibiting extremely different extensional flow properties. Only fordeformations that are either very small or very slow, the theory of linear visco-elasticity provides relationships between material functions determined using variouskinds of deformations (Dealy and Wissbrun, 1989). For instance, the followinglimiting relation between extensional and shear properties is established (Barneset al., 1989; Dealy, 1995):

(2.77)

where, ηE is the tensile or extensional viscosity and η is the shear viscosity. ForNewtonian fluids ηE = 3η for all values of strain rates. This relationship is namedas Trouton ratio, TR, defined as (Jones et al., 1987):

(2.78)

For calculating TR, the shear viscosity should be evaluated at a shear rate numericallyequal to . Trouton ratio is exactly 3 for inelastic flows, and any departure fromthe value of 3 is associated with viscoelastic effects (Jones et al., 1987; Barnes et al.,1989). It is clear that when the relation given in Equation 2.77 is valid there is noneed to make extensional tests since the extensional viscosity can be calculated fromthe shear viscosity function determined at small and slow shearing experiment (Dealyand Wissbrun, 1989). However, for large and rapid deformations the relation givenin Equation 2.77 is not valid, except at small strains, and therefore it is essential tomake extensional measurements.

There are several kinds of extensional-flow geometries such as uniaxial exten-sion, squeezing flow, sheet stretching, fiber spinning, bubble collapse, stagnationflows, and entrance flows (Macosko, 1994). Direct extensional-flow measurementshave an advantage over shear measurements in that the measurement does not involve

η ε η γε γE (˙) ˙˙ ˙→ →= ( )0 03

TRE==( )

η εη γ ε

(˙)

˙ ˙3

3ε


a sample–instrument interface, and thus there is no slip problem to consider(Cogswell, 1981). Some of these extensional methods are already applied to cheesewith some success, as described in Chapter 9. Here we limit our attention tolubricated squeezing flow (LSF) technique, which is the most popular and promisingmethod of studying extensional properties of (melted) cheese.

LUBRICATED SQUEEZING FLOW

Squeeze flow or squeezing flow is often used to determine flow properties of highlyviscous materials such as polymer melts and semiliquid or semisolid food products(e.g., cream cheese, peanut butter, melted cheese, tomato paste, butter, dough, etc).A schematic diagram of the squeezing-flow geometry is shown in Figure 2.55.Although it is a simple test to perform, the analysis of squeezing flow may not bestraightforward, particularly if there is friction between the specimen ends andcompression plates (i.e., unlubricated squeezing flow). In unlubricated squeezingflow, if a significant shearing component is present it alters the pattern of outwardflow of material between the plates. Thus, it is necessary to lubricate the sam-ple–platen contact surfaces in order to eliminate the shear in the sample and obtainpurely shear-free or biaxial extensional flow.

Lubricated or unlubricated squeezing flow can be conducted in constant volumeor constant area configurations depicted in Figure 2.55. The material is squeezedout between two parallel plates at either controlled force (or stress) or controlledspeed (or strain rate). Quite often the upper plate is moving at a constant speed whilethe lower plate is stationary. The squeezing-flow configuration represents one of thefew cases where specimen loading and cleaning of equipment are fairly easy. Thesimple geometry of the lubricated squeezing flow (LSF) makes it also convenientfor performing stress relaxation or creep experiments. Replacing the lower platewith a shallow dish results in a new configuration named as “imperfect squeezingflow” (Lee and Peleg, 1992) (Figure 2.55).

LSF has been developed and used first by Chatraei and Macosko (1981) tomeasure biaxial extensional viscosity of polydimethyl siloxane and polyisobutylenemelts under constant stress. The LSF technique was introduced to food rheology inthe mid-1980s (Casiraghi et al., 1985) and has since been applied to various kindsof food products (Campanella et al., 1987; Campanella and Peleg, 1987b; Hoffneret al., 1997; Shukla et al., 1995; Huang and Kokini, 1993; Bagley et al., 1990;Corradini et al., 2000; Suwonsichon and Peleg, 1999; Wang et al., 1998; Ak andGunasekaran, 1995). Recently, Campanella and Peleg (2002) reviewed LSF applica-tions to semiliquid foods. A good example of application of LSF for cheese is theUW Meltmeter, the cheese meltability measurement device developed by Wang et al.(1998). In this, the fat melting from cheese at high temperature self-lubricates thecompression plates, making it an ideal test method. The UW Meltmeter is discussedin detail in Chapter 8.

The LSF geometry and velocity profile in the specimen and the lubricant layerare depicted in Figure 2.56. In an ideal situation, the lubricant undergoes sheardeformation, and the sample undergoes biaxial extension. The working equationsfor LSF method are given as follows (Chatraei and Macosko, 1981; Macosko, 1994):


Axial Hencky strain:

(2.79)

Axial strain rate:

(2.80)

where Vz is the velocity in the vertical direction (e.g., crosshead speed of auniversal testing machine).

FIGURE 2.55 Configurations of unlubricated squeezing flow, lubricated squeezing flow, andimperfect squeezing flow tests.

R

Unlubricated constant volume squeezing flow Unlubricated constant area squeezing flow

Sample

r(t)

R

H

Lubricated constant volume squeezing flow

Sample

r(t)

R

H

R

Lubricated constant area squeezing flow

= Constant Load, W

or

= Constant Velocity, Vz

Sample

R

Imperfect squeezing flow

εHo

H

H=

ln

ε Hz

H

dH

dt

V

H= =1


Radial or biaxial strain:

(2.81)

where, the constant volume assumption, (R/R0) = (H0/H)1/2, is applied.Radial or biaxial strain rate:

(2.82)

It is assumed that at any moment the lubricant film thickness, δ, is smaller thanthe specimen thickness, H, and therefore, H + δ ≅ H. This is justified at the start ofthe test, but may be questionable at later stages when the specimen thickness becomessmall at large strains (e.g., when εΒ = 2.0, H/Ho = 0.018).

Biaxial (compressive) stress when the gap is fully filled with sample:

(2.83)

In this case Rspeciman ≥ Rplate = R.Biaxial (compressive) stress when the gap is partially filled with sample:

(2.84)

In this case r(t) represents the instantaneous radius of the specimen.

FIGURE 2.56 Lubricant and sample velocity profiles in ideal lubricated squeezing flow(the sample thickness H is much greater than the total lubricant layer thickness δ). (AfterPapanastasiou et al., 1986.)

Lubricant layer

Lubricant layer

Specimen H

δ/2

δ/2

The ideal velocityprofile

*Shear in the lubricant*Extension in the sample

Upper plate (moving)

Lower plate (fixed)

εBo o

R

R

H

H=

= −

ln ln

12

ε B H

dH

dt= − 1

2

σπB

F

R=

2

σπB

F= r(t)

2


Biaxial stress growth coefficient (Dealy, 1995):

(2.85)

Biaxial extensional or elongational viscosity:

(2.86)

For Newtonian fluids the biaxial elongational viscosity is six times the shearviscosity, ηB = 6η.

One important consideration in LSF, which is often not addressed in food-relatedstudies, is the loss of effective lubrication, which limits the maximum achievable strain.Macosko (1994) mentions that the strain in LSF is limited to 1.0–1.5 because of theloss of effective lubrication. It is experimentally demonstrated that lubrication ismaintained up to a higher total strain if the lubricant has a higher zero-shear viscosity(Chatraei and Macosko, 1981). The optimum ratio of the zero-shear viscosities of thesample to the lubricant is reported to range from 500 Pa.s to 1000 Pa.s (Papanastasiouet al., 1986; Soskey and Winter, 1985). The criterion for good lubrication is given as(Macosko, 1994):

(2.87)

where ηS is the sample viscosity, δ the lubricant thickness, H the sample thickness,ηL the lubricant viscosity, and R the plate radius.

EQUATIONS FOR DIFFERENT FLUIDS IN LUBRICATING SQUEEZING FLOW

Analytical solutions for lubricated-squeezing flow of Newtonian and non-Newtonianfluids are given in various publications in the rheology literature. We present belowthese equations describing the specimen thickness as a function of time underconstant load, or the load as a function of time under constant velocity for Newtonianand non-Newtonian fluids.

(1) Newtonian fluids(a) Flow under constant load–constant volume (Lee and Peleg, 1989):

(2.88)

where, W is the constant load, η the Newtonian viscosity, Λ thespecimen volume, and t the time.

η εσεB B

B

B

t+ ( ) ≡, ˙˙

η ε η εB B B B tt˙ lim ( , ˙ )( ) = [ ]+

→∞

220

2

2

δ ηη δH

RL

S

< <

1 13H t H

Wt

o( )= +

ηΛ


(b) Flow under constant load–constant area:

(2.89)

where, R is the radius of the plate (= radius of the sample).(c) Flow under constant velocity–constant volume:

(2.90)

where, Vz is the squeezing speed.(d) Flow under constant velocity–constant area:

(2.91)

(2) Power-law fluids(a) Flow under constant load–constant volume (Campanella and Peleg,

1987b):

(2.92)

where, K is the consistency index, and n the flow behavior index.(b) Flow under constant velocity–constant volume:

(2.93)

(c) Flow under constant load–constant area:

(2.94)

(d) Flow under constant velocity–constant area:

(2.95)

H t HW t

Ro( ) exp= −

3 2π η

F t Vz( ) =[ ]3

2

H(t)

η Λ

F tR

( ) =3 2π η V

H(t)z

1 1

31 1

2

1

H t H

t

n

W

Kon n

n n

( ) /

/

= +

+

Λ

F t KV

H t

nz

n

n( )( )

=( )

[ ]+

+31

21Λ

H t HW

R

to n

n

( ) exp

/

= −

+

31

2 2

1

Kπ

F t K RV

H t

nz

n

( )( )

=

+

31

2 2π


(3) Herschel-Bulkley fluids(a) Flow under constant load–constant volume (Ak and Gunasekaran, 2000):

(2.96)

where, Hypg2F1[a,b,c,z] is the hypergeometric function 2F1[a,b;c;z](Mathematica 3.0, Wolfram Research; Andrews, 1992). The validityof this hypergeometric solution, Equation 2.96, is verified by the factthat it reduces correctly to Equation 2.88 for n = 1 and τo = 0, andto Equation 2.92 for τo = 0 (Ak and Gunasekaran, 2000).

(b) Flow under constant velocity–constant volume:

(2.97)

(c) Flow under constant load–constant area:

(2.98)

(d) Flow under constant velocity–constant area:

(2.99)

REFERENCES

Abbott, J. et al. 1991. Experimental observations of particle migration in concentratedsuspensions: Couette flow. Journal of Rheology 35(5):773–795.

Ak, M.M. 1993. Rheological Measurements on Mozzarella Cheese. University of Wisconsin-Madison, Ph.D. thesis.

Ak, M.M. and S. Gunasekaran. 1992. Stress–strain curve analysis of Cheddar cheese underuniaxial compression. Journal of Food Science 57(5):1078–1081.

Ak, M.M. and S. Gunasekaran. 1995. Evaluating rheological properties of Mozzarella cheeseby the squeezing flow method. Journal of Texture Studies 26:695–711.

−( )

+

+

−

( )

+

= −

+

n

H t WHypg F

n n n H t W

n

H WHypg F

n n n H W K

no

o

no

on

( ), , ,

( )

, , ,

/

/ ( )

1

1 1

2 11 1

11 3

2 11 1

11 3 1

3

τ

τ

Λ

ΛΛ

1/ n

t

F tH(t)

KV

H toz

n

( )( )

= +

3 3 Λ τ

H t HW R

R Kto

on

n

( )

/

= −−

+ exp

π τπ

2

2 1

13

3

F t R KV

H toz

n

( )( )

= +

3 32 π τ



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Uniaxial Testingof Cheese

Uniaxial testing is the most popular configuration for evaluating mechanical andrheological properties of cheeses. In this chapter, we attempt to summarize theextensive literature on different cheeses. The available data are diverse and are oftencollected by various testing modes, which can be grouped under the word “uniaxial.”Uniaxial testing is also the most popular method for instrumental evaluation ofcheese texture (see Chapter 7). One way to handle such diverse literature on proper-ties of different cheeses would be to present the available data according to the typeof cheese. However, we organized the information according to the specific testmethod (e.g., uniaxial compression, tension, relaxation, etc.), since effects of manyexperimental factors (e.g., deformation rate, cheese age, etc.) on rheological proper-ties of different cheeses bear some similarities.

Rigorous analysis of the literature data is seriously hampered by the lack ofstandardization in terms of sample preparation, measurement conditions, parameterevaluations, and reporting style. It may not be feasible to specify particular require-ments for each of these issues since the objectives of measurements can be totallydifferent (e.g., quality control, correlations with sensory results, etc.), and the pre-vailing conditions under which the tests are made may also vary. However, minimumrequirements in data reporting may be (and perhaps should be) universally agreedupon, which would greatly facilitate comparison of results from different sources.

Masi (1987) reported a major attempt to improve the comparability of resultsfrom different laboratories and to identify the most suitable measurement conditionsfor generating reproducible mechanical data on cheese. Even in this collaborativework the participating laboratories used different experimental conditions (i.e., sam-ple size and shape, test temperature, sample handling, sample age at testing, numberof samples tested, etc.). The recommendations based on the results of this extensivestudy are given in Table 3.1 for cheese, as well as general recommendations forreporting compression results. Some of these suggestions are no longer relevant dueto advances in the instrumentation. For instance, the recommended crosshead speedsare naturally based on the characteristics of uniaxial testing machines available atthat time and the capabilities of the strip-chart recorders, which are practicallyobsolete now.

A group at the International Dairy Federation (IDF) also formed a workingteam (IDF E703) to develop standards for testing and reporting uniaxial test resultson cheese. Though a draft was prepared, it was never officially published.* Never-theless, the special bulletin of IDF (1991) includes expert opinions on importantissues related to cheese rheology and texture measurements, and recommendationson test methods.

* Philip Watkinson, Fonterra Research Center, New Zealand, personal communication.

3


The theory of fracture mechanics and the methods specially designed to studyfracture properties of materials are discussed in Chapter 4. Fracture propertiesreported in this chapter are those that are often routinely determined even thoughthe primary objective of the research is not to study fracture behavior. For instance,work-to-fracture (or area under stress–strain curve) values are given in this chapter,whereas the specific fracture energy data are reported in Chapter 4.

UNIAXIAL COMPRESSION MEASUREMENTS

Mechanical properties commonly determined from uniaxial compression tests oncheese include modulus of deformability

E

D

, fracture stress

σ

f

, fracture strain

ε

f

,and work to fracture

W

f

. All these variables are defined in Chapter 2 (see Figure 2.23).

TABLE 3.1ARecommendations for Compression Testing of Cheese

Measurement Conditions Data to Be Reported

a. Shape: vertical cylinder or prismb. Size: aspect ratio > 1

(aspect ratio = sample height/sample width or diameter)c. Crosshead speed: 5 cm/min and two other speeds in the range 0–20 cm/mind. Boundaries: Both bonded and lubricated platens

a. Rupture

a

(or yield) stressb. Rupture (or yield) strainc. Elastic modulusd. Rupture (or yield) work

per unit of volumee. Failure mode

a

If the cheese does not show rupture or yield, then the stress and the work per unit of volume shouldcorrespond to 80% deformation.

Source

: After Masi, 1987. With permission.

TABLE 3.1BInformation to be Included in Compression-Test Reports

Contextual Information Measurement Conditions Results

a. Detailed description of sampleb. Sample dimensionsc. Sample history (including

preparation and conditioning)

a. Temperature of environmentb. Relative humidity of environmentc. Sample temperatured. Interface between sample and

compression surfacesI. MaterialII. RoughnessIII. Dimensions

e. Compression ratef. Machine details

Accuracy of (1) compression rate,and (2) force measurement

g. Initial position of crosshead inrelation to the sample

h. Response time

a. All original and derivedresults

b. Completeforce–deformationcurve

Source:

After McKenna, 1987. With permission.


The numerical results for these properties extracted from many publications ondifferent cheeses are listed in Tables 3.2 to 3.5. In the following sections, we willfrequently refer to these compilations.

For viscoelastic materials, Mohsenin and Mittal (1977) suggested the term“modulus of deformability” instead of Young’s modulus, which is reserved forengineering materials obeying the Hooke’s law. The modulus of deformability is theslope of the “initial linear” part of the stress–strain curve. There are several methodsfor getting a representative value of the slope. One of these methods is to fit thestress–strain data to a polynomial equation (see Chapter 2, Equation 2.22) and todetermine properties from the resulting fit equation (Ak and Gunasekaran, 1992).The other approach is to take the maximum slope within the strain range from 0 to0.05 (Wium et al., 1997). Another method is to take the slope at a particular strainlevel (e.g., 5%) as the modulus of deformability (i.e., secant modulus described inChapter 2). Linear regression on the data pertaining to the initial part of thestress–strain curve is yet another option to calculate the modulus of deformability.

Watkinson and Jackson (1999) suggested a new procedure to calculate themodulus of deformability using the gradient of the inflection at the lowest strain ina stress vs. strain curve. This new procedure was used to calculate modulus ofdeformability

E

D

for three cheeses and compared with the results from three alter-native procedures, including the simple polynomial fitting suggested by Ak andGunasekaran (1992). As shown in Table 3.6, the ranking of

E

D

for each cheese wasthe same for each procedure, and the relative magnitude of

E

D

for each cheese alongwith the coefficient of variation was similar for each procedure. Watkinson andJackson (1999) discussed some special features of their procedure.

The usual practice in uniaxial compression of foods is to run the crosshead atconstant speed, since Universal Testing Machines (UTMs) machines are normallydesigned to do that. It is quite unusual, but perhaps highly necessary, to see com-pression tests made on cheese at constant true strain rate. The true strain ratecontinuously increases in uniaxial compression at a constant crosshead speed as thespecimen height decreases, and this has a great effect in uniaxial compression offoods (Peleg, 1977a; 1977b). We are not aware of any such studies on cheese exceptthat of Jaros and Rohm (1994). A simple device has been described earlier by Lutonet al. (1974) for use with Instron testing machines to produce a constant true strainrate in compression or tension tests.

Jaros and Rohm (1994) described a method to conduct uniaxial compressiontests at constant strain rate using an Instron testing machine. Based on the analysisof rheological data on 136 Swiss cheese samples, it was shown that stress and strainat fracture are significantly lower in constant strain rate compression than in constantspeed compression, due to the differences in strain history of the two modes. Themodulus of deformability, obtained at 0.04 strain level, is, however, not affected bythe test setup. The authors reported the following equations relating fracture stress

σ

f

and fracture strain

ε

f

from the two modes of deformation:

(3.1)

(3.2)

σ σf f(constant strain rate) 1.27 (constant speed)0.917=

ε εf f(constant strain rate) 1.01 (constant speed)0.867=


TABLE 3.2

V

alues of Modulus of Deformability from Uniaxial Testing of Several Cheeses

a

Cheese Variety

InitialStrain Rate

s

–1b

ModuluskPa Ref.

Apericube processed Bel, France — 70 Agrawal et al., 1997Appenzell — 22 Prentice et al., 1993Arzua-Ulloa Spanish soft cheese — type I 46 84 Almena et al., 1998Arzua-Ulloa Spanish soft cheese — type II 46 44 Almena et al., 1998Blue Brick UF-Feta 8–10 weeks 110 229 Wium and Qvist, 1997Blue Brick UF-Feta 8–10 weeks 220 221 Wium and Qvist, 1997Blue Brick UF-Feta 8–10 weeks 330 225 Wium and Qvist, 1997Blue Brick UF-Feta 8–10 weeks 440 176 Wium and Qvist, 1997Caciocavallo 4.2 687 Masi and Addeo, 1986Caerphilly — 8 Prentice et al., 1993Camembert 1-d before brining 5.56 357 Schlesser et al., 1992Camembert 1-d after brining 5.56 429 Schlesser et al., 1992Camembert 8-d-old 5.56 749 Schlesser et al., 1992Camembert 15-d-old 5.56 1070 Schlesser et al., 1992Camembert 22-d-old 5.56 251 Schlesser et al., 1992Camembert 29-d-old 5.56 0 Schlesser et al., 1992Cheddar — 48 Prentice et al., 1993Cheddar — 180 Prentice et al., 1993Cheddar 20 days 1.4–110 242 Ak and Gunasekaran, 1992Cheddar 8 weeks old 32 640 Hort and Le Grys, 2001Cheddar 64 weeks old 32 290 Hort and Le Grys, 2001Cracker Barrel Tasty: Kraft, USA — 580 Agrawal et al., 1997Danbo cheese with 45% fat 833 189 Madsen and Ardö, 2001Danish Feta — 470 Agrawal et al., 1997Double Gloucester — 1000 Prentice et al., 1993Double Gloucester — 850 Agrawal et al., 1997Edam — ~500 Prentice et al., 1993Edam — 290 Agrawal et al., 1997Emmental — 18 Prentice et al., 1993Emmental — 470 Agrawal et al., 1997Emmentaler 4 months 4.76 139 Rohm and Lederer, 1992Emmentaler 4 months 19 182 Rohm and Lederer, 1992Emmentaler 4 months 76.2 234 Rohm and Lederer, 1992Emmentaler 4 months 19 182 Rohm et al., 1992English Mature Cheddar — 890 Agrawal et al., 1997Galbanino 0.556 600 Masi, 1989Galbanino 11 1000 Masi, 1989Galbanino 28 1400 Masi, 1989Galbanino 56 1800 Masi, 1989Garrotxa-type goat milk cheese 500 343 Saldo et al., 2000Gouda — 405 Prentice et al., 1993Gouda — 390 Prentice et al., 1993


Gouda — 410 Agrawal et al., 1997Gruyère — 690 Agrawal et al., 1997Gruyère — 77 Prentice et al., 1993Gruyère-type strong cohesion 55.5 479 Pesenti and Luginbühl, 1999Gruyère-type strong cohesion — Tension 11 111 Pesenti and Luginbühl, 1999Gruyère-type weak cohesion 55.5 468 Pesenti and Luginbühl, 1999Gruyère-type weak cohesion — Tension 11 93 Pesenti and Luginbühl, 1999Jarlsberg — 350 Agrawal et al., 1997La Serena 2 days old, with lactic starter — 61 Medina et al., 1991La Serena 2 days old, without lactic starter — 32 Medina et al., 1991La Serena 60 days old, with lactic starter — 348 Medina et al., 1991La Serena 60 days old, without lactic starter — 104 Medina et al., 1991Lancashire — ~1250 Prentice et al., 1993Lancashire — 710 Agrawal et al., 1997Leicester — 650 Agrawal et al., 1997Mahon >150 days 8.33 2487 Benedito et al., 2000Mahon <60 days 8.33 497 Benedito et al., 2000Mahon from 60 to 150 days 8.33 1426 Benedito et al., 2000Mild Cheddar 3 349 Kamyab et al., 1998Mild Cheddar 37 days old 8.3–24 1176 Charalambides et al., 1995Mild Cheddar 182 days old 8.3–24 1050 Charalambides et al., 1995Mild Cheddar — Tension 3 747 Kamyab et al., 1998Montasio — 470 Prentice et al., 1993Monterey Jack 46 days old 8.3–24 1008 Charalambides et al., 1995Monterey Jack 185 days old 8.3–24 652 Charalambides et al., 1995Mozzarella — 15 Prentice et al., 1993Mozzarella — 150 Agrawal et al., 1997Mozzarella 4.2 49 Masi and Addeo, 1986Münster — 6 Prentice et al., 1993Parmesan — 1980 Prentice et al., 1993Parmesan — 2260 Agrawal et al., 1997Parmigiano Reggiano 12 months old 42 1340 Noel et al., 1996Parmigiano Reggiano 18 months old 42 1530 Noel et al., 1996Parmigiano Reggiano 28 months old 42 2280 Noel et al., 1996Pecorino Romano — 2840 Prentice et al., 1993Process cheese loaf, light 3 154 Kamyab et al., 1998Process cheese loaf, regular 3 107 Kamyab et al., 1998Process cheese slice, American 1 3 318 Kamyab et al., 1998Process cheese slice, American 1 — Tension 3 374 Kamyab et al., 1998Process cheese slice, American 2 3 138 Kamyab et al., 1998Process cheese slice, American 2 — Tension 3 162 Kamyab et al., 1998

TABLE 3.2 (continued)

V


a

Cheese Variety

InitialStrain Rate

s

–1b

ModuluskPa Ref.


Processed cheese analogs high fat,high moisture

5.56 27 Marshall, 1990


55.6 48 Marshall, 1990


556 50 Marshall, 1990

Processed cheese analogs low fat,low moisture

5.56 223 Marshall, 1990


55.6 231 Marshall, 1990


556 276 Marshall, 1990

Provolone — 240 Prentice et al., 1993Provolone 4.2 559 Masi and Addeo, 1986Raclette — 210 Agrawal et al., 1997Red Brick UF-Feta 8–10 weeks 110 301 Wium and Qvist, 1997Red Brick UF-Feta 8–10 weeks 220 256 Wium and Qvist, 1997Red Brick UF-Feta 8–10 weeks 330 260 Wium and Qvist, 1997Red Brick UF-Feta 8–10 weeks 440 190 Wium and Qvist, 1997Reduced Fat Cheddar Mainland, New Zealand — 940 Agrawal et al., 1997Sbrinz — 195 Prentice et al., 1993Sharp Cheddar 3 198 Kamyab et al., 1998Sharp Cheddar 1 month old 8.3–24 1580 Charalambides et al., 1995Sharp Cheddar 6 months old 8.3–24 1938 Charalambides et al., 1995Sharp Cheddar — Tension 3 220 Kamyab et al., 1998Silano 4.2 137 Masi and Addeo 1986Smoked Cheddar King Island, Australia — 990 Agrawal et al., 1997String 11 100 Taneya et al., 1992Swiss Appenzeller type — rapeseed-added diet 17 401 Jaros et al., 2001Swiss Appenzeller type — regular diet 17 490 Jaros et al., 2001Teleme 1 month old 36 175 Raphaelides and Antoniou,

1996Tilsit — 30 Prentice et al., 1993Tin UF-Feta 8–10 weeks 110 465 Wium and Qvist, 1997Tin UF-Feta 8–10 weeks 220 387 Wium and Qvist, 1997Tin UF-Feta 8–10 weeks 330 404 Wium and Qvist, 1997Tin UF-Feta 8–10 weeks 440 407 Wium and Qvist, 1997Vorarlberger Bergkase 16.7 600 Jaros and Rohm, 1997White Cheshire — 470 Agrawal et al., 1997

a

Data are from uniaxial compression test unless indicated otherwise by a remark next to the variety name.

b

Values in this column are already multiplied by a factor of 1000 to avoid small numbers.

TABLE 3.2 (continued)

V


a

Cheese Variety

InitialStrain Rate

s

–1b

ModuluskPa Ref.


TABLE 3.3 Values of Strain at Fracture from Uniaxial Testing of Several Cheeses

a

Cheese Variety

InitialStrain Rate

s

–1b

PeakStrain Ref.

American Light — Shear 261 1.05 Gwartney et al. 2002American — Shear 261 1.01 Gwartney et al., 2002Appenzell — 0.63 Prentice et al., 1993Arzua-Ulloa Spanish soft cheese — type I 46 0.37 Almena et al., 1998Arzua-Ulloa Spanish soft cheese — type II 46 0.71 Almena et al., 1998Blue Brick UF-Feta 8–10 weeks 110 0.31 Wium and Qvist, 1997Blue Brick UF-Feta 8–10 weeks 220 0.32 Wium and Qvist, 1997Blue Brick UF-Feta 8–10 weeks 330 0.34 Wium and Qvist, 1997Blue Brick UF-Feta 8–10 weeks 440 0.34 Wium and Qvist, 1997Caciocavallo — 0.80 Masi and Addeo, 1986Caerphilly — 0.17 Prentice et al., 1993Cheddar — 0.20 Prentice et al., 1993Cheddar — 0.21 Prentice et al., 1993Cheddar — 0.21 Prentice et al., 1993Cheddar 1.4–110 0.81–0.91 Ak and Gunasekaran, 1992Cheddar 11 0.85 Rosenau et al., 1978Cheddar 110 0.97 Rosenau et al., 1978Cheddar 225 d old 29 0.37 Fenelon and Guinee, 2000Cheddar 8 weeks old 32 0.73 Hort and Le Grys, 2001Cheddar 64 weeks old 32 0.27 Hort and Le Grys, 2001Cheddar 5-mo-old, full-fat: 32% 440 0.42 Kucukoner et al., 1998Cheddar 5-mo-old, low-fat: 5% 440 0.13 Kucukoner et al., 1998Cheshire — 0.33 Prentice et al., 1993Danbo 833 1.10 Madsen and Ardö, 2001Double Gloucester — 0.24 Prentice et al., 1993Edam — 0.63 Prentice et al., 1993Emmental — 1.05 Prentice et al., 1993Emmental 16 weeks 16.7 1.19 Rohm et al., 1996Emmental 16 weeks 16.7 1.21 Rohm et al., 1996Emmental 16 weeks 16.7 1.27 Rohm et al., 1996Emmental 7-d-old 16.7 1.47 Jaros et al., 1997Emmental 28-d-old 16.7 1.63 Jaros et al., 1997Emmental 70-d old 16.7 1.43 Jaros et al., 1997Emmental 112-d-old 16.7 1.25 Jaros et al., 1997Emmentaler 4 months 4.8 1.08 Rohm and Lederer, 1992Emmentaler 4 months 19 1.17 Rohm and Lederer, 1992Emmentaler 4 months 76.2 1.15 Rohm and Lederer, 1992Emmentaler 4-mo-old 19 1.12 Rohm et al., 1992Garrotxa-type goat milk cheese 500 0.24 Saldo et al., 2000Gouda — 0.72 Prentice et al., 1993Gouda — 0.37 Prentice et al., 1993Gouda 1 week, pH = 4.94 2.8 0.55 Luyten, 1988Gouda 1 week, pH = 4.94 28 0.60 Luyten, 1988


Gouda 1 week, pH = 4.94 140 0.61 Luyten, 1988Gouda 2 week, pH = 5.24 0.67 1.48 Luyten, 1988Gouda 2 week, pH = 5.24 2.7 1.39 Luyten, 1988Gouda 2 week, pH = 5.24 50 1.31 Luyten, 1988Gouda 2 week, pH = 5.24 250 1.07 Luyten, 1988Gouda 6 months 0.28 0.29 Luyten, 1988Gouda 6 months 2.8 0.31 Luyten, 1988Gouda 6 months 28 0.30 Luyten, 1988Gouda 6 months 170 0.32 Luyten, 1988Gruyère — 0.51 Prentice et al., 1993Gruyère-type strong cohesion 55.5 0.75 Pesenti and Luginbühl, 1999Gruyère-type strong cohesion — Tension 11 1.30 Pesenti and Luginbühl, 1999Gruyère-type weak cohesion 55.5 0.73 Pesenti and Luginbühl, 1999Gruyère-type weak cohesion — Tension 11 0.46 Pesenti and Luginbühl, 1999Lancashire — 0.20 Prentice et al., 1993Leicester — 0.30 Prentice et al., 1993Mild Cheddar — A Reduced Fat — Shear 261 1.28 Gwartney et al., 2002Mild Cheddar — A — Shear 261 1.13 Gwartney et al., 2002Mild Cheddar — B Light — Shear 261 1.47 Gwartney et al., 2002Mild Cheddar — B — Shear 261 0.95 Gwartney et al., 2002Montasio — 0.58 Prentice et al., 1993Monterey Jack Light — Shear 261 1.36 Gwartney et al., 2002Monterey Jack — Shear 261 1.41 Gwartney et al., 2002Mozzarella — 0.55 Prentice et al., 1993Mozzarella — 1.08 Masi and Addeo, 1986Münster — 0.10 Prentice et al., 1993Parmesan — 0.14 Prentice et al., 1993Parmigiano Reggiano 12 months old 42 0.22 Noel et al., 1996Parmigiano Reggiano 18 months old 42 0.18 Noel et al., 1996Parmigiano Reggiano 28 months old 42 0.12 Noel et al., 1996Pecorino Romano — 0.25 Prentice et al., 1993Processed American 11 0.86 Rosenau et al., 1978Processed American 110 0.79 Rosenau et al.,1978Processed cheese analogs high fat,high moisture

5.56 1.20 Marshall, 1990


55.6 1.43 Marshall, 1990


556 1.47 Marshall, 1990


5.56 0.92 Marshall, 1990


55.6 1.02 Marshall, 1990

TABLE 3.3 (continued)Values of Strain at Fracture from Uniaxial Testing of Several Cheeses

a

Cheese Variety

InitialStrain Rate

s

–1b

PeakStrain Ref.


The constant strain rate compression has also been applied to biopolymer gels(Rohm, et al., 1995).

Prentice (1992) discussed main issues related to the measurement and datainterpretation. Prentice (1992)* also listed the mechanical properties for a numberof cheeses, which are included in Tables 3.2 to 3.5. These properties are

zero-strainmodulus

,

E

o

, which we can take as modulus of deformability, peak stress, and peakstrain, which we can identify, as often done by many authors, as fracture stress andfracture strain. The zero-strain modulus is based on the following expression:

(3.3)

Where,

σ

is the true stress,

ε

is the Hencky strain below some critical level, and

c

is a constant.


556 1.02 Marshall, 1990

Provolone — 0.53 Prentice et al., 1993Provolone — 0.80 Masi and Addeo, 1986Red Brick UF-Feta 8–10 weeks 110 0.30 Wium and Qvist, 1997Red Brick UF-Feta 8–10 weeks 220 0.33 Wium and Qvist, 1997Red Brick UF-Feta 8–10 weeks 330 0.34 Wium and Qvist, 1997Red Brick UF-Feta 8–10 weeks 440 0.35 Wium and Qvist, 1997Sbrinz — 0.41 Prentice et al., 1993Sharp Cheddar Light — Shear 261 1.26 Gwartney et al., 2002Sharp Cheddar — Shear 261 0.94 Gwartney et al., 2002Silano — 0.99 Masi and Addeo, 1986Tilsit — 0.78 Prentice et al., 1993Tin UF-Feta 8–10 weeks 110 0.21 Wium and Qvist, 1997Tin UF-Feta 8-10 weeks 220 0.20 Wium and Qvist, 1997Tin UF-Feta 8-10 weeks 330 0.20 Wium and Qvist, 1997Tin UF-Feta 8-10 weeks 440 0.22 Wium and Qvist, 1997Tybo Argentino up to 114 days 42 1.20 Bertola et al., 1992Vorarlberger Bergkase 16.7 0.55 Jaros and Rohm, 1997

a


b


* The mechanical properties presented in Table 8.1 of Prentice (1992) were, however, different than thosereported by the same author and coworkers in a later publication (Prentice et al., 1993). Since ourcalculations based on data from the few original papers agreed better with the results of Prentice et al.(1993), these values are included in our Tables 3.2 to 3.5.

TABLE 3.3 (continued)Values of Strain at Fracture from Uniaxial Testing of Several Cheeses

a

Cheese Variety

InitialStrain Rate

s

–1b

PeakStrain Ref.

σ ε ε= −E co 2


TABLE 3.4 Values of Stress at Fracture from Uniaxial Testing of Several Cheeses

a

Cheese Variety

InitialStrain Rate

s

–1b

PeakStresskPa Ref.

American Light — Shear 261 38 Gwartney et al., 2002American — Shear 261 29 Gwartney et al., 2002Appenzell — 7 Prentice et al., 1993Arzua-Ulloa Spanish soft cheese — type I 46 39 Almena et al., 1998Arzua-Ulloa Spanish soft cheese — type II 46 220 Almena et al., 1998Blue Brick UF-Feta 8–10 weeks 110 20 Wium and Qvist, 1997Blue Brick UF-Feta 8–10 weeks 220 22 Wium and Qvist, 1997Blue Brick UF-Feta 8–10 weeks 330 23 Wium and Qvist, 1997Blue Brick UF-Feta 8–10 weeks 440 22 Wium and Qvist, 1997Caciocavallo 4.2 383 Masi and Addeo, 1986Caerphilly — 64 Prentice et al., 1993Cheddar — 8 Prentice et al., 1993Cheddar — 44 Prentice et al., 1993Cheddar — 23 Prentice et al., 1993Cheddar — 108 Prentice et al., 1993Cheddar 11.1 44 Rosenau et al., 1978Cheddar 110 59 Rosenau et al., 1978Cheddar 32.5% fat, 225 d old 29 220 Fenelon and Guinee, 2000Cheddar 6.3% fat, 225 d old 29 740 Fenelon and Guinee, 2000Cheddar 64 weeks old 32 30 Hort and Le Grys, 2001Cheddar 8 weeks old 32 60 Hort and Le Grys 2001Cheddar 20-d-old 1.4 39 Ak and Gunasekaran 1992Cheddar 20-d-old 2.2 45 Ak and Gunasekaran, 1992Cheddar 20-d-old 3.7 50 Ak and Gunasekaran, 1992Cheddar 20-d-old 5.6 57 Ak and Gunasekaran, 1992Cheddar 20-d-old 7.2 50 Ak and Gunasekaran, 1992Cheddar 20-d-old 11 68 Ak and Gunasekaran, 1992Cheddar 20-d-old 14.5 59 Ak and Gunasekaran, 1992Cheddar 20-d-old 22.2 72 Ak and Gunasekaran, 1992Cheddar 20-d-old 29.2 62 Ak and Gunasekaran, 1992Cheddar 20-d-old 44.6 82 Ak and Gunasekaran, 1992Cheddar 20-d-old 72.9 75 Ak and Gunasekaran, 1992Cheddar 20-d-old 111 100 Ak and Gunasekaran, 1992Cheddar 5-mo-old, full-fat: 32% 440 94 Kucukoner et al., 1998Cheddar 5-mo-old, low-fat: 5% 440 525 Kucukoner et al., 1998Cheshire — 44 Prentice et al., 1993Danbo 833 94 Madsen and Ardö, 2001Double Gloucester — 94 Prentice et al., 1993Edam — 146 Prentice et al., 1993Emmental — 12 Prentice et al., 1993Emmental 16 weeks 16.7 165 Rohm et al., 1996Emmental 16 weeks 16.7 126 Rohm et al., 1996Emmental 16 weeks 16.7 91 Rohm et al., 1996


Emmental 112-d-old 16.7 170 Jaros et al., 1997Emmental 28-d-old 16.7 265 Jaros et al., 1997Emmental 70-d-old 16.7 205 Jaros et al., 1997Emmental 7-day-old 16.7 280 Jaros et al., 1997Emmentaler 4 months 4.8 78 Rohm and Lederer, 1992Emmentaler 4 months 19 95 Rohm and Lederer, 1992Emmentaler 4 months 76.2 121 Rohm and Lederer, 1992Emmentaler 4-mo-old 19 96 Rohm et al., 1992Garrotxa-type goat milk cheese 500 65 Saldo et al., 2000Gouda — 69 Prentice et al., 1993Gouda — 68 Prentice et al., 1993Gouda 1 week, pH = 4.94 2.8 27 Luyten, 1988Gouda 1 week, pH = 4.94 28 41 Luyten, 1988Gouda 1 week, pH = 4.94 140 66 Luyten, 1988Gouda 2 week, pH = 5.24 0.67 35 Luyten, 1988Gouda 2 week, pH = 5.24 2.7 55 Luyten, 1988Gouda 2 week, pH = 5.24 50 108 Luyten, 1988Gouda 2 week, pH = 5.24 250 182 Luyten, 1988Gouda 6 months 0.28 42 Luyten, 1988Gouda 6 months 2.8 64 Luyten, 1988Gouda 6 months 28 82 Luyten, 1988Gouda 6 months 170 108 Luyten, 1988Gruyère — 15 Prentice et al., 1993Gruyère-type strong cohesion 55.5 1338 Pesenti and Luginbühl, 1999Gruyère-type strong cohesion — Tension 11.1 70 Pesenti and Luginbühl, 1999Gruyère-type weak cohesion 55.5 909 Pesenti and Luginbühl, 1999Gruyère-type weak cohesion — Tension 11.1 32 Pesenti and Luginbühl, 1999Lancashire — 87 Prentice et al., 1993Leicester — 48 Prentice et al., 1993Leicester — 50 Prentice et al., 1993Mild Cheddar 37 days old 8.3–24 170 Charalambides et al., 1995Mild Cheddar 182 days old 8.3–24 140 Charalambides et al., 1995Mild Cheddar — A Reduced Fat — Shear 261 43 Gwartney et al., 2002Mild Cheddar — A — Shear 261 37 Gwartney et al., 2002Mild Cheddar — B Light — Shear 261 50 Gwartney et al., 2002Mild Cheddar — B — Shear 261 33 Gwartney et al., 2002Montasio — 125 Prentice et al., 1993Monterey Jack 46 days old 8.3–24 110 Charalambides et al., 1995Monterey Jack 185 days old 8.3–24 80 Charalambides et al., 1995Monterey Jack Light — Shear 261 50 Gwartney et al., 2002Monterey Jack — Shear 261 25 Gwartney et al., 2002Mozzarella — 3 Prentice et al., 1993Mozzarella 4.2 147 Masi and Addeo, 1986

TABLE 3.4 (continued)Values of Stress at Fracture from Uniaxial Testing of Several Cheeses

a

Cheese Variety

InitialStrain Rate

s

–1b

PeakStresskPa Ref.


Münster — 3 Prentice et al., 1993Parmesan — 112 Prentice et al., 1993Parmigiano Reggiano 12 months old 42 211 Noel et al., 1996Parmigiano Reggiano 18 months old 42 199 Noel et al., 1996Parmigiano Reggiano 28 months old 42 186 Noel et al., 1996Pecorino Romano — 187 Prentice et al., 1993Processed American 11.1 20 Rosenau et al., 1978Processed American 110 31 Rosenau et al., 1978Processed cheese analogs high fat,high moisture

5.56 48 Marshall, 1990


55.6 79 Marshall, 1990


556 102 Marshall, 1990


5.56 368 Marshall, 1990


55.6 424 Marshall, 1990


556 453 Marshall,1990

Provolone — 57 Prentice et al., 1993Provolone 4.2 314 Masi and Addeo, 1986Red Brick UF-Feta 8–10 weeks 110 25 Wium and Qvist, 1997Red Brick UF-Feta 8–10 weeks 220 27 Wium and Qvist, 1997Red Brick UF-Feta 8–10 weeks 330 27 Wium and Qvist, 1997Red Brick UF-Feta 8–10 weeks 440 27 Wium and Qvist, 1997Sbrinz — 22 Prentice et al., 1993Sharp Cheddar 1 month old 8.3–24 120 Charalambides et al., 1995Sharp Cheddar 6 months old 8.3–24 155 Charalambides et al., 1995Sharp Cheddar Light — Shear 261 51 Gwartney et al., 2002Sharp Cheddar — Shear 261 44 Gwartney et al., 2002Silano 4.2 157 Masi and Addeo, 1986Swiss Appenzeller type — rapeseed diet 17 104 Jaros et al., 2001Swiss Appenzeller type — regular diet 17 135 Jaros et al., 2001Tilsit — 7 Prentice et al., 1993Tin UF-Feta 8–10 weeks 110 33 Wium and Qvist, 1997Tin UF-Feta 8–10 weeks 220 39 Wium and Qvist, 1997Tin UF-Feta 8–10 weeks 330 40 Wium and Qvist, 1997Tin UF-Feta 8–10 weeks 440 46 Wium and Qvist, 1997Vorarlberger Bergkase 17 123 Jaros and Rohm, 1997

a


b


TABLE 3.4 (continued)Values of Stress at Fracture from Uniaxial Testing of Several Cheeses

a

Cheese Variety

InitialStrain Rate

s

–1b

PeakStresskPa Ref.


TABLE 3.5 Values of Work-to-Fracture from Uniaxial Testing of Several Cheeses

a

Cheese Variety

InitialStrain Rate

s

–1b

ToughnesskJ/m

3c

Ref.

Arzua-Ulloa Spanish soft cheese — type I 46 7.1 Almena et al., 1998Arzua-Ulloa Spanish soft cheese — type II

46 31.7 Almena et al., 1998

Blue Brick UF-Feta 110 4.4 Wium and Qvist, 1997Blue Brick UF-Feta 220 5.2 Wium and Qvist, 1997Blue Brick UF-Feta 330 5.5 Wium and Qvist,1997Blue Brick UF-Feta 440 5.5 Wium and Qvist, 1997Caciocavallo 4.2 8 Masi and Addeo, 1986Cheddar 8 weeks old 32 42.3 Hort and Le Grys, 2001Cheddar 64 weeks old 32 7 Hort and Le Grys, 2001Cheddar cheese 20-d-old 1.4 23 Ak and Gunasekaran, 1992Cheddar cheese 20-d-old 2.2 27 Ak and Gunasekaran, 1992Cheddar cheese 20-d-old 3.7 26 Ak and Gunasekaran, 1992Cheddar cheese 20-d-old 5.6 32 Ak and Gunasekaran, 1992Cheddar cheese 20-d-old 7.2 34 Ak and Gunasekaran, 1992Cheddar cheese 20-d-old 11 42 Ak and Gunasekaran, 1992Cheddar cheese 20-d-old 14.5 30 Ak and Gunasekaran, 1992Cheddar cheese 20-d-old 22.2 35 Ak and Gunasekaran, 1992Cheddar cheese 20-d-old 29.2 40 Ak and Gunasekaran, 1992Cheddar cheese 20-d-old 44.6 47 Ak and Gunasekaran, 1992Cheddar cheese 20-d-old 72.9 51 Ak and Gunasekaran, 1992Cheddar cheese 20-d-old 111 61 Ak and Gunasekaran, 1992Danbo 833 61 Madsen and Ardö, 2001Garrotxa-type goat milk cheese 500 6.5 Saldo et al., 2000Gruyere-type strong cohesion 55.5 210 Pesenti and Luginbühl, 1999Gruyere-type strong cohesion — Tension 11.1 57 Pesenti and Luginbühl, 1999Gruyere-type weak cohesion 55.5 152 Pesenti and Luginbühl, 1999Gruyere-type weak cohesion — Tension 11.1 8 Pesenti and Luginbühl, 1999Mozzarella 4.2 2 Masi and Addeo, 1986Parmigiano Reggiano 12 months old 42 30.6 Noel et al., 1996Parmigiano Reggiano 18 months old 42 23.8 Noel et al., 1996Parmigiano Reggiano 28 months old 42 18.4 Noel et al., 1996Provolone 4.2 6.4 Masi and Addeo, 1986Red Brick UF-Feta 110 5.5 Wium and Qvist, 1997Red Brick UF-Feta 220 6.4 Wium and Qvist, 1997Red Brick UF-Feta 330 6.7 Wium and Qvist, 1997Red Brick UF-Feta 440 6.7 Wium and Qvist, 1997Silano 4.2 3.3 Masi and Addeo, 1986Tin UF-Feta 110 5 Wium and Qvist, 1997Tin UF-Feta 220 5.4 Wium and Qvist, 1997Tin UF-Feta 330 5.5 Wium and Qvist, 1997Tin UF-Feta 440 6.2 Wium and Qvist, 1997

a


b


c

Obtained from area under the stress–strain curve up to peak location.


As stated in Chapter 2, it is not sure at which stage and where the fracture actuallystarts in compression testing of cheese (Luyten et al., 1991b). Nevertheless, in theliterature it is common to identify the maximum point on the true stress–Henckystrain curve as the fracture point in order to extract fracture stress and fracture straindata. Fracture properties determined by this practical method are likely to be relatedto the actual stress and strain at fracture.

Luginbühl (1996) contested the use of true stress–Hencky strain curve for determi-nation of fracture parameters. He stated that the true stress calculation at largedeformation is based on incorrect assumptions. Two of these assumptions are the

constancy of volume

and the

retention of cylindrical shape

. He also stated that theshift of the apparent fracture strain towards smaller values is merely due to a mathe-matical effect. He advocated that the fracture parameters of hard and semihard cheesesshould be determined from the coordinates of the apparent fracture point in theengineering stress–engineering strain curve. If need arises, Equations 2.7 and 2.12can be used to convert fracture parameters from one set of coordinates to the other.

Following the criticisms of Luginbühl (1996), Rohm et al. (1997) conductedcompression tests on various foods, including Gouda cheese, where the contactsurfaces were generously lubricated with paraffin oil. The compression tests wererecorded, and the resulting video frames were analyzed using image-processingsoftware. Their results showed that the shape of Gouda cheese specimen remainednearly cylindrical even at a relative deformation of 60% or Hencky strain of 0.92.Furthermore, for Gouda cheese, the true stress calculated by Equation 2.17, wasshown to be in close agreement with the average stress based on the actual cross-sectional area obtained from the video image analysis. In addition to the previousfindings of other researchers (Culioli and Sherman, 1976; Calzada and Peleg, 1978;Luyten et al., 1991a), these results confirmed the assumptions of constant volume

TABLE 3.6Comparison of Modulus of Deformability Values Obtained Through Different Procedures for Three Cheeses at 20°C

ProcedureStandard Cheddar

(18-week-old)Granular Cheddar

(34-week-old)Standard Mozzarella

(7-week-old)

A 1210 (10)

a

958 (8) 144 (21)B 1150 (11) 946 (10) 133 (27)C 934 (13) 694 (3) 115 (21)D 996 (13) 685 (4) 93 (22)

A: Gradient at inflection (Inf.) method.

B: Gradient at strain range Inf./2 to 1.5 Inf.

C: Gradient at strain range 0 to 0.04.

D: Linear term of the polynomial fit (Equation 2.22, Chapter 2).

a

Numbers in parentheses are coefficients of variation (100*Std.Dev./Mean).

Source:

After Watkinson and Jackson, 1999.


and shape retention during uniaxial compression with lubrication, at least for Goudacheese. Taneya et al. (1992) calculated, using Equation 2.27, Poisson’s ratio of 0.493for string cheese, signifying that it is practically incompressible, and thus the constantvolume assumption is valid. Moreover, Brennan and Bourne (1994) and Charalambideset al. (2001) presented photographic evidence illustrating that cylindrical shapes inlubricated compression of mild Provolone, Gruyere, and Mozzarella cheeses weremaintained. On the other hand, compression between molar teeth in the mouthfollowed the nonlubricated pattern (i.e., barreling), although some lubrication wasprovided by the saliva (Brennan and Bourne, 1994).

For truly elastic solids or Hookean solids, the Young’s modulus will not beaffected by the deformation rate. Cheese, however, is a viscoelastic material, and,consequently, the rate of loading or deformation is expected to have a significantimpact on its rheological properties. Many researchers have actually observed therate effect for a variety of cheeses (Shama and Sherman, 1973; Culioli andSherman, 1976; Vernon-Carter and Sherman, 1978; Dickinson and Goulding,1980). The results of Shama and Sherman (1973) on double Gloucester cheeseclearly demonstrate the effect of deformation rate on cheese properties. Themodulus of deformability and the stress at fracture are usually more influencedby the deformation rate than the strain at fracture. For instance, the fracture stressof 20-day-old Cheddar cheese almost doubled upon increasing the initial strainrate (i.e., crosshead speed/original specimen height) by fiftyfold during the lubri-cated compression; meanwhile, only a small change in the fracture strain wasobserved (Ak and Gunasekaran, 1992). In a similar fashion, the modulus ofdeformability for 4-month-old Emmentaler cheese increased by 1.7 times whenthe initial strain rate was increased by sixteenfold. For this change in the rate ofdeformation the fracture strain increased only by 1.07 times (Rohm and Lederer,1992). A quick look at the data in Tables 3.2 to 3.5 will confirm the effect ofdeformation rate on the mechanical properties of various cheeses. Generally speak-ing, as the deformation rate of deformation is increased, the stress at fracture andthe modulus of deformability increase, whereas the strain at fracture may increase,decrease, or remain unchanged.

The common explanation for the rate effect is that at higher deformation rates theviscoelastic cheese has less time to relax some of the stress during the loading stageand therefore attains higher values of stress. In other words, Deborah number, whichis the ratio of the characteristic time of the material to the time-scale of the experiment,determines the way a viscoelastic material responds to mechanical perturbations.

The rate dependence of stress–strain relationship as a result of viscoelasticityof cheese can be represented by a power-law relationship:

(3.4)

Where,

C

is a constant and

n

is the exponent signifying the relative contributionsof viscous and elastic components. The

n

value is zero for an ideally elastic material(i.e., no viscous part) and increases with the extent of the viscous contribution.According to the analysis of Luyten et al. (1991a) the relation between

n

and the

tan

δ

at the same time scale is given by:

σ ε σ ε= = +C C nn˙ ln ln ln ˙ or


(3.5)

This equation forms a bridge between nonlinear property

n

from the static experi-ments and the linear property

tan

δ

from the dynamic experiments (see Chapter 5).The

n

values for a variety of cheeses are listed in Table 3.7.Luyten and van Vliet (1996) offered two mechanisms to explain the relation

between fracture strain and rate of deformation or time-scale of deformation. Thefirst mechanism is related to energy dissipation due to viscous flow. As the viscous-like character of a material increases with decreasing deformation rate (or increasingtime-scale of deformation), the energy dissipation due to viscous flow becomesrelatively more important (e.g., in cheese with high water content). Therefore, theamount of elastically-stored energy available for fracture at a given deformation (seeChapter 4) decreases so that fracture will not take place before the cheese is deformedfurther. Hence, the fracture strain will attain a larger value. Accordingly, a trulyviscous liquid will not fracture at all, and a truly elastic solid will store all mechanicalenergy until fracture. The second mechanism is related to another dissipative effectin cheese, which is internal friction due to relative motion of different components.The energy dissipation through friction, however, increases with increasing rate of

TABLE 3.7Values for the Exponent

n

in Equation 3.4 for Different Types of Cheese

Cheese

Range of InitialStrain Rate

s

–1a

n Ref.

Double Gloucester 20 fold 0.23 Luyten et al., (1991a)Gouda 20–300 0.19 Luyten et al., (1991a)Cream cheese 2–500 0.18 Luyten et al., (1991a)American 2–500 0.14 Luyten et al., (1991a)Cheddar 2–500 0.22 Luyten et al., (1991a)Cheddar 3–600 0.22 Luyten et al., (1991a)Leicester 3–600 0.21 Luyten et al., (1991a)Cheshire 3–600 0.14 Luyten et al., (1991a)Cheddar 2–400 0.19 Luyten et al., (1991a)Processed cheese 0.2–400 0.15 Luyten et al., (1991a)Provolone 4–200 0.19 Luyten et al., (1991a)Gouda-type 1 0.2–200 0.15–0.20 Luyten et al., (1991a)Cheddar 1.4–110 0.19 Ak and Gunasekaran, (1992)Emmentaler 4.8–76 0.16 Rohm and Lederer, (1992)Tin Feta 110–440 0.21 Wium and Qvist, (1997)Red Brick Feta 110–440 0.06 Wium and Qvist, (1997)Blue Brick Feta 110–440 0.09 Wium and Qvist, (1997)

a

Values in this column are already multiplied with a factor of 1000 to avoid small numbers.

tan δ π=2

n


deformation. Thus, this mechanism lowers more of the energy available for fractureat higher deformation rates, resulting in a larger fracture strain. There may also becheeses for which the fracture strain seems independent of the deformation rate dueto the balance between these two mechanisms.

The instrumental texture measurements often seek to obtain high correlationswith the sensory evaluations, so that the sensory panel can be replaced with instru-mental tests (Bourne, 1982; Peleg, 1983). The instrumental texture determinationsare discussed in Chapter 7. It is usually hoped that when instrumental tests are madeunder conditions similar to those prevailing during sensory evaluations, one canobtain good correlations. There are, however, many theoretical and practical issuesthat need to be addressed in order to obtain satisfactory and accurate correlations(Peleg, 1983). In addition, poor correlations may sometimes stem from other reasons;for instance, the difference in fracture mechanisms of Cheddar cheese and Cheshirecheese in the mouth and in compression testing (Green et al., 1985).

Often the deformation rates employed in instrumental measurements are smallerthan the rates estimated during the sensory evaluations (e.g., chewing rate). Thisdiscrepancy has long been considered to exert a negative effect on the correlationbetween instrumental and sensory measurements. However, a recent study on UF-Fetacheese indicated that the correlation between oral firmness and stress at fracture wasindependent of deformation rate (Wium et al., 1997). Whether this is a rule orexception is yet to be established with other cheeses. For instance, the effects ofdeformation level and deformation rate on the maximum compression force, whichis related to sensory hardness, were recently investigated for 26 commercial cheeses(Xiong et al., 2002). The highest correlation was obtained at a combination ofcompression level between 70 and 90% and deformation rate of 1.0 mm/s, whichwas not the highest rate used in the study (i.e., 10 mm/s). As for many other cheesevarieties, the compression force increased with the initial strain rate in log-linearfashion (Figure 3.1).

FIGURE 3.1

Relationship between maximum compression force and strain rate in uniaxialcompression of various cheeses. (After Xiong et al., 2002.)

0

100

200

300

400

0.01 0.1 1

Initial strain rate (1/s)

Max

imu

m c

om

pre

ssio

nfo

rce

(N)

Deli-ProvoloneFarmer’s

Edam

Gouda


STRUCTURE AND COMPOSITION EFFECTS

When cylindrical samples of cheese with oriented fibrous structure are evaluatedby uniaxial compression, according to Prentice et al. (1993), the values of Young’smodulus and maximum stress may be the same whether they are deformed alongor across the direction of the internal fibers. Prentice et al. (1993) commented thatduring uniaxial compression of cheese cylinders the stresses are distributed radiallythroughout the sample such that stresses will be both along and across the directionof the internal fibers.

Quantitative results for the effect of sampling direction on compression proper-ties of Mozzarella cheese have been presented in Ak (1993). The schematic drawingof compression test is given in Figure 3.2, and the experimental conditions are givenin Table 3.8. The deformability modulus

E

D

of samples with perpendicular orienta-tion was initially higher than those of parallel orientation. As the cheese matured,the difference in

E

D values first diminished at day 14, and later reversed (Figure 3.3).Examining the compression forces at three deformation levels (i.e., 25%, 50%, 75%),we see no definite trend emerging (Table 3.9) (Ak, 1993). Nevertheless, especiallyat 50% and 75% deformations, the force was usually higher when the fibers in thesample were perpendicular to the compression direction. This is consistent with thefindings of Cervantes et al. (1983) with Mozzarella cheese, where force at 50%

FIGURE 3.2 Sample preparations for parallel and perpendicular orientations.

PARALLEL

PERPENDICULAR

TENSION

COMPRESSION

Parallel Perpendicular

CHEESE BLOCK


compression was used for comparison. On the other hand, Pompei et al. (1987)examined whether the anisotropy of Provolone cheese, due to stretching of hot curd,affected its rheological behavior. For that purpose they applied force in directionparallel and normal to the run of the macroscopic fibers. The hardness, energy, andcohesiveness values from the texture profile analysis (TPA, see Chapter 7) tests didnot reveal sufficient evidence to claim the existence of anisotropic behavior inProvolone cheese of 5–6 mo old.

TABLE 3.8Details of Experimental Conditions in Uniaxial Compression ofMozzarella Cheese with Different Sampling Directions

Explanation

Cheese Commercial low-moisture, part-skim Mozzarella.Ambient temperature Tests were conducted at room temperature (~23°C). Specimen temperature Specimens were thermally conditioned in an incubator at 15°C. This

temperature was selected to reduce complications that may arise from melting of cheese fat. It was measured that the specimen temperature increased at most by 0.5°C during 40 s of testing

Crosshead speed It was set to 50 mm/min in order to reduce the time a specimen was exposed to ambient conditions during testing.

Storage time Tests were made 7, 14, 21, and 28 days after the production date. Samples stored at refrigeration temperature

Compression level 25, 50, and 75% compression level was applied separately on different daysReplication Sixteen specimens were tested for each orientation at each storage time

Source: After Ak, 1993.

FIGURE 3.3 Effect of aging on deformability modulus of cheese with parallel and perpen-dicular orientations. (After Ak, 1993.)

90

110

130

150

170

7 14 21 28

Storage time (day)

Def

orm

abili

ty m

od

ulu

s(k

Pa)

Parallel

Perpendicular


For some cheeses (e.g., Gruyère de Comté, a Swiss-type, hard cheese), aniso-tropy in the rheological properties is of commercial importance. As an example, wecite the study of Grappin et al. (1993), where significantly different rheologicalproperties were reported for samples taken according to the direction of pressing(axial) or perpendicular to it (Table 3.10). The authors established that the formationof slits favors large differences in stress and strain values at fracture for axial andperpendicular directions. They further established clearly that the difference infracture strains between the two directions is chiefly responsible for the formationof slits — a quality defect that downgrades commercial value of Comté cheese(Grappin et al., 1993).

It is known that rheological properties of cheeses vary with the composition(i.e., the amounts and states of constituents, namely casein, fat, water, salt, pH, etc.)and the degree of maturation. However, it may not be easy to establish sound relationsbetween composition and rheological properties of the cheeses. The reason for this,

TABLE 3.9Force Values at Different Compression Levels for Samples Taken Parallel and Perpendicular to the Fiber Orientation in Mozzarella Cheese During Refrigerated Storage

Mean Compressive Force (N)

Cheese Age(day)

25% Compression 50% Compression 75% Compression

ParallelPerpen-dicular

Sig.Levela Parallel

Perpen-dicular

Sig.Level Parallel

Perpen-dicular

Sig.Level

7142128

8.112.310.610.2

8.311.99.49.1

0.730.360.0090.005

21.229.225.026.0

23.531.125.123.7

0.0130.0500.930.027

51.565.151.457.7

61.173.757.854.0

0.00010.0030.0150.124

a Significance level

Source: After Ak, 1993.

TABLE 3.10Effect of Sampling Direction on Compression Properties of Gruyère de Comté Cheese

Rheological ParameterAxial

CompressionPerpendicularCompression

SignificanceLevel

Modulus (kPa) 367 429 **Fracture stress (kPa) 184 142 **Fracture strain (%) 43 38 **

Note: ** = significant p<0.01; comparison of the means by t-test.

Source: After Grappin et al., 1993. With permission.


as already acknowledged by many researchers (Creamer and Olson, 1982; Luytenet al., 1982; Marshall, 1990; Wium et al., 1998), is the difficulty of making cheesethat differs only in one constituent (e.g., fat content), while keeping others (e.g.,water content, salt content, pH, etc.) constant. In some cases, statistical methods areused to analyze the simultaneous variations in more than one variable. Rohm et al.(1992) evaluated chief compositional and maturation parameters affecting uniaxialcompression properties of Swiss-type cheese (4-month-old Emmental) by multipleregression analysis. The mean values for rheological and fracture parameters of thiswork are presented in Tables 3.2 to 3.5.

Casein is the main constituent in cheese that builds the structure and gives, whenintact, the elastic or solid character. Based on the data of Chen et al. (1979), therelation between penetration stress (required pushing the plunger, D = 0.64 cm, intothe sample for 1.91 cm) and protein content of different cheeses is shown inFigure 3.4. Based on the same study (excluding processed Cheddar cheese), Prentice(1992) concluded that about 25%* of the cheese by weight must be casein in orderto provide a rigid framework. A similar procedure is applied to the compression datataken from Lee et al. (1978), and the resulting plot is given in Figure 3.5. It is seenthat the compression stress at 80% deformation increases with the protein contentof different cheeses (protein values taken from Bassette and Acosta, 1988). In thestudy by Chen et al. (1979) the penetration tests were made at 12.2 to 13.3°C, whilethe compression tests by Lee et al. (1978) were made at room temperature. We shallremark that the composition of cheeses tested in these studies differed not only inprotein content but also in all other constituents (i.e., moisture, fat, salt, pH). How-ever, the results of Chen et al. and Lee et al. indicated that maximum compressionforce for cheese varieties with widely differing composition correlate most closelywith protein content and was not related to fat content. Other protein-containing

FIGURE 3.4 Relationship between penetration force and protein content of 11 differentcheeses. (After Chen et al., 1979.)

* Protein contents (%) in the original study and those that appear in Figure 8.6 of Prentice (1992) appearto be different.

y = 73 x − 1256

R2 = 0.76

0

400

800

1200

1600

10 20 30 40

Protein content (%)

Pen

etra

tio

n s

tres

s (k

Pa)


foods also exhibit similar relations (e.g., Hsieh and Regenstein, 1993). Therefore,although it may not be entirely correct to attribute the changes in rheologicalproperties fully to the protein content, the data presented in Figures 3.4 and 3.5demonstrate, however, that firmness is largely related to the protein content.

Another clear evidence of a strong relation between protein content and prop-erties by penetration method has been reported for heat-induced skim-milk gels(Kalab and Harwalkar, 1974; Holcomb et al., 1992). Besides, since hydrolysis ofprotein (i.e., casein fractions) during maturation weakens the structure and reducesthe magnitude of cheese strength, it is therefore consistent to observe an increasein strength of cheese with an increase in protein content, irrespective of the type ofcheese. Perhaps more compelling findings on the relation between protein contentand firmness of cheese are the results of de Jong (1978) for Meshanger cheese (oldDutch cheese). The relation between protein content and firmness (i.e., force byextrusion method) is shown in Figure 3.6. The firmness was determined by anextrusion method involving a close-fitting cylinder and piston, which is set to moveat a constant speed (de Jong, 1976). de Jong (1978) did not anticipate much contri-bution from the discontinuous fat to the overall firmness of Meshanger cheese.

The classification of cheese according to water content testifies for the importanceof this constituent. Chen et al. (1979) analyzed the relation between texture andcomposition (in relative unit of percent) of eleven cheeses to suggest the followingsequence of decreasing contribution to the texture parameters: protein > NaCl > water> pH > fat. However, in another investigation, the sequence obtained was different(Rüegg, 1985): water > fat > pH > Ca > (Nsol-NPN), where Nsol means solublenitrogen and NPN nonprotein nitrogen. Regardless of its position in such ranking,it is well established that a strong relation exists between water content and mechani-cal and textural properties for several cheeses (Amantea et al., 1986; Luyten, 1988;Tunick et al., 1993; Prentice, 1992; Visser, 1991; Taranto et al., 1979; Rohm et al.,1992; Tunick et al., 1991). As the moisture content increases, the resistance of cheeseto deformation, and hence its modulus of deformability, decreases. The stress at

FIGURE 3.5 Relationship between compression stress and protein content of differentcheeses. (After Lee et al., 1978.)

y = 0.41x − 2.95R2 = 0.57

0

2

4

6

8

10

12

5 10 15 20 25 30Protein content (%)

Str

ess

at 8

0% c

om

pre

ssio

n(k

Pa)


fracture also decreases with increasing water content. The strain at fracture, how-ever, either remains unaffected or increases with the moisture content, dependingon the age of cheese (Visser, 1991; Rohm et al., 1992). The effect of water contenton the modulus is usually explained by following reasons: (a) a high water contentmeans a low protein content, which is the stress-carrying component; (b) water isa low-viscosity liquid that occupies the space between the fat and protein, and actsas a good lubricant; and (c) more swollen protein particles due to high water contentoffers less resistance to deformation (Luyten, 1988; Prentice, 1992).

There can be significant variation in rheological properties within a single cheeseblock as a result of various reasons: (a) presence or absence of a rind; (b) frequencyof turning during ripening; (c) development of moisture gradient; and (d) nonuniformproteolytic activity (Prentice et al., 1993). It is likely that not only the magnitudesbut also the trends for a particular property (e.g., deformability modulus) can varywith the position in a cheese block, from surface (where moisture loss may dominate)to center (where proteolytic activities may dominate). Based on the data of Steffen(1976) reported by Prentice et al. (1993), there can be a variation of about 50% infirmness with distance from the surface in an otherwise uniform cheese. Recently,few studies have been conducted where hydrocolloid-based edible coatings wereapplied to semihard and brined cheeses for different purposes (e.g., moisture regula-tion, appearance, protection against microbial contamination) while still maintainingtheir desirable textural properties (Kampf and Nussinovitch, 2000). In terms ofmechanical properties, the outcome of such coatings was promising, especially forsemihard cheese (Kampf and Nussinovitch, 2000).

Fat is one of the primary constituents contributing greatly to rheology, texture,and organoleptic characteristics (e.g., imparting a desirable mouthfeel to cheese) ofcheeses (Marshall, 1990). It is also considered important in transport and packaging(Green et al., 1990). The contribution of fat to cheese quality is better appreciatedwhen it is removed or reduced in manufacturing low-fat varieties. A reduction in fatcontent often adversely affects texture and flavor of cheese (Olson and Johnson,

FIGURE 3.6 Strong contribution of protein content to the overall firmness of cheese. (Afterde Jong, 1978. With permission.)

0

50

100

150

200

250

0.20 0.30 0.40 0.50 0.60

Volume fraction of protein

Fir

mn

ess

(em

pir

ical

un

its)


1990; Jameson, 1990). The level of intact casein in 225-day-old Cheddar cheesewas twice higher in the reduced-fat cheese than that in the full-fat cheese. But therate of decrease in the levels of intact casein was practically independent of the fatcontent (Fenelon and Guinee, 2000). The technological strategies for coping withthe challenges in making of reduced-fat cheese and low-fat cheese and some regula-tory issues have been discussed in recent reviews (Olson and Johnson, 1990; Drakeand Swanson, 1995; Mistry, 2001).

Reduction in fat content of hard cheeses (e.g., Cheddar) affects not only theflavor development but also the texture. It is well known that the texture of a reducedfat cheese is firmer and more elastic than that with full-fat content. Marshall (1990)conducted a thorough study to determine effects of changing fat and moisture[as moisture in nonfat solids (MNFS)] contents on the sensory, rheological, andstructural properties of the processed cheese analogs. Numerical results from thiswork are presented in Tables 3.2 to 3.5. As can be seen from the data in these tables,the rheological parameters tended to decrease with an increase in MNFS, probablybecause of moisture acting as a plasticizer in the protein network.

The fat content affects the microstructure of cheese. Full-fat cheeses of allvarieties (i.e., Cheddar, Mozzarella, processed, and Swiss cheeses) are characterizedby a protein matrix interspersed with fat globules existing in various sizes andshapes. Low-fat cheeses, however, have fewer and smaller fat globules within thedense protein network. The consequence of the protein-dominated structure of low-fat cheeses, is a firm and rubbery body and texture (Mistry and Anderson, 1993).In an earlier work, Green et al. (1981) examined, by different microscopic tech-niques, the structure development in Cheddar cheese from concentrated milksthroughout cheese making and maturation. As the milk used in cheesemakingbecame more concentrated, the protein network became progressively coarser andthis, in addition to large loss of fat into whey, led to higher resistance to compression(i.e., higher firmness).

The role of fat in rheology of cheese was occasionally treated in terms ofcomposite material behavior (Prentice, 1992; Luyten and van Vliet, 1990). Thecheese is viewed as a composite material with casein-water forming the matrix andfat globules acting like fillers or inclusions. The mechanical properties of a compositematerial therefore depend on the properties of the matrix, the volume fraction andproperties of the filler, and the mechanical interaction between the filler and matrix.According to Prentice (1992) the only interaction between fat and casein is friction.

Green et al. (1990) studied the composite behavior of cheese analogs containingfat globules in a protein matrix. They varied fat concentration and fat hardness, andthey either emulsified the fat with a neutral detergent (minimizing interactionbetween fat globules and the matrix) or emulsified with sodium caseinate (increasinginteraction between fat globules and the matrix). The higher fat content at roomtemperature (70 to 80% liquid form) increased the lubrication effect of fat andreduced the fracture properties in compression and in wire cutting. Using differentamounts of sunflower oil (completely liquid at room temperature) instead of butterfatdecreased the maximum stress from 304 kPa at 6.2% oil to 165 kPa at 20.7% oil,and Young’s modulus from 115 kPa at 6.2% oil to 77 kPa at 20.7% oil. On the other


hand, substituting partially hydrogenated oil (50% solid) for butterfat decreased themaximum stress from 349 kPa at 6.8% fat to 282 at 21.5% fat, but increasedenormously the Young’s modulus from 152 kPa at 6.8% fat to 2061 kPa at 21.5%fat. Moreover, butterfat contributed more to the composite behavior when it wasemulsified with sodium caseinate (i.e., more interaction with the matrix).

It seems that simple substitution of fat by protein, water, and fat replacers resultsin a low-fat cheese that is inferior in many respects to its full-fat counterpart (Aryanaand Haque, 2001). Several characteristics of fat or lack of it in low-fat cheeses cancontribute to this result. Mechanical properties of fats, and their contribution to cheeseand probably to perception of texture by consumers, are influenced by their chemicalcomposition and temperature. The solid fraction of fat changes sharply in a relativelynarrow temperature range (e.g., 10 to 35°C). However, water, for instance, withinthis temperature range, will have more or less constant properties. The interactionbetween fat and protein is hard (if not impossible) to mimic by the interaction betweenwater and protein, or between fat replacers and protein. Commercially available fatreplacers, of which none can yet fully duplicate functional and sensory attributes offat, are one of three types: lipid based, carbohydrate based and protein based (Akoh,1998). Interaction between water and fat replacers, in contrast to water binding ofcasein (Geurts et al., 1974), can also have a large impact on the properties of the finalcheese. Another point worth mentioning is that during ripening of traditional cheeses,the fat globules can aggregate (and possibly coalesce) to increase in size and decreasein number, and this has an impact on the sensory properties of the cheese.

The clumping of fat globules was observed in Cheddar cheese (Kimber et al.,1974) and Mozzarella cheese of varying fat contents and aged for 6 weeks (Tunicket al., 1993) and 50 days (Kiely et al., 1993), as well as in Cheddar-type cheese(Guinee et al., 2000). Kiely et al. (1993) suggested that fat aggregates are formeddue to proteolytic destruction of the casein network. They also suggested thataggregation of fat globules could be the reason for the age-related increase in free-oil formation observed in low-moisture, part-skim Mozzarella cheese by Kiely et al.(1991). Tunick (1994) also reported that free-oil formation in Mozzarella cheeseincreased with the percentage of fat and protein breakdown. However, homogeni-zation of cheese milk and cream greatly reduced free-oil due to the reduction of fatdroplet size, while homogenization of skim milk had no effect (Tunick, 1994;Oommen, et al., 2000). Agglomeration of fat globules into larger particles wasmicroscopically observed in both stirred-curd and stretched-curd Mozzarella cheesesafter baking in a conventional oven (Paquet and Kalab, 1988). The agglomerationof fat globules is difficult to occur in low-fat cheese where the massive protein matrixkeeps the small fat droplets well dispersed. This contributes to the rubbery textureand mouthfeel of the low-fat cheeses. Lastly, the contribution of free fatty acids andfat-soluble flavors to the taste of traditional cheese must be mentioned. Even afteraging for 12 months, sensory panelists noted a flat flavor and lack of Cheddar flavorin reduced fat (50%) cheese (Olson and Johnson, 1990).

The physical state of the fat globules (i.e., proportion of solid fat) determinesits relative rigidity or stiffness in comparison to the casein matrix. Thus, the relativecontribution of milk fat to the overall cheese properties is highly temperature


dependent. Melting of milk-fat globules occurs over a large temperature range from–30 to 40°C due to varying melting points of triglycerides (Dufour et al., 2000). Itis entirely liquid above 40°C and completely solid below –30°C. Between theseextremes it is a mixture of crystals and oil, where the latter is a continuous phase.

Masi and Addeo (1986) reported a clear relation between the fat content(expressed as the ratio of fat to solids-nonfat, SNF) and the modulus of elasticityfor Mozzarella cheese (Figure 3.7). However, it may be incorrect to attribute thedecrease in the modulus entirely to the increase in fat content since moisture contentsof these experimental cheeses also changed. The size of variation in the fat contentwas 4.7 units, whereas that in the water content was 3.2 units; that is, rathercomparable numbers. As shown in Figure 3.7, we can also plot the modulus againstthe water content (as water/SNF ratio) for the same cheeses and still obtain a goodcorrelation. A recent study by Madsen and Ardö (2001) on Danbo cheese with threefat contents provides further results regarding effects of fat and water on rheologicalproperties (Table 3.11). On one hand, when the fat content of Danbo cheese is

FIGURE 3.7 Effects of fat and moisture contents on the elasticity modulus of different cheesevarieties. (Masi and Addeo, 1986.)

y = -34.4 x + 57.9 R2 = 0.96

10

20

30

40

0.7 0.8 0.9 1.0 1.1 1.2

Fat/SNF

Mo

du

lus

of

elas

tici

ty (

kPa)

y = -21.5 x + 66.9R2 = 0.90

10

20

30

40

1.5 1.9 2.3

Water/SNF

Mo

du

lus

of

elas

tici

ty (

kPa)

2.11.7


reduced from 25 to 16.7% (a change of 33%), there was no change in the rheologicalparameters except the modulus. On the other hand, when the fat content is furtherreduced from 16.7 to 13.6% (a change of 19%), all parameters increased dramati-cally. It was concluded that water is not an adequate substitute for fat in order toobtain good quality, low-fat Danbo cheese (Madsen and Ardö, 2001).

Considering Gouda cheese as a composite material, Luyten (1988) and Luytenand van Vliet (1990) determined the effect of temperature on the compressionproperties of the cheese. They pointed out that at 10°C the fat is stiffer than thematrix, and therefore the E for high-fat (60%) cheese is greater than the E for low-fat (10%) cheese. By the same token, the opposite is true at high temperature (26°C)where fat is nearly entirely liquid and contributes little to the modulus of the cheese.At the middle temperature (20°C), there was no influence of volume fraction of fat,indicating that the modulus of the fat is equal to the modulus of the protein matrixand is about 100 kPa (Luyten and van Vliet, 1990). The authors estimated that themodulus of the fat particles at 14°C to be 460 to 880 kPa. This is comparable to themodulus of deformability of a variety of cheeses listed in Table 3.2. It is alsoimportant to note that part of the temperature effect is due to the changes inrheological properties of the protein matrix.

The theory of composite materials predicts a decrease in fracture strain with anincrease in volume fraction of the filler. Since this was not observed in Gouda cheese,Luyten and van Vliet (1990) concluded that the milk-fat globules are relatively small(0.1–10 µm, Mulder and Walstra, 1974) and do not create stress concentrations tocause crack initiation. The fracture stress of Gouda cheese is, however, affected bythe fat content and test temperature. The fracture stress decreased with the increasingfat content, and the temperature effect was stronger in high-fat cheese than in low-fat cheese.

The importance of pH for a variety of cheese has been discussed from the cheese-manufacturing point of view (e.g., Lawrence et al., 1983; Lawrence et al., 1984;Chapter 1). The apparent effect of pH is more striking for Mozzarella and stringcheeses. It is known that the kneading and stretching process of Mozzarella cheesecurd is best performed at about pH 5.2 to 5.4 (Kosikowski, 1982). Kimura et al. (1992)

TABLE 3.11Uniaxial Compression Properties of Low-Fat, Reduced-Fat, and Normal-Fat Danbo Cheese

Parameter Low-Fat Reduced-Fat Normal-Fat

Deformability modulus (kPa) 208 143 189Fracture stress (kPa) 194 92 94Fracture strain (–) 1.3 1.1 1.1Work to fracture (kJ/m3) 127 55 61

Fat (%,w/w) 13.6 16.7 25.0Moisture (%,w/w) 52.9 53.3 47.4

Source: After Madsen and Ardö, 2001. With permission.


reported on the structure and properties of string cheese at different pH and dem-ineralization levels. Their results indicated that stringiness is limited by the cal-cium/phosphate (Ca/P) ratio in curd and not specifically by the curd pH. However,curd pH is an operational parameter that is associated with the Ca/P ratio.

It is known that cheese has a “short” consistency (i.e., small fracture strain) ifit has a low pH or a high salt content (Luyten et al., 1982). The effect of salt contenton rheological properties of unripened Camembert (Mpagana and Hardy, 1986) andGouda (Luyten, 1988) cheeses has been reported. Mpagana and Hardy (1986)adjusted the salt content of Camembert cheese by first keeping small, cylindricalpieces (2.4 cm diameter, 3.0 cm height) in saturated NaCl solution (pH = 5.0) at15°C and then storing the brined pieces at 15°C and relative humidity of 95% forthree days to assure homogeneous salt distribution within the samples. The testpieces (1.38 cm diameter, 1.0 cm height) were compressed to 20% of their originalheight (i.e., 80% deformation) at an initial strain rate 0.017 s–1. Although only thesalt content was intentionally altered by applying different brining times, the watercontent of cheese would have decreased as well due to brining. Nevertheless, themodulus of deformability and fracture stress of Camembert increased exponentially,while the fracture strain decreased linearly with the salt content of the cheese(Figure 3.8). These findings are consistent with the results on other cheeses, suchas Mozzarella cheese (Cervantes et al., 1983), Gouda (Luyten, 1988), and Fetacheese (Katsiari et al., 1997).

Watkinson et al. (2001) preferred to work with a model cheese system, obtainedby direct acidification, in order to study effects of pH on rheological propertiesduring ripening with minimal confounding from other variables. It is observed thatat a given ripening time, the fracture strain increased with pH in the range of 5.2 to6.2, except there was a distinct maximum at pH 5.8 for the 87-day data. At a givenpH value, the fracture strain increased with ripening time, with the exception of aconstant value after seven days for the pH 6.2 cheeses. It shall be recalled that thelocal maximum in fracture strain of young Gouda cheese (1-week-old) was posi-tioned at a lower pH 5.2 (Luyten et al., 1982). Further results from Watkinson et al.(2001) demonstrate that, in general, fracture stress increases with pH (e.g., at day7 from about 160 kPa at pH 5.2 to about 270 kPa at pH 6.2) and modulus ofdeformability decreases with pH (e.g., at day 2 from about 1200 kPa at pH 5.2 toabout 825 kPa at pH 6.2).

Changes in rheological properties of cheese curd during the initial stages ofripening were studied at 20°C as a function of pH (5.45–6.05) and storage time (2–14days) using a specially developed extrusion-flow technique (Ramkumar et al., 1998).The maximum force exerted on the grated curd during extrusion testing tended toincrease with pH, reaching the maximum at pH 5.90. Increasing solid-like behaviorwith pH was also observed in oscillatory shear results for the cheese curd, indicatingthat the effect of pH is persistent in both small and large deformation regimes.Moreover, the tendency to exhibit more solid-like response is in accordance withthe pH effect on the fracture stress (Watkinson et al., 2001).

Perhaps the most important factor affecting rheological and other properties ofcheese is proteolysis during maturation. The proteolytic activity that contributes


FIGURE 3.8 Effect of salt content on the mechanical properties of Camembert cheese. (AfterMpagana and Hardy, 1986.)

y = 109.3e0.09x

R2 = 0.91

10

100

1000

0 5 10 15 20 25

Salt content (g NaCl/100 H2O)

Mo

du

lus

of

def

orm

abili

ty (

kPa)

y = 37.6e0.10x

R2 = 0.91

10

100

1000

0 5 10 15 20 25

Salt content (g NaCl/100 g H2O)

En

gin

eeri

ng

fra

ctu

rest

ress

(kP

a)

y = -0.016 x + 0.85 R2 = 0.56

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 20 25

Salt content (g NaCl/100 g H2O)

Fra

ctu

re s

trai

n (

-)


greatly to the rheological and textural properties of cheeses basically means areduction in the levels of intact casein (i.e., αs1-casein and β-casein). It is usuallyobserved that αs1-casein fraction is hydrolyzed to a greater extent than β-casein,although the extent may depend on the cheese variety and the type of proteolyticenzyme (Fox, 1989; Trujillo et al., 1999; Dervisoglu and Yazici, 2001; Katsiari et al.,2000). Many ripening agents from different sources are responsible at different stagesfor the hydrolysis of caseins into small peptides and eventually to free amino acids,thus contributing to changes in both the texture and flavor during ripening (Foxet al., 1993; Farkye and Fox, 1990). It is of great importance to the cheese industryto be able to predict and control, and particularly accelerate, the ripening process(Fox et al., 1996; Fedrick, 1987; van den Berg and Exterkate, 1993; Folkertsmaet al., 1996; Law, 1987; Saldo et al., 2000).

Degradation of αs1-casein and β-casein during ripening of various cheeses isshown in Figure 3.9. We must note that only the trends should be considered andno comparison shall be made between different cheeses since the percent values arebased on different reference quantities (e.g., expressed as % of levels in milk, or %of levels in fresh curd, % of levels in 1-day-old cheese, etc). An interesting examplefor effect of hydrolysis of para-casein on properties of cheese was reported forCamembert cheese (Schlesser et al., 1992). During early stages of ripening (up to15 days) there was an increase in deformability modulus (called elasticity in theoriginal paper) of Camembert cheese, which later on decreased with further aginguntil zero. After aging for more than 29 days the samples became semifluid(Schlesser et al., 1992).

Consistent with the expectations based on previous findings, mechanical prop-erties of Tybo Argentino cheese (semihard variety) decreased with ripening at10°C and 60% relative humidity (Bertola et al., 1992). Although there was muchscatter in the results, the deformability modulus of this cheese decreased fromabout 65 to 15 kPa during 120 days of ripening. Assuming a linear dependency,this means a decrease of 0.4 kPa/day. Ak and Gunasekaran (1995) reported asimilar change for Mozzarella cheese over one month of aging. The strain atfracture did not vary with ripening time, and the average value was reported as70% or εf = 1.20 (Bertola et al., 1992).

Noël et al. (1996) determined rheological properties of Parmigiano Reggiano agedfor up to 28 months and established relationships with the sensory properties. Theseauthors reported not only standard rheological parameters, such as apparent elasticmodulus and fracture parameters, but also the proportional limit and the modulus ofresilience (see Chapter 2). The strain at apparent elastic limit of Parmigiano Reggianocheese was about 7.6%, regardless of its age, while the stress limit increased from117 kPa at 12 months to 191 kPa at 28 months. The apparent elastic modulus of thecheese increased with the age almost linearly with a rate of 60 kPa/month duringmaturation from 12 months to 28 months. The fracture strain and fracture stressvalues decreased linearly with the age of the cheese at a rate 0.006 units/month and1.5 kPa/month, respectively.

Raphaelides and Antoniou (1996) reported that for both traditional and UF-Telemecheeses, the main changes in cheese structure, as reflected in mechanical properties,took place within the first month of ripening (Figure 3.10). Wium and Qvist (1997)


reported on the fracture properties of three types of UF-Feta determined by uniaxialcompression and dynamic tests. As can be seen in Table 3.4 the stress at fracturefor these cheeses varied between 20 to 46 kPa, with the Tin Feta cheese alwayshaving higher values than the Red Brick Feta cheese and the Blue Brick Feta cheese.Moreover, when these cheeses were evaluated by sensory means (i.e., nonoralfirmness: the resistance of a cube of cheese to moderate squeezing between thumband forefinger; and oral firmness: the resistance of a cube of cheese during normalmastication), the Tin Feta cheese was selected as the firmest cheese, followed bythe Red Brick Feta cheese and the Blue Brick Feta cheese (Wium and Qvist, 1997).On the other hand, the Tin Feta cheese also had the highest n value (Table 3.7), aswell as tan δ, both signifying the more viscous character of this cheese. It seemsthat the parameters n and tan δ do not play a significant role in sensory evaluationof cheese.

The modulus of deformability (ED) values (Table 3.2) in uniaxial compression ofthree UF-Feta cheeses ranged from 176 to 465 kPa (Wium and Qvist, 1997). It can

FIGURE 3.9 Proteolysis in numerous cheeses as measured by the decrease in intact αs1-casein and β-casein. (Data from different sources referenced in text.)

0

20

40

60

80

100

0 10 20 30 40 50 60

Maturation time (week)

Alp

ha

(s1)

-cas

ein

(%

)Mild Cheddar

Monterey Jack

Sharp Cheddar

Cheddar

La Serena

Kulek

Feta

0

20

40

60

80

100

120

0 10 20 30 40 50 60Maturation time (week)

Bet

a-ca

sein

(%

)

Mild Cheddar

Monterey Jack

Sharp Cheddar

Cheddar

La Serena

Kulek

Feta


be seen that the Tin Feta* had higher ED values at all rates than the Red Brick Fetacheese and the Blue Brick Feta cheese, indicating that the Tin Feta cheese is the stiffest.

Wium and Qvist (1998) and Wium et al. (1998) reported on changes in rheo-logical properties of UF Feta cheese made by acidification using glucono-δ-lactone(GDL). In these studies, the gross chemical composition (e.g., moisture, salt, pH,total N, and fat) of the cheeses was kept essentially constant while studying theeffects of rennet concentration, coagulation method, and storage time. Measurementof proteolysis by capillary electrophoresis showed that αs1-casein was degraded morethan β-casein due to the relatively faster action of chymosin on the former caseinfraction, and also, the greater inhibitory influence of NaCl on the hydrolysis ofβ-casein by enzymes (Fox and Walley, 1971). Similarly, the ripening of Meshangercheese was characterized by a very rapid and complete hydrolysis of αs1-casein,while the β-casein remaining essentially unattacked (de Jong, 1976). Substantialamounts of αs1-casein and β-casein were hydrolyzed by the high level of residualrennet in Feta cheese having salt-in-moisture concentrations from 3.99 to 4.32 andpH from 4.65 to 4.71 (Samal et al., 1993).

The compression variables (ED, σf , εf , Wf) for UF-Feta cheese generallydecreased with storage time, and that was ascribed purely to the proteolysis sincethe gross chemical composition remained essentially constant. It was furtherobserved that stress at fracture, modulus of deformability, and work to fractureall increased significantly with rennet concentration, more so in the young cheese,with some showing a maximum at some intermediate levels (Figure 3.11). Thiswas associated with the formation of a coarser network at higher rennet concen-trations and viewed as a potential way of making soft variants of UF-Feta cheesewith a smooth texture by using less rennet. On the other hand, strain at fracturedecreased with increasing rennet concentration, again consistent with coarser

FIGURE 3.10 Effect of maturation time on the deformability modulus of different kinds ofFeta cheese. (After Raphaelides and Antoniou, 1996. With permission.)

* The Tin Feta is packed in tins containing brine and the Red Brick Feta and Blue Brick Feta are packedin Tetra-Brick packages without brine.

0

40

80

120

160

200

0 1 2 3 4 5

Maturation time (month)

Def

orm

abili

ty m

od

ulu

s (k

Pa)

Traditional

UF-unheated

UF-heated


structure explanation. Luyten and van Vliet (1996) stated that the strain at fractureis rather low for very young Gouda cheeses (e.g., 1-day- or 2-day-old) due to thelarge inherent defects (e.g., incomplete fusing of curd particles) present in suchcheeses (Luyten, 1988).

A recent interesting work on the fracture stress of fused curd grains (Lodaiteet al., 2002) indicated that the applied compressive stress, the degree of syneresisprior to fusion, and the fusion time exerted significant positive effects on the qualityof fusion and the magnitude of fracture stress.

A low fracture strain implies a short texture and possibly a crumbly behavior(Luyten et al., 1982). In general, the shortness of cheese increases with maturation.Watkinson et al. (1997) has shown that the strain at fracture of New ZealandCheddar cheese initially increased in the first 28 days, and thereafter it decreasedwith further aging. Their results, combined with those from Creamer and Olson(1982), are plotted in Figure 3.12, which shows a large decrease in fracture strainduring maturation of Cheddar cheese. Similar trends have been reported for severalother cheeses (Luyten, 1988; Ak et al., 1993; Luyten and van Vliet, 1996).

The initial increase in εf is attributed to the process of fusion until the proteolysisdominates and causes a decrease in εf or an increase in shortness. However, we mustnote that the relation between fracture strain and ripening time depends on otherfactors, such as pH. A fresh but acid cheese can have a fracture-strain value similarto that of a mature cheese (Luyten et al., 1982; Luyten and van Vliet, 1996; Rohmet al., 1992). Moreover, for 7-week-old Gouda cheese, a maximum in the strain atfracture was found at around pH 5.2 to 5.25 (Luyten et al., 1982). It is common tosee that effects of one compositional variable are confounded with another composi-tional variable and with ripening time.

Rohm et al. (1996) determined the impact of seasonal variations in raw-milkquality on the composition and fracture properties of Emmental cheeses. Regardingthe composition, the iodine value (IV), which is an indicator of the softness of the

FIGURE 3.11 Effect of rennet concentration on fracture stress and fracture strain of Fetacheese made from ultrafiltered milk. (After Wium and Qvist, 1998.)

0

20

40

60

80

0.001 0.01 0.1 1 10

Rennet concentration (g/kg)

Fra

ctu

re s

tres

s (k

Pa)

0

0.1

0.2

0.3

0.4

0.5

Fra

ctu

re s

trai

n (

-)

stress

strain


milk fat, and thus cheese, increased, as expected, from 34.3 in winter cheeses to41.5 in summer cheeses. Moreover, Emmental cheeses produced during wintershowed accelerated lactic-acid degradation and propionic-acid generation, andreduced secondary proteolysis than those produced during summer. It is observedthat the fracture strain of Emmental cheese is not affected by the seasonal variations,but decreased with the maturation time (Figure 3.13).

Emmental cheese made in different seasons exhibited considerably differentfracture stress (Figure 3.14), most probably due to the seasonal variations in fatty-acid composition of the milk fat (Rohm et al., 1996). The mean values of fracturestress, which correlates well with sensory firmness, are about 165, 126, and 91 kPafor mature cheeses (16 weeks) made in winter, spring, and summer, respectively.This is in line with the increase in iodine value of milk fat as the season changesfrom winter to summer. The iodine value is associated with the number of double

FIGURE 3.12 Variation of strain at fracture for Cheddar cheese as a function of maturationtime. (After Creamer and Olson, 1982; Watkinson et al., 1997.)

FIGURE 3.13 Fracture strain of Emmental cheese as affected by maturation. (After Rohmet al., 1996.)

0.0

0.4

0.8

1.2

1.6

0 100 200 300 400 500

Maturation time (day)

Str

ain

at

frac

ture

(-)

Watkinson et al. (1997)

Creamer and Olson (1982)

1.0

1.2

1.4

1.6

1.8

120100806040200

Age of cheese (day)

Str

ain

at

frac

ture

(-)


bonds in fat. As the number of double bonds increases, the solid fraction of milkfat at a given temperature decreases (Jaros et al. 2001). Therefore, the iodine valueof the milk fat serves as an indicator of the firmness of fat, and in turn, of cheese.

Jaros and Rohm (1997) reported on the seasonal variations in mechanical proper-ties of Vorarlberger Bergkäse (a smear-ripened, Gruyère-type, raw-milk hard cheese).Figure 3.15 shows apparent fracture stress for Bergkäse as a function of the produc-tion month. The mean values of fracture stress for summer and winter cheeses arereported to be 107 and 133 kPa, respectively. The corresponding fracture strainvalues for summer and winter cheeses are found to be 0.48 and 0.61, respectively(Jaros and Rohm, 1997).

FIGURE 3.14 Fracture stress of Emmental cheese as affected by maturation time and pro-duction season. (After Rohm et al., 1996.)

FIGURE 3.15 Seasonal variations in fracture stress of Vorarlberger Bergkäse. (After Jarosand Rohm, 1997.)

0

50

100

150

200

250

300

350

8020 40 600 100 120

Age of cheese (day)

Fra

ctu

re s

tres

s (k

Pa)

summer cheese

spring cheese

winter cheese

40

80

120

160

0 1 2 3 4 5 6 7 8 9 10 11 12

Production month

Str

ess

at f

ract

ure

(kP

a)


Without altering the gross chemical composition of the cheese (Swiss Appenzeller),Jaros et al. (2001) increased the amount of unsaturated fatty acids in milk fat byadding shredded rapeseed to the cattle diet. Those cheeses made with milk from themodified diet exhibited significantly lower values for the modulus of deformabilityand the fracture strain. The property values of the cheese with and without therapeseed are given in Tables 3.2 to 3.5. It is shown that the rapeseed feeding can beutilized advantageously to eliminate the firmness differences in cheeses of summerand winter periods, and therefore provide the consumer with more consistent products(Jaros et al., 2001).

Ohashi et al. (1982) demonstrated by wire-cutting tests the effect of seasonalvariations on mechanical properties of milk-rennet curd in connection with thecomposition of milk. In agreement with results of the other studies cited above, theelastic moduli of the curd were as follows for the spring, summer, autumn, andwinter seasons: 55.3, 37.1, 44.4, and 50.1 kPa, respectively.

STRESS-RELAXATION MEASUREMENTS

Stress-relaxation properties are very important in many industrial operations, as theycontrol the materials’ response to external mechanical forces. Generally speaking,stress relaxation can be due to physical events or chemical processes (Ferry, 1980;Grosberg and Khokhlov, 1997). In any case, the relaxation process is regulated bythe ratio of two variables: the characteristic time of a material (λ) to the characteristictime of observation (t), hence the Deborah number, De = λ/t. A high De (De>>1)corresponds to solid-like behavior (i.e., no relaxation), whereas a low De (De<<1)corresponds to a liquid-like behavior (i.e., instantaneous relaxation). The materialbehavior is called viscoelastic when the relaxation time and the observation time(e.g., experimentation time) are similar (i.e., De ≈ 1.0). The characteristic time of amaterial is often represented by its relaxation time. The relaxation time of materialsvaries in a wide range: for instance, at 20°C it is ~10–12 s for water, and at 27°C itis greater than 105 s for glass (Tanner, 1985). Thus, water will not exhibit an elasticresponse unless it is subjected to a deformation on a time scale less than 10–12 s.Due to various constituents present, single relaxation time is usually not sufficientto describe the relaxation behavior of foods.

There is a fundamental issue that needs attention, and it is related to the time ittakes to deform the sample (i.e., rise time mentioned in Chapter 2). If the rise timeis t1 seconds, then the rule-of-ten (Meissner, 1978) requires that only relaxation dataat times greater than 10t1 seconds should be used in analyzing the results. However,as pointed out by Masi (1989), if this rule is strictly obeyed, the relaxation processis very likely to be completed before starting the collection of “actual” data. Thesituation is, in fact, better with the advances in rheological instruments. In principleand practice, it is now possible to make t1 fairly short by using high-speed loading(e.g., 2500 mm/min), but the drawback of this is that at high-speed deformation,material may break before reaching the preset strain. In any case, the effect ofdeformation time or rise time on the subsequent relaxation behavior must be takeninto consideration. Theoretically, a viscoelastic solid deformed at a very slow ratecompletes its relaxation during the deformation stage, and the stress remains almost


the same during the relaxation stage, Figure 3.16 (Purkayastha and Peleg, 1986). InFigure 3.17 the relaxation time constants of Galbanino cheese obtained throughfitting the rheological data to the two-term Maxwell model (Masi, 1989) are presented.The relaxation time of the second Maxwell element is considerably longer than thatof the first element.

The apparent relaxation times (i.e., the time required for the stress to relax to1/e, or ~37%, of its initial value) of many cheeses obtained from published reportsare listed in Table 3.12, whereas the values of Maxwell model parameters arelisted in Table 3.13.

Nolan (1987) studied stress relaxation of commercial-stirred curd Cheddarcheese aged up to 14 months at a storage temperature of –2 to 0°C. Different

FIGURE 3.16 Schematic illustration of the deformation and relaxation stages of a stress-relaxation test. (After Purkayastha and Peleg, 1986.)

FIGURE 3.17 Effect of rise time or deformation time on the time constants of the two-element Maxwell model. (After Masi, 1989. With permission.)

Deformation stage

Rise time

High speedLow speed

Very low speed

Asymptoticstress

Time

StressRelaxation stage

0

1

10

100

1000

10.1 10

Rise time (s)

Rel

axat

ion

tim

e (s

)

1st relaxation time

2nd relaxation time


TABLE 3.12Calculated Apparent Relaxation Timesa for Some Cheeses

Cheese Rise Time (s) Temperature (°C) Relaxation Time (s) Reference No.

Mozzarella 24 23 47.5 AEmmentaler 0.5 15 60.8 BProcessed cheese 0.09 21 290 CMozzarella

0.43–0.7230405060

7.41.70.80.6

D

Stirred curd CheddarFresh2 mo old7 mo old14 mo old

0.9–1.6 20 3752805025

E

GoudaNormalLubricatedEmery paper

0.20 24 189183219

F

MozzarellaIIIIIIIVV.

2.4 20 3840505560

G

Gruyere-typeWeak cohesionStrong cohesion

1.8 15 141133

H

Garrotxa-type 0.5 19–21 140 I

A: Masi and Addeo, 1986. At less than 10% compression. Maximum load 150 g. Since crosshead speed forrelaxation tests is not explicitly specified it is taken to be 5 mm/min, which is the rate used in compression tests.

B: Rohm and Lederer, 1992. 5% deformation.

C: Atkin, 1990: Fit parameters given in the original paper are used to regenerate the stress–time plot andthen the apparent relaxation time is obtained as defined above. 10% deformation.

D: Ak and Gunasekaran, 1995: Compression levels varied from 30 to 50%.

E: Nolan, 1987. Average relaxation times are given at maturation of 2, 7, and 14 months. The level ofdeformation varied from 4 to 7%.

F: Goh and Sherman, 1987. Commercial Gouda cheese. 10% deformation.

G: Diefes et al., 1993. 20% compression. I: control cheese refrigerated (5°C) for only 14 days. II: cheeserefrigerated 90 days. III: cheese frozen (–20°C) for 90 days and tempered at 5°C for 21 days. IV: cheesefrozen for 30 days and thawed at 5°C for 24 h. V: cheese frozen for 90 days and thawed at 5°C for 24 h.

H: Pesenti and Luginbühl, 1999. 10% deformation.

I: Saldo et al., 2000. Goat’s milk cheese in Catalunya (Spain). 5% deformation.a Unless stated otherwise, apparent relaxation time is defined as the time for initial force or stress to relaxto 37% of its initial value.


TABLE 3.13Parameters of Maxwella Model Used to Describe Relaxation Curves of Cheeses in Compression

CheeseDeformation

(%)No. of

ElementsEo

(kPa)E1

(kPa)E2

(kPa)E3

(kPa)E4

(kPa)λλλλ1

(s)λλλλ2

(s)λλλλ3

(s)λλλλ4

(s)Temp(°C) Ref.

GoudaNormalLubricatedEmery

10 3 — 584788

483054

402654

— 320029002700

3400200200

6003030

— 24 Goh and Sherman, 1987

Processed cheese 10 3 — 30 9.3 29 — 1534 95 4.2 — 21 Atkin, 1990Cheddar cheese — 2 — 160 80 — — 156 6900 — — — Mohsenin and Morrow, 1967,

cited in Peleg andNormand, 1983

Processed cheese 10 3 — 84 42 41 — 2794 140 20 — 18–19 Robert and Sherman, 1988Tybo Argentinob

Day 3Day 114

40 2 0.240.16

0.350.51

0.400.32

— — 4.14.7

10458

— — 20 Bertola et al., 1992

Gruyere-typeWeak-cohesionStrong-cohesion

10 3 4852

6572

4855

4958

— 2.32.1

2625

267262

— 15Pesenti and Luginbühl, 1999

Cheddar8 weeks old64 weeks old

<10 2 5040

8040

6030

— — 18.216.6

388347

— — 20 Hort and Le Grys, 2001

Garrotxa-type(goat’s milk) 5 2 156 215 192 — — 9.2 105 — — 19–21 Saldo et al., 2000

a For Maxwell model, see Equation 2.46.b In the original article the data are fitted to a dimensionless force equation: F(t)/F(0) = A∞ + A1 exp (–t/λ1) + A2 exp(–t/λ2), and therefore quantities A∞, A1,and A2 are dimensionless even though they are listed in this table for Ei′s, which have units of kPa.


empirical models, including the two forms of the Peleg model, Equation 2.47, havebeen evaluated for their ability to describe relaxation curves of aging Cheddar cheese.Here, we utilize Nolan’s data to regenerate the relaxation curves in terms of truestress vs. time for calculating apparent relaxation time as a function of cheese age.The resulting values are plotted in Figure 3.18. From this graph, it is evident thatthe relaxation time decreases with the age of stirred-curd Cheddar cheese, especiallyduring the first six months (Nolan, 1987). Similar trends have been reported forMozzarella cheese during one month of refrigerated storage (Ak and Gunasekaran,1995). The rheological changes occurring during cheese aging are due to changesin pH, moisture, and salt content, and mainly due to the degradation of differentcasein fractions by residual rennet, indigenous milk proteinases, and starter enzymes(Desmazeaud and Gripon, 1997; Fox, 1989; Visser, 1993).

Goh and Sherman (1987) studied stress relaxation of commercial Gouda cheeseunder reduced (by lubrication) and intensified (by inserting emery paper) friction atseveral compression levels (10 to 60%). The crosshead speed was set to a relativelyhigh value, 100 cm/min, except few cases where it was 5 cm/min. The relaxationtests were conducted at room temperature on samples taken from the central regionof the cheese. The apparent relaxation times for different friction conditions areplotted against the compression level in Figure 3.19. It is clear that at each crossheadspeed and surface condition the relaxation time decreases with increasing percentcompression. It is interesting to note that lubrication resulted in lower relaxationtimes as compared to normal and high friction conditions only when the compressionwas 20% or less. This was thought to be due to cracks developing, for instance, inGouda cheese at compressions exceeding 20%. Hence, lubrication and compressionless than 20% were suggested as test conditions to obtain true stress-relaxationbehavior of Gouda cheese. In the same figure, the relaxation time of processed cheese(Atkin, 1990) at different compression levels is also shown. It is seen that therelaxation time for processed cheese drops nearly to zero at compressions above30%, probably due to cracking (Atkin, 1990). The other factor that may affect theresults for lubricated case, particularly at large compressions, is the loss or depletionof lubricant to a different extent at different compression levels (Atkin, 1990). More

FIGURE 3.18 Variation in apparent relaxation time of Cheddar cheese as a function ofmaturation time. (After Nolan, 1987.)

0

100

200

300

400

9630 12 15

Cheese age (month)

Ap

par

ent

rela

xati

on

tim

e (s

)


detailed analyses of the data in terms of multiple-element Maxwell model (withoutthe asymptotic parameter corresponding to the single spring — see Equation 2.46and Figure 2.42) resulted in parameter values given in Table 3.13. We must, however,state here that the interpretation of model parameters is difficult and often notmeaningful since they depend on the number of Maxwell (or Kelvin-Voigt in creep)elements included in the model.

Robert and Sherman (1988) determined the influence of friction on stress-relaxation parameters of commercial processed cheese tested at ambient temperature(18°C to 19°C) and compression levels from 5 to 20%. The researchers used a rathernovel approach and compressed simultaneously from one to four specimens in orderto determine the components of the total force, FT: a) the force to compress thecheese, FC, and b) the force to overcome the surface friction, FF. Only the formercomponent relaxes. By plotting the compression results as FT/N versus 1/N, whereN is the number of specimens tested simultaneously, it was possible to determinethe FC from the intercept and FF from the slope of the linear relation. The resultssuggested that cracks develop in processed cheese somewhere between 15 and 20%compression, which is in good agreement with the conclusions of Atkin (1990)discussed above. Maxwell model parameters for processed cheese obtained in thetwo investigations were however considerably different (Table 3.13).

For Emmentaler cheese, a significant relationship was reported between apparentfracture strain and apparent relaxation time at any deformation rate between 0.5 and80 mm/min. An inverse relation was observed between the relaxation time and thefracture strain. For instance, Emmentaler cheese that fractured at a strain of 0.84had a longer relaxation time (~90 s) than that fractured at a strain of 1.28 (~35 s)(Rohm and Lederer, 1992).

Low-moisture, part-skim (LMPS) Mozzarella cheese was subjected to severalstorage treatments (e.g., freezing, thawing, refrigeration) before measuring its

FIGURE 3.19 Apparent relaxation times of Gouda cheese (after Goh and Sherman, 1987)and processed cheese (after Robert and Sherman, 1988) under different surface conditions(5 and 100 means the initial compression was imposed at a crosshead speed of 5 cm/minand 100 cm/min, respectively).

0

50

100

150

200

250

300

350

7550250

Compression level (%)

Ap

par

ent

rela

xati

on

tim

e (s

) Gouda Normal-100

Gouda Lubricated-100

Gouda Emery-100

Gouda Normal-5

Gouda Lubricated-5

Gouda Emery-5

Proc. cheese-100


properties by stress-relaxation tests made at 20°C and 20% compression (Diefeset al., 1993). The reasons for changes in mechanical properties observed in freezingand refrigeration were considered to be different. In refrigerated storage, theproteolysis was the main factor for progressive softening of cheese. During freez-ing and subsequent frozen storage, local dehydration, compaction, and disulfide-bond formation as well as modified water-binding ability after thawing wereconsidered to be possible causes for the observed changes in mechanical properties(Diefes et al., 1993). The apparent relaxation time of Mozzarella subjected todifferent storage treatments was highest for cheese frozen for 90 days and thawedin a refrigerator over 24 h, and lowest for control cheese that was only refrigeratedfor 14 days before measurements.

Ak and Gunasekaran (1995) reported on temperature effect on rheological prop-erties of Mozzarella cheese during one month of refrigerated storage. Figure 3.20shows that both the apparent relaxation time and the initial relaxation modulusdecrease significantly with temperature; more steeply in the range from 10 to 40°C.

Korolczuk (1996) analyzed stress-relaxation curves for five types of commercialacid-fresh cheeses (7 to 12% protein, 0 to 58% fat) using different models, such astwo-parameter Maxwell model, power-law model, Peleg model, and kinetic (Avrami)model. Based on the average coefficients of variation for these equations, the Avramimodel was decided to best represent the stress-relaxation data of the cheeses. Thebehavior of acid-type fresh cheese was characterized more like a viscoelastic liquidsince the residual stress after relaxation was fairly low and independent of the appliedstrain (Korolczuk, 1996).

Stress-relaxation behavior of Gouda cheese packed in plastic films of low gaseouspermeability was studied at 10 and 20°C during ripening up to 70 days (Bertola et al.,2000). The packaging did not offer any advantage in terms of textural properties ofGouda cheese. The asymptotic (residual) modulus, an indicator of the degree ofsolidity (Peleg, 1987), was independent of ripening temperature, but increased from

FIGURE 3.20 Stress-relaxation parameters of Mozzarella cheese as a function of temperature.(After Ak and Gunasekaran, 1995.)

0.1

1

10

100

1000

0 20 40 60 80

Temperature (°C)

Ap

par

ent

rela

xati

on

tim

e (s

)

0

50

100

150

200

250

Init

ial r

elax

atio

n m

od

ulu

s(k

Pa)

Relx time-tension Relx time-comp Relx modulus-tension Relx modulus-comp


44 kPa at day 15 to 54 kPa at day 70. The changes in mechanical properties wererelated to the decrease in the water content and increase in the proteolytic activity.Although relaxation behavior was modeled using a Maxwell model, the values ofmodel parameters were not reported completely.

It is no doubt that acceleration of ripening, especially in long-ripened varieties, ishighly desirable for both economical and safety reasons. One of the relatively newways being investigated for accelerating cheese ripening is to apply high pressure.Under high pressure, ripening is accelerated due to increased water retention, releasingbacterial enzymes, and increased enzyme activity (Saldo et al., 2000). It was shownthat the values of the elastic constants in the Maxwell model were greater and therelaxation times were longer for the high-pressure-treated (≥400 MPa), Garrotxa-typecheese (Spanish cheese made from goat milk) than for the control and the cheesetreated with 50 MPa pressure (Saldo et al., 2000). According to Trujillo et al. (1999),goat cheeses made with high-pressure-treated milk matured more quickly than thecontrol cheeses. Thus, high-pressure treatment may be an alternative way of accelera-ting cheese ripening.

Hort and Le Grys (2001) examined the effect of ripening time at 8°C oncompression and relaxation parameters of commercial English Cheddar cheese.Plotted in Figure 3.21 are the progressive changes in fracture strain of Cheddarcheese from Hort and Le Grys (2001) and Creamer and Olson (1982). It is observedthat there is a clear negative relation between fracture strain and maturation time.The overall agreement between the values from the two studies is satisfactory.

TORSION MEASUREMENTS

Torsion test was used by Wodecki et al. (1984) to study mechanical properties ofEdam cheese in relation to its moisture content at different stages (i.e., after pressing,during ripening, and as marketed). The authors found no significant correlationbetween modulus determined from torsion test and water content for fresh cheese

FIGURE 3.21 Variation in fracture strain of Cheddar cheese as a function of ripening time.(After Creamer and Olson, 1982; Hort and Le Grys, 2001.)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1008060200 40 120

Cheese age (week)

Fra

ctu

re s

trai

n (

-)Hort & Le Grys

Creamer & Olson


(i.e., after pressing). However, once the cheese was matured for 12 weeks beforemarketing, its modulus as a function of water content varied according to thefollowing equation:

(3.6)

where, W2 is the water content of the marketed cheese (Wodecki et al., 1984). Theyfurther developed other equations relating modulus of Edam cheese (determined byimpressing a sphere to a particular depth) to the moisture content as described inTable 3.14. Based on this study, they suggested that the modulus of Edam cheesecan be controlled by adjusting the moisture content of freshly made cheese accordingto the equation given in Table 3.14, indicated as (*).

Bowland and Foegeding (1999) showed that fracture stress of a model processedcheese, formulated to contain 20% protein, 27% fat, and 1.5% NaCl as fixed ingre-dients, can be varied from about 25 to 80 kPa by manipulating processing variablesand usual ingredients (e.g., processing time, solution pH, percentage of disodiumphosphate). The fracture strain of the model cheeses varied from 0.66 to 1.88. Itwas found that the model processed cheese fractured in tension regardless of changesin processing variables. Moreover, the results of this work suggest that a wide varietyof textures from soft and ductile to firm and brittle can be obtained by carefullycontrolling compositional and processing factors. Recently, casein hydrolysate frac-tions were shown to have potential to replace traditional emulsifiers (e.g., sodiumphosphates) in process cheese (Kwak et al., 2002).

TABLE 3.14Equations Relating Hardness of Edam Cheese to Its Moisture Contenta

Equation Descriptions

W1: water content after pressing (%)H1: Hardness modulusb after pressing

(Pa)R2 = 0.886W2: water content at marketing time (%)H2: Hardness modulus at marketing

time (Pa)R2 = 0.773

(*)c ∆W: Change in water content through maturation

a Authors emphasize that “the coefficients throughout this analysis refer only to that milk and thoseprocessing conditions which were used in this particular study; they should not be regarded as general forall Edam cheese.”b Hardness modulus “measured as the pressure to impress a test sphere to a particular depth.”c This equation is applicable for: 41 ≤ W1 (%) ≤ 46; 2.2 ≤ ∆W (%) ≤ 6.6; 45 × 103 ≤ H2 (Pa) ≤ 10.5

Source: After Wodecki et al., 1984.

H Pa W17

164059 3 1 10 0 55( ) . exp( . )= − ⋅ −

H Pa W26

21 15 10 0 0685( ) . exp( . )= ⋅ −

W W H15

24 185 10 3 16 4 10 43 1(%) . log . . .= + − ⋅[ ] +− ∆

M Pa Ws ( ) = −8219 174 2


Gwartney et al. (2002) carried out torsion tests on capstan-shaped specimens(see Chapter 2) of various commercial cheese products to determine their fractureproperties at 20°C. As expected, full-fat cheeses are characterized by lower fracture-stress values than their reduced-fat counterparts. The impact of fat reduction on thefracture stress is highly dependent on the cheese type (e.g., Monterey Jack vs. SharpCheddar), as well as the processing factors (e.g., Mild Cheddar-A vs. Mild Cheddar-B),as shown in Figure 3.22.

TENSION MEASUREMENTS

Tension tests are considered particularly good for determining fracture properties (vanVliet and Luyten, 1995). The rheological information collected by tension test is alsofree of serious complications, such as friction, and thus easier, in general, to interpretcorrectly. The main obstacle preventing a broader use of tension tests in cheeserheology (or in food rheology, for that matter) is the problem and difficulty of propergripping. Nevertheless, several research reports on tensile properties of various foodshave been published (Gillett et al., 1978; Schoorl and Holt, 1983; Nussinovitch et al.,1990; Lelievre et al., 1992; Tang et al., 1997; Teratsubo et al., 2001). Tensile measure-ments on foods and cheeses are expected to increase since special and creative gripsand testing machines are designed particularly for measurements on foods.

There are few investigations on the tensile properties of cheeses. Luyten et al.(1992) provided an in-depth analysis and comparison of tension, compression, andbending methods for cheese and potato-starch gels. Fracture data reported by Luyten(1988) and Luyten et al. (1992) for Gouda cheese are included in Chapter 4.Moreover, we utilized quite heavily in Chapter 2 the information on the merits ofeach specific method as presented in detail by Luyten et al. (1992).

Tensile properties of low-moisture, part-skim Mozzarella cheese have beendetermined as a function of age (up to one month), temperature (10 to 40°C), anddeformation rate (5 to 50 cm/min) using a uniaxial horizontal extension apparatus

FIGURE 3.22 Effect of fat reduction on fracture stress of different kinds of natural andprocessed cheeses. (After Gwartney et al., 1999.)

0

10

20

30

40

50

60

30 40 50 60

Change in fat (%)

Ch

ang

e in

fra

ctu

rest

ress

(%

)Monterey Jack

Mild Cheddar-A

Sharp Cheddar

Mild Cheddar-B

American


by Ak et al. (1993). For Mozzarella cheese, which is one of the main ingredients ofpizza, the tensile properties (though at higher temperatures than could be realizedin this particular study) are of practical and commercial importance, since it willundergo stretching during consumption. The mean values of tensile properties areshown in Figure 3.23 as a function of age, temperature, and initial strain rate. Amongthe three rheological parameters, the modulus of deformability exhibited a simpledependency on the independent variables: it decreased with aging at a rate 2.2 kPa/day,

FIGURE 3.23 Tensile properties of Mozzarella cheese as affected by as a function of age,temperature, and initial strain rate. (After Ak et al., 1993.)

Fra

ctu

re s

tres

s (k

Pa)

Def

orm

abili

tym

od

ulu

s (k

Pa)

0

30

60

90

120

0 5 10 15 20 25 30

Maturation time (day)

Fra

ctu

re s

tres

s (k

Pa)

Def

orm

abili

tym

od

ulu

s (k

Pa)

0

0.2

0.4

0.6

Fra

ctu

re s

trai

n (

-)

stress modulus strain

0

50

100

150

200

Fra

ctu

re s

tres

s (k

Pa)

Def

orm

abili

tym

od

ulu

s (k

Pa)

0

50

100

150

200

0 40302010

Temperature (°C)

0

0.2

0.4

0.6

0.8

Fra

ctu

re s

trai

n (

-)

stress modulus strain

0 0.05 0.1 0.15

Initial strain rate (1/s)

0

0.2

0.4

0.6

Fra

ctu

re s

trai

n (

-)

Stress Modulus Strain


it decreased with temperature at a rate about 8.9 kPa/°C, and it increased with initialstrain rate at a rate 453 kPa/s–1. Ak and Gunasekaran (1995) reported the correspond-ing average values from the squeezing flow of Mozzarella cheese as: 0.4 kPa/day(one month aging), 0.5 kPa/°C (in the range 30 to 60°C), and 48 kPa/s–1. Thus, thetensile properties appear to be more sensitive to changes in the experimental variablesthan the compressive properties (of course, for a moment we are neglecting the largedifferences between the two experimental setups).

Kamyab et al. (1998) determined the rheological and fracture properties ofseveral cheeses by using various methods, including the tension test with single-edge-notched specimens. The modulus of deformability values for Cheddar (sharpand mild) and two American processed cheese varieties are given in Table 3.2. Acomparison of the tensile and compression moduli indicated that in general, anacceptable difference from 10 to 20% between tensile and compression moduli wasobserved, with the exception for mild Cheddar where there was a difference byfactor of 2. Major results of this study concerning fracture properties of variouscheeses are given in Chapter 4.

In a majority of rheological studies on cheese, it is accepted that cheese is anisotropic material, meaning that if test pieces are taken at various directions from acheese block, they will all yield essentially the same stress–strain curve. Althoughthis may practically be true for many cheeses, it is worth investigating for pasta filatacheeses since the curd-stretching step during their manufacture induces orientationof the structural components. Scanning electron micrographs of Mozzarella cheesecurd after it passed through the stretcher clearly showed the formation of a fibrous,oriented structure of the cheese (Kalab, 1977; Oberg et al., 1993; Kalab, 1993; Kielyet al., 1993; Paquet and Kalab, 1988), as shown in Figure 3.24. The protein matrixis largely modified by the stretching process to form a bundle of long, parallel caseinstrands interspersed with channels containing serum, fat globules, and starter culture.In reduced-fat cheeses, fewer channels exist between the protein strands. This meansmore interaction of proteins and a firmer and rubbery cheese body (McMahon et al.,1996; McMahon and Oberg, 1999). In fact, scanning electron micrographs revealed

FIGURE 3.24 Scanning electron micrograph of2-day-old Mozzarella cheese showing that stretch-ing the curd results in longitudinally directedfibers (scale bar = 8 µm). (After Kuo, 2001.)


that the size of casein aggregates increased as the fat content of Feta cheese wasreduced. Furthermore, the addition of tapioca starch and lecithin as fat mimeticsimproved overall acceptability of the reduced-fat (16.4% fat) and low-fat (12.5% fat)Feta cheeses to the level not too far from the full-fat (19.8% fat) sample (Sipahiogluet al., 1999). Although substantial improvements in the textural quality of low-fatCheddar cheese (5% fat) were realized by incorporating commercial fat replacers,neither the microstructure nor the stress–strain behavior of full-fat cheese (32% fat)could be satisfactorily duplicated (Kucukoner et al., 1998).

The microscopic observations mentioned above and the theoretical notion thatalmost no material is truly uniform and isotropic, led Ak and Gunasekaran (1997) tomeasure fracture properties of Mozzarella cheese by taking samples parallel andperpendicular to the long axis (Figure 3.2) of the cheese block (i.e., presumablyrepresenting protein orientation). The mean tensile fracture properties are presentedin Table 3.15. The results indicated that the fracture toughness, fracture stress, andfracture strain of Mozzarella cheese were 2.8, 2.1, and 1.4 times greater in paralleldirection than in perpendicular direction. This considerable variation in propertiesindicated anisotropic nature of the cheese. Orientation of protein strands in a particulardirection in the cheese block appears to enhance fracture properties significantly inthat direction. Furthermore, reduced-fat variety had significantly higher fracturevalues than the regular LMPS Mozzarella cheese, consistent with the expectations.

Pesenti and Luginbühl (1999) determined rheological properties of Gruyere-typecheese using tensile test, among others. The numerical property data from thisresearch for the weak-cohesion and strong-cohesion types of cheese are listed inTables 3.2 to 3.5. The authors remarked that the tension test, in accord with theo-retical expectations, proved to be the most powerful test also in practice.

TABLE 3.15Mean Tensile Properties of 14-Day-Old Mozzarella Cheese

VariablesFracture Strain

(–)Fracture Stress

(kPa)Fracture Toughness

(kJ/m3)

Sampling directionParallelPerpendicular

0.460.32

70.733.5

16.25.8

Cheese typeReduced-fata

Low-moisture part-skimb

0.430.34

112.521.0

23.64.0

Deformation rate25.0 cm/min5.0 cm/min

0.390.38

59.339.8

12.47.6

a Composition: 57.2% moisture, 31.7% protein, 7% fat, 3.5% carbohydrate, 0.6% sodium.b Composition: 50% moisture, 28.2% protein, 17.6% fat, 3.5% carbohydrate, 0.7% sodium.

Source: After Ak and Gunasekaran, 1997.


CREEP MEASUREMENTS

Creep is another characteristic behavior of a viscoelastic material. Most often, thecreep response of cheese is described by the Kelvin–Voigt model with a varyingnumber of elements. This model has been described in Chapter 2; see Equation 2.50and Figure 2.46. The analysis of creep behavior of cheese, or any foods for thatmatter, involves determination of model constants (individual elasticities Ei,Newtonian viscosity η, and individual viscosities ηi) from creep data (i.e., strain vs.time or compliance vs. time data). The tedious task of parameter determination ismade easy and faster by using computers and optimized calculation procedures(Balaban et al., 1988). As mentioned in Chapter 2, the alternative method to analyzecreep curves is to employ the Peleg model (Purkayastha et al., 1984), which issimpler to apply* as demonstrated for various foods (e.g., apple, pectin gel, orange,potato, cheese) (Peleg, 1980; Purkayastha, et al., 1984; Purkayastha et al., 1985).Using parameters of the Peleg model, one can also estimate an asymptotic compli-ance (Purkayastha and Peleg, 1986), which is of practical importance, since con-ducting long duration tests (i.e., creep and relaxation) on foods is not feasible dueto physical, biological, and chemical alterations.

Purkayastha et al. (1985) represented creep curves of potato and Cheddar cheeseusing a four-parameter Peleg model [i.e., D(t) = ko + k1t + t/(k2 + k3t), where, D iscompliance, t time and ko, k1, k2, and k3 are constants] and the discrete Kelvin–Voigtmodel with 4 to 6 constants. The values of parameters for corrected compliance ofmild Cheddar cheese are tabulated in Table 3.16 along with those for many othercheeses. Purkayastha et al. (1985) stated that the yielding nature of the cheese wasevident in the values of k1 and its dependency on the initial stress.

Kuo et al. (2000) used the viscoelastic parameters derived from analysis of creepcurves to successfully predict meltability of Cheddar cheese with two fat contents.This procedure is further described in Chapter 8.

Creep tests are used to study effects of formulation changes on properties of white,fresh cheese by adding different levels of sodium caseinate up to 13.92 g/L (Lobato-Calleros et al., 2000). These authors also represented the creep curves of white, freshcheese with a 6 parameter Kelvin–Voigt model. The parameter values for the standardwhite cheese (59.7% moisture, 19% fat, 17.3% protein, pH = 5.7) are given inTable 3.16. The effects of some factors on the creep parameters are summarized inTable 3.17. The authors also reported that white cheese with sodium caseinateaddition showed higher yield and lower syneresis compared to the standard cheese.

Creep measurements were made to determine effects of milk fat and lecithin(Ma et al., 1996) and commercial fat mimetics (Ma et al., 1997) on viscoelastic

* Nolan (1987) expressed concerns regarding one form of the Peleg model, Equation 2.47, where thesame variable (i.e., time) appears in both ordinate and abscissa. As stated by Nolan (1987), this kindof plotting, according to Mickley et al. (1957), may cause misleading correlations and is a poor test ofthe experimental data. Moreover, Hunston (1974) compared three linear forms of the model and foundthat when a variable appears only in abscissa, the model does not provide as good a representation ofthe data as when it appears in both ordinate and abscissa. Nevertheless, the Peleg model is frequentlyused not only in rheological studies but also in diffusion studies (e.g., Abu-Ghannam and McKenna,1997; Sopade et al., 1992).


TABLE 3.16Values of Parameters of Kelvin–Voigta Model Used to Describe Creep Curves of Cheeses

CheeseInitial Stress

(kPa)No. of

ElementsKo

(MPa)-1

K1

(MPa s)–1

K2

(MPa)–1

ττττ2

(s)K3

(MPa)-1

ττττ3

(s)K4

(MPa)–1

ττττ4

(s)Temp.(°C)

Type oftestb Ref.

Mild Cheddar 18.5 2 1.32 4.54 × 10–3 5.39 9.42 0.95 82.2 — — Room C Purkayastha et al., 198540.0 — 1.31 8.17 × 10–3 0.85 5.04 1.36 54.6 — — Room C Purkayastha et al., 1985

White fresh (6-d-old) 76.6 2 310 1.96 440 131 410 21.1 — — 20 S Lobato-Calleros et al., 2000Velveeta 2.0 Four-element

modelc

20.5 1 × 10–2 36 540 — — — — Room C Chang et al., 1986

Velveeta 2.9 19.3 8.3 × 10–3 24 420 — — — Room C Chang et al., 1986Cheddar full fat(3-mo-old)

2 e 2 7.54 9.3 × 10–2 13.4 32.9 9.9 3.0 — — 20 S Ma et al., 1996

Cheddar reduced fat 2d 2 12 0.24 23.5 23.3 15.6 2.5 — — 20 S Ma et al., 1996Cheddar full fat(3-mo- old)

1e 2 6.9 9.0 × 10–2 11.3 25.3 8.2 2 — — 20 S Ma et al., 1997

Cheddar low-fat(3-mo- old)

1e 2 11.8 0.2 21.7 24.3 15.3 1.8 — — 20 S Ma et al., 1997

Gruyere-type(weak cohesion)

43.3 3 3.4 8.8 × 10–3 4.1 119.9 1.8 16.4 1.0 1.16 15 C Pesenti and Luginbühl, 1999

Gruyere-type(strong cohesion)

43.3 3 3.8 9.2 × 10–3 4.4 119.5 2.0 15.8 1.0 1.12 15 C Pesenti and Luginbühl, 1999

Cheesef — 1 1.89 3.23 × 10–4 0.88 152 — — — — — — Purkayastha et al., 1984

a For Kelvin–Voigt model, see Equation 2.50: Kη = 1/η = 1/ηN; K1: first retarded compliance; τ1: first retardation time; K2: second retarded compliance; τ2: second retardationtime; Kn: nth retarded compliance; τn: nth retardation time. Although we use the same symbol Ko to represent Do in compression and Jo in shear, Do and Jo are not equal, butrelated to each other as D(t) = J(t)/3 in the linear viscoelastic region of an incompressible material.b C: compression; S: shear. For shear creep the letter J is normally used (i.e., Jo, η, J1, J2, τ1, τ2, etc.).c Combination of a Maxwell and a Kelvin element in series.d The initial applied stress is not explicitly specified, but 2 kPa was reported to be limit of linear viscoelasticity.e The initial applied stress is not explicitly specified, but 1 kPa was reported to be limit of linear viscoelasticity.f The type of cheese is not specified in the original article by Datta and Morrow, 1983. It is probably Cheddar.


properties of Cheddar cheese. The values of six-parameter Kelvin–Voigt model arepresented in Table 3.16 for full-fat (35.6%), reduced-fat (21%, estimated), andlow-fat (13.5%) varieties. Addition of lecithin at a rate of 0.2–0.5% apparentlyimproved the protein matrix of reduced-fat cheese, but not enough to simulate thebehavior of full-fat Cheddar cheese (Ma et al., 1996). In a similar fashion, additionof carbohydrate-based fat mimetic improved rheological properties of low-fat cheese,but not enough to simulate the behavior of the full-fat Cheddar cheese. It was alsofound that both granular lecithin at concentrations of 0.05% and higher and hydro-genated lecithin at concentration of 0.2% decreased creep recovery* of reduced-fatprocessed cheeses (Drake et al., 1999b). These results were consistent with thesensory evaluations by trained panelists.

A number of different cheeses containing varying amounts fat all exhibited creeprecovery to some extent upon releasing the applied stress (Drake et al., 1999a). Thecheeses that were evaluated as firm (e.g., Parmesan, Feta, Cheddar cheeses)responded in a more elastic manner (74 to 80% recovery) than the soft cheeses (e.g.,Velveeta™ and Brie) that recovered less (52 to 64%).

In a recent study on viscoelastic properties of Tetilla cheese (soft-paste, washed-rind Spanish cheese), creep response was modeled by the generalized Burgers model(Equation 2.50 with n = 9), but only the instantaneous compliance and Newtonianviscosity were reported (Tovar et al., 2002). There was a significant variation in thecreep behavior of this cheese collected from several factories complying with theregulations of Tetilla cheese denominations. A positive relation was obtained

TABLE 3.17Effect of Experimental Factors on Different Creep Parameters of White Fresh Cheese

Creep Parameter Main Variable Nature of Effect

Instantaneous compliance, Jo MoistureNa-caseinate

(+)(+)

Retarded compliance (1st), J1 MoistureNa-caseinatepHAging

(+)(+)(–)(+)

Retarded compliance (2nd), J2 Na-caseinateAging

(+)(+)

Newtonian viscosity, ηN Na-caseinatepH

(–)(+)

Retardation time (1st), τ1 Aging (–)

Note: (+): Parameter value increases with increasing value of the variable;(–): Paremeter value decreases with increasing value of the variable.

Source: After Lobato-Calleros et al., 2000.

* Creep recovery test involves removal of stress at a time during creep test and measuring the height ofsample after allowing sufficiently long time for recovery.


between the instantaneous creep compliance in shear and the dry extract of thecheese (Figure 3.25).

BENDING MEASUREMENTS

The three-point bending test is considered to mimic the way cheese graders evaluatebody and texture by bending a plug of cheese until it breaks (Pesenti and Luginbühl,1999; van Vliet, 1991a). One of the key requirements for a proper bending test isto assure sufficiently high length-to-diameter (or thickness) ratio of the test piece.This ratio seems to vary with the material being tested: it is required to be 8 and 24for metal beams and rectangular timber beams, respectively (van Vliet and Luyten;1995). For paperboard, a span-to-thickness ratio greater than 100 was used (Fellersand Carlsson, 1979). For cheese, at least for Gouda, a length-to-diameter ratio of3.3 or more was observed to be sufficient (Luyten, 1988; van Vliet and Luyten,1995). This ratio was higher than 3.5 in other studies on different cheeses: Mozzarella(Cervantes et al., 1983), Gruyere-type (Pesenti and Luginbühl, 1999), and Cheddar(Charalambides et al., 1995).

Cervantes et al. (1983) reported that increasing the salt content of Mozzarellacheese from 0.24 to 2.40% caused an increase in sensory firmness, which wasdetected by compression and beam-bending tests. A nonlinear strong interactionexisted between salt content and age of the cheese affecting textural and mechanicalproperties. However, no effect of the freeze–thaw cycle and frozen storage (–15°C)was detected on mechanical properties and textural characteristics of Mozzarellaaged up to 39 days.

Results of Charalambides et al. (1995) on fracture properties of sharp Cheddar,mild Cheddar, and Monterey Jack by bending test are presented in Chapter 4. Ingeneral, the fracture toughness of the cheeses decreased with aging, indicating morebrittle behavior with maturation. This is associated with the breakdown of αs1-caseinduring maturation.

FIGURE 3.25 Relationship between instantaneous creep compliance and dry-matter contentof Tetilla cheese from Spain. (After Tovar et al., 2002.)

0

10

20

30

40

50

60

40 45 50 55 60

Dry extract (%)

Inst

anta

neo

us

shea

rco

mp

lian

ce (

MP

a−1)


The quantitative assessment of cohesion in Gruyere-type (unripened hard) cheesehas been done using a number of static and transient methods, including three-pointbending (Pesenti and Luginbühl, 1999). Although all static methods were able todifferentiate different levels of cohesion in Gruyere-type cheese, the uniaxial tensiontest has been selected as the most powerful test for quantitative measurements ofcohesive properties of the cheese. Rheological properties of the cheese from bendingtests are given in Table 3.18. Also given in this table are the tensile properties, sincein a bending test the fracture is expected to occur on the outer surface (tensile side)of the samples. The fracture parameters are affected by the level of cohesion andthe type of test. For Gouda cheese, no significant difference was found for deform-ability modulus from tension, bending, and compression tests (Luyten et al., 1992)(see Table 4.3).

VANE MEASUREMENTS

Whey protein concentrates (WPC) and whey protein isolates (WPI) are finding moreuse as food ingredients in various applications due to their nutritional quality andfunctional properties, such as water binding, viscosity, gelation, etc. (de Wit, 1984;Harper, 1991). Mleko and Foegeding (2000) investigated physical properties ofprocessed cheese analogs containing various amounts of WPI and whey proteinpolymers obtained by heating WPI solutions. They used a four-blade vane attachedto a rotational viscometer to measure the yield stress of processed cheese analogs.Both addition of WPI and substitution of casein with WPI increased the yield stressof the processed cheese analogs, more effectively when whey proteins are formedinto polymers before addition. In the same study, yield-stress values of commercial-processed cheeses are reported to vary between 2 and 4 kPa; values that are veryclose to those obtained for the cheese analogs. The addition of whey protein polymersto replace a portion of rennet casein in processed cheese analogs also increased theyield stress of the cheese, the effect being stronger with the double-heated wheyprotein polymers (Mleko and Foegeding, 2001).

TABLE 3.18Rheological Properties of Gruyere-Type Cheese in Bending and Tension

Type Parameter Bending Tension Ratio (B/T)

Weak cohesion Deformability modulus (kPa) 193 93 2.10Fracture strain (–) 0.34 0.46 0.74Fracture stress (kPa) 41 32 1.28Work to fracture (kJ/m3) 0.9 8 0.11

Strong cohesion Deformability modulus (kPa) 204 111 1.84Fracture strain (–) 1.01 1.30 0.78Fracture stress (kPa) 130 70 1.86Work to fracture (kJ/m3) 8.7 57 0.15

Source: After Pesenti and Luginbühl, 1999. With permission.


DeMartine and Cussler (1975) proposed the following reciprocal relationbetween the subjective spreadability, which is evaluated by spreading the samplesalong the plate with the index finger:

(3.7)

This relation is shown to hold true for both Newtonian and non-Newtonian (shearthinning without yield stress) fluids with a high correlation coefficient of 0.95(log–log scale) (DeMartine and Cussler, 1975). Later, Kokini and Cussler (1987)demonstrated that the same kind of relation is valid for numerous foods (e.g.,ketchup, mustard, margarine, whipped cream cheese, peanut butter, etc.) where thesensory assessment of spreadability is made using a knife (hence, ττττspread is replacedwith ττττknife. In these studies, the stress on the index finger or the knife is predictedusing psychophysical models and fluid mechanics analysis.

Spreadability is certainly one of the key textural attributes of semisolid foodsaffecting their quality and acceptance (van Vliet, 1991b). Consumers have come toexpect and demand such foods (e.g., margarine, butter, peanut butter) to spread easilyeven at low temperatures (e.g., refrigeration temperature). A strong link between sensoryspreadability and yield stress has already been established for butter by Mortensen andDanmark (1982) and Rohm and Weidinger (1991), where the yield stress is measuredby penetrometers and sectilometer. Mortensen and Danmark (1982) concluded that theyield stress alone is a sufficient measure for the spreadability of butter. Thus, theaccurate measurement of yield stress becomes crucial for quantitative evaluation ofthe quality of semisolid products. In this respect, the vane method stands out as asimple and powerful tool for direct and accurate measurement of the yield stress.

Daubert et al. (1998) found that not only yield stress but also yield strain, perhapsto a lesser degree, plays an important role in the spreadability of foods. They prepareda plot of yield stress vs. yield strain (more correctly the angular rotation at the yieldpoint) and named the resulting graph as a “spreadability map.” They calculated yieldstrain γγγγo using the following approximate equation:

(3.8)

where, tmax is the time (s) to the peak torque, ΩΩΩΩ the rotational speed (rad/s), Cs

the spring constant for the viscometer (rad/torque reading), and R the viscometertorque reading.* These researchers established three categories of spreadability bysensory analysis as easy, mild and hard, and associated them with the yield stressand yield strain results from the vane measurements. It is seen that materials witha combination of high yield stress and yield strain will be most difficult to spread.The spreadability map is considered to be a simple tool for direct comparison of

* It must be noted that differences in the wind-up characteristics of rotational viscometers are to betaken into account when evaluating yield stresses determined using the vane method (see Steffe, 1992,for a numerical example).

subjective

spreadability ~

1

τspread

γ o st C R= −max Ω


similar materials, as well as for quantifying the impact of changes in processing andcomposition variables on the spreadability of products.

Breidinger and Steffe (2001) used the vane method in the controlled rate modeto construct a texture map by plotting yield stress vs. apparent yield strain for variousregular and light cream cheeses. They determined yield stress using Equation 2.43and apparent yield strain γγγγo (rad) using the following equation:

(3.9)

where, the vane rotational speed ΩΩΩΩ is given in (rev/s). No attempt was made todevelop sensory spreadability categories in order to correlate with the instrumentaldata. Their results and those from Daubert et al. (1998) are presented in Figure 3.26in the form of yield stress vs. angular rotation. Some trends can be noticed in theseplots: (a) a decrease in yield stress corresponds to an increase in apparent yield strain;(b) at refrigeration temperature, cream cheese with regular fat level is generally lessspreadable than its reduced-fat counterparts; (c) variations in temperature (from 5 to22°C) caused relatively small changes in rheological behavior of fat-free samples;(d) fat-free varieties from different manufacturers show significantly different resultsat both temperatures (i.e., 1-FF vs. 6-FF in Figure 3.26); and (e) differences in prop-erties of the regular varieties from different manufacturers are less at 22°C than at5°C. Many factors can contribute to the differences observed among cream cheeses:ingredients and exact compositions of products; total fat content and percent of solidand liquid fractions at a specific temperature; type and level of stabilizers in fat-freetypes; emulsion characteristics of the products; and processing conditions.

Commercially acceptable spreadability of cream cheese is given in terms ofyield stress and apparent yield strain in Table 3.19 (Breidinger and Steffe, 2001).These values may be useful as a guide in quality-control and product-developmentefforts. There is, however, a need for more thorough sensory analysis and correlationsbetween sensory and instrumental results, since we note that values in Table 3.19would fall all over the three parts (i.e., easy, mild, and hard) of the spreadabilitymap developed by Daubert et al. (1998).*

The vane technique has also been employed to study the characteristics ofcheeses with different textures such as firm (Cheddar), rubbery (Mozzarella), andsoft (Processed cheese) (Truong and Daubert, 2001). In these types of cheeses it isthe fracture, rather than flow, that ensues the peak stress. The fracture is likely tostart at the tips of vane blades, where stress is concentrated, and propagates outward(Truong and Daubert, 2001; Yan and James, 1997). The shear stress at the peak pointis calculated from Equation 2.43, and the corresponding strain is computed from:

(3.10)

* We must, of course, state that the spreadability map of Daubert et al. (1998) is made not for creamcheese but for elastoplastic foods, including a few cream cheese samples. It may be more helpful ifsuch maps are made for individual foods at a constant temperature.

γπo

t= max

Ω2

γ = ⋅

−

td

df

Ω

1


FIGURE 3.26 Texture map for various cheeses at two temperatures. (5 and 22°C). (After Daubert et al., 1998; Breidinger and Steffe, 2001.)

22°C

0

1

2

3

4

5

6

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Angular rotation (rad)

Yie

ld s

tres

s (k

Pa)

1-FF

2-R5-R

6-FF

7-L8-N

10-W

4-R9-N

PCS

CC

5°C

0

1

2

3

4

5

6

7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Angular rotation (rad)

Yie

ld s

tres

s (k

Pa)

1-FF 2-R

3-L

5-R6-FF

7-L8-N

10-W

4-R

9-N

CC

FCC

ABBREVIATION DESCRIPTION REFERENCEPCS Processed Cheese SpreadCC Cream Cheese

FCC Free Cream Cheese

Daubert et al., 1998

ABBREVIATION DESCRIPTION REFERENCE1-FF Kraft Philly Fat Free6-FF Store Brand Fat Free2-R Bruegger’s Regular4-R Store Brand Regular5-R Kraft Philly Regular 3-L Kraft Philly Light7-L Bruegger’s Light8-N Store Brand Neufchatel9-N Kraft Philly Neufchatel

10-W Kraft Philly Whipped

Breidinger andSteffe, 2001.

3-L


where df is the diameter of the fractured surface measured with a caliper (Truongand Daubert, 2001). Both the maximum shear stress and the parameter quantifyingsubsequent structural breakdown (i.e., maximum stress–final stress) are found usefulto monitor textural characteristics of these cheeses. At low strain-rate range, the peakstress is dependent on the shear rate (Figure 3.27). The slopes of the individual linesfor each cheese show that extra-sharp Cheddar (firm) cheese is the most sensitive,and American yellow type processed cheese (soft, elastic) is the least sensitive tothe increases in shear rate (Figure 3.27). Therefore, the concept of texture map basedon vane data provides a rapid and useful way to compare textural characteristics ofa wide range of cheeses (see Chapter 7 for more on texture map of cheeses).

It is clear that vane method is convenient to determine yield stresses of a varietyof materials, including numerous cheeses. Vanes can, however, be used also for themeasurement of steady-state flow curves of Newtonian and non-Newtonian fluids(Barnes and Nguyen, 2001). Additional details on procedures for shear rate estima-tions for vane attachments and examples of flow-curves for Newtonian and non-Newtonian fluids obtained with the vane method have been published (Steffe, 1996;Barnes and Carnali, 1990; Glenn III et al., 2000).

SHEAR MEASUREMENTS

Experiments based on shear deformation have often been utilized to study visco-elastic properties of solid cheeses, and part of these studies has been discussed inother chapters. For instance, in Chapter 5 we present the small amplitude oscillatoryshear properties, and in Chapter 6 the large amplitude oscillatory shear properties.Moreover, flow curves of melted Mozzarella cheese obtained by the capillary piston-driven rheometer have been discussed in Chapter 8. The rheometers based on thePoiseuille flow, for instance, capillary and slit rheometers, make it possible to studymaterial properties at velocities (or shear rates) comparable to those found in mostprocessing operations (Pérez-Trejo et al., 2001). Shukla and Rizvi (1995) used thecapillary rheometry to study and compare the rheological behaviors of butters madefrom supercritically-fractionated, high-melting triglyceride and anhydrous milk fatat different temperatures (17°C, 22°C, 27°C). They also showed the application ofcorrection procedures (i.e., Bagley pressure correction and wall slip correction; seeChapter 2) to the capillary rheometry data on butter.

TABLE 3.19Acceptable Yield Stress and Yield Strain Ranges for Commercial Cream Cheeses

Temperature (°C) Stress Range (Pa) Strain Range (rad)

5 3500–6100 0.23–0.4622 1200–2000 0.23–0.42

Source: After Breidinger and Steffe, 2001.


Flow properties of string cheese were measured at temperatures from 45 to 70°Cusing a piston-driven capillary rheometer (Taneya et al., 1992). The resulting rheo-logical data were analyzed with the power-law equation:

(3.11)

The end effects are corrected according to the Bagley procedure. Both the flowindex n and the consistency index K decreased expectedly with temperature.Similar to the increase in the maximum extrusion force with pH of grated cheesecurd (Ramkumar et al., 1998), the K value of the string cheese curd was highest(~180 kPa sn) for the highest pH = 5.9 (Taneya et al., 1992).

FIGURE 3.27 Peak stress dependency on the shear rate for a number of cheeses. (AfterTruong and Daubert, 2001.)

0

4

8

12

16

20

0 0.01 0.02 0.03 0.04

Shear rate (1/s)

Pea

k st

ress

(kP

a)

P3-CP

P2-Light

P1-Full

P4-Amer

Mozzarella

Ched-2

Ched-1

Cheese type SymbolTextural

CharacteristicsSlope

R2(kPa.s)

Extra sharp Cheddar Ched-1 Firm 182 0.986

Deluxe Cheddar Ched-2 Firm 90 0.984

Mozzarella Mozzarella Rubbery 54 0.984Processed cheese low-fat P2-Light Soft, Elastic, Sticky 46 0.971

Processed cheese American white P4-Amer Firm 42 0.725Processed cheese full-fat P1-full Soft, Sticky 36 0.966

Processed cheese American yellow P3-CP Soft, Elastic 23 1.000

τ γ= K n˙


Rheology of enzyme-modified cheese (EMC) has been studied with a cone-and-plate viscometer equipped with a temperature control unit (Jao et al., 1981). Therheological properties of EMC were essential for development of a manufacturingprocess and selection of proper equipment for processing. The shear viscosity vs.shear rate curves in the range from 1.92 s–1 to 384 s–1 showed hysteresis, whichdisappeared after two cycles of up and down shearing. The authors also examinedthe effect of temperature and moisture content on the rheology of EMC to providethe following equations describing viscosity of the cheese in terms of significanttechnological variables:

(3.12)

where, η the apparent viscosity (mPa.s), the shear rate (s–1), T the temperature(°C), M the moisture content (%), a, b, and c are constants. The rheological behaviorof EMC was characterized as thixotropic shear thinning. Table 3.20 lists the valuesof the model coefficients and the applicability ranges for temperature and moisture.

Massaguer-Roig et al. (1984) modeled shear-dependent and time-dependentbehavior of experimental cheese spreads and two commercial Neufchatel cheeses(plain and chocolate flavored) using the following rheological equation proposed byTiu and Boger (1974):

(3.13)

where, k1 is the rate constant for structural decay, the shear rate, η the apparentviscosity at time t, ηo the initial apparent viscosity, ηe the apparent viscosity atequilibrium, K the flow-consistency index and n the flow-behavior index. The loadingof a small volume of sample (0.5 mL) on a cone-and-plate viscometer was madeusing a modified plastic syringe with maximum care in order not to damage thesample before actual testing. The model parameters accounting for the shear depen-dency of cheeses are presented in Table 3.21. It is evident from the table thatexperimental cheeses have at least three times higher yield stress than the reference

TABLE 3.20Parameter Values for the Viscosity Equation of Enzyme Modified Cheese

Shear Rate Range A1 a b c

Up curve: 1.92–384 s-1 56.3 –0.72 94.6 –0.076Down curve: 384–1.92 s-1 18.4 –0.61 88.5 –0.064

Note: Temperature range: 24–72°C; moisture range: 42.3–59.3%

Source: After Jao et al., 1981. With permission.

η γ= A e ea b T c M1 ˙ /

γ

1 1 1

η η η ηγ

τ γ−=

−+

+e o e yn

k t

K

˙

˙

γ


Neufchatel cheeses. The other point deserving a mention is that two, instead of oneas suggested in the model, structural decay constants (k ′1 and k ″1) is needed toadequately describe the 1/(η – ηe) vs. time plots.

Other studies reporting time-dependent rheological behavior are Sanchez et al.(1996) for double cream cheese and Korolczuk and Mahaut (1990) for two types offresh-acid cheese. In the former study, a coaxial cylinder rheometer with a cup-to-bob diameter ratio of 1.08 was used while obtaining flow curves at 20°C and in theshear rate up to 300 s–1. Korolczuk and Mahaut (1990) employed a coaxial cylinderviscometer with a cup-to-bob diameter ratio from 1.08 to 4 at temperatures from5 to 40°C in two different shear rate range: (a) lower shear rate from 1.7 × 10–4 s–1

and 2.0 × 10–3 s–1, and (b) high shear rate from 9 s–1 to 482 s–1.The flow curves (i.e., shear stress vs. shear rate) of double cream cheese at 20°C

exhibited hysteresis loops that did not disappear even after seven to nine days ofstorage at 5°C, signifying only a partial recovery of the original structure or perma-nent damage to the structure. The hysteresis loops also contained at least two stresspeaks generally below the shear rate of 100 s–1. In spite of all precautions, the damageto sample during preparation could not be eliminated, making us think that for suchmaterials the lubricated squeezing flow (see below) may be a better method forrheological characterization.

The apparent viscosity of the fresh cheese was found to depend more on theshear rate than on the time of shearing, but the latter factor was not negligible. Thus,the authors developed the following equation to describe the thixotropic behaviorof fresh cheeses:

(3.14)

where, is the apparent viscosity (mPa.s) at a given time and shear rate. Itwas also determined that the temperature effect on the apparent viscosity could bedescribed by an Arrhenius-type expression with the activation energy of flow increas-ing from 13.4 kJ/mol for nonfat cheese to about 48 kJ/mol for the cheese containing20% fat in dry matter and for the temperature range between 15 and 20°C. Such

TABLE 3.21Values of Rheological Model Parameters for Neufchatel and Experimental Cheeses

Model Parameter

Neufchatel Cheese Experimental Cheese Spreads

Plain Chocolate Flavored A B

K (Pa.sn) 142 435 1001 787

n (–) 0.37 0.22 0.07 0.12

τy (Pa) 72 114 334 350

Source: After Massaguer-Roig et al., 1984. With permission.

log . . log ˙ . log . log ˙ log, ˙ η γ γγt t t= − − +4 32 0 569 0 0529 0 0169

η γt, ˙


equations relating shear viscosity to shear rate and time are expected to be usefulfor process designers and technologists.

LUBRICATED SQUEEZING FLOW MEASUREMENTS

Chatraei et al. (1981) developed and used the lubricated squeezing flow (LSF)technique to obtain biaxial viscosity data on polymer melts. Casiraghi et al. (1985)introduced the LSF technique to food research in the mid-1980s. We must alsorecognize the fundamental contributions of Peleg and his coworkers, which widenedthe use of the LSF method in food rheology. Recent review by Campanella andPeleg (2002) provides a detailed account of the theory and application of the LSFtechnique to semiliquid foods. We will limit our discussion in this section to theLSF studies on cheese.

Casiraghi et al. (1985) conducted LSF measurements on processed cheese spread(at 7 and 22°C) and Mozzarella cheese (at 22°C). It may seem unusual to talk about“flow” at such temperatures, but one must remember that cheese in general is aviscoelastic material and will normally have a viscous component, which may besmall for some varieties at low temperatures. In many respects, the LSF techniqueis similar to the uniaxial compression under lubrication, but it focuses on thedetermination of viscous properties of the materials.

Plots of apparent elongational viscosity (or biaxial stress-growth coefficient asdefined in Chapter 2, Equation 2.85) as a function of biaxial extension rates (Equation2.82) approached asymptotically a straight line, as schematically shown inFigure 3.28. This is a fairly typical response observed for cheeses. For example, Akand Gunasekaran (1992) reported the same type of behavior for Cheddar cheese,

FIGURE 3.28 Schematic drawing of elongational viscosity vs. biaxial strain-rate relationshipfor fluids in lubricated squeezing flow. V: deformation rate. (After Ak and Gunasekaran, 1992.)

V1

V3 > V2 > V1

V2

V3

Asymptotic line

log-log scale

Biaxial extension rate

Ap

par

ent

elo

ng

atio

nal

vis

cosi

ty


although at 22°C. In fact, the slope of the apparent elongational viscosity vs. strain-rate curve was similar: –0.85 and –0.88 for processed cheese spread at 7 and 22°C(Casiraghi et al., 1985); –0.85 for 20-day-old Cheddar cheese (Ak and Gunasekaran,1992); and ranged from –0.80 to –0.85 for Gouda and a number of other cheeses(Luyten et al., 1991a). The slope corresponds to the flow-behavior index of power-law model, which is widely used in modeling of steady-shear behavior of liquid andsemisolid foods (e.g., Barbosa-Canovas and Peleg, 1983).

The elongational viscosity against temperature at two extension rates (0.15 s–1

and 0.015 s–1) for two kinds of process American cheeses (national and supermarketbrands) and low-moisture part-skim Mozzarella cheese are shown in Figure 3.29.As expected, the viscosity decreases almost linearly with the temperature on semi-log coordinates. The biaxial extension rates experienced by a melting cheese in asandwich or on a pizza pie are expected to be very low (Campanella et al., 1987),perhaps similar to those reported in the figure. Ak and Gunasekaran (1995) and laterWang et al. (1998) suggested that the apparent elongational viscosity, as determinedby LSF technique, might be used as a quantitative measure of the cheese meltability,since its variations with maturation (i.e., decreasing with age of cheese) and tempera-ture are consistent with practice. However, in order to relate this parameter to cheesemeltability, the approximate extension rates during melting of cheese over pizza pieand other surfaces must be estimated.

Based on the LSF technique, Wang et al. (1998) developed and used an instrumentcalled “UW-meltmeter” (see Chapter 8) to determine apparent elongational viscosityof full-fat (43%) and reduced-fat (14%) Mozzarella cheeses. The behavior of meltedMozzarella cheese was characterized as strain-rate thinning at 40 and 60°C andcovering the strain rate 10–4 s–1 to 10–1 s–1. The elongational viscosity vs. extension-rate curves for all conditions appeared to fall within a relatively narrow band(see Figure 8.19), which might be divided into a few regions of different meltabilityfrom the upper-left corner to the lower-right corner. Cheese meltability measurementswith the UW-meltmeter and other methods are discussed in detail in Chapter 8.

FIGURE 3.29 Elongational viscosity of two cheeses as a function of temperature at slowstrain rates. (After Companella et al., 1987; Ak and Gunasekaran, 1995.))

1

10

100

1000

10000

25 35 45 55 65

Temperature (°C)

Ap

par

ent

elo

ng

atio

nal

visc

osi

ty (

kPa.

s)

Mozzarella:0.015 1/sMozzarella:0.15 1/s

ProcessAmerican-N:0.015 1/s

ProcessAmerican-S:0.015 1/s


The LSF technique was employed by Suwonsichon and Peleg (1999b) to studyrheological properties of Ricotta cheeses (whole-milk, part-skim, and fat-free kinds)of different brands. The imperfect squeezing-flow (see Chapter 2) method enablescharacterization of rheological behavior of the cheese without causing structuraldamage. It was observed that the Ricotta cheeses had a significant yield stress onthe time scale of the experiments (i.e., 3 min). The results, for instance the residualstresses at t = 60 s and t = 120 s, were sufficiently sensitive to variations inconsistency of the cheese so that the different brands and fat contents of ricottacheeses could be distinguished on the basis of yield stress.

Thus, the LSF technique, in either perfect or imperfect geometry, is expectedto find increased applications in food research, since it offers a practical solutionto serious problems encountered in coaxial and capillary viscometry, namely theslip and the partial destruction of the specimen’s microstructure during sampleloading (Hoffner et al., 1998; Suwonsichon and Peleg, 1999a). An additional benefitmay be the relatively low cost of an LSF instrument as compared to that ofcommercial rheometers.

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Fracture Properties of Cheese

Fractures, cracks, or damage may originate from different aspects: debonding of atoms, nucleation, or growth and coalescence of microcracks and microcavities (Lemaitre, 2001). From an engineering materials point of view, the following damage categories can be defined:

1. Brittle or quasi-brittle failure — fracture occurs without significant irre-versible strain

2. Ductile failure — failure at large plastic strain at low temperature (~1/4 of the melting temperature)

3. Creep failure — failure at large plastic strain at high temperature (>1/3 of the melting temperature)

4. Fatigue failure — failure due to repetitious loading either above or below yield stress; may be further classified into low-cycle, high-cycle, and giga-cycle fatigue damage

It must be emphasized that any fracture or crack mechanism is closely related to the material’s microstructure. In polymers, these mechanisms are dominated by the long and flexible macromolecules (Schirrer, 2001). Macromolecules are long series of monomers whose backbones are composed of linked carbon atoms. The cone angle of carbon atoms is fixed at about 70º (Figure 4.1). Therefore, the relative position of the linked carbon atom chain, i.e., the macromolecular backbone, is limited to some extent. The stiffness of the monomer and the space it occupies dictate the stiffness of the macromolecule. A large condensed assembly of macromolecules is the polymer. It may exist in either amorphous or crystalline structure, depending on its temperature. At material temperatures below its glass transition temperature, Tg, the macromole-cules assume a glassy or amorphous disordered structure in which the smallest elementary volume of the material is about the size of the monomer. At temperatures above Tg, the material is said to be in the “rubbery” state. Figure 4.2 shows a typical modulus vs. temperature relationship for a polymer. In the glassy state, interactions between nonlinked atoms are strong, and any applied load is distributed atom to atom. When a small elastic load is applied, all carbon–carbon bonds are stressed, and their cone angles are strained. Larger loads lead to nonrecoverable plastic deformations. In the rubbery state, molecular interaction at the atomic level does not exist. Under applied loads, the entanglements deform about each other, and the atoms are free to twist on the carbon–carbon cone. The elastic properties are due primarily to the entropy variations of the entanglement positions, which are nearly proportional to the macroscopic strain (Schirrer, 2001). True rubbery materials may exhibit linearity between applied stress and strain up to strain levels of 10.

4


Sometimes a third state, semicrystalline, can be defined when the material temperature is close to Tg. The semicrystalline state is characterized by a more or less regular small rigid lamellar arrangement of macromolecules with flexible amor-phous macromolecules connecting the crystalline states.

FIGURE 4.1 Schematic representation of a macromolecule as a string of monomers whose backbone is comprised of linked carbon atoms with limited movement (within the cone angle of 70°) about each other. (After Schirrer, 2001.)

FIGURE 4.2 Modulus vs. temperature relation for a typical polymer. Glass transition tem-perature, Tg, is identified at the transition from glassy to leathery state.

70° Cone

Linked carbonatoms

Tg Temperature

Glassy

Leathery

Rubbery

Iog

(Mod

ulus

)

ViscousFlow


When strained, a network of entanglements in both glassy and rubbery states deform with increasing (in tension) or decreasing (in compression) distance between the entanglements. In the glassy state, the elongation is irreversible due to the atomic interactions, and the energy input is converted to heat. In some cases, a few molecules may break, creating a crack or cavity. Such an event entirely changes the material microstructure.

FRACTURE MECHANICS

A fracture in a material is a failure mechanism that involves stable or unstable propagation of a flaw (e.g., a crack) within the material structure. Often the purpose of fracture-mechanics analysis is to prevent fracture (or propagation of an existing flaw). This criterion also applies to undesirable fracture in cheeses that will lower the overall quality and consumer appeal. However, the eye (slit) formation in some cheeses is not only desirable but is facilitated. In such cases, the focus is to limit the extent of crack growth. Regardless, it is useful to consider various factors that contribute to crack growth and those factors that tend to resist it. These factors are (Figure 4.3): (1) crack driving force – applied stress, crack size, crack geometry, and loading rate/cycles; and (2) material resistance factors — type of material, environment (temperature, chemical/physicochemical factors), loading rate, and fatigue. Naturally, when the driving force exceeds the material resistance, the crack will propagate. Under a specific set of conditions, the crack size that balances the driving force and resistance is known as the critical flaw size.

These forces can be considered to act in one of three basic modes schematically illustrated in Figure 4.4. They are: Mode I — opening; Mode II — sliding; and Mode III — tearing. In the case of cheese and many other materials, Mode I, the opening mode, is most relevant. It represents the crack pulling open due to forces

FIGURE 4.3 Various factors contributing to material resistance to fracture and crack driving force.

Material Environment Loading Rate Fatigue

Material Resistance

Applied Stress Crack Size Crack GeometryLoading

Rate/Cycles

Crack Driving Force


acting perpendicular to the crack. Mode III is relevant when forces are applied perpendicular to a crack, causing the material to tear and slide along itself, and thus move out of its original plane. Separating strings from string cheese (Izutsu et al., 1991) is as an extreme example of Mode III behavior. In Mode II, the forces are acting parallel to the crack, causing an in-plane shear.

There are three broad regimes to analyze the fracture mechanics of materials: linear elastic, elastic–plastic, and limit load. These regimes are illustrated in Figure 4.5. In linear elastic fracture mechanics (LEFM), only localized yielding around the crack tip is considered. A stress intensity factor, KI , represents the crack driving force. This is defined as:

(4.1)

where σ = applied stress, a = crack size, and Y = a dimensionless constant depending on material geometry and loading mode (more on this later under Determi-nation of KI). The subscript I refers to Mode I described above (Figure 4.4). Since Mode I is the most common, the subscript I is sometimes omitted. The material resistance is measured by fracture toughness KIc. Fracture occurs when KI = KIc. Fracture toughness is a material property, i.e., it is independent of material geometry and test procedure. It is a measure of the energy per unit area necessary to give a new crack surface (Williams, 1984).

In elastic–plastic fracture mechanics (EPFM) analysis, a large section around the crack tip is considered yielding. Depending of the extent of yielding, it may be termed “contained” or “full.” The crack driving force represents the work done under applied stress in the area around the crack tip. It is a function of crack and material geometry, applied stress, and elastic–plastic stress–strain relationship of the material.

The limit load analysis or diffuse dissipation assumes that the entire cross-section of the material becomes fully plastic before it begins to fail. This is appropriate for highly ductile materials. It is possible to have this regime in conjunction with one of the other regimes (Williams, 1984).

FIGURE 4.4 Typical failure modes in engineering materials.

Mode I (Opening) Mode II (Sliding) Mode III (Tearing)

K Y aI = σ π


The effect of fracture toughness on the governing failure mechanism is depicted in Figure 4.6. As can be noticed, within LEFM (for material with low KIc) brittle fracture is the governing failure mechanism. As KIc increases, LEFM is no longer valid, the failure mechanism is dominated by material flow properties, and EPFM will be prevalent. At extremely high KIc, fracture mechanics is no longer valid

FIGURE 4.5 Failure mechanisms: 1. LEFM — Linear elastic fracture mechanism, td<<a, w, and material thickness; 2. EPFM — elastic–plastic fracture mechanics, contained yielding i.e., td<w-a; 3. EPFM, fully yielded i.e., td>w-a; 4. Limit load or diffuse dissipation. (After Williams, 1984.)

2

3 4

σ

Crack

σLEFM

td

a

1

w

σ

Crack

σEPFM (fully yielded)

σ

Crack

σEPFM (contained yielding)

σ

Crack

σLimit Load (diffuse dissipation)


because the failure stress is insensitive to toughness. In such cases, limit load analysis is sufficient to predict failure (Anderson, 1995).

In most materials, plasticity effects precede failure, gross yielding effects pre-dominate, and failure occurs by plastic collapse. To account for elastic fracture and plastic collapse, a two-parameter approach to failure has been developed. This is represented by a failure assessment diagram (Figure 4.7) with the following ratios:

FIGURE 4.6 Effect of fracture toughness on governing failure mechanism. (After Anderson, 1995.)

FIGURE 4.7 Failure assessment diagram. (After BSI, 1991.)

LEFM EPFM Limit Load Analysis

Fracture Toughness

Fai

lure

Str

ess

Brittle

Fra

ctur

e

Collapse

0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8

1.0

Kr

σr


(4.2)

where σ = applied stress and σf = flow stress. If Kr = 1, failure will occur by brittle fracture. If σf = 1, failure will occur by plastic collapse. In the failure assessment diagram, the region under the curve represents insignificant risk of failure, and the region outside the line represents a potential for failure.

BRITTLE FRACTURE

A material is considered brittle if it breaks at small strains (and has small fracture toughness). Therefore, it is possible to study brittle failure using the theory of LEFM. An existing microcrack propagates when the stresses and strains at a critical distance ahead of the crack tip reach the fracture criterion of a fictitious tiny specimen (Francois, 2001).

Consider an average stress σ applied to a plane of dimensions width w and thickness B of ideal isotropic, elastic material. Consider also a through-the-thickness crack of elliptical geometry (major and minor axes are 2a and 2b units, respectively) as shown in Figure 4.8. The stress distribution around the crack can be indicated by the stress σxx measured along the x-direction and the stress σyy along the y-direction. As shown, σxx is zero at the crack tip, reaching the maximum at a short distance away and falling back to zero again. However, σyy increases exponentially from σ at a distance away from the crack and reaches a maximum of σm at the crack tip. The maximum stress amplification or stress concentration (σm/σ) is measured as below (Riande et al., 2000):

(4.3)

where, ρ = radius of curvature of the crack tip = b2/a. The same σm can be considered to be present at the other end of the crack when present centrally within the material. For a circle (a = b) the stress concentration factor is 3 and for narrow cracks (a>>b) the stress concentration increases to a large value and can be approxi-mated as:

(4.4)

Therefore, even at an acceptably low applied stress the maximum stress can exceed that of the material fracture stress. If the material cannot relieve this stress concentration by plastic flow around the crack tip, the crack will grow, thereby lowering the total energy of the system.

Bui and Ehrlacher (1981) described the damaged zone around a crack propa-gating in a brittle material. If the material was elastic and fails when the maximum

KK

Kandr

I

Icr

f

= =σ σσ

σσ

ρm a

ba= + = +1

21 2

σσ

ρm a= 2


principal stress reaches a critical value σc, the thickness of this damaged zone td is given by:

(4.5)

where k = initial stiffness. The theoretical failure stress is the stress needed to break atomic bonds. This is on the order of E/10, where E = Young’s modulus of the material. However, the actual fracture stresses are several orders of magnitude lower. This is due to the heterogeneous distribution of the stresses in the material. For example, in a material containing several microcracks scattered within the entire volume, stress concentrations easily approach the fracture stress. In materials without such microcracks, inclusions or impurities contribute to the lowering of fracture stress. Given the high stress concentration at local flaws in a material, fracture is always considered to originate from such locations (Gordon, 1968). Various inhomogeneities and flaws in cheese may range from 10–5 mm to 10 mm or larger (Table 4.1).

The practical problem with the stress-concentration approach is that σm

approaches infinity as ρ approaches zero, as would be the case for an infinitely sharp

FIGURE 4.8 Distribution of local stresses around an elliptical crack inside an elastic plane subjected to stress σ (After Riande et al., 2000.)

σm

σ

σyy

σxx

x

y

σ

σ

2a

2b

tk

dc

=⎛

⎝⎜⎞

⎠⎟σ

2


crack. Since all materials are considered to contain infinitely small flaws, they all should fail upon application of an infinitesimal stress.

GRIFFITH CRITERION

To overcome problems due to the local stress concentration approach, Griffith (1920) proposed an energy balance approach. According to this, an existing crack can grow or a new crack can form if and only if such a process would result in net decrease or, at best, no change in total energy of the system. The energy needed for the process is given in terms of specific surface energy (γs, J/m2) of the two new surfaces created (Williams, 1984):

(4.6)

where σf = failure stress; E = Young’s modulus; and a = flaw size.For a typical elastic system where applied energy is absorbed locally around the

tip of a sharp crack the energy balance may be written as (Williams, 1984):

(4.7)

where U1 = energy input; U2 = stored energy; U3 = energy dissipated (around the crack tip); and U4 = kinetic energy. If we further consider that the crack is growing such that increase in crack area is given as ∆a, then we can write:

(4.8)

TABLE 4.1Estimated Size of Various Inhomogeneities and Flaws in Cheese

Type of Inhomogeneity/Flaw Estimated Size (mm)

Casein sub-micelle 10–5

Paracasein micelle 10–4

Protein network strands 10–3

Fat globule 10–3 to 10–2

Unevenness of network 0.01 to 0.1Precipitates of salts, amino acids 1 Curd grains 1 to 10Acid spots 10Holes 10Curd pieces (in Cheddar cheese) 20Difference rind-center 10 to 100

Source: After Walstra and van Vliet, 1982; Luyten, 1988.

γσ π

sf a

E=

2

2

∆ ∆ ∆ ∆U U U U1 2 3 4= + +

∆∆

∆∆

∆∆

∆∆

U

a

U

a

U

a

U

a1 2 3 4−

⎛⎝⎜

⎞⎠⎟

= +


It is important to note that the changes in energy occur not due to crack displace-ment in the material, but due to increase in area. The left hand side of Equation 4.8

is known as the energy release rate (G) and on the right hand side, is the

fracture resistance (R). The fracture resistance represents the work required to fracture a material. For crack initiation, U4 = 0. Therefore, we can write the following differential form for incremental values of the variables:

(4.9)

Incidentally, the symbol G is used in fracture mechanics after Griffith, who introduced the energy-balance approach. Williams (1984) provides a detailed account of evaluating G for different test configurations.

It can be assumed that the energy required to produce a crack is the same for each increment (i.e., R = a constant). Therefore, G = GIc where GIc is known as the critical energy release rate. It can be shown that:

(4.10)

(4.11)

where ν = Poisson’s ratio and E = Young’s modulus. When Equation 4.9 is first satisfied, the crack propagates in a stable manner. However, uncontrolled fracture occurs when (Williams, 1984):

(4.12)

The material’s resistance to fracture R can be determined by knowing σf , fracture stress of a sample with a crack of size a in a fracture test (Broek, 2001).

Typically, a residual strength vs. crack size diagram can be drawn. Such a plot can be used advantageously when combined with a crack growth curve (Figure 4.9) to determine the permissible crack size ap corresponding to permissible residual strength pp and the time taken for the crack to grow to that limit (tp).

The surface-energy approach helps to understand fracture mechanics without having to assume infinitely sharp cracks and infinitely high stress concentrations within the material. It should be emphasized, however, that in LEFM only the elastic deformation (stored) energy is available for fracture. The energy dissipated due to material flow does not contribute to creating new surfaces, and hence is not available for crack propagation. The EPFM considers plastic flow around the crack

∆∆U

a3

dU

da

dU

da

dU

daor G R1 2 3−⎡

⎣⎢⎤⎦⎥

= =

GE

KIc I= −⎛⎝⎜

⎞⎠⎟

1 22ν

for plane (biaxial) strain

GK

EIc = 12

for plane (biaxial) stress

dG

da

dR

da≥


tip (see Figure 4.5). For the EPFM the resistance to crack propagation R is GIc plus the energy dissipation in the flow region beyond the vicinity of crack tip. Thus, R is denoted by J (or JR) to account for this additional component. We should note that for the limiting elastic case J + R = GIc. It is worth pointing out that G is the energy release rate of the entire system and can include energy stored, whereas, R and J describe material behavior. Williams (1984) presents additional discussion on fracture mechanics of polymeric systems that exhibit such energy dissipation.

Cheese being a viscoelastic material, strictly speaking, the LEFM is not directly applicable. However, unfortunately, theories suitable for evaluating combined frac-ture and flow in cheese are not available, and reasonable predictions can be made using the theory of LEFM. This is especially true if the flow region around the crack tip is small compared to the size of the crack (case 1 in Figure 4.5).

In engineering materials, cracks usually occur rapidly. For cheese, crack prop-agation is a slow and prolonged process. For example, formation of eyes or holes in Gouda cheese takes about one week (Luyten, 1988). Based on the LEPM concept, the slow crack growth rate is measured as a function of KI or GI. That is,

(4.13)

where A = material constant and n = exponent. As tends to zero, KI reduces towards a low threshold value Kth, and as tends to infinity, KI tends to approach KIc, the fracture toughness. Near Kth the crack growth is slow, and at Kc the crack growth is rapid. The material constant A varies, depending on the material and environmental conditions (e.g., temperature).

FIGURE 4.9 Residual strength and crack growth curve. (After Broek, 2001.)

Crack size, a

Crack G

rowth T

ime, t

Pp

Res

idua

l Str

engt

h, P

res

ap

tp

a=0

a

ada

dtA KI

n= =

aa


DETERMINATION OF KI

The stress-intensity factor KI is normally determined experimentally by “v-notch” test or other similar tests. As shown earlier for the case of a through-the-thickness crack of length 2a in an infinite plate subjected to a tensile stress σ, the stress-intensity factor is given by

(4.14)

The Equation 4.14 is the same as Equation 4.1 given Y = 1. However, for finitespecimens Y¦1 and alternate expressions have been developed (Williams, 1984; Anderson, 1995):

(4.15)

where w = width of the plate. Note that as a/w approaches zero (i.e., for a large plate), KI approaches that of infinite plate value. Therefore, for all geometries, KI is written as:

(4.16)

where, P = applied force, B = thickness of the plate and φ(a/w) is a calibration factor. Some common test specimen and notch geometries and the corresponding solutions for KI based on finite element analysis are presented in Table 4.2.

The American Society for Testing and Materials (ASTM) has defined a certain specimen size to obtain valid results for KIc in metals. Recommendations are also available for plastics. Such recommendations do not exist for food and biological materials. Therefore, even if the experiments were performed carefully, the test results of cheese should be treated with this fact in mind — i.e., test geometry does affect the validity of the LEFM theories. Moreover, for viscoelastic materials, even though the testing and data analysis procedure are the same, the validity of K and J are not guaranteed (Anderson, 1995).

FRACTURE TESTS ON CHEESE

Fracture properties of cheese can be determined by any of the fundamental materials testing methods discussed in Chapters 2 and 3. These methods include compression, tension, shear, torsion, and bending. Details of these methods and accompanying results have been presented in previous chapters. Here we will briefly discuss some results that are directly relevant to determining fracture of cheese using notched-tension and notched-bending tests. In general, tension or bending is best suited for determining fracture properties because it is easy to observe the crack initiation and propagation. However, tension tests are difficult to perform with soft materials such

K aI = σ π

K aw

a

a

wI = ⎛⎝

⎞⎠

⎡⎣⎢

⎤⎦⎥

σ ππ

π22

12

tan

KP

B wa wI = φ( )


TABLE 4.2Stress Intensity (KI) Factors (φ(a/w) in Equation [4.16]) for Different Test Geometries

Crack Geometry φ(a/w)1

1 m = πa/2w; n = a/w

Source: After Anderson, 1995.

20 752 2 02 0 37 1 3tan

cos. . . ( sin )

m

mn m+ + −[ ]

3

2 1 2 11 99 1 2 15 3 93 2 71 5

2

S

wn

n nn n n n

( )( ). ( )( . . . ).+ −

− − − +[ ]

m

nn n n n

11 122 0 561 0 205 0 471 0 1902 3 4

−− − + +( . . . . . )


as cheese and other food and biological materials. Therefore, bending is the preferred fracture-test mode. The fracture properties can be determined using compression tests, and a good set of data may be obtained due to the small sample size used and small effect of sample inhomogeneities (Luyten, 1988). We shall note that compres-sion tests are often carried out until sample failure even when the object of the test is not to determine the fracture properties. Luyten (1988) evaluated fracture prop-erties of Gouda cheese in tension, compression, and bending. The stress–strain curves in all three modes agree well for small strains (Figure 4.10). However, large differences are noticed in fracture stress and strain values (normally estimated at the peak of stress–strain curve). As presented in Table 4.3, the results indicate the modulus values are fairly similar because they correspond to linear (initial) part of the curve (measured as the initial slope). The fracture stress and strain values in tension, bending, and compression are low, intermediate, and high, respectively. With some corrections (Luyten, 1988), the fracture stress values from three testing modes may agree better than the fracture strain values.

NOTCH TESTS

Testing of specimens in tension and bending with known crack size by means of a notch is perhaps the most popular fracture test for engineering materials. In fact, the tension test results presented in Figure 4.10 and Table 4.3 for Gouda cheese are for notched specimens. For a proper notch test, the initial crack should be sharp (so that the stress concentration is high). Therefore, the notch is made by pressing a razor blade into the material to a measured distance (the crack length).

Luyten (1988) performed notched tension tests on Gouda cheese of different ages with different notch lengths (0 mm to 5 mm) to determine the notch sensitivity for crack initiation and propagation. The aged Gouda cheese is less notch-sensitive than the young cheese for crack initiation, and once initiated the crack propagates more rapidly in mature cheese than in the young cheese (Figure 4.11). The perceived “brittleness” of mature cheese is thought to be due to its propensity for higher crack propagation rate compared to the younger cheese.

FIGURE 4.10 Stress–strain curves of A: six-week-old and B: 10-week-old Gouda cheese in compression (____), tension (— — -), and bending (-.-.-.-). (After Luyten, 1988. With permission.)

Strain (-)A

Strain (-)B

Str

ess

(kP

a)

00 0.1 0.2 0 0.2 0.4 0.6 0.8 1.00.3 0.4 0.5 0.6

12.5

25

37

50

0

10

20

30


TABLE 4.3Comparison of Modulus (E) Fracture Stress (σf) and Strain (εf) of 6-week-old Gouda Cheese at 21°C Measured in Compression, Tension, and Bending Tests

Test Mode

AppliedStrain Rate

(1/s) E (kPa) σf (kPa) εf

Tension 0.0139 189 30.5 0.33201 26.4 0.31221 28.9 0.31230 22.4 0.28

Bending 0.0181 188 41.3 0.48173 40.8 0.43169 37.6 0.47188 43.6 0.62165 44.1 0.54

Compression 0.0167 202 49.7 0.87203 45.7 0.80173 45.8 0.89154 45.3 0.96244 53.3 0.82

Source: After Luyten, 1988.

FIGURE 4.11 Results of notch sensitivity tests on young (A) and mature (B) Gouda cheese samples in tension. The dotted lines connecting solid circles (•) and open circles (o) indicate decreasing stress with increase in notch length for crack initiation and crack propagation, respec-tively. Some points (x) are calculated values. (After van Vliet et al., 1991. With permission.)


Charalambides et al. (1995) and Kamyab et al. (1998) performed single-edge notched bending (SENB) tests on cheese. They followed the LEFM test protocol of the European Structural Integrity Society for testing of polymers (Williams and Cawood, 1990) using the test geometry for SENB as given in Table 4.2. This protocol has also been used for a model food system (Langley et al., 1994). For sufficiently large samples, the bending test specimen is prepared such that width (w) is twice the thickness (B), and the ratio of span (S = distance between supports) to B is four (Kamyab et al., 1998). Accordingly, samples of length, L = 88 mm, w = 18.5 mm, B = 9.3 mm, S = 74 mm, were used. Five-millimeter- to 6-millimeter-long notches were made using a razor blade at the center such that 0.45<a/w<0.55, where a is the notch length. Such deep notches apparently lead to brittle fracture during the test (Kamyab et al., 1998). The typical force–deflection diagrams for sharp and mild Cheddar cheeses are presented in Figure 4.12. The curves are nonlinear due to viscoelastic effects. However, the fracture toughness calculated using the area under the curve (A) until the crack initiation point (the peak of the curve) is considered to reasonably satisfy the LEFM assumption. The fracture toughness is calculated as:

(4.17)

where, φ(a/w) is the calibration factor.

FIGURE 4.12 Force–deflection curves from single-edge notched bending tests at a loading rate of 10 mm/min. (After Charalambides et al. 1995. With permission.)

GA

Bw a wc =φ( )


The measured fracture toughness values for sharp and mild Cheddar and MontereryJack cheeses at 4°C are summarized in Table 4.4. These results show, as Luyten (1988) observed (Figure 4.11), that cheeses tend to be more brittle with age, i.e., fracture toughness decreases with maturation, which correlated well with the αs1-casein breakdown during storage. Kamyab et al. (1998) reported also performing single-edge notch tension tests, SENT (see Table 4.2) with rigid clamps to avoid any rotation at the sample-test grip interface. Several samples of different a/w ratios were used. The tensile stress–strain curves are shown in Figure 4.13. The arrows on this figure indicate the fracture stress (σf) of the corresponding cheese obtained

TABLE 4.4Fracture Toughness of Different Cheeses Measured by Single-Edge Notched Bending (SENB) and Single-Edge Notched Tension (SENT) Tests

Cheese Age (day)

FractureToughness

(J/m2) Test Modea

Sharp Cheddar 30 31.2 SENB

60 23.6 SENB

90 21.5 SENB

120 19.8 SENB

150 15.7 SENB

180 16.5 SENB

— 2.7 SENT

Mild Cheddar 37 41 SENB

89 29.3 SENB

155 17.9 SENB

182 30.6 SENB

— 13.8 SENB

Monterey Jack 46 26.5 SENB

102 24.6 SENB

152 20.4 SENB

185 17.5 SENB

Process cheese, regular 4.1 SENT

Process cheese, light 2.4 SENT

Process American 1 5.6 SENT

Process American 2 3.8 SENT

a SENB test results are from Charalambides et al. (1995); SENT test results are from Kamyab et al. (1998).


in SENT tests. As in the case of SENB (Figure 4.12), the nonlinearity is also apparent in tensile tests. The fracture toughness is calculated as:

(4.18)

where, E = tensile modulus obtained from the curves in Figure 4.13, and Kc = stress intensity factor for the rigid clamp case (Williams, 1984):

(4.19)

Luyten and van Vliet (1996) reported results of notched-tension tests on Gouda cheese at different ages. The relative values of fracture stress and strain (with respect to samples without notch) as a function of notch length are plotted in Figure 4.14. The fracture strain is small initially for the cheese as it is rather brittle before the curd particles fuse together. Fracture strain increased as the cheese matured. The same was true for other cheeses such as Gruyere, Appenzeller, and Cheddar. Further, due to viscoelastic effects the fracture strain decreased with strain rate. At low strain rates, a significant part of the energy is lost as viscous dissipation due to the material flow and the energy available for fracture is small. Therefore, for fracture to occur at lower strain rates the materials have to be deformed to a larger extent. This strain rate effect is rather large for young (2-week-old) Gouda cheese. For the 9-month-old

FIGURE 4.13 Stress–strain curves from tension tests of different cheeses. 1- mild Cheddar cheese; 2- sharp Cheddar cheese; 3- American process cheese1; 4- American process cheese 2. Arrows indicate fracture stress obtained in single-edge notched tension tests. (After Kamyab et al., 1998. With permission.)

GK

Ecc=

2

K ac f= 1 12. σ π


Gouda cheese, though the fracture strain is considerably smaller than that for the young cheese, the strain-rate effect is not observable (Figure 4.15).

Luyten (1988) also reported fracture energy for crack initiation and propagation estimated from SENT experiments (Table 4.5). These values were obtained assuming negligible energy dissipation, and thus are lower than the actual energy available for fracture. It has been estimated perhaps only 20 to 40% of the energies reported in Table 4.5 are actually available for fracture. Though not consistent, it can be observed that, in general, the energy for crack initiation and propagation decrease with age.

FIGURE 4.14 Relative change (with respect to corresponding values of unnotched speci-mens) in fracture stress (circles) and fracture strain (squares) as a function of notch length in 2-week-old (open symbols) and 6-month-old (closed symbols) Gouda cheese. (After Luyten and van Vliet, 1996.)

FIGURE 4.15 Fracture strain as a function of strain rate. (After Luyten and van Vliet, 1996.)

Notch length (mm)

Rel

ativ

e σ f

or

ε f1.0

0.75

0.5

0.25

0

0 1 2 3 4 5 6

2-week-old

9-month-old

Strain rate (1/s)

Fra

ctur

e st

rain

(-)

10−4 10−3 10−2 10−1 100

0.5

1.0

1.5Gouda cheese


CUTTING, SLICING, AND SHREDDING

Cutting, slicing, and shredding are routine for both natural and process cheeses in retail marketing. Natural cheeses are made in huge blocks as large as 640 pounds. For supermarket sale, these blocks are cut into bricks ranging from one-half to two pounds and shrink-wrapped, or cut into small cubes or thin strips and packaged in plastic bags (Figure 4.16). Sliced and shredded cheeses are also popular for food service, restaurants, and other ready-to-eat end uses. These products represent a huge share of the cheese market. Shredded cheese has captured nearly 25% of the cheese market, and its share is still growing, obviously due to increased use in the ready-to-eat and heat-and-serve food categories. The top 10 vendors of natural shredded cheese had sales of more than $1.7 billion (U.S.) in 2001, a 7% increase from the previous year (www.dairyfoods.com).

TABLE 4.5Fracture Energy for Gouda Cheese at 20°C in Notched Tension Tests Performed at a Strain Rate of 0.0028 s–1

Cheese Age(months)

Fracture Energy (J/m2)

Crack Initiation Crack Propagation

0.5 6.3–9.2 11.0–12.51 4.5–8.1 —2 2.9–7.8 —4 5.3–6.8 —6 6.6–9.1 —

10 1.3–3.1 —12 0.6–3.1 0.8–1.5

Source: From Luyten, 1988.

FIGURE 4.16 Sliced, cubed, and shredded cheese samples. (After DMI, 2002.)

http://www.dairyfoods.com/


Much of the shredded cheese market is based on the integrity and uniformity of the shreds. In addition to being appealing to the eyes, the shreds that retain their integrity melt uniformly, and are easier to sprinkle on foods (Dubuy, 1980). These attributes enhance sales and use of shredded cheese as a food ingredient. Machined cheeses make portion control and fill-weight control easy (Andres, 1983). However, the shreds often crumble, stick, or mat. Special processes are used to maintain the length of each shred so that breakage or crumbling is held to a minimum. Microcrystalline cellulose is used to prevent caking or stickiness. Consequently, the cheese will not mat together on storage and can be easily sprinkled onto formulated food. The consistency of the shreds, plus the fact that it does not mat together, makes better portion control possible (Andres, 1983). Use of the cellulose additive must be done carefully, because if used improperly, it shows up as a white dusting, which is mistaken for mold, hurting cheese sales. Therefore, to take full advantage of the growing shredded-cheese market, it is essential to offer cheese shreds that do not mat or fragment. However, cheese processors often find it difficult to maintain the integrity of cheese shreds, especially when composition and manufacturing parameters vary widely. The lower-fat cheeses are especially hard to cut satisfactorily. The other major problems are “stickiness,” primarily due to high moisture content, and the inability to increase the speed of cutting without compromis-ing product quality. These problems are encountered in the industry due to, in part, lack of adequate understanding of the relationships between shredding process and cheese properties. Computer-vision techniques have been proposed to examine cheese shreds individually (Apostopoulos and Marshall, 1994) or en masse (Ni and Gunasekaran, 1998 and 2002) to quantify shred integrity and uniformity.

Machining of cheeses, as with most other foods and biological materials, is still largely performed empirically. The design and operation of food-cutting equipment are mostly adapted from equipment used in the lumber and metal industries (Pomerantz and Feeney, 1985; Antonissen, 1986). Little published information is available about fracture properties of cheeses, which are undoubtedly affected by several physico-chemical properties (moisture content, temperature, composition, pH, etc.), rheological properties (modulus, toughness, failure stress and strain, etc.), and operating parameters (cutting speed, blade type, contact angle, etc.) Typical commercial shredders take precut cheese cubes and pass them over a series of cutting blades or cutting heads by centrifugal action. Shred shape is controlled by the form of the cutting heads (Barritt, 1985). Conventional shredded cheese has a diameter of 1/8" while a new line of cheese shreds, called fancy shreds, has shred diameters ranging from 1/32" and 1/64". Several designs for shredding and application of cheese shreds have been described (Dubuy, 1980). The fancy shreds give the appearance of significant increase in volume of cheese per given weight — the volume of cheese is increased by as much as 50% (Andres, 1983).

CUTTING WITH WIRE AND BLADE

Cutting cheese with wire and blade is very popular. Wire cutters range from small tabletop units to large-scale cutters at the factory level. Cutting with wire and blade comprise fracture, plastic deformation, and friction. They can be schematically represented as shown in Figure 4.17. The elastic–plastic fracture mechanics theory deems that the material flows only in a small area around the crack tip. Therefore,


the stored and flow energies are limited. During wire cutting, it can be assumed that only the material in the vicinity of the wire undergoes plastic deformation.

The total energy during cutting may be considered to comprise of three major components (Atkins and Vincent, 1984): friction, flow, and fracture. The net energy balance during slicing or cutting may be written following the form of Equation (4.7) (Atkins and Mai, 1985; Luyten, 1988; van Vliet et al., 1991):

(4.20)

where U1 = total energy; U2 = stored energy; U3 = dissipated energy; Uf = dissi-pated energy due to fracture; and Ud = dissipated energy due to plastic deformation, curling, etc.

When cutting a sample of width B, with a wire diameter of d at a cutting speed v, the total energy input to the sample during time t is:

(4.21)

where Fc = cutting force, the constant force obtained on the force–time curve (Figure 4.18). This energy is used primarily for fracture and plastic deformation. Therefore,

(4.22)

where γs = specific fracture energy (J/m2) and B = sample width. The surface energy γs can be replaced by Gc, the energy release rate (Williams, 1984). Therefore, when d = 0,

(4.23)

which can be obtained by extrapolating the Fc /B vs. d curve to d = 0 (Figure 4.19).Luyten (1988) and Kamyab et al. (1998) performed wire-cutting tests on natural

FIGURE 4.17 Schematic of cutting cheese with a blade (left) and wire of diameter d (right). (After Luyten, 1988; Kamyab et al., 1998.)

Fracture

PlasticDeformation

Cutting Blade

Cheese Cheese

Cutting wire

d

2d

Fracture

B

Fc PlasticDeformation

U U U U Uf d1 2 3= + + +

U F vtc1 =

F vt vtB U U dBvtc s= + +( )γ 2 3 2

GF

Bcc d= =( ) 0


and process cheeses. Their data are summarized in Table 4.6. The cheese type and cutting speed appear to have significant effect on the specific fracture energy, which is in the range of about 3 J/m2 to 10 J/m2.

Luyten (1988) also reported a decrease in fracture energy as Gouda cheese matured, apparently due to casein breakdown as it aged. The value of fracture energy is considered to be on the order of the theoretical energy needed to break all chemical bonds in one plane, which is estimated to be 1 J/m2 (Gordon, 1978). For most materials,

FIGURE 4.18 Force–deflection diagram during wire-cutting of process cheese. Cutting force Fc is the constant force developed during the test. (After Kamyab et al., 1998.)

FIGURE 4.19 Effect of wire diameter and rate of cutting on cutting force for process cheese. The intercept of each line represent the fracture toughness of the cheese. (After Kamyab et al., 1998.)

1 mm/min

10 mm/min

100 mm/min

Wire diameter (mm)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Fc/

B (

J/m

2 )

0

20

40

60

80

10

30

50

70


the fracture energy is higher than this theoretical limit because of plastic deformation in the vicinity of fractured surfaces. The low fracture energy for cheeses is believed to be due to rather incomplete network throughout the cheese (Luyten, 1988).

Brown et al. (2000) studied the effect of cutting speed and cheese temperature while cutting a mature Cheddar cheese using a knife blade mounted at a 45° angle to the sample. Their results of peak average cutting force (Figure 4.20) indicate expected trends — higher forces at higher cutting speeds and at lower temperatures. The effect of temperature is greater than that of the cutting speed. Atkins and Vincent (1984) remark that the angle the blade makes with the cutting surface is critical. At angles greater than optimum, the forces are higher due to energy expended in curling of the cut section.

The cutting studies also allow measuring friction forces. Brown et al. (2000) measured the friction forces of the knife blade slicing the cheese. The trends of the friction forces are the same as that of the cutting force, i.e., friction force increases with cutting speed and decreases with cheese temperature (Figure 4.21).

Kamyab et al. (1998) determined the coefficient of friction µ from the wire-cutting force vs. deformation curve. This is based on the fact that the cutting force Fc should also sustain yield stress σy normal to the surface and frictional force µσy . Therefore,

(4.24)

where d = diameter of cutting wire. Therefore, the slope of Fc /B vs. d curve (Figure 4.19) is (1 + µ)σy . If σy is determined from another test (e.g., compression test), µ can be determined from wire-cutting data. The µ determined from friction tests, wire-cutting tests, and compression tests are comparable for different cheeses (Table 4.7).

The friction force for slicing cheese with a blade (Brown et al., 2000) is higher than for cutting with a wire (Kamyab et al., 1998) by about an order of magnitude, mainly due to larger blade-to-cheese contact area during slicing. Of course, the

TABLE 4.6Specific Fracture Energy of Some Natural and Processes Cheeses Determined By Wire Cutting Tests

Cutting Speed(mm/min)

Cheese Type

Goudaa Regular Processb Light Processb Mild Cheddarb

1 4.9 2.9 — —10 6.7 4.6 3.44 5.320 9.6 — — —

100 — 8.1 — —

a From Luyten, 1988.b From Kanyab et al., 1998.

F

BG dc

c y= + +( )1 µ σ


FIGURE 4.20 Maximum cutting force as a function of cutting speed and cheese temperature during blade cutting of mature Cheddar cheese. (After Brown et al., 2000.)

FIGURE 4.21 Maximum friction force as a function of cutting speed and cheese temperature during blade cutting of mature Cheddar cheese. (After Brown et al., 2000.)

60

50

40

20

10

0

239

105

26 15

5

−5

30

Cut

ting

forc

e (N

)

Cheese te

mperature (°C)

Cutting speed (mm/s)

Cheese temperature ( oC) Cutting sp

eed (mm/s)

Fric

tion

5

5

15

239

0

10

20

30

105

26

forc

e(N

)


differences are further exacerbated by cheese temperatures and composition (e.g., moisture content).

EYE/SLIT FORMATION AND GROWTH

Small, round holes distributed throughout a cheese mass is a characteristic and desirable feature of Emmentaler (e.g., Swiss), Gouda, and Edam cheeses. These holes, known as eyes, are formed primarily from CO2 produced as propionic and citric acids are fermented by the starter organisms and from N2 dissolved in the cheese milk (Akkerman et al., 1989; Polychroniadou, 2001). Holes formed in other cheeses (e.g., Tilsit and Havarti) are not called eyes but still are considered typical of these varieties (Polychroniadou, 2001). However, holes present in Cheddar-type cheeses caused by some spoilage organisms producing CO2, H2, or H2S are an indication of a quality defect (Table 4.8). Even in cheeses where eyes or holes are expected and accepted, slits or cracks are formed under certain conditions. This is a quality defect. Biochemi-cal and microbiological aspects of hole formation has been well researched (Zoon and Allersma, 1996; Akkerman et al., 1989; Polychroniadou, 2001).

A nucleus is required in order for a hole to form. Small air bubbles (N2 in milk) attached to curd particles may form as nuclei along with some impurities and small mechanical openings. The nuclei grow into eyes due to diffusion of CO2. The size, number and distribution of eyes can be related to the time, quantity, intensity, and rate of CO2 production in cheese (Polychroniadou, 2001). Akkerman et al. (1989) discussed the mechanism of eye formation and growth in detail.

From a fracture mechanics viewpoint, the formation of holes, slits, and cracks in cheese can be considered as controlled by the rheological and fracture properties of the cheese. Walstra (1991) presented a succinct discussion on the rheological foundation of eyes and slits. The driving force for hole growth is the differential gas pressure ∆P between the inside and outside of the hole. In Gouda-type cheeses, this is estimated to be on the order of 5 kPa to 10 kPa (Walstra, 1991). The hole growth, which can be measured in terms of the biaxial elongational strain rate (BESR), is dictated by the biaxial elongational viscosity (BEV). Therefore,

TABLE 4.7Comparison of Friction Coefficient of Different Cheeses Determined By Different Tests

Cheese TypeFriction

TestCutting

TestCompression

Test

Regular process cheese 0.77–0.85 0.75 0.69Light process cheese 0.82–0.93 0.86 0.39Sharp Cheddar 0.97–1.04 1.07 0.54Mild Cheddar 0.61–0.65 0.52 0.54Process American 1 0.98–1.06 1.13 0.57Process American 2 1.13–1.28 1.25 0.53

Source: From Kamyab et al., 1998.


(4.25)

(4.26)

where r = radius of the hole at time t. If the rate of gas diffusion into the hole is higher, for a cheese of certain BEV, the hole growth will be faster. Due to the strain rate thinning nature of the cheese, at higher BESR, the BEV is lower, leading to a faster hole growth. However, the faster the growth of the hole, the faster the decrease in ∆P. It has been estimated that the BESR is on the order of 10–6 s–1 and rapidly decreases during the hole growth (Akkerman et al, 1989). In the event that ∆P is greater than the fracture stress of the cheese, a slit will form and progress until the slit area grows sufficiently to lower the ∆P below the fracture stress. Luyten (1988) estimated a fracture stress of about 6 kPa at a strain rate of 10–6 s–1

based on compression tests on Gouda cheese in the strain rate range of 0.001 to 0.1 (Figure 4.22). Walstra (1991) questioned such an estimate because hole growth

TABLE 4.8Eyes in Different Cheese Types

Cheese TypeAppearance of

Eyes Cause (Organism)Stage of

FormationCurdpH

Cheese Texture

Dutch Small and round (φ < 1 cm); smooth and shiny internal surface

Citrate fermentation (mesophilic lactococci and leuconostocs)

Over-long ripening period

5.4 Flexible, pliable body

Emmental Large and round (φ = 1–3 cm); smooth and shiny internal surface

Lactate fermentation (thermophilic and meso-philic lactic acid and propionic acid bacteria)

Over-long ripening period

5.4 Firm, flexible body

Havarti Small and irregular Mechanical and citrate fermentation (mesophilic lactococci and leuconostocs)

During manufacture and first weeks of ripening

5.2 Firm, flexible body

Blue-veined Open structure; irregular slits

Mechanical and possibly citrate fermentation (mesophilic lactococci and leuconostocs)

Mainly during manufacture

4.7 Firm (friable) body

Cheddar Normally no holes; slits and cracks in defective cheeses

Mechanical and citrate fermentation (gas forming starters and nonstarter lactic acid bacteria, e.g., lactococci)

During manufacture and ripening

5.0 Short texture

Source: After Polychroniadou, 2001.

BEVP

BER= ∆

BESRd r

dt= (ln )


is an elongational property, the linear extrapolation may not hold in the low strain rate range, and the temperature at which the testing was done (20°C) was higher than the refrigerator conditions at which the cheese is normally aged. Nonetheless, the estimated fracture stress is well within the ∆P estimated by Walstra (1991). There are indications that low cheese pH (<5.2) may be the key factor in determining the tendency for cheese to develop eyes or slits. Walstra (1991) also points out that there may be a pH optimum around which conditions are detrimental with respect to eye formation.

REFERENCES

Akkerman, J.C., P. Walstra, and H.J.M. van Dijk. 1989. Holes in Dutch-type cheese. 1. Conditions allowing eye formation. Netherlands Milk and Dairy Journal 43:453–476.

Anderson, T.L. 1995. Fracture Mechanics — Fundamental and Applications, 2nd ed. Boca Raton, FL: CRC Press.

Andres, C. 1983. Natural cheese in new form provides improved aesthetic and functional qualities. Food Processing 44(12):64,66.

Antonissen, P. 1986. Method and apparatus for slicing a product in accordance with its anticipated weight distribution. Patent No. US4572044.

Apostopoulos, C. and Marshall, R.J. (1994). A Quantitative method for determination of shred quality of cheese. Journal of Food Quality 17:115–128.

Atkins, A.G. and Y.-M. Mai. 1985. Elastic and Plastic Fracture. Chichester, U.K.: Horwood Publishers.

Atkins, A.G. and J.F.V. Vincent. 1984. An instrumented microtome for improved histological sections and the measurement of fracture toughness. Journal of Materials Science Letters 3:310–312.

Barritt, S. 1985. Slicing up the cheese market. Food Manufacture 60(6):41.

FIGURE 4.22 Fracture stress as a function of strain rate for Gouda cheese. Dotted line extrapolates fracture stress to a strain rate of 10–6 s–1 prevalent during eye or slit formation. (After Walstra 1991. With permission.)

Strain rate (1/s)

Fra

ctur

e st

ress

(kP

a)100

10

10−6 10−5 10−4 10−3 10−2 10−1 100

1-week-old, pH=4.94

2-week-old, pH=5.24


Broek, D. 2001. Practical application of fracture mechanics — fracture control, in Handbook of Materials Behavior Models 2, J. Lemaitre, Ed., San Diego: Academic Press, pp. 661–671.

Brown, T. et al. 2000. Improving food cutting systems. Food and Drink 2000: Processing Solutions for Innovative Products. Warwickshire, U.K.: Institution of Chemical Engineers.

BSI. 1991. Guidance on methods for assessing the acceptability of flaws in fusion welded structures. PD6493. London: British Standards Institution.

Bui, H.D. and A. Ehrlacher. 1981. Propagation of damage in elastic and plastic solids, in Advances in Fracture Mechanic, Vol. 3, D. Francois, Ed., New York: Pergamon Press, p. 533.

Charalambides, M.N., J.G. Williams, and S. Chakrabarti. 1995. A study of the influence of aging on the mechanical properties of Cheddar cheese. Journal of Material Science30(16):3959–3967.

DMI. 2002. Putting the flavor back in reduced-fat cheese. Dairy Dimensions 5(1):1.Dubuy, M.M. 1980. The French art of shredding cheese. Food Processing Industry 49:52–53.Francois, D. 2001. Brittle fracture, in Handbook of Materials Behavior Models 2, J. Lemaitre,

Ed., San Diego: Academic Press, pp. 566–576.Gordon, J.E. 1978. Structures, or Why Things Don’t Fall Down. London: Penguin Books.Gordon, J.E. 1968. The New Science of Strong Materials. London: Penguin Books.Griffith, A.A. 1920. The phenomena of rupture and flow in solids. Philosophical Transactions,

Series A 221:163–198.Izutsu, T. et al. 1991. Rheological properties of fibrous structured cheese. Nippon Kagaku

Kaishi 8:1059–1065.Kamyab, I., S. Chakrabarti, and J.G. Williams. 1998. Cutting cheese with wire. Journal of

Materials Science 33:2763–2770.Langley, K.R., A. Martin, and S.L. Ogin. 1994. The effect of filler volume fraction on the

fracture–toughness of a model food composite. Composites Science and Technology50(2):259–264.

Lemaitre, J. 2001. Handbook of Materials Behavior Models, Vol. II, Failures of Materials. New York: Academic Press.

Luyten, H. 1988. The Rheological and Fracture Properties of Gouda Cheese. Ph.D. thesis, Wageningen Agricultural University, Wageningen, The Netherlands.

Luyten, H. and T. van Vliet. 1996. Effect of maturation on large deformation and fracture properties of (semi-)hard cheeses. Netherlands Milk and Dairy Journal 50:295–307.

Ni, H. and S. Gunasekaran. 1998. Computer vision method for determining length of shredded cheese. Artificial Intelligence Review. 12:27–37.

Ni, H. and S. Gunasekaran. 2002. Image Processing Algorithm for Cheese Shred Evaluation. Journal of Food Engineering (submitted).

Polychroniadou, A. 2001. Eyes in cheese: a concise review. Milchwissenschaft 56(2):74–77.Pomerantz, J. and P. Feeney. 1985. Slicing device for food stuffs [e.g., cheese]. Patent No.

US4516458.Riande, E. et al. 2000. Polymer Viscoelasticity — Stress and Strain in Parctice. Marcell Dekker,

Inc., New York. pp. 616–638.Schirrer, R. 2001. Damage mechanisms in amorphous glassy polymers, in Handbook of Mate-

rials Behavior Models 2, J. Lemaitre, Ed., San Diego: Academic Press, pp. 488–499.Van Vliet, T., H. Luyten, and P. Walstra. 1991. Fracture and yielding of gels, in Food Polymers,

Gels and Colloids, E. Dickinson, Ed., Cambridge, England: The Royal Society of Chemistry, pp. 392–403.

Walstra, P. 1991. Rheological foundation of eye or slit formation, in Bulletin of the IDF, No. 268, Rheological and Fracture Properties of Cheese, Brussels, Belgium: International Dairy Federation.


Walstra, P. and van Vliet, T. 1982. Rheology of cheese. Bulletin of the IDF, No. 153. Brussels, Belgium: International Dairy Federation.

Williams, J.G. 1984. Fracture Mechanics of Polymers. Chichester, England: Ellis Harwood Limited Publishers.

Williams, J.G. and M.J. Cawood. 1990. European group on fracture-kc and Gc method for polymers. Polymer Testing 9(1):15–20.

Zoon, P. and D. Allersma. 1996. Eye and crack formation in cheese by carbon dioxide from decarboxylation of gluconic acid. Netherlands Milk and Dairy Journal 50(2):309–318.

Linear Viscoelasticityof Cheese

The rheological behavior of cheese is viscoelastic. A viscoelastic material exhibitsboth elastic solid and viscous liquid behavior simultaneously under a wide range ofconditions. An elastic solid stores mechanical energy during deformation and revertsto its original form (shape and size) upon removal of external forces; a viscous liquiddissipates such energy. Though no material is a “true solid” or a “true liquid,” a steelspring or rubber band is a good example of an elastic solid, and water is an ubiquitousexample of a viscous liquid. The simplest type of viscoelastic behavior is linearviscoelasticity, where the measured properties are independent of magnitude of theinput variable (Ferry, 1980). This type of behavior is observed when the deformationis so small that the structure of a material is disturbed only to a negligible extent.

The small amplitude oscillatory shear (SAOS) measurements are commonlyused to study the linear viscoelasticity of cheese and other foods. SAOS is a specialsubset of the dynamic mechanical analysis (DMA). DMA is used to measuremechanical properties of materials while they are subjected to an oscillating strain(or stress), usually applied sinusoidally. When DMA accounts for temperatureeffects, it is termed “dynamic mechanical thermal analysis” (DMTA). DMA andDMTA are extremely useful material characterization techniques. The main featureof SAOS tests is that, due to small strain (and stress) used, they can be consideredas objective and nondestructive tests suitable for probing material structure andstructure development during different processes. We have recently reviewed the useof SAOS technique in food and dairy research (Gunasekaran and Ak, 2000; Ak andGunasekaran, 2001).

SAOS measurements allow determination of shear moduli, (i) storage modulus(or elastic modulus) and (ii) loss modulus (or viscous modulus) as a function of testfrequency (

ω

) in the linear viscoelastic (LVE) region of the test material. The storagemodulus G

′

(

ω

) is a measure of the energy stored and recovered per cycle, and theloss modulus G

″

(

ω

) is a measure of the energy dissipated or lost as heat per cycleof imposed deformation (Ferry, 1980). In addition, phase angle (or mechanical lossangle)

δ

and loss tangent

tan

δ

, relative measures of the ratio of viscous to elasticcomponent, can be determined.

MATHEMATICAL RELATIONS INLINEAR VISCOELASTICITY

In dynamic testing, a sample is subjected to an alternating strain, and the resultingstress is measured. Most often the form of the alternating strain is sinusoidal, andthe deformation is usually in shear mode. In food rheology, dynamic measurements

5


are rarely made in compression mode (e.g., Weipert, 1997). The amplitude of strainis usually chosen to be small (often less than 1% for cheese) so that the stressresponse is proportional to the input strain amplitude, or, in other words, the responseis in the LVE region. Then the material properties,

G

′

(

ω

),

G

″

(

ω

), and

tan

δ

aredetermined.

Applying a sinusoidal stress and measuring the resulting strain is another way toconduct dynamic measurements. In principle, measurements in an LVE region willyield the same result regardless of how it is performed. In actuality, there may be somedifferences due to the accuracy of measurements with strain-controlled

vs.

stress-controlled instruments. This aspect will be briefly discussed later in this chapter.

In SAOS experiments, the material is subjected to a sinusoidal shear strain ofconstant amplitude

γ

ο

and frequency

ω

so that the shear strain varies with time as:

(5.1)

When the strain amplitude is sufficiently small the stress response will also besinusoidal:

(5.2)

where,

σ

ο

is the stress amplitude. Using a trigonometric identity* Equation 5.2can alternatively be written as:

(5.3)

Multiplying the right hand side of Equation (5.3)by (

γ

ο

/

γ

ο

) and using the fol-lowing relations

(5.4)

(5.5)

Equation 5.3 can be rewritten as:

(5.6)

* sin(A + B) = sin(A) cos(B) + cos(A) sin(B)

γ γ ω( ) sint to= ( )

σ σ ω δ( ) sin( )t to= +

σ σ ω δ ω δ( ) cos cos( ) sin( )t to= ( ) +[ ] sin( t)

′ = ( )G o

o

( ) cosωσγ

δ

′′( ) = ( )G o

o

ωσγ

δ sin

σ γ ω ω ω ω( ) sin( ) cost G t G to= ′( ) + ′′( ) ( )[ ]


The ratio (

σ

o

/

γ

o

) in Equations 5.4 and 5.5 is the magnitude of the complexmodulus (

G*

) and it is related to the storage (

G

′

) and loss (

G

″

) moduli by thefollowing expression:

(5.7)

Quite often the dynamic response of materials is expressed in terms of the losstangent defined as:

(5.8)

For a Hookean (ideal elastic) solid the loss angle

δ

= 0, so all the energy isstored (i.e., recoverable). For a Newtonian (ideal viscous) liquid

δ

=

π

/2, so all theenergy is dissipated (i.e., lost) during deformation. The corresponding values for

tan

δ

are 0 and

∞

. For a viscoelastic material, 0<

δ

<

π

/2, and thus the relative amountof energy stored or dissipated is determined from the magnitude of phase angle. Thetypical SAOS responses for these materials are illustrated in Figure 5.1.

An increase in

tan

δ

indicates that the material is reacting to an external stressin a relatively more viscous and less elastic manner. For instance,

tan

δ

is used asa measure of the dynamic character (life–time) of protein–protein bonds in rennet

FIGURE 5.1

Sinusoidal strain input and typical stress–strain responses of elastic solid, vis-cous liquid and viscoelastic materials.

G G G* ( ) )= ′ + ′′2 ( 2

tan GG

δ ω ωω

( ) = ′′( )′( )

Newtonian Liquid

δ = π/2

Hookean Solid

σ0γ0 ωt

Strain input

Strain inputStress output

ωt

Stress output

Viscoelastic Material

0<δ<π/2

ωt

Strain inputStress output


casein gels (van Vliet et al., 1989). When,

G

′

=

G

″

,

tan

δ

= 1 and the modulusvalue at this point is called the “crossover modulus.” At

tan

δ

= 1, the material isequally liquid and solid. When

tan

δ

<1, the material is more solid-like, and when

tan

δ

>1, the material is more liquid-like. Hence, change in

tan

δ

value around 1signifies that the state of the material is crossing over from predominantly solid toliquid or

vice versa.

Another way to present results of oscillatory experiments is to use complexviscosity

η

*

, which is related to its viscous and elastic components,

η′

and

η″

,as follows:

(5.9)

The real part of the complex viscosity (i.e.,

η

′

) is called the dynamic viscosity,and for a Newtonian fluid, it corresponds to shear viscosity. The complex viscosityis also related to the complex modulus as given below:

(5.10)

Furthermore, we can write the loss tangent in terms of the components ofcomplex viscosity:

(5.11)

The physical significance of these dynamic quantities may be appreciated betterin terms of energy stored and dissipated during sinusoidal deformation. The energy,or work, is given by (Ward and Hadley, 1993):

(5.12)

It has been shown (Ferry, 1980; Tschoegl, 1989) that the average energy perunit volume stored in a cycle is given by:

(5.13)

The energy dissipated in a complete cycle is given by:

(5.14)

η η η* = ′( ) + ′′( )2 2

ηω

* *= 1 G

tan δ ω ηη

( ) = ′′′

W E d dt= = =∫ ∫∆ σ γ σ γ ˙

E Gstored o( ) ( )ω γ ω= ′14

2

E Gdissipated o( ) ( )ω π γ ω= ′′ 2


In a similar fashion, the stored energy is proportional to

η

″

,

and dissipated energyis proportional to

η

′

as shown in Equations (5.15) and (5.16):

(5.15)

and

(5.16)

TYPES OF SAOS MEASUREMENTS

There are four major experimental variables in any dynamic test: strain (or stress),frequency, temperature, and time. Thus, different types of dynamic tests can be setup changing one or more of these experimental variables. The commonly performedtests are: strain (or stress) sweep; frequency sweep; temperature sweep, and timesweep (gel cure). Each of these tests serves to fulfill a certain objective.

Depending on the input variable, two types of rheometers are commerciallyavailable: “controlled strain” (or controlled strain rate) with torque measurementand “controlled stress” with angular motion measurement. Detailed discussion ofsuch rheometers is outside the scope of this book, but interested readers can findadditional information elsewhere (Macosko, 1994). We shall only mention here thatwith most of the commercial rheometers it is possible, through the versatility of theoperating software, to conduct measurements in either the constant stress or theconstant strain mode. This, however, may have some problems related to the preci-sion of dynamic measurements. Bafna (1996) examined the precision of complexviscosity measurements in the constant stress and constant strain modes. One of theimportant findings of Bafna’s work is that constant stress measurements provideimproved precision at lower frequencies, whereas constant strain measurements aremore precise at higher frequencies.

S

TRAIN

(

OR

S

TRESS

) S

WEEP

In this type of oscillatory tests the moduli are measured as a function of increasingstrain while the frequency is fixed, for instance, at 1 Hz (Figure 5.2). Usually, theobjective of a strain sweep test is to determine the critical point beyond which thedynamic shear moduli (

G*

,

G

′

,

G

″

) become dependent on the input variable, strain.In other words, it is carried out to determine the limits of linear viscoelasticity. Thestrain sweep test is the first step in dynamic mechanical analysis and always per-formed prior to a frequency sweep test in order to specify the strain level forfrequency sweeps.

In case of controlled stress dynamic rheometers, a stress sweep is performedand serves the same purpose of identifying the limit of LVE region.

Estored o( )ω γ ω η= ′′14

2

Edissipated o( )ω π γ ω η= ′ 2


FIGURE 5.2

Schematic representation of a strain sweep test at constant frequency (e.g., 1 Hz) with an example of response in termsof complex modulus. (LVE stands for linear viscoelasticity.) (After Ak and Gunasekaran, 1996.)

amplitude: 0.5%

−0.024

0

0.024

0 0.2 0.4 0.6 0.8 1

Time (s)

Str

ain

(-)

amplitude: 1%

−0.024

0

0.024

0 0.2 0.4 0.6 0.8 1

Time (s)

Str

ain

(-)

amplitude: 2%

−0.024

0

0.024

0 0.2 0.4 0.6 0.8 1

Time (s)

Str

ain

(-)

40

50

60

70

80

90

0 0.5 1 1.5 2

Strain amplitude (%)

Com

plex

mod

ulus

(kP

a)

LVE limit


F

REQUENCY

S

WEEP

The frequency sweep is probably the most versatile rheological test to characterizeviscoelastic behavior of materials. In this test, a sinusoidal strain (or stress) of fixedamplitude is imposed on the material and the dynamic moduli are determined overa wide range of frequencies (Figure 5.3). The resultant plot is also known as the“mechanical spectrum” of the material. The strain amplitude must be selected withcare and, under all conditions, should be less than the strain limit of linear visco-elasticity. Contemporary rheometers are capable of measuring dynamic propertiesat a wide range of frequencies, typically from 0.01 Hz to 100 Hz. With advancedrheometers one can even conduct oscillatory measurements at frequencies as low as10

–5

Hz. With such instruments, the low frequency selection is dictated mainly bythe stability of the sample and the researcher’s patience in performing long dynamicmeasurements. For instance, it takes nearly 28 h to complete one oscillation cycleat 10

–5

Hz. An efficient way to shorten the total experimental time is to use, wheneverapplicable, the time–temperature superposition (TTS) procedure, which will bediscussed later. In the high-frequency range, the measurements have been limiteddue to inertia effects. However, performance improvements at high frequencies arereported for new rheometers (Eidam et al., 2001). When using a controlled stressinstrument, test software allows setting a “target strain,” which should be below thestrain amplitude limit of LVE region.

One of the enhancements in rheometry is the introduction of multiwave oscilla-tion mode, where the sample is exposed simultaneously to oscillations at two ormore frequencies (Holly et al., 1988; Anon, 2002a; Anon, 2002b). Multiwave oscilla-tion mode reduces experimental time, as compared to running several experimentseach at a different frequency, while providing the same standard dynamic parameters.This is a significant advantage especially when large numbers of tests must be donein a limited time (e.g., quality-control testing). It is important that the sum of strainamplitudes, which are additive in multiwave oscillation, remains within the LVEregion of the material (Holly et al., 1988). Multiwave oscillation is particularly usefulfor materials with transient structure, and therefore it may be suitable for studyingmilk gelation.

T

EMPERATURE

SWEEP

The temperature-sweep test involves measurement of dynamic moduli over atemperature range at constant frequency and constant strain (or stress) amplitude.Temperature sweeps can be carried out in a ramp or stepwise fashion (Figure 5.4).If the ramp mode is employed, then the rate of temperature change and frequencyof oscillation must be selected carefully. For instance, if one conducts the test at1 Hz and 1°C/min, then the temperature change per cycle (0.017°C) can be consid-ered insignificant. Temperature sweeps are essential to investigate phase transitions.For example, during a temperature sweep, the temperature at crossover modulus(G′ = G″) is considered to signify the beginning of gel forming (or gel melting)temperature (Gunasekaran and Ak, 2000). During cheese melting, the temperatureat crossover modulus is an indication of the “softening point” of cheese, the onset


FIGURE 5.3 Schematic representation of a frequency sweep test at constant strain amplitude (e.g., 0.5%) with an example of responsein terms of complex modulus. (After Ak and Gunasekaran, 1996.)

1 Hz

0 0.5 1

Time (s)

Str

ain

2 Hz

0 0.5 1

Time (s)

Str

ain

5 Hz

0 0.5 1

Time (s)

Str

ain

100

1000

0.1 1 10 100 1000

Frequency (rad/s)

Com

plex

mod

ulus

(kP

a)


temperature of rapid melt and flow (Gunasekaran et al., 2002) (see Chapter 8 fordetails). This is illustrated in Figure 5.5 for Mozzarella cheese. The temperaturesweep test is also helpful to detect changes that would occur at rather high, andpossibly inaccessible, frequencies if measurements were made at room temperature.

TIME SWEEP

Time-sweep measurements are often made isothermally at constant strain (or stress)amplitude and frequency (Figure 5.6). It is also known as a “gel cure” test, and maybe performed along with a temperature-sweep program to examine changes inrheological behavior due to combined effects of time and temperature. It is commonpractice to set the oscillation frequency at 1 Hz.

Time-sweep measurements are very useful in monitoring the build-up or break-down of structure. For instance, the evolution of milk gel (i.e., firming) after theaddition of rennet or another coagulant is usually monitored by time-sweep mea-surements of viscoelastic parameters, G′, G″, and tan δ (Gunasekaran and Ak, 2000;Renault et al., 2000; Singh and Waungana, 2001). The time at which crossovermodulus is observed during gel cure can indicate gelation time in systems that gelat isothermal conditions. An example of this is presented in Figure 1.4 (Chapter 1)for determining the gelation time of rennetted milk gel.

FIGURE 5.4 Schematic representation of a temperature sweep test (in ramps or steps) withan example of response in terms of storage modulus. (After Wetton and Marsh, 1990.)

Time

Tem

pera

ture

Tem

pera

ture

Example:Ramp rate = 5° C/min

Time

Ramp change Step change

00

1

2

34

5

6

7

20 40 60 100

Temperature (°C)

log

Sto

rage

mod

ulus

(P

a)

80


TIME-TEMPERATURE SUPERPOSITION

Rheological properties of cheese are strongly dependent on temperature. Thus,measurements at different temperatures are made for full characterization of thecheese behavior. For some materials it is well known that the linear viscoelasticproperties measured at several temperatures can be represented on one curve, calledthe “master curve,” at a reference temperature by means of time–temperature super-position (TTS) procedure (Ferry, 1980; Dealy and Wissbrun, 1989; Honerkamp andWeese, 1993). The resulting master curve will have a largely expanded time orfrequency scale, which is very valuable for characterization of material behavior attimes or frequencies that are not directly accessible with a single instrument ormeasurement technique. Materials for which TTS procedure is applicable are termed“thermorheologically simple.”

Although cheese is less likely to be a thermorheologically simple material dueto its multi-component nature and thermal phase changes, there have beensuccessful applications of TTS (or more correctly frequency–temperature super-position) to cheese (Taneya et al., 1979; Subramanian and Gunasekaran, 1997b).Whenever TTS is applicable to foods it makes it possible to estimate long-termviscoelastic properties from the short-term data. This is significant consideringthat lengthy experiments with foods are hampered due to considerations for samplestability (i.e., physical, chemical, and enzymatic alterations).

Time–temperature or frequency–temperature equivalence simply implies that theviscoelastic properties at one temperature are related by a constant ratio (i.e., the

FIGURE 5.5 Temperature at crossover modulus correspond to cheese softening point. (AfterGunasekaran et al., 2002.)

0.1

1

10

100

20 30 40 50 60 70 80

Temperature (°C)

Mod

ulus

(kP

a)

Mozzarella cheese(10-day-old)

G¢¢

G¢

Crossover modulus

Softening point


shift factor) to the corresponding property at the reference temperature. Ferry (1980)gives three criteria for the applicability of TTS procedure:

1. The shapes of adjacent curves should match closely.2. The same values of empirical shift factors (aT) must superpose all the

viscoelastic functions.3. The temperature dependence of aT must have a reasonable form consistent

with experience (e.g., Arrhenius-type or WLF type relation).

If viscoelastic data are not superposable, it is often taken as an indication oftwo-phase behavior or a phase change caused by the changing temperature. Suchmaterials are termed “thermorheologically complex,” for which the shift factorbecomes a function of time in addition to temperature. Furthermore, chemical changescan also interfere with the superposition procedure (Gordon and Shaw, 1994).

Several companies are making different rheometers of varying sophistication(and cost) to be used in routine quality control applications, or in advanced research-and-development activities. In most cases, these instruments are furnished with

FIGURE 5.6 Schematic representation of an isothermal time-sweep test at constant frequencyand amplitude with an example of response for milk gelation at 40°C by glucono-δ-lactone.(After Lucey and Singh, 1998.)

1

10

100

1000

0 2 4 6 8 10 12 14 16

Time (h) after GDL addition

Sto

rage

mod

ulus

, G′ (

Pa)

UnheatedHeated (80°C, 30 min)

Time (h)

Str

ain

(-)


user-friendly software to control the operation of the instrument, and to collect andanalyze the data. In advanced systems, the TTS module will be integrated into thesoftware package so that the user can readily carry out the superposition of transientor dynamic rheological data. We must mention, for the readers who are savvycomputer programmers, the book by Gordon and Shaw (1994) that gives the fullsource code of computer algorithms for performing rheological computational taskssuch as TTS. In the example in the section on Mozzarella chesse, we will illustratethe TTS procedure using a spreadsheet program.

APPLICATION OF SAOS IN CHEESE RHEOLOGY

The viscoelastic behavior of cheese is mostly dictated by the properties of theprincipal component forming the continuous network, that is the protein network.The other main constituents are fat and moisture, which contribute to the overallbehavior by modifying the properties of the protein network. There are, of course,numerous other factors (e.g., proteolysis, temperature, pH, salt content) that greatlyinfluence the viscoelastic behavior of cheeses (Walstra et al., 1987a; Luyten, 1988).

As described earlier, SAOS measurements enable quantification of elastic andviscous effects simultaneously. Elastic response in cheese is primarily due to theprotein–protein bonds. The viscous dissipation in cheese may be due to flow of thematrix material (i.e., protein), flow of liquid through the matrix, and movement ofother structural elements relative to each other, causing friction (Luyten et al., 1991b).

LINEAR VISCOELASTIC REGION OF CHEESES

Measurements in LVE region are most useful in enhancing our understanding ofcheese structure (bond formation and subsequent alterations). It is therefore impor-tant to correctly determine the LVE region of the sample. The SAOS strain (or stress)sweep test offers a rapid and accurate way to determine the critical limits of strain(or stress) for the LVE region.

Shown in Figure 5.7 is an example of a strain-sweep test made on Mozzarellacheese to determine the LVE strain limit. It is evident that the critical strain oflow-moisture, part-skim Mozzarella cheese is about 0.5%. It is further seen thata higher strain limit is observed at 0.1 Hz than at 1 Hz test frequency. Tchir andSaucier (1991) reported a strong dependence of the linear viscoelastic strain limitfor a polymeric material on the test frequency. The linear range for this materialended at approximately 10% strain for 100 rad/s (15.9 Hz), but it extended muchbeyond 100% strain for 0.1 rad/s (0.0159 Hz). It is worth remarking that thesestrain limits of linear viscoelasticity are much higher than those observed forcheese and other foods. Taking advantage of the inverse relation between the linearstrain limit and frequency, Tchir and Saucier (1991) suggested the variable straintechnique to improve the quality of data, particularly at low frequencies where thetorque noise may dominate. In this technique, the strain amplitude is manuallyadjusted so that a measurable torque is obtained while remaining in the domainof linear viscoelasticity.


Subramanian and Gunasekaran (1997a) have conducted a detailed study on thevariation of linear viscoelastic range of Mozzarella with age and temperature. Theyfound that the region of linear viscoelasticity decreased with increasing cheese ageand test temperature (Figure 5.8). A critical strain of 0.05% was determined for12-week-old, low-fat, part-skim Mozzarella cheese at 70°C.

A compilation of the critical strain values for the linear viscoelastic region ofvarious cheeses is presented in Table 5.1. As evident from this table, for the majorityof cheeses the linear viscoelastic strain limit is 1% or less. The exception is therange given by Luyten et al. (1991b) as 3–5% for Gouda cheese. The table servesonly as a guide and does not eliminate the need to determine LVE region for thecheese according to the experimental conditions. It is important to recall that thelimits of LVE vary with factors like temperature. Therefore, if tests are to beperformed over a range of experimental conditions, one should use the smallestcritical strain limit for all tests so that the results can be analyzed together.

FIGURE 5.7 Linear viscoelastic region (LVE) for Mozzarella cheese determined at roomtemperature for two frequencies. (After Ak and Gunasekaran, 1996.)

FIGURE 5.8 Shear strain dispersion of storage modulus for 1-week-old low-moisture, part-skim Mozzarella cheese tested at 1.5 Hz. (After Subramanian and Gunasekaran, 1997a.)

0

20

40

60

80

100

120

0 0.5 1 1.5 2 2.5

Shear strain (%)

Com

plex

mod

ulus

G*

(kP

a)

0.1 Hz1 Hz

critical strains

LVE

1

10

100

1000

0.01 0.1 1

Shear strain (%)

Sto

rage

mod

ulus

(kP

a) 10°C20°C30°C

40°C50°C60°C70°C


CHEDDAR CHEESE

There is considerable interest in the properties of cheese as a function of temperaturesince the amount of cheese used as an ingredient in prepared foods has been rising,especially in the U.S. (Mann, 2000). Since prepared foods often undergo thermalprocessing before consumption, it is important to know how cheese behavior changeswith heating. The properties of cheeses during refrigerated and frozen storage maybe studied by cooling or freezing the sample.

Initial investigation of dynamic properties of cheese as a function of temperatureappears to be made by Taneya et al. (1979). They measured viscoelastic propertiesof Cheddar, Gouda, and processed cheese. Experimental conditions are given inTable 5.2 and chemical composition in Table 5.3. We note at this point that experi-mental conditions of each pertinent report examined in this chapter are presented inTable 5.2 with no further reference at the actual point of discussion.

The temperature dispersion of the loss tangent for Cheddar cheese is plotted inFigure 5.9. One or more peaks are discernible in these plots for Cheddar cheese.The loss tangent peak locations for Cheddar cheese are dependent on the maturationperiod. It is worth to note that the dynamic response of cheese is both qualitativelyand quantitatively different below and above 35°C. For example, the loss tangent of5-month-old Cheddar cheese is the highest and lowest below and above 35°C,respectively. A few important points not addressed by Taneya et al. are (a) influence

TABLE 5.1Strain Limits of Linear Viscoelastic Region for Various Cheeses

Cheese Critical Straina (%) Reference

Cheddar 0.55 Nolan et al., 1989aCheddar-type 0.6 Guinee et al., 2000Cheese curd 0.1–0.3 Ramkumar et al., 1998Feta <1 Wium and Qvist, 1997Gouda 1 Dewettinck et al., 1999Gouda 1 Messens et al., 2000Imitation 1 Mounsey and O’Riordan, 1999Mozzarella 1 Hsieh et al., 1993Mozzarella 0.5 Nolan et al., 1989bMozzarella 0.5 Ak and Gunasekaran, 1996Mozzarella 0.05–1 Subramanian and Gunasekaran, 1997aMozzarella 0.5 Diefes et al., 1993Mozzarella 1 Yun et al., 1994Process 0.35–0.7 Sutheerawattananonda and Bastian, 1998Process 0.70 Nolan et al., 1989aQuarg 1 Kelly and O’Donnell, 1998Several cheeses 0.4 Drake et al., 1999

a In some occasions, the value given in this column represents the strain actually used in theexperiment rather than the true limit of linear viscoelasticity.


TABLE 5.2Experimental Conditions Used in Small Amplitude Oscillatory Shear Measurements on Cheese

Cheese Equipment

Sample Dimensions

(mm)a

Storage Conditions

Test Temperature

(°C)

Test Frequency

(Hz)

Strain Amplitude

(%)Contact Surface Notes Ref.

Gouda: 1, 3, 5 mo old; Cheddar: 1, 3, 5 mo old; Process: hard and soft types

Sanki Eng. Co. Ltd. IRCL-SL type: vertical oscillation

Sample container: 15 mm in diameter and depth; oscillating rod: 3 mm diameter penetrating 12.5 mm into the specimen

Natural cheeses matured at 13°C and tempered at 5°C for 2 weeks; process cheese stored at 5°C

From –5 to 95 3, 10, 30, 100 Vertical amplitude:0.1 mm

No mention of sample bonding or serrated surface

Samples taken from central part of natural cheeses to avoid moisture variation

Taneya et al., 1979

Cheddar: mild and mature

Polymer Laboratories-DMTA

— — 0–100 1 — — — Wetton and Marsh, 1990

CheddarPasteurized Process American Cheese

Rheometrics Dynamics Analyzer 700

Parallel Plate

D = 25H = 4 or 8

— ~22–60 0.0159–15.9 0.55–0.70 Specimens bonded to pitted plates with cyanoacrylate

Initial force of 100 g applied to ensure bonding

Nolan et al., 1989a


TABLE 5.2 (continued)Experimental Conditions Used in Small Amplitude Oscillatory Shear Measurements on Cheese

Cheese Equipment

Sample Dimensions

(mm)a

Storage Conditions

Test Temperature

(°C)

Test Frequency

(Hz)

Strain Amplitude


20-wk-old Cheshire

60-wk-old Cheshire

60-wk-old Cheddar

Rheometrics Dynamics Analyzer 700,

0–200 g–cm torque transducer,

Parallel Plate

D = 25 mmH = 4 mm

Commercial,Tempered 5 h prior to tests

20, except for η* measurements between20 and 40

Strain and temperature sweeps:0.159

Strain sweep: 0–20; temperature sweep: 2.5

Cheese samples bonded to the plates with cyanoacrylate

Heating rate: 2°C/min

Tunick et al., 1990

Cheddar from pasteurized or raw milk

TA Instruments

Carri-Med CSL100,

Parallel Plate

D = 20 mmH = 2, 5, and 10 m (10 mm was selected)

Pasteurized: 19, 240, and 470 days; raw: 246 and 475 days, both at 5°C

25 for torque sweep; 10, 15, 25, 35 for frequency sweep

Torque sweep: 4; frequency sweep: 0.1–10

Torque sweep: 0–1000 µN m;

frequency sweep:700 µN m

A special rough upper plate with 80 µm teeth

A custom-made plastic compartment was used to prevent drying and maintain consistent sample temperature

Rosenberg et al., 1995

Cheddar Rheometrics 8400 fluid spectrometer,

Parallel Plate

D = 60 mmH = 1–2 mm

Ripened at 7°C for 4 months in packages vacuumed

25–90 0.159 0.1 No mention of sample bonding or serrated surface

Heating rate: 2°C/min; fat content: from <1% to 34.3%

Ustunol et al., 1994

Cheddar(2- and24-week-old)

Haake CV20,Parallel Plate

D = 20.4H = 3.6

— 25–60 on heating;

60–25 on cooling

1 0.5 — Heating and cooling rate:1°C/min; gap setting: 3.5 mm; fat content: 8.2–28.4%

Venugopal and Muthukumar-appan, 2001


Cheddar type TA Instruments Carri-Med CSL500,

Parallel Plate

D = 40H = 2

Vacuum wrapped and stored first at 4°C 30 days and then at 7°C up to 190 days

20–90 1 0.6 Serrated plates Tempering 15 min and equilibration 3 min at 20°C; heating rate: 3°C/min; fat content:1.3–30.6%

Guinee et al., 2000

Cheddar Physica MC20/UM Parallel Plate,

Stress-controlled mode

D = 30H = 3

Vacuum-sealed in plastic bags and stored 3 months at 7.2°C

20 0.05–20 — Normal plates Full fat, reduced fat with or without lecithin; 5-min relaxation after sample loading; for frequency sweeps: 2 kPa

Ma et al., 1996

Cheddar Physica MC20/UM

Parallel Plate,Stress controlled mode

D = 30H = 3

Vacuum-sealed in plastic bags and stored 3 months at 7.2°C

20 0.05–20 — Normal plates 1 carbohydrate- and 2 whey-based fat mimetics are used;

5-min relaxation after sample loading; for frequency sweeps: 1 kPa

Ma et al., 1997

Cremoso Argentino

Haake RV20,Parallel Plate

— Ripened 20 days at 5°C and 80% relative humidity

30 0.1–9.6 5 Normal plates Sample dimensions are not specified

Zalazar et al., 2002



Cheese Equipment

Sample Dimensions

(mm)a

Storage Conditions

Test Temperature

(°C)

Test Frequency

(Hz)

Strain Amplitude


Gouda Deer Rheometer PDR 81, Parallel plate

D = 15H = 9–10

Ripening at 13–14°C; tempering 1.5 h in a closed tube

20 0.005–0.05 3–5 Plates covered with emery paper

Upper plate made of Perspex; wet cotton wool around sample to limit maximum weight loss in 45 min was 0.4%; cheese age: 1 week and 1, 3, and 6 months

Luyten et al., 1991b

Gouda Bohlin CVO, Parallel Plate

D = 25H = 5

— 20 1 1 Serrated plates Stress amplitude sweep: 0–4000 Pa; frequency sweep: 0.001–20; cheese: young (1–2 months), medium (6 months), old (12 months)

Dewettinck et al., 1999

Gouda Bohlin CVO, Parallel Plate

D = 25H = 5

Salted 6 h at 14°C in brine, and vacuum-packed and stored 3 days at 14°C

14 1 1 Serrated plates Gap setting 4.5 mm (thus compression of 0.5 mm)

Messens et al., 2000


Natural LMPS Mozzarella and Imitation Mozzarella

Rheometrics Dynamics Analyzer 700, Parallel Plate

D = 25H = 4 or 8

Stored at 4.4°C

25–70 0.0159–15.9 0.5 Bonding sample to pitted aluminum plates with cyanoacrylate

5-min relaxation after sample loading

Nolan et al., 1989b

Part-skim Mozzarella with protein fillers

Carri-Med Am. Inc.

Carri-Med CSL100

Cone and Plate (4 cm diameter, 2° angle)

— Refrigeration: 8–10°C

60–10 1 1 Normal cone and plate

Sample dimensions not specified; cooling from 60 to 10°C in 10 min

Hsieh et al., 1993

LMPS Mozzarella

Rheometrics RDS 7700 for 20°C tests;

Bohlin Rheometer for 60°C; Parallel Plate

For 20°C:D = 25H = 4For 60 °C:D = 25H = 2

Frozen: –20°C;

Refrigerated: 5°C

20 and 60 Frequency sweep: 0.0159–15.9 for 20°C tests; 0.1–20 for 60°C tests

0.5 in 20 °C tests; 2.5% in 60°C tests.

Serrated plates in 60°C tests

Mineral-oil coating of the exposed sample surfaces; water activity controlled

Diefes et al., 1993

LMPS Mozzarella

Bohlin VOR Melt Rheometer,

Parallel Plate

D = 30H = 3.7

6–8°C up to 1 mo

10 and 20 Frequency sweep: 0.005–20; strain sweep: 0.1 and 1

Strain sweep: up to 2.5;

frequency sweep: 0.5

Normal plates Mineral-oil coating of the exposed sample surfaces; wet paper towel to minimize drying

Ak and Gunasekaran, 1996

LMPS and LFPS Mozzarella

Bohlin VOR,Parallel Plate

D = 30H = 3.5

4°C; 1 week to 12 week

10–70 Frequency sweep:0.314 and 125.6 rad/s

Strain sweep: 0.0001–0.01

Coarse sand paper glued to upper plate

Rheometer housed in an environmental chamber

Subramanian and Guansekaran, 1997a, b



Cheese Equipment

Sample Dimensions

(mm)a

Storage Conditions

Test Temperature

(°C)

Test Frequency

(Hz)

Strain Amplitude


LMPS Mozzarella

Rheometrics RDA-II,

Parallel Plate

D = 25H = 2–2.5

3 weeks at 4°C 22 Strain sweep: 1.59; frequency sweep: 0.0159–15.9

Strain sweep:0–20;

frequency sweep: 1

Serrated plates Fiber direction in cheese ⊥ to parallel plated

Yun et al., 1993

UF-Feta Bohlin VOR Rheometer, Parallel Plate

D = 30H = 4.2

8–10 weeks old at reception and stored at 5°C

13 Strain sweep: 0.15;

frequency sweep:.009–7

Strain sweep: 0.5–45,

frequency sweep:0.9

Serrated plates Samples conditioned at 13°C for 16 h before testing;

specimens with weights within 1% of mean value are tested

Wium and Qvist, 1997

Deli-style Cheddar and pre-sliced Mozzarella

TA Instruments TA-1000 N

D = 40H = ?

Stored at 4°C 25 11 Stress sweep:0.1–1000 Pa

Smooth ss plates and serrated plates

5 or 20 N loading normal force applied

Pearce and Bellmer, 2002

Several commercial and experimental varieties

Bohlin VOR,Parallel plates

D = 35H = 3.5

Tempering 1 h at room temperature

23 Frequency sweep: 0.01–15

0.4 Normal plates Gap setting: 3.2 mm;5-min relaxation after loading;

petroleum jelly applied to the exposed sample surfaces

Drake et al., 1999


Imitation cheese

Rheometrics SR 2000,

Parallel plate

D = 24H = 2.4

4°C Strain sweep:22;

temperature sweep:22–100

1 <1 Normal plates Imitation cheeses contained up to 9% pregelatinized starch; samples are compressed 0.2 mm before testing

Mounsey and O’Riordan, 1999, 2001

Quarg cheese TA Instruments

CSL 100, Parallel Plate

Not explicitly given

4–5°C, maximum 3 days

5 1 0.2–0.8 Normal plates Samples compressed before testing; 15-min rest for relaxation

Kelly and O’Donnell, 1998

Process cheese Rheometrics DSR,

Parallel Plate

D = 25H = 2, 3, or 4

1 week at 4°C Frequency sweep: 23; temperature sweep: 25–90

Temperature sweep: 0.8;

stress sweep: 0.8

Stress sweep: 63–6300 Pa

Serrated plates and bonding with cyanoacrylate

Sample edges lubricated with silicone oil; heating rate: 10°C/min

Sutheerawatta-nanonda and Bastian, 1998

Model processed cheese spreads

TA Instruments Carri-Med CSL100,

Parallel Plate

D = 20H = 1

Stored 3 weeks at 20°C

20 Frequency sweep: 0.01–10

— Normal plates Moist filter paper used to prevent drying

Lee and Klostermeyer, 2001

a D: diameter, H: thickness


of fat separation at high temperatures and potential for sample slippage; (b) effectrod insertion on structure; and (c) assertion that strain amplitude is in LVE region.

Wetton and Marsh (1990) applied DMTA technique to a series of productsincluding Cheddar cheese of different maturation grades to determine transitiontemperatures. The plots of loss tangent against temperature for mild and matureCheddar cheeses are shown in Figure 5.10. Two peaks of loss tangent are evident ataround 25 and 75°C. The first transition is thought to be associated with the meltingof fat phase in the cheese and the second one with the mobilization of protein matrix.It is also seen that the peak temperatures for Cheddar cheese decreased with matura-tion, which is contrary to the results of Taneya et al. (1979). Wetton and Marsh (1990)proposed that the reason for this conflict might be the higher moisture content of themature cheese as compared to that of the mild cheese in their work; however, themoisture contents of the cheeses are not specified. It is known that water can act asa plasticizer and modify certain properties (e.g., glass transition temperature, Tg) offood polymers (Slade and Levine, 1995; Roos, 1995; Noel et al., 1990). Moreover,the primary effect of plasticizers (i.e., low molecular weight diluents) is to reduce,for instance, the stiffness of polymers. However, it is also shown that an opposite

TABLE 5.3Chemical Composition of Cheeses Tested by Taneya et al. (1979)

CheeseMaturationPeriod (mo) Moisture (%) Fat (%) pH

CaseinousNitrogen

Gouda 1/3/5 39.9/33.7/32.7 26.4/31.3/31.5 5.89/5.78/5.80 80/70/70Cheddar 1/3/5 42.4/37.9/35.8 23.6/28.6/30.2 6.92/5.81/5.77 87/80/73Processed — hard — 44.5 26.0 6.00 77Processed — soft — 42.5 27.5 5.75 77

Source: After Tanya et al., 1979. With permission.

FIGURE 5.9 Dynamic loss tangent of Cheddar cheese at different maturation stages. (AfterTaneya et al., 1979. With permission.)

0

0.5

1

1.5

2

-5 10 25 40 55 70 85

Temperature (°C)

tan d(-

)

1-mo

3-mo

5-mo


effect (“antiplasticization”) is possible, depending on the nature and amount of theplasticizer (Peleg, 1996; Seow et al., 1999). Wetton and Marsh (1990) in factdemonstrated the plasticization effect of water on the casein samples manufacturedby two processes. The loss tangent peaks for casein samples with 10 and 25% moisturecontent are at about 55 and 98°C, respectively (Figure 5.11).

Nolan et al. (1989a) determined dynamic properties of Cheddar and pasteurizedprocess American cheeses using SAOS measurements, expecting that the data wouldaid in establishing quality criteria for purchase of cheese to be used in the schoollunch program and other food donation programs. The loss tangent values of Cheddarcheese are essentially independent of frequency in the range 10 to 100 rad/s for alltemperatures except 60°C and seen to exceed unity only at 60°C (Figure 5.12). The

FIGURE 5.10 Temperature dispersion of the loss tangent for Cheddar cheese at two matu-ration stages. (After Wetton and Marsh, 1990.)

FIGURE 5.11 The loss tangent of casein samples with different moisture contents from twoalternative manufacturing methods. (After Wetton and Marsh, 1990.)

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100

Temperature (°C)

tan d(-

)

mild

mature

fat melting

proteinphase

0

0.1

0.2

0.3

0.4

0.5

-50 -25 0 25 50 75 100 125 150

Temperature (°C)

tan d(-

)

hot press moldedextruded

10% moisture

25% moisture


complex viscosity of Cheddar cheese is highly dependent on both temperature andfrequency (Table 5.4) and decreases, for instance, at 40°C by a factor of 40 forincreasing frequency from 1 to 100 rad/s, signifying a shear thinning character formelting cheese.

Cheddar and Cheshire cheeses are quite similar in composition but significantlydifferent in texture. The curd manipulation of Cheddar cheese results in matting ofthe curd particles into a close texture and firm body; while that in Cheshire cheesekeeps the individual curd particles separate to obtain a crumbly texture. Expectingthat this large difference in texture will be reflected in the rheological properties,Tunick et al. (1990) applied oscillatory shear tests to distinguish between Cheddarand Cheshire cheeses.

The strain-sweep tests up to 20% shear strain did not reveal a clear linear region,but below 2.5% strain the complex modulus (G*) was practically constant for bothcheeses. The complex viscosity (η*) values of Cheshire and Cheddar cheeses against

FIGURE 5.12 Variation of loss tangent with frequency for Cheddar cheese tested at differenttemperatures. (After Nolan et al., 1989a.)

TABLE 5.4Equation of Complex Viscosity at Different Frequencies for Cheddar Cheese

Frequency(rad/s) Complex Viscosity Equation (kPa.s)

Evisc

(cal/g mol)

1 η* = 1.06 × 10–25 exp(Evisc/RT) 3670010 η* = 1.84 × 10–23 exp(Evisc/RT) 32600100 η* = 3.37 × 10–21 exp(Evisc/RT) 28300

Note: These equations are valid between 22 and 50°C.

Source: After Nolan et al., 1989a.

0.1

0.4

0.7

1.0

1.3

10 100

Frequency (rad/s)

tan d (

-)

26°C

35°C

45°C

60°C


temperature at 2.5% strain and 1 rad/s are presented in Figure 5.13. The temperaturedependence of η* is well described by an Arrhenius-type equation:

(5.17)

where, Avisc preexponential factor, Evisc activation energy, R gas constant, and Tabsolute temperature. The resulting equations with numerical values of fitting param-eters are listed in Table 5.5. It is shown that the complex viscosity and activationenergy of Cheshire cheese decrease 17% during aging from 20 to 60 weeks, whichis ascribed to the proteolysis. The activation energy of Cheddar cheese is significantlyhigher than that of Cheshire cheese. Thus, these authors concluded that the SAOSmeasurements provide an objective way of distinguishing between Cheddar andCheshire cheeses and can be used for detecting mislabeled cheese.

The majority of the rennet-coagulated cheeses are ripened, often under carefullycontrolled conditions, for periods ranging from four weeks to more than two years.

FIGURE 5.13 Dynamic viscosities of Cheshire and Cheddar cheeses at 2.5% strain amplitudeand 1 rad/s frequency. (After Tunick et al., 1990.)

TABLE 5.5Arrhenius Equation with Fitting Parameters for Cheddar and Cheshire Cheeses

Cheese Maturation (week) Arrhenius Equationa Activation Energy (kJ/mol)

Cheddar 60 Y = 7195 X – 19.4 137Cheshire 20 Y = 5380 X – 13.2 103Cheshire 60 Y = 4475 X – 10.3 86

1 Y = log η*; X = 1/T; the unit of dynamic viscosity is Pa.s.

Source: After Tunick et al., 1990.

3

3.5

4

4.5

5

5.5

15 20 25 30 35 40 45

Temperature (°C)

log

η* (

Pa.

s)

20-wk Cheshire

60-wk Cheshire60-wk Cheddar

ln * ln 1T

η = +

AE

Rviscvisc


For Cheddar cheese, the ripening time varies depending upon the flavor profiledesired: Mild Cheddar is aged three months, medium Cheddar is aged four to ninemonths, and strong or sharp (old, extra old) Cheddars are aged from nine monthsto several years. During ripening, a series of physical and chemical/biochemicalchanges take place in the principal constituents of the cheese (i.e., drying, proteolysis,lipolysis, and glycolysis) (Fox, 1989). For most cheese varieties the primary proteo-lysis during ripening (Grappin et al., 1985; Rank et al., 1985) is the major biochemi-cal event responsible for the changes in texture.

Rosenberg et al. (1995) studied the linear viscoelastic properties of pasteurized(P-) and raw milk (R-) Cheddar cheese during ripening using SAOS technique. Theseresearchers used a custom-made upper plate with a rough surface to prevent sampleslippage during the oscillation tests. For P-Cheddar cheese, higher G′ values arereported for samples aged longer (PS vs. PM in Figure 5.14). On the other hand,for the same ripening, an opposite trend is observed for R-Cheddar cheese, where

FIGURE 5.14 The dynamic storage modulus of Cheddar cheese as a function of frequencyand test temperature. Numbers 10, 25, and 35 represent test temperatures in °C; PS: Cheesemade from pasteurized milk and aged 470 days; PM: Cheese made from pasteurized milkand aged 240 days; RS: Cheese made from raw milk and aged 475 days; RM: Cheese madefrom raw milk and aged 246 days. (After Rosenberg et al., 1995. With permission.)

3.5

4.5

5.5

6.5

0.1 1 10 100

Frequency (rad/s)

log

G′ (

Pa)

PS-10PM-10PS-25PM-25PS-35PM-35

5.5

3.5

4.5

6.5

0.1 1 10 100

Frequency (rad/s)

log

G′ (

Pa)

RS-10RM-10RS-25RM-25RS-35RM-35


the G′ values decreased with aging (RS vs. RM in Figure 5.14). The levels of solublenitrogen in different cheese extracts are lower in R-cheese than in P-cheese. Like-wise, as expected, the magnitudes of G′ values in P-cheese are smaller than thosein R-cheese. These authors attributed the disparity in G′ trends to the differences inpeptide profiles between pasteurized and raw milk cheeses. They suggested that theincrease in the elastic character of P-Cheddar cheese is related to decrease in theamount of water previously available for solvation of the protein chains. As moreionic groups are formed due to cleavage of peptide bonds, and these groups bindwater, then less water is available to provide lubrication and solvation. We shall notehere that Creamer and Olson (1982) previously used this argument to explain thebrittleness of maturing (up to 109 week) Cheddar cheese, as measured by thedecrease in percent compression at the yield point.

The effect of temperature on complex modulus (G*) is graphed in Figure 5.15.This figure shows that the change in complex modulus for each cheese is a gradualprocess, as pointed out by Rüegg et al. (1991). Rosenberg et al. (1995) stated thatthe inverse relation between dynamic properties and temperature is an indication ofthe thermal softening of the matrix. At this temperature range (10 to 35°C) meltingof milk fat is likely to influence G′ and G″ of Cheddar cheese (Wetton and Marsh,1990; Visser, 1991).

Meltability is the key functional property of cheese when used as an ingredient(e.g., pizza, toasts, hamburgers, sauces). As discussed in Chapter 8, several empiricaland fundamental methods exist to quantify cheese meltability. The definition pro-posed for meltability has two aspects that need to be quantified: (a) ease of melting,and (b) extent of flow. In terms of dynamic testing, the first aspect may be quantifiedwith the temperature at which the viscous contribution becomes equal to the elasticcontribution (i.e., transition temperature where tan δ = 1), and the second aspectmay be quantified with the magnitude of the complex modulus, or more preferably

FIGURE 5.15 Effect of test temperature on dynamic modulus of Cheddar cheese made frompasteurized and raw milks. PS: Cheese made from pasteurized milk and aged 470 days; PM:Cheese made from pasteurized milk and aged 240 days; RS: Cheese made from raw milkand aged 475 days; RM: Cheese made from raw milk and aged 246 days. (After Rosenberget al., 1995.)

4

5

6

403020100

Temperature (°C)

log

G*

(Pa)

PSPMRSRM


with the complex viscosity, at that transition temperature as well as the temperaturedependence of the complex viscosity. The relationship between complex viscosityand complex modulus is given above by Equation (5.10). Figure 8.38 (Chapter 8)compares the softening point of cheeses measured by different tests, including usingSAOS crossover modulus (Figure 5.5).

As an objective method for meltability, Ustunol et al. (1994) applied SAOS toCheddar cheese of different fat contents and correlated the complex modulus withmeltability measurements from the traditional empirical test (i.e., Arnott test). Exceptfor the very low-fat Cheddar cheeses (12.6 and <1% fat) that did not melt uponheating, the meltability of Cheddar cheese decreased with decrease in fat content.More results from this study are given in Chapter 8. Ustunol et al. (1994) pointedout that the G′ is greater than the G″ prior to melting, and the opposite is valid aftermelting. This observation gives support to the proposal of using tan δ = 1 as acriterion for detection of the transition temperature in meltability.

Reduction in the fat content of cheese has a direct impact on texture, flavorprofile, functional properties, and thus overall acceptability (Olson and Johnson,1990; Fife et al., 1996). During the past two decades, the demand for reduced-fatand low-fat dairy products and other foods has been rising due to consumer concernsfor health and dietary fat intake (Mistry, 2001). As a result, the legal standards ofidentity for cheeses containing a reduced amount of fat have also developed(Table 5.6). Meanwhile, the cheese industry has been dealing with the challenge ofproducing good-quality, reduced-fat cheeses that meet the consumer expectations.The consumers expect reduced-fat cheeses to have the functional and organolepticcharacteristics of their traditional regular-fat counterparts. This challenge hasprompted many investigations to understand and improve rheological properties of

TABLE 5.6Description of Terms Used to Classify Cheese with Reduced-Fat Content

In United States In Codex

Fat-free: Less than 0.5 g fat per reference amount and per labeled serving size and no added fat or oil ingredient

High fat: >60% fat on dry basis

Low fat: Maximum 3 g total fat per serving for serving size of more than 30 g or more than 2 tablespoons. 3 g or less of fat per 50 g product if serving size is 30 g or less or 2 tablespoons or less

Full fat: 45–60% fat on dry basis

Light or Lite: If less than 50% of calories come from fat: minimum 33 1/3% reduction in calories per reference amount or minimum 50% reduction in fat per reference. If more than 50% of the calories come from fat: minimum 50% reduction in fat per reference amount.

Medium fat: 25–45% fat on dry basis

Reduced fat: Minimum 25% reduction in total fat per reference amount

Low fat: 10–25% fat on dry basis

Skim: <10% fat on dry basis

Source: After Mistry, 2001. With permission.


reduced-fat cheeses (Tunick et al., 1993; Tunick et al., 1995; Bryant et al., 1995; Maet al., 1996; Ma et al., 1997; Rudan et al., 1998; Guinee et al., 2000).

Venugopal and Muthukumarappan (2001) conducted SAOS measurements intime-sweep mode while heating and cooling Cheddar cheese to simulate conditionsduring preparation and consumption of foods containing cheese, for instance, pizza.Dynamic moduli of Cheddar cheese with 8.2 and 28.4% fat contents are measuredas a function of temperature during melting and subsequent solidification. It is seenthat a temperature hysteresis forms between heating (melting) and cooling (solidify-ing) curves. For Cheddar cheese with 8.2% fat content the moduli values duringcooling are always higher than those during heating. The response is different,however, for Cheddar cheese with high-fat content (28.4%). In this case, G′ and G″during cooling are greater than those during heating only at temperatures above~43°C. Furthermore, it is observed that the slopes of G′ and G″ vs. temperature ofhigher-fat cheeses (22.8 and 28.4% fat) are steeper than those of lower-fat cheeses(8.2 and 16.5% fat). This is consistent with the results of Ustunol et al. (1995) wherethe fat content varied from 13 to 34%. The rheological differences of low-fat andhigh-fat Cheddar cheeses (i.e., more elastic character of low-fat type) certainly affectfunctionality and consumer acceptance of these products, in a negative way forreduced-fat cheese.

Heating causes the cheese to melt and release fat, and therefore alter the originalstructure. Melted fat may coalesce and result in separation of fat from the proteinmatrix. This causes the undesirable effect of oiling-off or fat leakage. The resolidifyingof fat during cooling may cause a less homogeneous distribution of fat and significantalteration in the cheese structure. It was also reported that both G′ and G″ decreased,as expected, with aging. The decrease in G′ is linked to proteolysis and that in G″ towater binding by ionic groups liberated in proteolysis, which presumably reducesavailability of water to act as a lubricant (Venugopal and Muthukumarappan, 2001).

The heat-induced changes on viscoelasticity of 5-day-old Cheddar-type cheesesof different fat contents have been recently reported (Guinee et al., 2000). Asexpected, increasing the temperature causes a large decrease in G′ and thus anincrease in the phase angle (δ) of Cheddar cheese at different fat levels. This meansthat temperature effect on G″ is not as severe as that on G′. Much of the changestake place within the temperature range from 20 to 45°C. The factors that may affectthe heat-induced softening of cheese, as evidenced by the reduction in G′, can be(a) melting of milk fat and (b) an increase in para-casein solvation or hydration(Guinee et al., 2000). It is known that milk fat is fully liquid above 40°C andcompletely solid below –40°C (Mulder and Walstra, 1974). Prentice (1992) com-mented that at low temperatures the fat globules are mainly solid and contribute tothe rigidity of the casein matrix. At intermediate temperatures the fat is plastic andcontributes to the rheological properties in a complex way. At 20°C and above mostof the fat (nearly 80% of fat in milk) is already liquid, and it adds little to thefirmness. It is interesting, however, to note that very low-fat cheese (1.3% fat) madefrom skim milk exhibited a greater decrease in G′ within this temperature range ascompared to those with higher fat contents. This result indicates that between 20 and40°C, more than the melting of fat, other factors such as solvation of protein arelikely to govern the thermal softening of the cheese. Results of Guinee et al. (2000)


further indicate that effect of fat reduction on rheological properties is better moni-tored via G′ at temperatures less than 50°C, and via the phase angle (δ) at tempera-tures greater than 50°C.

Ma et al. (1996) compared viscoelastic properties of Cheddar cheeses of full fat,reduced fat, and reduced fat with added lecithin. The full-fat Cheddar cheese at 20°Cpossessed greater G′ and G″ than the reduced-fat kind with or without lecithinaddition. These authors did not specify the fat contents of the samples. However, ifwe assume that the fat content of cheese is about 10 times the amount of fat in milk,we can estimate full-fat samples to contain 32%, and reduced-fat samples to contain21% fat. Addition of lecithin, irrespective of the level (0.2 or 0.5%), contributes tothe elastic part of the reduced-fat Cheddar cheese but not sufficient to fully simulatethe full-fat kind. Results of Ma et al. (1996) regarding the effect of fat reduction ondynamic moduli are not in agreement with the other studies. For instance, anexamination of the data of Ustunol et al. (1995) reveals that at 30°C (lowest in thatstudy) the values G′ and G″ for 34%-fat cheese is smaller than those for 20%-fatcheese. Similarly, at 20°C, Guinee et al. (2000) reported nearly twice the G′ valuesfor very low-fat (1.3%) cheese than full-fat (30%) cheese. The discrepancies inresults of different studies are probably due to the difference in fat content (32%vs. 21% and 30% to 1.3%), the exact ratio of solid-to-liquid fat at respectivetemperatures (20 vs. 30°C), and thermal history before testing (Guinee et al., 2000).

Another means of reducing the fat in natural and processed cheeses is to use fatreplacers — a group of compounds developed to perform the functions of fat inreduced-fat foods (Drake and Swanson, 1995; Drake et al., 1996). Fat replacers aredivided into two categories as fat substitutes and fat mimetics. Fat substitutes arenonpolar substances with physical and functional properties of fats and oils, excepttaste. They can be used to fully replace the fat for texture and mouthfeel. Fat mimeticsare water-soluble substances that are used to partially replace the sensory andfunctional characteristics of fat (Drake and Swanson, 1995). Both protein-based(e.g., whey protein-based) and carbohydrate-based (e.g., starch-based) fat mimeticsare commercially available.

Ma et al. (1997) compared effects of three types of fat mimetics (dosage: 0.125to 0.5%) on dynamic moduli of Cheddar cheese aged for three months at 7.2°C.The carbohydrate-based fat mimetic (consisting of microcrystalline cellulose, guargum, and carrageenan) better mimics the functions of fat, as judged by the pairwisestatistical comparison of G′ and G″ values for the resulting cheeses. Despite thecontributions from the carbohydrate-based mimetic, the textural characteristics ofreduced-fat cheeses are still inferior when compared to those of the full-fat cheeses.

A recent report shows that attempts to replicate textural characteristics of full-fat Cremoso Argentino soft cheese with elevated moisture content or by addition ofa fat replacer are not successful (Zalazar et al., 2002). Dynamic parameters of G′and G″ are similar for the low-fat cheeses with and without Dairy-Lo fat replacer.But the moduli, particularly G′, for low-fat kind are significantly higher than thosefor full-fat version. It is seen that the sensory panel did not detect the texturaldifferences manifested in the dynamic properties. It is concluded that, good-quality,low-fat Cremoso cheese can be made without fat replacers if 60% final moisturecontent is attained by technological means.


GOUDA CHEESE

Gouda cheese is one of the traditional and most popular Dutch-type cheeses with aclassic shape of flat cylinder with bulging sides. It is produced today in severalcountries around the world (Scott, 1986). The cheese usually contains 49% fat (asFDM*) and 59 to 62% water (as WFFC**), and is matured for one to 20 monthsin the Netherlands (Walstra et al., 1987b; Visser, 1991). Gouda cheese is expectedto contain some round holes evenly distributed over the body, and the number, sizeand shape of these holes are important aspects of its quality (Polychroniadou, 2001).

Since Gouda cheese is produced and consumed worldwide, it is an active subjectof rheological investigations (Culioli and Sherman, 1976; Goh and Sherman, 1987;Luyten, 1988; Luyten et al., 1991a; Luyten et al., 1991b; Dewettinck et al., 1999).

The temperature dispersion of loss tangent for Gouda cheese matured for onemonth had a small peak at around 10°C and a large peak at about 45°C, as seen inFigure 5.16 (Taneya et al., 1979). Moreover, for Gouda cheese aged longer (i.e., threeor five months) the locations of loss tangent peaks occur at higher temperatures. Thedata also indicate that 1-month-old Gouda cheese assumes a more viscous character(i.e., tan δ>1) at above 30°C. On the other hand, this character is observed only after50°C for 3-month-old and 5-month-old cheeses. This is probably related to the highermoisture content (39.9% vs. 32.7 and 33.7%, Table 5.3) of young Gouda cheese.

Luyten et al. (1991b) conducted a comprehensive rheological study on maturingGouda cheese, including its dynamic properties. The tan δ values of Gouda cheeseat different maturation stages varied between 0.3 and 0.4 for frequencies rangingfrom 0.005 and 0.05 Hz. This indicates strong viscoelastic solid character of thecheese. Furthermore, the loss tangent is higher at lower frequencies, showing thateffective bonds in Gouda cheese have a more viscous character at longer time scales.A comparison of the loss tangent between Gouda and Feta cheeses indicates that Feta(tan δ = 0.17 – 0.25) is less viscous than Gouda cheese (tan δ = 0.32 – 0.4) (Wium and

FIGURE 5.16 Dynamic loss tangent of Gouda cheese at different maturation stages. (AfterTaneya et al., 1979. With permission.)

* FDM: fat content in the dry matter.** WFFC: water content of fat-free cheese, when young.

0

0.5

1

1.5

2

80706050403020100

Temperature (°C)

tan d(-

)

1-mo

3-mo

5-mo


Qvist, 1997). Wium and Qvist (1997) suggest that the lower pH of Feta (4.5–4.7) ascompared to that of Gouda (5.2 or higher) is probably the main reason for dominantelastic character of the Feta cheese. It is known that high pH milk gels exhibitsignificantly higher tan δ values as compared to those with low pH values, while amaximum in tan δ may appear at pH 5.2 (van Vliet et al., 1989; Roefs et al., 1990).

Dewettinck et al. (1999) investigated dependence of dynamic rheological proper-ties of commercial Gouda cheese on the sampling location using SAOS technique.The four sampling locations are 2.5, 6.5, 10.5, and 14.5 cm away from the crust.The dry matter content of Gouda increased with the position from 57.09% at thecenter to 58.75% at the crust, and with the cheese age from 58.75% for young(1 to 2 mo) and 67.41 for old (12 mo). The linear viscoelastic strain limit of thecheese with different ages was determined to be 1%. This value is lower than therange reported by Luyten et al. (1991b). The storage and loss moduli both changedduring ripening in such a way that tan δ remained constant. This result is explainedby the simultaneous and opposing effects of decrease in water and increase inproteolyis (Dewettinck et al., 1999).

The high inventory cost associated with controlled storage during ripening hasstimulated interest in accelerated ripening and resulted in several approaches, eachwith some advantages and disadvantages (Folkertsma et al., 1996). The major eventof ripening is proteolysis that has direct and important influences on the texture andflavor of cheese (Law, 1987).

One of the recent applications to accelerate ripening in cheese is the use of high-pressure treatment. Isostatic high-pressure treatment (up to 1000 MPa) can influenceprotein conformation, and thus alter its functional properties (Messens et al., 1997). Itis reported that the ripening time of Cheddar cheese could be reduced from six monthsto three days using continuous pressures of 50 and 250 MPa at 25°C (Messens et al.,1997). On the contrary, for Gouda cheese, the pressure treatment (50 to 400 MPa) didnot influence the extent of proteolysis assessed by means of various nonspecificmethods. Even the steady application of 50 MPa pressure for three days did notaccelerate ripening of this cheese (Messens et al., 1999). Nevertheless, some texturaldifferences detected manually have prompted a further study of rheological changesin Gouda cheese as a result of pressure treatment (Messens et al., 2000). The dynamicproperties of high-pressure-treated (50 to 400 MPa, one hour) and untreated Goudacheese indicate that pressure treatment leads to a decrease in both G′ and G″, moreso in G′. Since proteolysis and other parameters presumably play no part immediatelyafter pressure release, the changes in dynamic properties are attributed to weakeningof hydrophobic interactions by pressure treatment (Messens et al., 1997; Messens et al.,2000). As the ripening progressed, the differences in rheological (dynamic and creep)and textural properties of treated and untreated samples become smaller and eventuallynot statistically significant at the end of 42-d ripening, indicating almost completefading of pressure effects, or full restoration of hydrophobic interactions (Messenset al., 2000). It is interesting to note that the pressure treatment at 400 MPa for onehour brought about a reduction of about 150 kPa in G′ of Gouda cheese.*

* Units of G ′ and G″ in Figure 1 of the original paper must be kPa instead of Pa (Dewettinck, personalcommunication).


MOZZARELLA CHEESE

Mozzarella cheese is the famous member of pasta filata cheese family. Pasta filatacheeses are characterized by a unique texturization process where the curd is con-tinually kneaded and stretched in hot water until a smooth, fibrous structure isobtained (Reinbold, 1963; Casiraghi and Lucisano, 1991). Traditional Mozzarellacheese, made from high-fat water-buffalo milk, is consumed as a dessert or appetizerin combination with fresh vegetables and cured meat. On the other hand, todayMozzarella cheese is made from cow’s milk and primarily used as an ingredient invarious prepared foods.

Introduction of Mozzarella into the United States at the start of 20th century byItalian immigrants greatly changed the fate of this traditional cheese (Bruno, 1999).

Standards of identity in the U.S. specify four types of Mozzarella cheese accord-ing to moisture and fat contents, as shown in Table 5.7. The low-moisture, part-skimMozzarella cheese makes the greatest proportion and is mainly used as a toppingon pizza. Reports indicate that about 69 and 26% of all cheese manufactured in theU.S. and European Union, respectively, is used as an ingredient (Mann, 2000). Morethan 70% of Mozzarella cheese produced in the U.S. was used for pizza in 1986(Alvarez, 1986; Kindstedt, 1993), and 96% of all American households eat pizzaabout 30 times a year, whether it is frozen, delivered, made-from-scratch, or eatenat pizzerias, (Anon, 1986; Sauber, 1990).

Mozzarella cheese must have certain characteristics for use on pizzas and otherfoods. The desirable characteristics of the cheese in the solid and melted states arecollectively referred to as “functional properties,” which, in a way, express consumerexpectations of how the cheese should perform when used as an ingredient. Thefunctional properties of Mozzarella cheese include shreddability for the solid cheese,and meltability, stretchability, elasticity, free oil formation, and browning for themelted cheese (Kindstedt, 1991; Kindstedt, 1993; McMahon et al., 1993). Clearly,a majority of these functional properties are associated with the rheology of the solidand melted cheese. Hence, there have been many studies on rheological propertiesof Mozzarella cheese and many attempts to relate them to the so-called functionalproperties, as discussed in other chapters.

TABLE 5.7USDA Specifications for Mozzarella Cheeses

TypeMoisture Content

(%)Fat Content (FDMa)

(%)

Mozzarella cheese >52 but ≤60 ≥45Low-moisture Mozzarella cheese >45 but ≤52 ≥45Part-skim Mozzarella cheese >52 but ≤60 ≥30 but <45Low-moisture, part-skim Mozzarella cheese >45 but ≤52 ≥30 but <45

a FDM: fat in the dry matter.

Source: After Anon, 1980.


Dynamic rheological properties of low-moisture, part-skim (LMPS) Mozzarellacheese appear to be first reported by Nolan et al. (1989a; 1989b), where they areused as an objective basis to distinguish between natural and imitation Mozzarellacheeses for purchasing purposes. The specimen slippage due to the lubrication ofcontact surfaces by melting milk fat was of serious concern for proper measurements.For this reason, Nolan et al. (1989b) have taken two critical precautions: (a) bondingof cheese sample directly to the pitted aluminum plates by cyanoacrylate esteradhesive, and (b) checking presence of slippage by following the analytical proce-dure suggested by Yoshimura and Prud’homme (1988). This procedure requiresmeasurements of stress waveforms with at least two gap separations at the samestrain and frequency. Identical stress waveforms from the two gap settings indicatethat no slip is occurring. On the other hand, if the waveforms differ, then slip isoccurring (Yoshimura and Prud’homme, 1988). The data obtained under a differentset of conditions demonstrated that repeatable results with no evidence of slip couldbe obtained with Mozzarella (as well as Cheddar) samples bonded to the aluminumplates of the rheometer with cyanoacrylate resin adhesive. Moreover, it is shownthat up to a 0.5% shear strain amplitude the G* values are almost constant, indicatinglinear behavior in the frequency range 0.1 to 100 rad/s. Further results from Nolanet al. (1989b) are given in the form of equations in Table 5.8. The sensitivity of thecomplex viscosity to added calcium caseinate is significant and used to differentiatebetween natural and imitation LMPS Mozzarella cheeses. Sutheerawattananondaand Bastian (1998) investigated the sample slippage during SAOS experiments forprocess cheeses by varying the gap setting. Their observations are discussed laterin the Processed Cheese section.

Hsieh et al. (1993) investigated changes in dynamic properties of Mozzarellacheese to which various protein fillers are either mixed with the shredded cheeseand then heated, or added during cheesemaking. Figure 5.17 shows variation of tan δwith temperature for Mozzarella cheese mixed with 3% egg white. Among all theprotein-filled Mozzarella cheeses, this one had the highest G′ and G″ values. Thesignificant changes in tan δ occurred between 10 and 25°C and 40 to 60°C, and anearly constant region in between. The addition of egg white seemed to contributemore to the elastic character than viscous character of Mozzarella cheese, and therebyreducing the tan δ in comparison with the control cheese.

TABLE 5.8Dynamic Shear Moduli (20°C) and Complex Viscosity ofNatural LMPS Mozzarella and Imitation Cheeses

Cheese G′′′′ (Pa) G″″″″ (Pa) ηηηη* (Pa.s)

Natural Mozzarella 2.27 × 104 ω0.17 1.03 × 104 ω0.19 3.2 × 10–3 e4100/T

Imitation with 1% Ca caseinate 5.92 × 104 ω0.20 1.98 × 104 ω0.14 —Imitation with 2% Ca caseinate 1.59 × 104 ω0.21 1.98 × 104 ω0.16 5.0 × 10–4 e4750/T

Note: T: absolute temperature (K).

Source: After Nolan et al., 1989b.


Freezing and frozen storage of cheese is practiced to arrest the changes in cheeseduring ripening, to preserve flavor and physical properties, and thus extend shelf-life during marketing, especially those varieties of high-moisture contents (Olson,1982). There are a number of research reports on the effects of freezing and frozenstorage on various functional properties of cheese (Cervantes et al., 1983; Tunicket al., 1991; Viotto and Grosso, 1999). It seems that the effects of freezing on cheesequality are determined by the cheese type and conditions of freezing, frozen storage,and subsequent thawing. Unless frozen rapidly, the cheese may require some tem-pering time to regain desired flavor and, more importantly, functional attributes ofunfrozen cheese (Olson, 1982). It is worth indicating here that a survey of pizzarestaurants in the state of Vermont (U.S.) revealed that nearly all of the pizzarestaurants (96% of 22 respondents) stored cheese in refrigerated condition ratherthan frozen condition (Pilcher and Kindstedt, 1990).

Diefes et al. (1993) investigated the rheological changes in LMPS Mozzarelladuring a commercially usable freeze-thaw protocol. Data from Diefes et al. (1993)are plotted in Figure 5.18 as the loss tangent against frequency. Since the loss tangentrepresents the ratio of energy lost (viscous effects) to energy stored (elastic effects)in a cyclic deformation, it provides an overall picture of changes. The loss tangentat 20°C is always less than unity regardless of the storage treatment. Furthermore,there is a slight decrease in tan δ as the cheese aged either in refrigerated or frozenstorage for 90 days. The difference in tan δ of cheese refrigerated or frozen duringstorage is minimal and seemed to vary with frequency; at low frequencies it is slightlylower for the refrigerated sample than for the frozen sample and opposite at higherfrequencies. It is interesting to note that for similar ages of LMPS Mozzarella, theresults from two studies (Diefes et al., 1993; Nolan et al., 1989b) differ much morethan the difference due to the storage effect. Another point to highlight is that at 20°Cthe LMPS Mozzarella has a more viscous character at shorter time scales (higherfrequencies). An opposite trend has been reported, for instance, by Zoon et al. (1989)for rennet-induced skim milk gels of different pH at 30°C and 0.00159 to 0.159 Hz;

FIGURE 5.17 Temperature dependence of loss tangent for Mozzarella cheese containing 3%egg white. (After Hsieh et al., 1993.)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10 20 30 40 50 60Temperature (°C)

tan

δ (-

)


by Luyten et al. (1991) for Gouda cheese (1 week old to 6 months old) at 20°C and0.005 to 0.05 Hz; and by Ak and Gunasekaran (1996) for LMPS Mozzarella cheese(1 week old to 4 weeks old) at 20°C and 0.005 to 20 Hz. Furthermore, Figure 5.18shows that at 60°C the trend is reversed, and now the cheese has a more viscouscharacter at longer time scales (lower frequencies) at all storage treatments. Anotherinteresting behavior is reported in the literature for casein gels, which are moreliquid-like at 20°C and lower frequencies (0.001 to 1 Hz) but more solid-like at40°C (Roefs, 1986). Besides a host of compositional factors (moisture content,amount and kind of proteins, pH, salt content, etc.), perhaps another factor that maylead to such seemingly opposite results is the range of frequency involved.

For theoretical analysis of loss tangent–frequency relationship, Campanella andPeleg (1997) used discrete relaxation times to calculate the frequencies where the

FIGURE 5.18 Loss tangent profiles at 20°C (upper plot) and 60°C (lower plot) of LMPSMozzarella cheese subjected to different storage treatments. (After Diefes et al., 1993; Nolanet al., 1989b.)

0.2

0.3

0.4

0.5

0.6

0.01 0.1 1 10 100

Frequency (Hz)

tan

δ (-

)Nolan et al.

0

0.5

1

1.5

2

2.5

3

0.1 1 10 100

Frequency (Hz)

tan

δ (-

)

Control: 14-d refrigerated90-d refrigerated90-d frozen

Control: 14-d refrigerated

90-d frozen, 1-d tempered

Nolan et al.90-d frozen, 21-d tempered

90-d refrigerated


loss tangent peaks are observed. They examined a variety of commodities, includinga fresh cheese called tybo Argentino (Bertola et al., 1992). They calculated two losstangent peaks for this cheese at 4.3 × 10–3 and 1.0 × 10–1 Hz using the limitedrelaxation constants. Below and above the peak locations, the loss tangent–frequencyrelationship is, of course, opposite (i.e., increasing and decreasing). Moreover, fora given material the peak can appear at a higher or lower frequency depending onthe material characteristics, which, of course, change with the conditions. It issuggested that the frequency at which a peak appears can be used to evaluate thedegree of solidity of materials: the lower it is the more solid is the material on thecorresponding time scale.

As mentioned before, refrigerated storage of Mozzarella cheese is preferablypracticed in pizza establishments. Although Mozzarella is classified as an unripenedvariety and can be consumed immediately after production, it is well known thatsignificant and desirable changes occur during a brief refrigerated storage. FreshMozzarella cheese melts poorly to a tough and overly elastic consistency, and there-fore is unacceptable for use on pizza (Kindstedt, 1991). It usually takes one to threeweeks of storage for desired functional properties to develop, primarily as a result ofsignificant proteolysis (Kindstedt et al., 1989; Farkye et al., 1991; Kiely et al., 1993).

Ak and Gunasekaran (1996) determined the dynamic rheological properties ofcommercial LMPS Mozzarella cheese during one month of refrigerated storage. Theirresults confirm the expected decrease of G′ and G″ with aging due to limited break-down of protein matrix. One of the significant features of this publication is that Akand Gunasekaran compared the measured G′ values with those calculated from stressrelaxation data using an approximation equation known as the Alfrey’s rule (Tobolsky,1960; Ferry, 1980). This relatively simple and useful procedure generated results inFigure 5.19. Hence, the comparison between measured and calculated G′ values ofMozzarella cheese provides a way of checking the validity of measurements. Theresulting satisfactory agreement (Figure 5.19) is taken to indicate that true materialproperties are measured (Zoon et al., 1990). Interested readers will find many publi-cations on other approximation equations and conversion techniques of varyingcomplexity and precision (Ferry, 1980; Baumgaertel and Winter, 1989; Zoon et al.,1990; Elster et al., 1991; Emri and Tschoegl, 1993; Tschoegl and Emri, 1993). Someof these techniques are integrated into the analysis software of advanced rheometers.

After three weeks of storage at refrigeration temperature, dynamic viscoelasticparameters of Mozzarella cheese made at three cooking temperatures (38, 41, and44°C) are determined using SAOS measurements (Yun et al., 1994). Dynamic para-meters, G′ and G″, are not affected by different cooking temperatures. It is well knownthat within the linear viscoelastic region G′ of Mozzarella cheese is greater than G″.In the nonlinear region, specifically at strain amplitudes of 10% and higher, theviscous contributions became dominant (G″ > G′), most likely due to structuraldamage by large deformations (Yun et al., 1994). This type of shift in behavior is notobserved for Cheddar (60 week old) and Cheshire (20 week old and 60 week old)cheeses although the same strain range (0 to 20%) is examined (Tunick et al., 1990).Applying different cooking temperatures does not result in different proteolyticactivity of the residual coagulant, and therefore the percentages of intact αs-caseinsand β-casein remaining in the cheeses after two weeks of storage at 4°C are similar.


The experimental data from various reports on dynamic rheological propertiesof Mozzarella cheese are compared in Table 5.9. It is fair to conclude that the resultsfrom several studies show good agreement.

MOZZARELLA: TIME–TEMPERATURE SUPERPOSITION EXAMPLE

Here we illustrate a bit tedious but quite simple approach and carry out the TTS(or time–frequency superposition) procedure with the help of a spreadsheet program.Data are taken from Subramanian and Gunasekaran (1997b). The original values ofstorage modulus for low-fat, part-skim Mozzarella are plotted in Figure 5.20 andalso given for 30, 40 and 50°C in Table 5.10, along with columns of some manipu-lations. The last column (log shifted frequency) is plotted against the log G′ values,

FIGURE 5.19 Calculation of dynamic storage modulus from linear stress relaxation datausing the Alfrey’s rule. (a) Shear stress relaxation of LMPS Mozzarella cheese at 20°C. Theslope of the regression line = –2.303 H*. (b) Measured and calculated shear relaxation modulusof LMPS Mozzarella cheese at 20°C. (After Ak and Gunasekaran, 1996. With permission.)

0

20

40

60

80

100

−3 −2 −1 0 1 2 3

log time (s)

G(t

) (k

Pa)

Data

Fitting

1

10

100

1000

0.01 0.1 101 100 1000

Frequency (rad/s)

G′ (

kPa) Measured

Calculated

(a)

(b)


as shown in Figure 5.21. The reference temperature for shifting is chosen to be 40°C.The superposition shown in the figure is obtained by the logarithmic shift factorsof 0.35, 0, and –1 for 30, 40, and 50°C, respectively. Three points shall be noted:(a) shift factor is zero at the reference temperature; (b) size of shifting is differentfor the same temperature difference, that is, the shift factor is temperature dependent;and (c) at a temperature lower than the reference temperature the shift factor isgreater than 1 (i.e., log aT is positive) and smaller than 1 at a temperature higherthan the reference. The entire master curve is shown in Figure 5.22. One may ofcourse obtain better and faster superposition by using more rigorous shiftingschemes, such as those described in Gordon and Shaw (1994).

FETA CHEESE

Feta cheese is the most famous member of the pickled cheese category, whereripening takes place in brine. Feta is a white, soft cheese with a salty and slightly

TABLE 5.9Magnitudes of Linear Viscoelastic Properties for Low-Moisture,Part-Skim Mozzarella Cheese during Refrigerated Storage (ωωωω = 10 rad/s)

Dynamic PropertyNolan et al.

(1989b)Diefes et al.

(1993)Yun et al.

(1994)Ak and Gunasekaran

(1996)

G′ (kPa) 33.6 95.5 58–64 105.7G″ (kPa) 16 34.1 19–21 35.6tan δ (-) 0.48 0.36 0.33–0.35 0.34Test conditions 20°C

0.5% strain—

20°C0.5%

2 weeks

22°C1%

3 weeks

20°C0.5%

3 weeks

FIGURE 5.20 Frequency dispersion of storage modulus (G′) of 1-week-old low-fat, part-skim Mozzarella cheese at indicated temperatures and 0.05% strain amplitude. (After Subra-manian and Gunasekaran, 1997b. With permission.)

1

10

100

1000

0.1 101 100 1000

Frequency (rad/s)

Sto

rage

mod

ulus

(kP

a)

10°C20°C30°C40°C50°C60°C70°C


acid taste. It is traditionally made from sheep’s milk or a mixture of sheep and goat’smilk (Anifantakis, 1991). However, significant amounts of Feta cheese are nowproduced from cow’s milk (Scott, 1986; Tamime et al., 1991).

Many types of pickled cheeses have traditionally been made and consumed forcenturies in the Balkans and the Mediterranean region (Abd El-Salam et al., 1993).Today, Feta cheese is no longer a regional variety but marketed and consumed allover the world (Tamime et al., 1991).

One of the main steps in cheesemaking is the concentration of the major con-stituents by means of whey removal. Ultrafiltration (UF) process offers an alternativeway of concentrating milk before the formation and handling of the curd. It issuccessfully applied in Feta cheesemaking (Tamime and Kirkegaard, 1991).

There are several publications on sensory, textural, and rheological propertiesof Feta cheese (Samal et al., 1993; Pappas et al., 1996; Lalos et al., 1996; Katsiariet al., 1997; Wium et al., 1997; Wium and Qvist, 1997; Sipahioglu et al., 1999), andonly a few of them included dynamic properties (Wium and Qvist, 1997; Wium and

TABLE 5.10Data for Time–Temperature Superposition Example

Temperature(°C)

Frequency(rad/s)

G’(Pa) log frequency log G’

Shifted Frequencylog freq + log aT

30 0.63 62250 –0.202 4.794 0.148

3.14 84650 0.497 4.928 0.847

6.28 96100 0.798 4.983 1.148

31.42 129000 1.497 5.111 1.847

62.83 147000 1.798 5.167 2.148

125.66 168000 2.099 5.225 2.449

40 0.63 54000 –0.202 4.732 –0.202

3.14 74400 0.497 4.872 0.497

6.28 84150 0.798 4.925 0.798

31.42 113000 1.497 5.053 1.497

62.83 128000 1.798 5.107 1.798

125.66 149000 2.099 5.173 2.099

50 0.63 29250 –0.202 4.466 –1.202

3.14 43250 0.497 4.636 –0.503

6.28 51500 0.798 4.712 –0.202

31.42 75500 1.497 4.878 0.497

62.83 87900 1.798 4.944 0.798

125.66 104000 2.099 5.017 1.099

Source: After Subramanian and Gunasekaran, 1997b.


Qvist, 1998). Wium and Qvist (1997) determined rheological properties of threetypes of UF-Feta cheese using uniaxial compression and dynamic testing. Beforewe present some results from this study, it is useful to highlight two important issuesnoted by Wium and Qvist. The first one is related to the effect of loading normalforce (i.e., compression) on the dynamic properties. They stated “a variation of 5%in the size of the gap between the parallel plates, and thereby of the compressionof the sample, may change the moduli by a factor of two (or more).” When experi-mental conditions of dynamic rheological investigations are carefully examined, itis possible to see cases where the gap setting is smaller than thickness of the sample(see Table 5.2), implying that the specimen is actually compressed before the oscilla-tory shear tests.

FIGURE 5.21 Partial time–temperature superposition for G′ of 1-week-old low-fat, part-skimMozzarella cheese with Tref = 40°C. (After Subramanian and Gunasekaran, 1997b. Withpermission.)

FIGURE 5.22 Master curve for G′ of 1-week-old low-fat, part-skim Mozzarella cheese withTref = 40°C. (After Subramanian and Gunasekaran, 1997b. With permission.)

4.4

4.6

4.8

5

5.2

5.4

−1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3

log (ω aT)

log

G′ (

Pa)

30°C40°C50°C

3

3.5

4

4.5

5

5.5

6

−3 −1 1 3 5

Log (ω aT) (rad/s)

Log

G′ (

Pa)


In a recent study, Pearce and Bellmer (2002) showed that higher loading normalforce (20 vs. 5 N) results in greater initial G′ values for commercial Cheddar andMozzarella cheese, among other food products. For instance, the mean initial G′values of Mozzarella cheese loaded to 5 and 20 N were 52 and 62 kPa (i.e., 1.2 times).That ratio for Cheddar cheese is 1.06. Similar but smaller effect of normal force onthe average G″ values is observed (Pearce and Bellmer, 2002). We shall note thatwhenever normal forces are applied to prevent slippage the cheese samples areallowed for stress relaxation to occur before starting the oscillatory measurements(Nolan et al., 1989a; Diefes et al., 1993; Ma et al., 1996; Mounsey and O’Riordan,1999; Messens et al., 2000). However, Pearce and Bellmer (2002) stated that theeffects of loading normal force on some semisolid materials are not eliminated orminimized by simply allowing the sample to rest prior to testing. All these, on onehand, may explain partially the variation in property values reported by separatelaboratories for the same cheese, but on the other hand, and perhaps more impor-tantly, point out the urgent need for standardized test protocols in terms of sampledimension, preparation, contact surface conditions, and so on, as remarked also byWium and Qvist (1997) and Pearce and Bellmer (2002). The second important pointemphasized by Wium and Qvist (1997) is that when the same gap setting is usedwith all samples, the exact weight/size of the individual specimen would affect theresult. This is probably one of the factors contributing largely to the variations indynamic property data from different investigations. To eliminate this source ofvariation, Wium and Qvist (1997) determined the weight of individual specimensand used only those with weights within 1% of the mean.

Returning to the results of Wium and Qvist (1997), we note that the complexmodulus of the three types of UF Feta cheese ranged from 40 to 173 kPa, and theloss tangent (tan δ) varied between 0.17–0.25 (Figure 5.23), indicating more elasticthan viscous character. These two viscoelastic parameters are useful to differentiatetexture among UF Feta cheeses. Drake et al. (1999) also employed SAOS tests on13 commercial and experimental cheeses to inspect if dynamic data can be used todifferentiate firmness of these cheeses. They found out that, in general, the frequency

FIGURE 5.23 Variation of loss tangent with the frequency of oscillation for three kinds ofUF Feta cheeses. (After Wium and Qvist, 1997. With permission.)

0.15

0.2

0.25

0.01 0.1 1 10

Frequency (Hz)

tan

δ (-

)

Tin Feta

Red Brick Feta

Blue Brick Feta


sweep tests are useful to distinguish the cheese types. However, within a cheesetype, especially for commercial cheeses, the differences in G′ and G″ of full-fat andlow-fat kinds are not significant (e.g., Velveeta and Velveeta Lite).

IMITATION CHEESE

Imitation cheeses may offer some significant advantages, such as lower price, flexi-bility to better manipulate functional properties suitable for some applications, andlonger shelf life. The main disadvantages are inferior flavor quality compared to thenatural cheese and an image of being unnatural (Anon, 1989). Many types ofimitation cheese are produced and sold in the U.S., with the major portion ofproduction being Mozzarella, to be used as an ingredient (Graf, 1981; Bachmann,2001). In line with increasing use of ingredient cheese, several investigations on thetextural and functional characteristics of imitation cheeses have been reported (e.g.,Yang and Taranto, 1982; Kiely et al., 1991; Mulvihill and McCarthy, 1994).

Dynamic rheological properties of imitation Mozzarella cheese have lately beenstudied by many researchers (Nolan et al., 1989b; Mounsey and O’Riordan, 1999;Mounsey and O’Riordan, 2001). Nolan et al. (1989b) reported that both elastic andviscous components of the shear modulus increase with 1% addition of calciumcaseinate, but a 2% addition causes a large and unexpected decrease in storagemodulus and an increase in loss modulus. Mounsey and O’Riordan (1999) assessedthe usefulness of dynamic quantities from SAOS tests as indicators of meltabilityfor imitation cheese manufactured with various levels of pregelatinized maize starch.The loss tangent values measured at 22°C decreased from 0.4 to 0.28 when thestarch content increased from 0 to 9%, signifying that the addition of starch resultedin more solid behavior. The increasing starch content also causes considerablereduction in meltability as determined by the modified version of tube method (seeChapter 8). It is further noted that the effect of starch on dynamic viscoelasticproperties is more pronounced at higher temperatures (Figure 5.24).

FIGURE 5.24 Temperature dependency of the loss tangent for imitation cheeses containing0 and 9% pregelatinized starch. (After Mounsey and O’Riordan, 1999.)

0

0.4

0.8

1.2

1.6

20 30 40 50 60 70 80 90 100

Temperature (°C)

Loss

tang

ent (

-)

control with no starch

with 9% starch


In another study, Mounsey and O’Riordan (2001) examined the rheology, melt-ability, and microstructure of imitation cheese as affected by the addition of nativestarches from different sources (maize, waxy-maize, potato, wheat, rice). The useof native starches to partially replace (15%) casein in the control cheese resulted inmarked differences in microstructure of imitation cheese, such as smaller fat glob-ules, better emulsification of fat, and greater disruption of protein matrix. Thesemodifications in the structure decreased meltability of the cheese regardless of thetype of starch added. On the other hand, the effect of starch addition on dynamicproperties of the cheese varied greatly depending on the origin of starch and thetemperature range. Among the different starches examined, the rice starch appearsto have potential to partially replace the casein, as it has the least effect on theproperties of imitation cheese.

QUARG CHEESE

Quarg or Quark is an acid-coagulated (pH 4.6), soft, fresh cheese with high moisturecontent (often 80% or more) (Scott, 1986). It is normally prepared from pasteurizedskim milk, but half-fat and full-fat Quarg-based products with a range of vegetablesand fruits may also be prepared. Other uses of Quarg cheese include blending intoa sauce or dressing, adding to bakery products, and consuming as is at breakfast.Small amounts of rennet are sometimes used in the production of Quarg to obtainfirmer coagula and minimize casein losses during whey separation (Kroger, 1979;Kelly and O’Donnell, 1998).

Kelly and O’Donnell (1998) studied the rheological characteristics of experi-mental Quarg cheese by SAOS. The storage modulus as a function of strain amplitudeis shown in Figure 5.25. The data in this figure indicate that the plasmin hydrolyzedpasteurized milk Quarg cheese has lower G′ values than that treated with potassium

FIGURE 5.25 Strain-sweep test for different experimental quargs. PC: quarg prepared frompasteurized milk; PK: quarg prepared from pasteurized milk containing potassium iodate; PP:quarg prepared from pasteurized milk digested premanufacture with plasmin. (After Kellyand O’Donnell, 1998.)

1

10

100

0.1 1 10

Strain amplitude (%)

Sto

rage

mod

ulus

(kP

a) PCPKPP


iodate prior to pasteurization and acidification. Similar trends, but with lower magni-tudes, are observed for heat-treated Quarg cheeses.

PROCESSED CHEESE

Processed cheese is manufactured by heating and blending comminuted naturalcheeses of different types and maturity into a homogeneous mass in the presenceof an emulsifying agent and other ingredients (Price and Bush, 1974; Caric andKalab, 1987; Zehren and Nusbaum, 1992). The use of other dairy and nondairyingredients in the manufacture of processed cheese make it possible to obtain avariety of textures and functional properties (Rayan et al., 1980; Savello et al., 1989;Kalab et al., 1991).

Taneya et al. (1979) reported on viscoelastic properties of hard and soft pro-cessed cheeses. Their results show that for hard processed cheese, unlike for Cheddarand Gouda cheeses, only a feeble peak appears at about 60°C (Figure 5.26). Thesignificant modification of protein matrix, fat globule clumping, and redistributionof fat during processed cheesemaking (Rayan et al., 1980) are probably responsiblefor the observed differences in dynamic properties of natural and processed cheeses.

As mentioned before, Nolan et al. (1989a) studied dynamic properties ofCheddar and pasteurized process American cheeses as a function of frequency andtemperature. Significant temperature and frequency effects on the complex viscosityof process cheese are observed (Table 5.11). For instance, the complex viscosity at60°C for 1 rad/s is 100 times that for 100 rad/s. It is interesting to note that theelastic character of pasteurized process cheese is dominant even at 60°C, wheretan δ values are below 0.5 (Figure 5.27). This finding is significant, as it shows thatthe criterion used as meltability index for natural cheeses (e.g., temperature at whichtan δ = 1.0) may not be applicable to pasteurized processed cheese.

Meltability of process cheese containing 14-week-old Cheddar and differentemulsifying salts (disodium phosphate or trisodium citrate) has been measuredby dynamic stress rheometry (Sutheerawattananonda and Bastian, 1998) in the

FIGURE 5.26 Temperature dispersion of loss tangent for two types of process cheese. (AfterTaneya et al., 1979. With permission.)

0

0.5

1

−5 10 25 40 55 70

Temperature (°C)

tan

δ (−

)

Soft

Hard


temperature range from 25 to 90°C at a rate of 10°C/min. These researchers cautiouslyshow that there was no more variation in dynamic moduli measured at two gapsettings (2 and 4 mm) if the cheese samples are bonded to the plates with ethyl-2-cyanoacrylate and the exposed cheese surfaces are coated with silicone oil(Figure 5.28). It is further demonstrated that at room temperature both the serratedplates and the cyanoacrylate bonding produce repeatable results, but at highertemperature the former technique gives better repeatability.

The lowest temperature at which the loss tangent became equal to one (i.e., G′= G″) is called the transition temperature and is used as a parameter for quantitativecomparison (Sutheerawattananonda and Bastian, 1998). The process cheese madewith trisodium citrate, TSC, has a lower transition temperature (56.5°C) than thatformulated with disodium phosphate, DSP, (64.6°C). It is also remarked that thetexture of process cheese containing DSP as an emulsifying salt is more elastic thanprocess cheese containing TSC. Considering the ease of flow, the dynamic viscositygraphs of process cheese with TSC and DSP as a function of temperature are shownin Figure 5.29. It is clear that process cheese with TSC has a better overall meltability

TABLE 5.11Equation of Complex Viscosity at Different Frequencies for Pasteurized Process Cheese

Frequency (rad/s)Complex Viscosity (kPa.s)

Equation Evisc (cal/g mol)

1 η* = 1.50 × 10–6 exp(Evisc/RT) 1180410 η* = 1.09 × 10–6 exp(Evisc/RT) 10192

100 η* = 8.65 × 10–7 exp(Evisc/RT) 9138

Note: These equations are valid between 26 and 60°C.

Source: After Nolan et al., 1989a.

FIGURE 5.27 Dependence of loss tangent of pasteurized processed cheese on frequency atdifferent temperatures. (After Nolan et al., 1989a.)

0.1

0.2

0.3

0.4

0.5

10 100Frequency (rad/s)

tan d(-

)

26°C35°C45°C60°C


than that with DSP, as both the transition temperature and dynamic viscosity valuesare lower for the former type. Similarly, Savello et al. (1989), using the empiricalmethod of Olson and Price (1958), report that rennet casein process cheese modelsprepared with DSP have poor meltability, whereas those prepared with TSC meltwell. However, it is further shown that the acid casein cheese emulsified with DSPhas good meltability.

At this point a comparison of complex viscosity results from the two reportsmentioned above may be given. There is considerable difference in complex viscosi-ties from the two studies (Figure 5.30): for instance, at 35°C the process cheese (PC)of Nolan et al. (1989a) has complex viscosity nearly six and three times bigger thanthe process cheeses (PC–TSC and PC–DSP) of Sutheerawattananonda and Bastian

FIGURE 5.28 Storage and loss moduli of process Cheddar cheese measured at 2 and 4 mmgap settings. (After Sutheerawattananonda and Bastian, 1998. With permission.)

FIGURE 5.29 Variation of dynamic viscosity with temperature for process cheeses con-taining two emulsifying salts. DSP: disodium phosphate; TSC: trisodium citrate. (AfterSutheerawattananonda and Bastian, 1998. With permission.)

10

100

1000

0.01 0.1 1 10

Applied stress (kPa)

Mod

uli (

kPa)

G' - 2 mm

G' - 4 mm

G" - 2 mm

G" - 4 mm

2

4

6

8

10

20 40 60 80 100

Temperature (ºC)

ln η

* (

Pa.

s)

DSPTSC


(1998), respectively. The moisture content of process cheeses in the latter study varybetween 38.59 and 39.75%, and pH vary between 5.52 and 5.73. No compositioninformation is given in the former study, but the moisture content can be expectedto be similar based on USDA specifications for processed American cheese. Morethan the moisture, it is probably the difference in pH that causes such large variationsin numerical values of dynamic properties of processed cheese, as also evidenced inthe next paragraph.

Lee and Klostermeyer (2001) have recently reported on the effect of pH on dynamicoscillatory properties of reduced-fat model processed cheese spreads made from sodiumcaseinate. The fat content is largely replaced by water, and the resulting processedcheese spreads have a composition of fat, protein, and moisture as 12, 12, and 73%,respectively. The pH adjustment between 5.0 and 6.0 is made using sodium polyphos-phate salts. The authors report that the visual evaluation of properties of the processedcheese spreads indicate a change from a brittle, soft solid to a sticky liquid with the pHincreasing from 5.0 to 6.0. At high pH the dynamic rheological response of the cheesespread resembles that of a dilute polymeric solution, where the G″ is greater than G′,the moduli increase rapidly with frequency, and the complex viscosity is practicallyindependent of frequency. At low pH the dynamic behavior of the cheese spreadresembles that of a weak gel where the G′ is greater than G″, the moduli weaklydependent on frequency, and the complex viscosity decrease rapidly with frequency(Ross-Murphy and Shatwell, 1993). The remarkable changes in rheological behaviorof processed cheese within one pH unit are probably related to protein–protein andprotein–water interactions (Lee and Klostermeyer, 2001). The increase in pH results ina decrease in protein–protein interactions and an increase in hydration of proteins, allof which lead to an increased liquid-like behavior (Figure 5.31). In this figure, it canbe noticed that for the same pH the reduced-fat model spread (20°C) has a considerablyhigher tan δ value than process Cheddar cheese (23°C). It is also of interest to remarkthat at 92°C the tan δ values of process Cheddar cheeses are 1.5 (pH 5.64) and 2.8(pH 5.62), depending upon the emulsifying salt (Sutheerawattananonda and Bastian,

FIGURE 5.30 Comparison of complex viscosity of pasteurized processed cheese from twostudies. (After Nolan et al., 1989a; and Sutheerawattananonda and Bastian, 1998, for PC-DSPand PC-TDC data.)

100

1000

10000

100000

20 30 40 50 60 70

Temperature (ºC)

Com

plex

vis

cosi

ty (

Pa.

s)

PCPC-DSPPC-TSC


1998), whereas that of reduced-fat cheese spread at 20°C and pH 6.0 is about 4.0(Figure 5.31). These results assert the importance of accurate pH control for obtainingand maintaining the desirable textural and rheological properties of processed cheese.

COX–MERZ RULE

The similarity between the shear rate dependence of the steady shear viscosity, ηand the frequency dependence of the complex viscosity, η*(ω) has lead to anempirical correlation known as Cox–Merz rule (Cox and Merz, 1958). TheCox–Merz rule can be expressed as:

(5.18)

The rule is unusual, as it relates a linear viscoelastic property to a nonlinearproperty. It has, however, been found to be valid for a variety of polymer melts andsolutions (Dealy and Wissbrun, 1989; Ferry, 1980). Doraiswamy et al. (1991)showed that by using effective shear rates the Cox–Merz rule is applicable toproducts with yield stress. This is also reported to be valid for tomato paste (Raoand Cooley, 1992).

The main utility of the rule is probably for estimating steady shear viscosity,particularly at high shear rates, from oscillatory measurements. Of course, one canas well predict dynamic viscoelastic properties from the steady shear viscosity. Inboth cases only the steady state values are used.

For food materials, Bistany and Kokini (1983) reported that many products (e.g.,whipped cream cheese, butter, margarine, ketchup) do not obey the Cox–Merz rule,where the complex viscosity is greater than the steady shear viscosity. Moreover,

FIGURE 5.31 Effect of pH on loss tangent of reduced-fat caseinate processed cheese (afterLee and Klostermeyer, 2001) and processed Cheddar cheese (after Sutheerawattananonda andBastian, 1998).

0

1

2

3

4

5 5.2 5.4 5.6 5.8 6

pH

Loss

tang

ent (

-)reduced-fat

regular

γ

η γ η ωω

ω γ

˙ *

˙

( ) = ( ) = ′′ + ′′′

=

G G

G1

2


the Cox–Merz rule is also not followed by stirred yogurt (Skriver, 1995). Bistanyand Kokini (1983) further showed that using the following modified form of theCox–Merz rule, the complex viscosities of fluid and semisolid foods are correlatedwell to their steady viscosities:

(5.19)

where, C and α are constants to be determined experimentally.Recently, Yu and Gunasekaran (2001) examined the applicability of the

Cox–Merz rule or its other forms to a variety of foods, including cream cheese,Mozzarella cheese, and process cheese. Their results show that for cream cheese at30 and 35°C, the generalized Cox–Merz rule (Equation 5.19) gives satisfactorycorrelation between dynamic and steady shear vicosities (Figure 5.32). On the otherhand, for Mozzarella and process cheeses tested at 60°C, the resulting data do notpermit any Cox–Merz type relation to be established. For these cheeses, a sharpdrop in steady shear viscosity (Figures 5.33 a and b) is observed when shear rate isbetween 1 s–1 and 10 s–1. The reason for failure of the Cox–Merz rule or its variantsin Mozzarella and process cheeses is not clear. Sample slippage at the rheometerinterface due to free-oil formation during melting is a possibility. However, somematerial property may be in play as well. Aubry et al. (2000) observed a sharp dropin steady shear viscosity in associating polymer solutions and attributed it to theexistence of clusters of associating polymers (microgel) that behave like soft particlesin a low viscous dispersing medium once the associative network is destroyed.

FIGURE 5.32 Steady shear apparent viscosity and complex viscosity data and fit of generalizedCox–Merz rule for cream cheese at 30°C. (After Yu and Gunasekaran, 2001. With permission.)

η ω η γα

ω γ* ˙

˙( ) = ( )[ ]

=C


The utility of the Cox–Merz rule has led researchers to seek similar relationshipsbetween other rheological quantities; for instance, prediction of the first normalstress coefficient from dynamic moduli (Laun, 1986; Al-Hadithi et al., 1992).

(a)

(b)

FIGURE 5.33 Steady shear apparent viscosity and complex viscosity data for Mozzarellacheese (a) and processed cheese (b) at 60°C. (After Yu and Gunasekaran, 2001. With permission.)


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Nonlinear Viscoelasticity of Cheese

When the current state of stress of a material depends on both its current rate ofdeformation and its past history of deformation, the material is said to be viscoelastic.When a material is only slightly perturbed from its equilibrium state it generallyexhibits a type of behavior called linear viscoelasticity, for which the rheologicalmaterial functions are independent of strain amplitude. Curves of frequency-depen-dent storage modulus,

G

′

(

ω

) and loss modulus,

G

″

(

ω

) are commonly used to describelinear viscoelastic behavior.

As discussed in the previous chapter, linear viscoelasticity is ideally suited toprovide information to understand material structure and its implications on rheo-logical behavior. However, most food-processing operations such as extrusion,mixing of dough, and stretching and molding operation during Mozzarella cheesemaking, etc., involve large and rapid deformations that cannot be modeled using thetheory of linear viscoelasticity. Hence, there is a clear need for measuring nonlinearviscoelastic properties. Moreover, many important rheological phenomena are com-pletely absent from the predictions of linear viscoelastic theory. These effects areobserved even in the simplest flow types such as simple steady shear, with linearbehavior observed only at very low shear rates. The most predominant and oftenobserved among the nonlinear phenomena are the nonzero first normal stressdifference and the dependence of the viscosity on shear rate. The first normal stressdifference gives rise to the Weissenberg effect — the tendency of the free surfaceof an elastic liquid to rise around a partially immersed rotating rod. Another nonlineareffect is the dependence of the relaxation modulus on strain magnitude. These effectsare interesting and give rise to curious and fascinating phenomena. However, theycomplicate the representation of nonlinear data. Additional parameters such as shearstrain or shear rate must be introduced, and in other cases, entirely new materialfunctions must be defined (Dealy and Wissbrun, 1990).

The deformations involved in nonlinear viscoelasticity are neither small norslow. The distinction between the linear and nonlinear viscoelasticity is schemati-cally represented in terms of the rate and extent of the deformations involved by aVenn diagram in Figure 6.1. The material response to an imposed deformationdepends on size, rate, and kinematics of the deformation. This means that to duplicateresponses in a particular type of deformation, the magnitude, rate, and kinematicsof the deformation must match. Therefore, the Boltzmann superposition principle,the essential condition for linear viscoelasticity, is no longer valid. Sometimes astrain-amplitude dependent complex modulus or complex viscosity is used todescribe nonlinear viscoelasticity if the deviation from linearity is small (Ohta et al.,1987). However, the algorithms usually employed to calculate

G

′

(

ω

) and

G

″

(

ω

) from

6


σ

(

t

) signal from a rheometer cannot discriminate between linear (sinusoidal) andnonlinear responses. Therefore, the software that processes signals from a typicaldynamic rheometer will produce values for material property functions even if thestress is not sinusoidal. For example, cross-correlation gives only the first harmonicof the stress signal, even if higher harmonics are present (Dealy and Wissbrun, 1990).Therefore, it is essential to look at unprocessed stress signal to detect nonlinearity.

PIPKIN DIAGRAM

Material behavior at various frequency-strain amplitude (

ω

–

γ

0

) regimes can bedepicted in a general way. This was first proposed by Pipkin (1972). In fact, Pipkinplotted (Figure 6.2) a dimensionless quantity,

λω

(the Deborah number) vs. a charac-teristic strain amplitude which is also dimensionless, A (=

λ

, the Weissenbergnumber). Where

λ

is the relaxation time of the sample and (=

ωγ

0

) is the strainrate amplitude. The Deborah number represents the extent to which elastic or memoryeffects will play a role in a fluid’s response, i.e., high Deborah number correspondsto solid-like behavior. The Weissenberg number measures the extent to which aniso-tropy, i.e. nonlinearity, will be exhibited in the response, i.e., large Weissenbergnumber means high nonlinearity. Later, Tanner (1985) suggested plotting

ω

vs. and named it the “Pipkin diagram.” A schematic of the Pipkin diagram is shown inFigure 6.3. It is important to note that this diagram is not drawn to scale, and theregions of viscometric flow and linear viscoelasticity are in reality very narrow.

At low frequencies, because the shear rate varies slowly with time, the defor-mation approaches that of simple, steady shear. Thus, in the zone along the left sideof the Pipkin diagram, the flow is governed by viscometric functions. Under thiscondition, if the shear rate amplitude is also small (i.e., near the origin) the flowwill be Newtonian. The boundary of the viscometric flow is depicted by a verticalline, though in reality the line may bend to the right toward the top of the diagram

FIGURE 6.1

Venn diagram to illustrate the region of linear and nonlinear viscoelasticity withrespect to S = small strain; L = low strain rate. (After Tariq, 1998.)

Nonlinear Viscoelasticity

Linear Viscoelasticity

S L

Linear: L c S c (L 1 S)Nonlinear: (L c S)N

γ 0

γ 0

γ


FIGURE 6.2

Different flow regimes presented by Pipkin (1972). (A = Wiessenberg number;

ω

= test frequency;

λ

= sample relaxation time.)

FIGURE 6.3

Pipkin diagram. (After Dealy and Wissbrun, 1990.)

Navier-Stokes(Newtonian)

Linear Viscoelasticity InfinitesimalElasticity

Vis

com

etric

Flo

w

Fin

ite E

last

icity

?

ωλ0 ∞

A

∞

Frequency (ω)

Str

ain

rate

am

plitu

de (

ωγ o ) Nonlinear Viscoelasticity

Newtonian

Vis

com

etric

Flo

w

Non

linea

r E

last

icity

Linear Viscoelasticity

Constant γ o

Line

ar E

last

icity


(i.e., at high ). This is because viscosity and effective relaxation time decrease as increases (Dealy and Wissbrun, 1990).

As the frequency is increased, the stress will begin to lag the strain, as thematerial will exhibit viscoelasticity. Identifying the boundary between the linear andnonlinear viscoelasticity is of interest. It has been shown, using the fundamentalconcepts of continuum mechanics, that strain rate amplitude ( ) governs the depar-ture from linearity at low frequencies, and strain amplitude (

γ

0

) governs the onsetof nonlinearity at high frequencies (Astarita and Jongschaap, 1977, 1978; Dealy andWissbrun, 1990). On the Pipkin diagram,

γ

0

is constant along straight lines runningthrough the origin. One such line is depicted on Figure 6.3 is the boundary betweenlinear and nonlinear viscoelasticity. The region of nonlinearity is rather large.According to Pipkin (1972), nothing very systematic is known about this region,and he placed a question mark to indicate many phenomena still not clearly knownin this region (Figure 6.2). Pipkin also remarked that a kind of equation that woulddescribe the nonlinear viscoelastic behavior is stress as an analytical function ofstrain increments.

At very high frequencies the response becomes more and more elastic. The region,along the right-hand side of the Pipkin diagram, represents this nondissipative (purelyelastic) response. Increasing

γ

0

in this zone, i.e., getting into the nonlinear visco-elasticity zone, it has been suggested that there may be a region where stress issinusoidal, but the amplitude ratio and loss angle depend on the strain amplitude(Dealy and Wissbrun, 1990). This region is marked as nonlinear elasticity on thePipkin diagram. It has been suggested that at some critical strain amplitude, for moltenmaterials the melt will slip at the wall, causing the stress signal to become erratic inoscillatory shear (Hatzikiriakos and Dealy, 1991). Therefore, when the slip happens,it may be difficult to distinguish the effects of slip and nonlinear viscoelasticity.

SLIDING PLATE RHEOMETER

The nonlinear viscoelastic measurements are rare in food literature. It is due, at leastin part, to the limitations of the available instruments to accurately create andmeasure nonlinear viscoelasticity. Also, there is a lack of suitable theoretical frame-work to describe and analyze nonlinear material behavior. Nonlinear viscoelasticproperties of cheese and other polymeric materials can be measured using an instru-ment that can generate large, uniform, transient deformations involving high shearrates. Such a rheometer is particularly useful for studying time-dependent structuralchanges in rheologically complex food materials such as cheese, bread dough, etc.The commonly available rotational, parallel-disk, or similar rheometers are notsuitable for this purpose. These rheometers generate heterogeneous flow fields nearthe sample edges at high shear rates, which can cause significant errors in materialproperty determination. The relative advantages and disadvantages of several rheo-meter geometries for large strain oscillatory shear (LAOS) measurements to studynonlinear viscoelasticity are summarized in Table 6.1.

Giacomin et al. (1989) developed a sliding-plate rheometer (SPR). As required,this rheometer can generate large, uniform, transient deformations involving highshear rates. It was developed for studying nonlinear viscoelasticity of molten plastics,

γγ

γ


concentrated polymer solutions, raw elastomers, and other viscoelastic or thixotropicmaterials. A schematic diagram of SPR is presented in Figure 6.4. An importantfeature of SPR is the flush-mounted shear-stress transducer in the stationary platethat comes in contact with the sample. Using this, the shear stress can be measuredlocally in a region of uniform deformation, away from free boundaries, and henceavoid errors due to flow heterogeneity near the edges. Therefore, this rheometer canalso be called a true shear sliding-plate rheometer. The SPR employs a computer-controlled servo-hydraulic linear actuator to generate user-programmed deformations.The shear stress and displacement of the sliding plate can be measured. The shearstrain is simply the plate displacement per gap thickness. Unlike the parallel-diskflow (parallel-plate configuration available) and sliding-cylinder flow (concentriccylinder configuration) that generate a heterogeneous flow field, sliding-plate flowgenerates homogeneously simple shear, except near the edges of the sample due to

TABLE 6.1Advantages and Disadvantages of Different Rheometer Geometries forLAOS Measurements

Rheometer Geometry Advantages Disadvantages Reference

Cone-and-plate Homogeneous flow field; suitable for strain amplitudes less than one

Large strains cause sample outflow, degradation, and fracture at edges; normal stress effects distort free boundary

MacSporran and Spiers, 1984; Pearson and Rochefort, 1982

Parallel disk Suitable for small strain measurements in the linear viscoelastic region

Heterogeneous flow field; sample outflow and degradation at edges leading to fracture; normal stress effects distort free boundary

MacSporran and Spiers, 1984; Powell and Schwarz, 1979

Concentric cylinder

Nearly homogeneous flow field at small strains

Weissenberg effect causes severe distortion of free boundary at strains greater than 10

Onogi et al., 1970, 1981; Dealy et al., 1973

Sliding cylinder Nearly homogeneous flow field at small strains

Large strains cause sample outflow and degradation at edges

Tsai and Soong, 1985; McCarthy 1978; Hibberd et al., 1966

Total force sliding plate

Nearly homogeneous flow field at small strains

Edge effects at large strains; error due to friction in guide mechanisms

Liu et al., 1983; Sivashinsky et al., 1984

True shear sliding plate

Homogeneous flow field; can neglect flow heterogeneity near sample edges; prolonged sample life

Limited displacement of sliding plate

Giacomin et al., 1989

Source

: After Giacomin and Dealy, 1993; Tariq, 1998.


LAOS conditions. Degradation near the exposed sample edges does not affect themeasurement until it has penetrated to the sample center. When this diffusionalprocess is slow, the sample life is no longer limited by this effect. Furthermore, theexact size and shape of the sample need not be known. This greatly simplifies samplepreparation and shear stress determination. Only a small sample (few grams) is neededto perform the test. The SPR can generate rapid shear rates (250 s

–1

in a period of2 s) as well as high shear strain (

γ

0

≤

500). The gap thickness of the rheometer isusually 0.25 mm to 2 mm. A larger gap is used to provide maximum resolution ofthe motion-control system for linear viscoelasticity studies, while a small gap is usedto maximize the total shear strain for nonlinear viscoelasticity studies. The samplesare typically 50 mm

×

80 mm

×

1 mm. The sample is positioned so that the transducerface, with a diameter of about 7 mm, is centered. In addition to LAOS, the SPR iscapable of generating many types of nonlinear deformations, such as exponentialshear, step shear, and interrupted shear as well as linear deformations.

LARGE AMPLITUDE OSCILLATORY SHEAR FLOW

The large amplitude oscillatory shear (LAOS) flow occurs usually when strainamplitude,

γ

o

is more than unity. A typical LAOS test conducted on reduced-fat

FIGURE 6.4

Schematic of the true shear sliding plate rheometer. (After Tariq et al., 1998.)

Actuator

Shear StressTransducer

Sample

Sliding Plate

LinearBearings

AdjustableSample Gap


Mozzarella cheese sample at 60°C is illustrated in Figure 6.5. In this case, the stressresulting from an imposed sinusoidal

γ

o

= 6 (i.e. 600% strain) is recorded. It is easyto see that the stress amplitude becomes a standing wave within about four cycles.When nonlinearities are present the stress amplitude will no longer be sinusoidal,as is the case for Cheddar cheese at 40°C at

γ

o

= 4 and 7 (Figure 6.6). Thecompositions of cheeses used in the nonlinear viscoelastic study are listed inTable 6.2, except for the fat-free process Mozzarella cheese, which is store bought.

The LAOS test is particularly useful for characterizing nonlinear viscoelasticity,because the Weissenberg number (proportional to the strain rate amplitude) and theDeborah number (proportional to the frequency) can be varied independently. It isdesirable to be able to use constitutive theories to interpret such responses. Then,the response can be described in terms of parameters of a rheological model.However, there is no unifying theory (such as the Boltzmann superposition theorythat is suitable for linear viscoelasticity) that forms the basis for describing thenonlinear viscoelastic behavior. Therefore, we do not have generally valid formulaefor calculating one material function from experimental data for another. Nonethe-less, several approaches have been taken including those based on continuummechanics and molecular theory. The continuum mechanics theories establish aninitial model based on certain general hypotheses and use experimental data toimprove the model (Tanner, 1985; Larson, 1988). The molecular-theory approachstarts with a model based on the molecular behavior and uses statistical mechanicsto derive a constitutive equation (Bird et al., 1987; Doi and Edwards, 1986). Despite

FIGURE 6.5

LAOS test strain input [

γ

(t), small signal] and stress output signal [

σ

(t), largesignal]. Test conditions: reduced-fat Mozzarella cheese; frequency = 0.4 Hz; T = 60°C; age =1 week. (After Tariq, 1998.)

−25.0

−20.0

−15.0

−10.0

−5.0

0.0

5.0

10.0

15.0

20.0

25.0

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0

Time (s)

γ(t)

; σ(t

) (k

Pa)


FIGURE 6.6

Nonlinearity as observed in the stress amplitude vs. time signal at two largestrain amplitudes (

γ

0

= 4___;

γ

0

= 7----), as they are nonsinusoidal. Test conditions: Cheddarcheese; frequency = 0.4 Hz; T = 60°C; age = 6 week. (After Wang, 1998.)

TABLE 6.2Composition of Cheddar, Mozzarella, and Pizza Cheeses Used in Nonlinear Viscoelasticity Studies

CheeseFat(%)

Moisture(%)

MNFP

a

(%)FDM

b

(%)Salt(%)

S/M

c

(%)Initial

pH

Cheddar 33.0 38.8 57.9 53.9 1.05 2.71 5.14Reduced-fat Cheddar 20.6 43.1 54.2 36.1 2.02 4.69 5.60No-fat Cheddar 1.6 53.3 54.1 3.4 1.94 3.64 5.59Mozzarella 21.7 46.4 59.2 40.5 1.53 3.30 5.21Reduced-fat Mozzarella 7.3 54.0 58.2 15.9 1.61 2.99 5.16Pizza 22.3 47.0 60.5 42.1 1.63 3.47 5.17Reduced-fat Pizza 8.5 54.5 59.6 18.6 1.65 3.30 5.28

a

Moisture in the non-fat portion.

b

Fat in the dry matter.

c

Salt/moisture ratio.

Source:

After Wang, 1998.

−4

−2

0

2

4

She

ar s

tres

s (k

Pa)

0 2 4 6 8 10

Time (s)


the problems in developing models to describe the nonlinear behavior, the abovetechniques are useful as they (Dealy and Wissbrun, 1990):

1. Provide criteria for the appearance of nonlinear effects.2. Predict the nature of the incipient departures from linear behavior.3. Suggest methods for representing the experimental data.

As a result, several constitutive equations have been developed to describe non-linear behavior under LAOS. They include the upper-convected Maxwell (UCM), theBernstein-Kearsley-Zappas (BKZ), the Phan Thien-Tanner (PTT) models, Wagner’sequation, the Doi-Edwards theory, and the Lodge rubber-like liquid model (Baird andCollias, 1995; Giacomin and Dealy, 1993).

For example, the Doi-Edwards theory can predict the behavior for monodispersepolystyrene melts with

γ

o

<1.5 (Pearson and Rochefort, 1982). The BKZ model,Lodge rubber-like liquid model, generalized Maxwell model, and some kineticnetwork theories have been used to interpret the behavior of LAOS for differentmaterials (Giacomin and Dealy, 1993). Giacomin and Oakley (1992) demonstratedthat the UCM model with a structure-dependent relaxation spectrum incorporatingthe three-parameter kinetic rate equation proposed by Mewis and Denn (1983) worksextremely well for molten, low-density polyethylene (LDPE) in LAOS. Giacominand Jeyaseelan (1995) used a simple constitutive theory based on entanglementkinetics, which employs a kinetic rate expression proposed by Liu et al. (1984), tointerpret the LAOS data of seven polyolefins. They also used a structural-networktheory proposed by DeKee and Fong (1992) to study LAOS behavior of high-densitypolyethylene (HDPE) pipe resin containing carbon black.

SPECTRAL ANALYSIS

The spectral analysis is the most direct way to evaluate LAOS data. For nonlinearviscoelasticity,

σ

(

t

) is no longer sinusoidal (Figure 6.5), and, as mentioned before,

σ

(

t

) cannot be described in terms of two functions of frequency [modulus and lossangle or

G

′

(

ω

)

and G

″

(

ω

)]. A few cycles after starting the test, the shear stressnormally becomes a standing wave that can be represented using the Fourier series.For an isotropic material with fading memory, it can be shown that the stress canbe represented as a Fourier series of odd harmonics:

(6.1)

where the amplitudes,

σ

m

(

ω

,

γ

o

), and phase contents,

δ

m

(

ω

,

γ

o

), of the odd harmonicsdepend upon both strain amplitude and frequency. The value of M is normally notgreater than 7.

For a fundamental interpretation of rheological behavior, one requires a consti-tutive equation. These predictions are frequently given in terms of

G

′

(

ω

,

γ

o

) and

σ σ ω δ( ) sin( ),

t m tm m

m odd

M

= +=∑

1


G

″

(

ω

,

γ

o

), which have no unique definitions for nonlinear behavior. It is helpful tohave a general representation of the stress response in LAOS. By separating eachFourier component into in-phase and out-phase parts, and factoring out

γ

o

, a set ofnonlinear viscoelastic moduli can be defined:

(6.2)

According to a number of viscoelastic equations of state, the nonlinear storageand loss moduli,

G

′

n

(

ω

,

γ

o

) and

G

″

n

(ω, γo), can be expanded in odd powers of γo,and stress can thus be represented as:

(6.3)

which conveniently separates the strain dependence from frequency dependence.Algorithms for calculating the discrete Fourier transform (DFT) make it easy toreliably extract the Fourier components from a stress signal even when noisy(Ramirez, 1985).

Typically, LAOS data are analyzed by evaluating and comparing the materialproperties σm (f0, γ0) and δm(f0, γ0) of Equation 6.1, where, f0 = test frequency (Hz).A DFT can be used to determine these material properties as described below.

DISCRETE FOURIER TRANSFORM

The shear-stress signal from the SPR is usually recorded digitally. When stress, σ(t),is sampled N times with a constant time interval, ∆t, a time series of stress, σ(n∆t),is obtained, where n is the time sample index and its range is 0, 1, 2, …, N–1. TheDFT of σ(n∆t) is:

(6.4)

Where, j = √–1, ∆f0 is the frequency resolution, ∆f0 = 1/N∆t, and k is the discretefrequency component index and its range is 0, 1, 2, …, N–1.

The DFT yields a set of complex numbers, the amplitudes and phase contentsof which are:

(6.5)

σ γ ω γ ω ω γ ω(t) [G )cos(m t)]m 1,odd

= ′ + ′′=∑0 0 0m mm t G( , )sin( ) ( ,

σ γ ω ω ω ω( ) [ ( )sin( ) ( ) cos( ), ,

t G n t G n tn odd

mn mn

m odd

n

= ′ + ′′=

∞

=∑ ∑0

1 1

σ σ π σ πd

n

N

k fN

n tkn

Nj n t

kn

N( ) ( )[

cos] ( )[

sin]∆ ∆ ∆0

0

11 2 2= −

=

−

∑

σ σ σd d dk f k f k f( ) Re [ ( )] Im [ ( )]∆ ∆ ∆02

02

0= +


(6.6)

Where Re and Im are the real and imaginary parts, respectively.

DETERMINING MATERIAL PROPERTIES

The material property, σm defined in Equation 6.1 can be inferred from the amplitudesof σd(k∆f0):

(6.7)

Where, |σd(k∆f0)| is the amplitude of the discrete transform; C is the integer ofcycle analyzed; and m = 1 denotes the fundamental harmonic and occurs at the testfrequency, f0. For a proper LAOS test, the fundamental harmonic should be the onlysignificant peak in the shear-strain amplitude spectrum.

Obtaining the phase-shift angles of higher harmonics, σm is an involved process.The command shear-strain wave prescribed to SPR gives nearly perfect, slightlydisplaced sinusoid. Hence, the command and actual shear strain will be slightly outof phase depending on the frequency response of the system. The actual shear strainwill be:

(6.8)

where δγ is its phase content. The phase spectra for the shear-stress signal mustbe corrected with δγ before the material property δm can be determined. A DFT,therefore, must also be applied to the shear strain to obtain δγ . Once δγ is known,δm can be computed (Giacomin and Dealy, 1993):

(6.9)

where, δd(k∆f0) is given by Equation 6.6 for k = mC.Therefore, phase differences for the first three odd harmonics are as follows:

(6.10)

This procedure is called frequency modulation. By convention, reported phase-shift angles are between 0 and 2π radians.

δσσd

d

d

k fk f

k f( ) tan

Im (

Re (∆

∆∆0

1 0

0

=( )( )

−

σ σm d k f k mC= =2 0( );∆

γ γ π δγ( ) cos( )t f t= +0 02

δ δ δγm df k f m0 0( ) = ( ) −∆

δ δ δ

δ δ δ

δ δ δ

γ

γ

γ

1

3

5

3 3

5 5

f f

f f

f f

d

d

d

( ) = ( ) −

( ) = ( ) −

( ) = ( ) −


AMPLITUDE SPECTRUM

The amplitude spectrum, vs. frequency, is plotted for Mozzarella cheeseat two strain amplitudes γ0 = 0.27 and 1.38 in Figure 6.7. At the smaller strainamplitude (γ0 = 0.27), only the first harmonic is detectable, which occurs at the testfrequency f0. When the strain amplitude is increased, the higher harmonics (thirdand fifth) become significant, and occur at the multiples of f0, indicating nonlinearity.The data can also be plotted as σm vs. γ0 and δm vs. γ0 (Figure 6.8). The increase inthe higher harmonic terms is clearly noticeable with increasing γ0. Alternately, σd,γ0, and f can be graphed on a three-dimensional (3-D) plot (Figure 6.9) to providethe combined results of stress vs. frequency and stress vs. strain amplitude. This isvery useful to observe the emergence of nonlinearity as a function of strain amplitudeat different frequencies. The higher odd harmonic components (peaks in Figure 6.9)exceed the signal noise and appear very pronounced as γ0 is increased. The smaller,

FIGURE 6.7 Stress amplitude spectrum for cheese at two strain amplitudes, γ0. At low γ0,only the first harmonic (1) is prominent; at high γ0 third and fifth harmonics (3, 5) are alsoprominent. Test conditions: fat-free process Mozzarella cheese; T = 30°C; frequency = 0.25Hz. (After Tariq, 1998.)

LOG

σm

LO

G σ

m

−3.5

−3.0

−2.5

−2.0

−1.5

−1.0

−0.5

0.00.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

1 γo = 0.27

γo = 1.38

−4.0

−3.5

−3.0

−2.5

−2.0

−1.5

−1.0

−0.50.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

1

3

5

f (Hz)

σd k f( )∆ 0


even harmonics peaks are also observable, which are caused by mechanical inter-ference. Plots like these are helpful to approximate the conditions at which the stressresponse is no longer sinusoidal, and the degree of nonlinearity with respect to strainamplitude (Tariq et al., 1998).

STRESS–SHEAR RATE LOOPS

The above representations based on the Fourier analysis provide a complete mathe-matical description of LAOS data. However, presence of many harmonics makes

FIGURE 6.8 Effect of strain amplitude on the odd (first, third, and fifth) harmonics of stress(σ1, σ2, σ3) and phase angle (δ1, δ2, δ3) for cheese (fat-free process Mozzarella cheese; T = 30°C;frequency = 0.25 Hz) (After Tariq, 1998.)

FIGURE 6.9 Three-dimensional amplitude spectrum for cheese. (fat-free process Mozzarellacheese; T = 30°C; frequency = 0.25 Hz) (After Tariq, 1998.)

σ1

σ3σ5

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0.3 0.5 0.8 1.0 1.3 1.5 1.80.0 2.0

Str

ess

ampl

itude

, σm

(kP

a)

Strain amplitude, γo

δ1

δ3

δ5

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.3 0.5 0.8 1.0 1.3 1.5 1.8 2.0

Pha

se a

ngle

, δm

Strain amplitude, γo

0.5 1.0 1.5 2.0 2.5 3.0 3.54.5

4.05.0 0.5

1.01.5

2.02.5

3.03.5

4.54.0

5.05.5

−1.0

−2.0

0

log

(Str

ess,

kP

a)

Frequency (Hz)

Strain amplitu

de


them rather complex. Therefore, LAOS response is ideally presented as σ(t) vs. γor σ(t) vs. closed loop plots. The σ(t) vs. plot especially allows for a rapidqualitative and quantitative evaluation of the presence of nonlinearity (Tee and Dealy,1975). Such representation can also be used to present small amplitude oscillatoryshear (SAOS) linear viscoelastic data, in which case the loop is ellipsoidal. For thenonlinear case, the presence of higher harmonics distorts the loops and they are nolonger elliptic. The typical stress vs. shear rate loops for different regimes identifiedin the Pipkin diagram are illustrated in Figure 6.10.

In the σm vs. γ0 and δm vs. γ0 plots small, higher harmonic components may beconstrued as insignificant. However, they can profoundly distort the stress vs. shearrate loops signifying the presence of nonlinearity. Another useful feature of the σ(t)vs. plot is that the area inside the loop represents energy dissipated per cycle perunit volume. The cyclic integral of the shear stress with respect to shear strain givesthe energy dissipation per cycle per unit volume, WL (Onogi and Matsumoto, 1981):

(6.11)

Hence, all dissipated energy is in the first harmonic.

FIGURE 6.10 Example stress-shear rate loops for different flow regimes in the Pipkin dia-gram (Figure 6.3). A: Newtonian and linear elastic; B: viscometric flow and nonlinear elastic;C: linear viscoelastic; D: nonlinear viscoelastic.

γ. (s−1)γ. (s−1)

γ. (s−1)γ. (s−1)

σ (k

Pa)

σ (kP

a)σ (

kPa)

σ (kP

a)A

DC

B

γ γ

γ

W dL = =∫ σ γ πσ γ δ1 0 1sin( )


From the second law of thermodynamics, WL ≥ 0. Therefore,

(6.12)

The measured values of phase angle of the first harmonic are always in the first

quadrant, , and by convention, phase angles of higher harmonics lie

between 0 and 2π radians.Figure 6.11 shows the shear stress vs. shear strain rate loops for 6-week-old,

reduced-fat Cheddar cheese tested at temperature 40°C, frequency of 0.4 Hz, andγo from 0.1 to 7. The loop deviates from being an ellipse at γ0 > 0.7 indicatingsignificant nonlinearities at γ0 ≥ 1. The area inside the loops increases with γo,indicating increased energy storage at higher strain amplitude.

Figure 6.12 shows the effect of temperature (40 and 60°C) and test frequency(0.4 and 0.7 Hz) on the σ vs. loops for 6-week-old, reduced-fat Cheddar cheese.At γo = 0.7, the shear stress response at 40°C is about 10 times as large as at 60°C,and the area inside the loop at 40°C is larger, i.e., the cheese retains more of thenetwork structure and can store more energy at 40°C than at 60°C, a logical findingconsidering the effect of heating on cheese microstructure. The effects frequencyshows that, as would be expected, the shear-stress response is larger at the higherfrequency at both 40 and 60°C than at the lower frequency. The results at 60°C show,at both strain amplitudes, at the lower test frequency (0.4 Hz) the distorted ellipseshave sharper ends than those at the higher frequency (0.8 Hz). This result followsthe trends presented in the Pipkin diagram, i.e., at higher frequency (in proper range),the linear viscoelastic behavior covers a larger range.

FIGURE 6.11 Effect of strain amplitude (γ0) on stress-shear rate loops for cheese (6-week-old reduced-fat Cheddar cheese; T = 40°C; frequency = 0.4 Hz). (After Wang, 1998.)

−3

−2

−1

0

1

2

3

She

ar s

tres

s (k

Pa)

She

ar s

tres

s (k

Pa)

−2 −1 0 1 2

Shear rate (s−1) Shear rate (s−1)

0.1

0.2

0.4

0.7

γ0 γ0

−15

−10

−5

0

5

10

15

−20 −10 0 10 20

1

2

4

7

sin δ

δ π

1

1

0

0

≥

≤ ≤

and

021≤ ≤δ π

γ

γ


The σ vs. loops for four cheeses at 40 and 60°C, tested at 0.4 Hz and γo = 0.7,are shown in Figure 6.13. At 40°C, reduced-fat Mozzarella cheese has the highestshear-stress response and area inside the loop (i.e., stronger protein network). Asexpected, the full-fat Cheddar has the lowest stress response and loop area at bothtemperatures. Cheddar and pizza cheeses have similar responses at 40°C, but themagnitude of the pizza cheese responses is higher than that of the Cheddar cheeseat 60°C. The only difference between Mozzarella and pizza cheeses is that pizzacheese was made without the typical mixing and molding process. Thus, the micro-structure of the pizza cheese does not exhibit the usual oriented protein fibers foundin the Mozzarella cheese. This may also explain the relatively larger loop areas forMozzarella compared to pizza cheese at both temperatures.

FIGURE 6.12 Effect of temperature (40°C on left and 60°C on right) on stress-shear rateloops for 6-week-old reduced-fat Cheddar cheese at different test frequencies and strainamplitudes (γ0). (After Wang, 1998.)

FIGURE 6.13 Stress-shear rate loops for different reduced-fat (RF) and full-fat (FF) cheeses(40°C on left and 60°C on right) at 0.4 Hz and γo = 0.7. (After Wang, 1998.)

−0.8

−0.4

0

0.4

0.8

−4 −2 0 2 4−6

−3

0

3

6

She

ar s

tres

s (k

Pa)

She

ar s

tres

s (k

Pa)

−6 −4 −2 0 2 4 6


0.4 Hz, γ0 = 0.4

0.4 Hz, γ0 = 0.7

0.4 Hz, γ0 = 0.4

0.4 Hz, γ0 = 0.7

0.8 Hz, SA = 0.4

0.8 Hz, SA = 0.7

0.8 Hz, SA = 0.4

0.8 Hz, SA = 0.7

−3

−1.5

0

1.5

3

She

ar s

tres

s (k

Pa)

She

ar s

tres

s (k

Pa)

−2 −1 0 1 2


RF Mozzarella

RF Pizza

RF Mozzarella

RF Pizza

FF Cheddar

RF Cheddar

FF Cheddar

RF Cheddar−0.8

−0.4

0

0.4

0.8

−2 −1 0 1 2

γ


The effects of age for reduced-fat Cheddar and Mozzarella cheeses at 40°C areshown in Figure 6.14. For Cheddar, the shear-stress response and the loop areadecreased as cheese ripened from one to six weeks, but the changes are not asnoticeable between six and 12 weeks of aging. In the case of Mozzarella, the agingeffects are noticeable throughout the 12-week aging. The proteolysis-induced caseinnetwork breakdown is responsible for these observations. It has been experimentallyconfirmed that proteolysis of Cheddar cheeses occur more slowly (but over a longertime) compared to the Mozzarella cheese.

EFFECT OF WALL SLIP

Cheese is particularly notorious in posing slippage problems at the sample-machineinterfaces during rheological testing. The melting of fat at temperatures above 35°Cis the main reason for this to occur. The slippage problems during LAOS tests areobserved even at 40°C, especially at high strain amplitudes. This is confirmed by theknotted σ vs. loop for γo = 7, which is not present at γo = 4 (Figure 6.15). Slip alsocauses double peaks (and the resulting knotted σ vs. loop) in stress vs. time curvefor other cheeses (Tariq, 1998). Hatzikiriakos and Dealy (1991) observed similar slip-related distortions in their stress vs. time plots of high-density polyethylene.

CONSTITUTIVE MODEL FOR CHEESE

The Lodge rubber-like liquid model parameters can be determined using the measuredG′ and G″ values. In this model, the Finger tensor, B, is used to generalize theBoltzmann superposition principle and to formulate the following general (materialobjective) theory (Bird et al., 1987):

(6.13)

FIGURE 6.14 Effect of ageing on stress-shear rate loops for reduced-fat Cheddar (on left)and reduced-fat Mozzarella (on right) cheeses at 0.4 Hz and γo = 0.7. (After Wang, 1998.)

Shear rate (s−1)

−8

−4

0

4

8

She

ar s

tres

s (k

Pa)

−2 −1 0 1 2

1 week4 week

6 week12 week

−10

−5

0

5

10

She

ar s

tres

s (k

Pa)

−2 −1 0 1 2Shear rate, (s−1)

1 week4 week

6 week12 week

γγ

ij

t

(t) = m(t t ) σ − ′ ′ ′−∞∫ ijB (t , t ) dt


where, m(t – t′) is called the memory function. The Finger tensor B is:

(6.14)

The relation between the memory function and relaxation modulus of the rubber-like liquid is (Dealy and Wissbrun, 1990):

(6.15)

(6.16)

FIGURE 6.15 Effect of slip on stress-shear rate loops at two strain amplitudes (γ0 = 7 -∇-;γ0 = 4 -•-). (6-week-old full-fat Cheddar cheese; frequency = 0.4 Hz; T = 40°C). (After Wang,1998.)

−4

−2

0

2

4

She

ar s

tres

s (k

Pa)

−20 −10 0 10 20

Shear rate (s−1)

Bij

t t t t

t t=+ ( ) − ′( )[ ] ( ) − ′( )[ ]

( ) − ′( )[ ]

1 0

1 0

0 0 1

2γ γ γ γ

γ γ

G(t) = m t t dt

m t t =d G t t

dt

− ′( ) ′

− ′( ) − ′( )′

−∞∫0

m t t =G t ti

i ii

N

− ′( ) −− ′( )

=∑ λ λexp

1


Where, Gi and λi are, respectively, the initial modulus and relaxation timecorresponding to each Maxwell element in the generalized Maxwell model. UsingEquation 6.15, it can be shown that the relaxation modulus corresponding to thismemory function matches that of the generalized Maxwell model.

For the rubber-like liquid in simple shear, the shear stress, σ(t), is obtainedfrom Equation 6.13:

(6.17)

or

(6.18)

For sinusoidal oscillatory shear flow, γ (t) = γo sin(ωt), the shear stress, σ(t), is thus:

(6.19)

where, s = t – t′.If a generalized Maxwell model is used to represent the relaxation modulus,

(6.20)

then:

(6.21)

(6.22)

where, Gi and λi are the initial moduli and relaxation times corresponding toeach Maxwell element. This is how G′ and G″ can be calculated from Gi and λi.The parsimonious modeling technique by Winter et al. (1993) can be used todetermine the discrete relaxation spectrum.

RELAXATION MODULUS OBTAINED FROM SAOS

The discrete relaxation spectrum (Gi, λi) for 6-week-old reduced-fat Mozzarellacheese obtained by SAOS tests at 40°C and γ0 = 1% is presented in Figure 6.16.Table 6.3 contains the summary of (Gi, λi) data for both Cheddar and Mozzarella

σ σ γ γ(t) (t) = m t t t t dt21

t

≡ − ′( ) ( ) − ′( )[ ] ′−∞∫

σ γ(t) = G t t d tt

− ′( ) ′( )−∞∫

σ γ ω ω ω ω ωt G s s ds t G s s ds to( ) = ( ) ( )

( ) + ( ) ( )

( )

∞ ∞

∫ ∫sin sin cos coso o

G t G ti ii

N

( ) = −( )[ ]=∑ exp λ

1

′( ) = ( ) ( ) =( )

+ ( )[ ]∞

=∫ ∑G G s s dsG

o

i i

ii

N

ω ω ωωλ

ωλsin

2

21 1

′′( ) = ( ) ( ) =( )

+ ( )[ ]∞

=∫ ∑G G s s dsG

o

i i

ii

N

ω ω ωωλ

ωλcos

121


FIGURE 6.16 Discrete relaxation spectrum for 6-week-old reduced-fat Mozzarella at 40°Cand γ0 = 0.01. (After Wang et al., 2001.)

TABLE 6.3Relaxation Spectrum for 6-Week-Old Cheddar and Mozzarella Cheeses Based on Small Amplitude Oscillatory Shear Test Data

CheeseTemperature

(°C)Initial modulus,

Gi (Pa)Relaxation time,

λλλλi (s)

Cheddar 40 1.48 × 105

4.33 × 103

6.79 × 103

6.48 × 103

6.94 × 10–4

7.18 × 10–1

6.80 × 10–2

1.35 × 101

60 6.80 × 105

9.89 × 103

7.95 × 103

1.59 × 104

4.65 × 10–4

4.22 × 100

6.18 × 10–1

9.01 × 10–2

Mozzarella 40 6.12 × 105

1.72 × 104

8.54 × 103

6.96 × 103

5.90 × 103

5.37 × 10–4

6.94 × 10–2

4.40 × 10–1

2.30 × 100

2.73 × 101

60 4.93 × 105

1.40 × 104

3.96 × 103

6.24 × 103

5.32 × 103

3.51 × 102

4.83 × 10–4

6.06 × 10–2

4.11 × 100

3.04 × 10–1

1.09 × 100

1.20 × 102

Source: After Wang et al., 2001.


cheeses at 40 and 60°C. In Figure 6.17 the measured loops (γo = 1, ω = 0.4 Hz) canbe compared with those predicted from the Lodge rubber-like liquid for both Cheddarand Mozzarella at 40 and 60°C. The loops are all elliptical, but at 40°C the theoryoverpredicts by a factor of five for Cheddar cheese and by a factor of ten forMozzarella, and at 60°C by a factor of 20 for both cheeses. Thus, the Lodge rubber-like liquid model, though qualitatively correct, is remarkably invalid for cheeses.

RELAXATION MODULUS CONFORMING TO LAOS

Strain sweep using SPR (Figure 6.18) revealed that at large strain amplitudes, thestress is nearly free of higher harmonics, and its amplitude is again linear with strainamplitude. The slope in this large strain linear regime is lower than that in the lowstrain linear regime. Specifically, when γ0 > 1, the cheese has switched to the largestrain linear behavior.

The predictions using the relaxation spectrum for the large strain linear regimeare in Figure 6.19. The measured σ vs. loops are elliptical at γ0 = 0.2 for bothcheeses at 40 and 60°C. The predicted and experimental σ vs loops match at 60°Cfor both cheeses. At 40°C, the predicted slightly exceed the experimental σ vs. loops for Cheddar cheese, but do not fit the Mozzarella data well. Figure 6.20 showsthe predicted and experimental σ vs loops for Cheddar cheese at 60°C: 0.4 Hzand γo < 1 and γo > 1, respectively. Figure 6.21 shows similar results for theMozzarella cheese. The predicted and experimental data match up to γo = 4 forCheddar, and up to γo = 1 for Mozzarella. Comparing these, we can state that the

FIGURE 6.17 The experimental (•) and predicted (——) shear stress (σ) vs. shear strainrate ( ) loop for Cheddar cheese (on left) and Mozzarella cheese (on right) at (a) 40°C and(b) 60°C using the relaxation spectrum determined from small amplitude oscillatory sheartest at 0.4 Hz and γo = 0.01. (After Wang et al., 2001.)

31−1−3−20

20

−10

10

0

She

ar s

tress

, kP

a

Shear rate, 1/s

(a)

(b)

31−1−3−40

40

−20

20

0

She

ar s

tress

, kP

a

Shear rate, 1/s

31−1−3−40

40

−20

20

0

She

ar s

tres

s, k

Pa

Shear rate, 1/s

(a)

(b)

31−1−3−30

30

−10

10

0

She

ar s

tres

s, k

Pa

Shear rate, 1/s

γ

γγ

γ

γ


FIGURE 6.18 Shear stress vs. shear strain amplitude data for 6-week-old reduced-fat Cheddarcheese at 60°C at 0.4 Hz (top) and 0.8 Hz (bottom) over γ0 = 0.1 to 10. The virtual absenceof 3rd and 5th harmonics indicates linear viscoelastic properties at large strain amplitudes.(After Wang et al., 2001.)

FIGURE 6.19 The experimental (•) and predicted (——) shear stress (σ) vs. shear strain rate( ) loop for Cheddar cheese (left) and Mozzarella cheese (right) at (a) 40°C and (b) 60°Cusing the relaxation spectrum determined from LAOS test at the test condition: 0.4 Hz andγo = 0.2. (After Wang et al., 2001.)

1st

3rd

5th

1st

3rd

5th

She

ar s

tres

s, k

Pa

She

ar s

tres

s, k

Pa

Shear rate, 1/s

Shear rate, 1/s

6

3

0

−3

−6

0.6

0.3

0

−0.3

−0.6

−3 −1 31

−3 −1 31

(a)

(b)

She

ar s

tres

s, k

Pa

She

ar s

tres

s, k

Pa

Shear rate, 1/s

Shear rate, 1/s

6

3

0

−3

−6

1.5

0.5

−0.5

−1.5

−3 −1 31

−3 −1 31

(a)

(b)

γ


Cheddar cheese exhibits large strain linear viscoelastic behavior over a wider strainrange than Mozzarella — γo ≤ 4 for Cheddar compared to γo ≤ 1 for Mozzarella.Microstructurally, Cheddar cheese may be considered more uniform and homoge-neous than Mozzarella. The mixing–molding step in the Mozzarella manufacture

FIGURE 6.20 The predicted shear stress (σ) vs. shear strain rate ( ) loops (——) forCheddar cheese at 60°C using the relaxation spectrum determined from LAOS test comparedwith the experimental σ vs. loop (•) at the test condition: 0.4 Hz and strain amplitude(SA), γo, from 0.1 to 0.7 (on left) and γo, from 1 to 7 (on right). (After Wang et al., 2001.)

FIGURE 6.21 The predicted shear stress (σ) vs. shear strain rate ( ) loop (——) forMozzarella cheese at 60°C using the relaxation spectrum determined from LAOS test com-pared with the experimental σ vs. loop (•) at the test condition: 0.4 Hz and strain amplitude(SA), γo, from 0.1 to 0.7 (on left) and γo, from 1 to 7 (on right). (After Wang et al., 2001.)

She

ar s

tres

s, k

Pa

−0.1−0.6 −0.3 0 0.3 0.6

0.1

0SA = 0.1

SA = 0.2

Shear rate, 1/s

She

ar s

tres

s, k

Pa

−0.1−0.2−0.3−0.4

−2 −1 0 1 2

0.40.30.20.1

0SA = 0.4

SA = 0.7

Shear rate, 1/s

(a)

(b)S

hear

str

ess,

kP

a

−1

−0.5

−6 −3 0 3 6

1

0.5

0SA = 1

SA = 2

Shear rate, 1/s

She

ar s

tres

s, k

Pa

−2

−4−20 −10 0 10 20

4

2

0

SA = 0

SA = 7

Shear rate, 1/s

(a)

(b)

γ

γ

She

ar s

tres

s, k

Pa

−0.1

−0.2

−0.3−0.6 −0.3 0 0.3 0.6

0.1

0.2

0.3

0SA = 0.1

SA = 0.2

Shear rate, 1/s

She

ar s

tres

s, k

Pa

−0.4−0.6

−0.2

−0.8−2 −1 0 1 2

0.80.60.40.2

0SA = 0.4

SA = 0.7

Shear rate, 1/s

(a)

(b)

She

ar s

tres

s, k

Pa

−3

−2

−1

−6 −3 0 3 6

3

2

1

0SA = 1

SA = 2

Shear rate, 1/s

She

ar s

tres

s, k

Pa

−4−6

−2

−8−20 −10 0 10 20

86420

SA = 0

SA = 7

Shear rate, 1/s

(a)

(b)

γ

γ


orients the protein fiber structure. The effect of this oriented structure has also beenobserved in other rheological measurements (see Chapter 3).

The large strain linear behavior is equally difficult to explain. It would appearthat at rest (and in small amplitude oscillatory shear), the cheese has one equilibriumstructure, and that in large amplitude oscillatory shear, it converts to another non-equilibrium structure. Whereas the equilibrium structure is independent of smallamplitude deformations, its nonequilibrium counterpart appears to be equally inde-pendent of large amplitude deformations.

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of viscoelastic fluids with a sliding cylinder rheometer executing coaxial displace-ments. Journal of Rheology 29(1):1–18

Wang, Y.-C. 1998. Rheological properties of cheeses at high temperatures. Ph.D. Thesis,University of Wisconsin-Madison, Madison, WI.

Wang, Y.-C., S. Gunasekaran, and A.J. Giacomin. 2001. The Lodge rubberlike liquid behaviorfor cheese in large amplitude oscillatory shear. Journal of Applied Rheology11(6):312–319.

Winter, H.H., M. Baumgaertel, and P.R. Soskey. 1993. A parsimonious model for viscoelasticliquids and solids, in Techniques in Rheological Measurement, A.A. Collyer, Ed. NewYork: Chapman & Hall.



Cheese Texture

Texture of foods is a highly subjective human experience with foods during their consumption. It is, in essence, the “eating quality” of foods encompassing many properties of foods that excite our senses of sight, touch, and sound. The International Organization for Standardization (ISO, 1992) defines texture of a food product as, “all the rheological and structural (geometric and surface) attributes of the product perceptible by means of mechanical, tactile, and, where appropriate, visual and auditory receptors.” The textural attributes of foods play a major role in consumer appeal, buying decisions, and eventual consumption. For some foods, texture is more important to consumers than flavor and color (Szczesniak and Kleyn, 1963). In fact, Rohm (1990) indicated, based on several studies, that food texture is the single most dominant attribute for consumer preference of foods. Needless to say, developing “proper” texture is an ongoing industry effort in marketing a variety of foods. This, however, is easier said than done. Developing foods with “proper” texture implies that we know (a) what is the expected texture; (b) how to formulate the product to achieve that texture; and (c) how to measure and characterize texture. Each of these is, and has been, an area of active research.

Texture means different things to different people, and the textural attributes expected from different foods vary widely. The perceived textural attributes of a given food are also influenced by a variety of factors, including one or more of other textural qualities. It has also been established that chewing force and chewing movements are strongly influenced by food texture (Ahlgren, 1966; Kawamura, 1981, Horio and Kamuwara, 1989). Given these, objectively measuring and characterizing texture is a virtually impossible task. Therefore, human sensory evaluation has been the corner-stone of food-texture evaluation. Due to limitations of cost, lack of suitable experience, and subjectivity of the sensory panels, efforts are continually made in designing instrumented methods for texture measurement. These range from simple penetro-meters to measure firmness to sophisticated rheometers to determine the viscosity of the bolus. In this chapter, our focus is primarily on measurement of perceived mechani-cal textural attributes of cheeses during consumption. For general discussions on food texture and sensory texture evaluation methods, the readers are referred to several recent books and reviews on the subject (Bourne, 2002; Dijksterhuis and Piggott, 2001; Lawless and Heymann, 1998; Rosenthal, 1999; Wilkinson et al., 2000).

TEXTURE DEVELOPMENT IN CHEESE

CHEESE MANUFACTURING FACTORS THAT AFFECT TEXTURE

Texture is the primary quality attribute of cheeses. The overall appearance and mouthfeel of cheeses are appreciated before their flavor (Lawrence et al., 1987).

7


Cheeses offer a variety of textures. For each cheese type, there is an expected dominant textural attribute. For example, Mozzarella cheese is “stretchy” or “stringy” and Parmesan cheese is “crumbly,” etc. A good example of how dominant textural attributes are to quality of cheese is the description of acceptability of Mozzarella cheese on pizza by Kindstedt (1991): “The cheese must melt readily but not excessively so as to become ‘soupy.’ The cheese must exhibit ‘stretchability’ and ‘elasticity’ but should not be ‘tough’ and overly ‘chewy.’” The textural attributes expected of Mozzarella cheese in this description are highlighted by enclosing them within quote marks.

There are literally hundreds of terms used in describing food texture. Many of the terms used in the literature to describe cheese texture are summarized in Table 7.1. Pagliarini et al. (1991) developed a “cheese wheel,” similar to the aroma wheel developed for wine (Noble et al., 1987). The cheese wheel (Figure 7.1) comprises five major sectors: flavor, texture, aroma, appearance, and taste. The sectors are further divided into classes and subclasses to list corresponding sensory attributes.

Major structure-forming constituent in cheese is the casein matrix in which fat globules are entrapped; water or serum is both bound to casein and fills interstices of the matrix (Jack and Paterson, 1992; Hort and Grys, 2001). This network structure is critically affected by the relative content of protein, fat, and water, as well as by the biochemical activities that occur almost continually during storage. The strong interrelationship between food structure and texture is well known (Aguilera and Stanley, 1999). Based on spectroscopic data, Dufour et al. (2001) noted that cheese texture is a reflection of its structure at the molecular level.

During manufacture of cheeses, several factors can contribute to the eventual cheese texture. These include those factors that affect the curd moisture content (scalding temperature, fineness of the curd, duration of stirring, etc.), acidity, and pH. Higher curd scalding temperature leaves the curd springy, and the resulting cheese rubbery (e.g., Emmental) (Jack and Paterson, 1992). Lower pH of milk at the time of enzyme addition or that of the curd at milling results in harder cheese (Jack and Paterson, 1992). Low acidity weakens the protein bonds through charge repulsion, as the negative charges on casein molecules increase with pH. The hydro-phobic interactions, important for a stable casein matrix structure, are weakened by adsorption of water by proteins to solvate the ionic charges. In high-pH cheese, the absorption of water by protein limits the amount of water in matrix interstices. Creamer and Olson (1982) suggested that the high-pH cheese may be considered as concentrated protein emulsion, and the low-pH cheese as porous mass of casein and fat particles. The “shortness” of low-pH cheese and its propensity to crumble are well established (Creamer and Olson, 1982; Watkinson et al., 2001). Higher pH cheese (in pH 5.2 to 6.2 range) is “long” (high fracture strain) and is less adhesive (Watkinson et al., 2001). Lawrence et al. (1987) prepared a schematic representation of the effect of pH on cheese texture based on electron micrographs of protein breakdown during ripening reported by de Jong (1987) and Hall and Creamer (1972). This figure (Figure 7.2) represents the changes in cheese microstructure and the concomitant change in its texture at 14 day after manufacture. As the pH changes from 5.4 to 4.6, the casein submicelles progressively dissociate into smaller aggre-


TABLE 7.1 Different Terms Used in the Literature to Describe Cheese Texture

Sensory Term Definition Reference

Adhesiveness Stickiness of sample in the mouth throughout mastication

Civille and Szczesniak, 1973

Force required to remove the cheese from the palate during eating

Zoon, 1991

Brittleness Breakability of the sample at the first bite Civille and Szczesniak, 1973

Deformation at fracture during slow bending of a stick Wium et al., 1997

Creaminess The extent to which the cheese has a velvety mouthfeel Hort and Grys, 2001The extent to which the texture has broken down to a creamy, semiliquid texture, assessed between tongue and palate during mastication

Cooper, 1987

Crumbliness The ease of fragmenting cheese into small particles Hwang and Gunasekaran, 2001

The extent to which the cheese structure breaks up during the initial two to three chews

Cooper, 1987

Deformation at fracture during first bite of a cheese cube between molars

Wium et al., 1997

The extent to which the sample breaks when chewed or compressed

Hort and Grys, 2001

Tendency to break down readily into small irregular pieces

van Vliet, 1991

Chewiness Number of chews required to swallow a certain amount of sample


Total amount of work necessary to chew a sample to a state ready for swallowing

Meullenet et al., 1997

Length of time required to masticate a sample in order to reduce the consistency satisfactory for swallowing

Zoon, 1991

Cohesiveness Amount of deformation undergone by a material before rupture when biting completely through the sample using molars


Ease with which a sample crumbles Zoon, 1991

Crustiness The force required to break through the crust of the cheese when taking the first bite, assessed using the front teeth

Cooper, 1987

Curdiness The extent to which a curdy or mealy texture perceived in the mouth during mastication

Cooper, 1987

Firmness The force required to compress the cheese with the fingers

Hort and Grys, 2001

The amount of force required to take the first bite of cheese, assessed using the front teeth

Cooper, 1987

Force required to squeeze a cube (1.5-cm × 1.5-cm × 1.5-cm) of cheese flat between the first finger and thumb

Cooper, 1987


The resistance of a cube of cheese to moderate squeezing between thumb and forefinger

Wium et al., 1997

Resistance of a cube of cheese during normal mastication

Wium et al., 1997

Reciprocal of the ease of indentation by teeth van Vliet, 1991

Graininess The extent to which the cheese is bitty towards the end of chewing

Hort and Grys, 2001

Inhomogeneities in the cheese evaluated in the mouth Zoon, 1991

Hardness Force required to penetrate the sample with the molar teeth


Force required to bite completely through the sample when placed between molars


Long/Longness Tendency to fracture only after a relatively large deformation

van Vliet, 1991

Lumpiness Heterogeneous mouthfeeling of sample throughout mastication


Residual Mouth Feel The degree of “bittiness” or graininess in the mouth just before swallowing

Cooper, 1987

Rubberiness The extent to which the cheese returns to its initial form after biting, assessed during the first two chews

Cooper, 1987

Short/Shortness Tendency to fracture at small deformation van Vliet, 1991Slipperiness Related to the flowability of the food in the mouth Omar et al., 1995Smoothness The smoothness of the cheese against the palate as it

breaks down during masticationCooper, 1987

The friction force assessed during the contact of the food with the tongue

Omar et al., 1995

Spreadability Ease of spreading of a cube of cheese with a knife Wium et al., 1997Springiness Degree or rate at which the sample returns to its

original size/shape after partial compression between the tongue and palate


Bouncing property of sample through several consecutive bites


Stickiness Extent to which a cube of cheese sticks to the tongue and palate after normal mastication, just before swallowing

Wium et al., 1997

The stickiness of the cheese against the palate and around the teeth during mastication

Cooper, 1987

Stiffness Resistance to deformation due to an applied force that is insufficient to cause yielding or fracture

van Vliet, 1991

Thickness In-mouth consistency assessed as the force developed by the tongue during the compression of the food between the roof of the mouth and the tongue

Omar et al., 1995

TABLE 7.1 (continued) Different Terms Used in the Literature to Describe Cheese Texture

Sensory Term Definition Reference


gates and eventually into nonlinear strands rendering cheese from springy at high pH (5.3 to 5.4) to noncohesive at pH below about 4.8.

The moisture, salt, and calcium contents of cheese can alter the effect of pH on cheese texture. It is well established that higher-moisture content cheeses, at a given pH and salt content, are less firm than their lower-moisture content counter parts. This has been attributed to the extent of swelling of casein submicelles with the increase in casein-to-moisture ratio. Accordingly, even small variations in moisture content can have significant effect on cheese texture. Olson (1982) reported that Mozzarella cheese with a higher salt content (1.78 vs. 1.06%) is less stringy. A good example of the effect of lower-acidity and higher-moisture curd is the more open texture of Cheshire cheese compared to the closed texture of Cheddar cheese, which is also due to the matting of the curd particle during pressing.

The effect of fat content on cheese microstructure and texture has been widely investigated. The texture of higher-fat cheeses is generally more acceptable than texture of their lower-fat counterparts (Muir et al., 1997). The intricate microstructure

FIGURE 7.1 Cheese wheel showing five major organoleptic sectors and several attributes in each. (After Pagliarini et al., 1991. With permission.)


of Cheddar cheese is altered with a decrease in fat content. Consequently, compared to the microstructure of a regular-fat cheese, the microstructure of lower-fat Cheddar cheese has a more compact protein matrix with less open spaces, which would have been otherwise occupied by fat globules (Bryant et al., 1995). This is associated with hard texture even when the moisture content is high. Reduced-fat cheeses also tend to be more elastic and more adhesive (Emmons et al., 1980; Olson and Johnson, 1990; Bryant et al., 1995). Higher fat and water content tends to weaken the protein structure, and vice versa. Increase in fat content results in smoother and softer cheese, and increase in casein content results in firmer cheese (Chen et al., 1979; Jack and Peterson, 1992; Lawrence et al., 1983; Lawrence et al., 1987; Guinee et al., 2001). Cheeses containing more unsaturated fats have a softer body (Adda et al., 1982). The cohesiveness of cheese decreases with fat content. Reduced-fat Cheddar cheese is springier because of fewer fat globules with more casein being deformed per unit volume. Because lower-fat cheese is springier, it resists deformation and does not rupture easily, and hence it may appear to be more cohesive. Increase in moisture content or addition of water binders generally improves texture of low-fat cheeses (Drake et al., 1996a; Mistry, 2001). The effect of moisture content on springiness is not clear, i.e., both increase and decrease in springiness with moisture content have been reported (Tunick et al., 1991, Bryant et al., 1995, Chen et al., 1979). Thus, the nature of cheese protein matrix rather than the moisture content may be more impor-tant in dictating cheese textural attributes (Bryant et al., 1995).

Despite the fact that there is an extensive literature on the effect of various manufacturing factors on cheese structure and texture, the actual practice of manu-facturing a given cheese of all the stipulated textural attributes is a challenging task due to the complex interrelationships among the many factors involved. A good example is the suggested modifications required for manufacturing harder or softer hard/semihard cheeses presented in Tables 1.7a and 1.7b, respectively.

FIGURE 7.2 Effect of pH on cheese texture. (After Lawrence et al., 1987. With permission.)


TEXTURAL CHANGES DURING STORAGE

Texture of many cheeses change almost continuously after it is manufactured due to the proteolytic action of the residual enzyme. The most notable change with age, due to proteolytic breakdown of the protein matrix, is decrease in fracture strain and springiness and increase in creaminess. In fact, after 64 weeks the Cheddar cheese is very soft, having lost its structural integrity due to extensive proteolysis (Hort and Grys, 2001). Lawrence et al. (1987) list the following three factors as having an effect on cheese texture during ripening: (a) pH at which whey is drained from the curd. This determines the proportions of chymosin and plasmin in the cheese; (b) salt-in-moisture ratio that controls, along with temperature, the activity of resid-ual rennet and plasmin in cheese; (c) pH of cheese after salting. The cheese pH has been described as the single most important factor that influences the texture. The temperature and relative humidity conditions of storage also affect the texture development (Jack and Paterson, 1992). Increasing the ripening temperature from 0 to 15°C results in a significant decrease in the mean concentration of intact casein, a decrease in the level of expressible serum in low-moisture Mozzarella cheese, and concomitant changes in texture and functional properties of the cheese (Guinee et al., 2001). Lawrence et al. (1987) described the effect of these factors with specific case of Cheddar, Gouda, Swiss, and Camembert cheeses. The main factors that determine textural changes in Cheddar cheese during ripening are illustrated in Figure 7.3. Since moisture content of low-fat cheeses is higher, the proteolysis during

FIGURE 7.3 Factors affecting textural changes in Cheddar cheese during ripening. (After Lawrence et al., 1987. With permission.)


storage leaves them more adhesive. However, Braynt et al. (1995) reported low-fat cheese to be less adhesive regardless of moisture content. Kiley et al. (1993) observed a decrease in porosity of the paracasein matrix during ripening attributed to proteo-lysis. The rate of proteolysis is affected by the amount of residual enzymes and native milk proteinases in the cheese post manufacture, salt-to-moisture ratio, pH change, and temperature during ripening. These factors are described in more detail in Lawrence et al. (1987). Some additional discussion is also presented with respect to changes in cheese functional properties in Chapter 10.

The textural changes in cheese during storage may be considered to occur in two phases (Lawrence et al., 1987). In phase 1, the first two weeks after manufacture, there is a rapid change during which the casein network is greatly weakened when only a single bond in about 20% of the αs1-casein is hydrolyzed. The resulting peptide αs1-I causes the initial softening of the cheese (Creamer and Olson, 1982). This peptide is present in all types of cheeses, at least during the early stages of ripening. In phase 2, the period subsequent to the first two weeks, the proteolytic changes are fairly gradual. The extent of textural change during this phase is based on the rate of proteolysis and increase in pH. As each peptide is cleaved, two new ionic groups are generated. This reduces the amount of free water in the matrix by increasing the solvation of the protein chains. Thus, as the Cheddar-type cheese ages, it hardens, and the protein matrix becomes less cohesive (Lawrence et al., 1987; Jack and Paterson, 1992). Hort and Grys (2001) suggested that the changing texture of Cheddar cheese might be divided into three distinct stages corresponding to the commercial classification of mild, medium, and mature Cheddar cheese.

Although Mozzarella cheese is regarded as unripened cheese, it does undergo changes during storage (Kindstedt, 1993). Due to the proteolytic breakdown of αs1-casein in Mozzarella cheese, the protein matrix is both reorganized and weakened, resulting in a softer, less elastic, and more meltable cheese (Tunick et al., 1993; Tunick et al., 1997). The changes in submicelle size and distribution of the casein submicelle could explain some of the textural differences between fresh and stored Mozzarella cheeses, and between cheeses made from homogenized and nonhomog-enized milk (Tunick et al., 1997). Insufficient proteolysis due to high salt content can cause “curdy” texture in Mozzarella cheese (Olson, 1982).

During Feta cheesemaking, a relatively high concentration of rennet is used. This leads to high aggregation rate and a coarse casein network that is responsible for the firm gel and cheese. In the young Feta cheese, this firming effect is greater than the softening effect of proteolysis. But as storage time is prolonged, the proteo-lytic effect increases to an extent that the cheese becomes softer and shorter (Wium et al., 1998; Wium and Qvist, 1998).

MEASUREMENT OF TEXTURE

Since texture encompasses many attributes, it is fairly intuitive that one instrument may not be able to measure all attributes of various foods or not even single food type. Hamann and Webb (1979) and Montejano et al. (1985) demonstrated this in their studies with protein gels; and Breuil and Meullenet (2001) concluded similarly after testing texture of 29 types of cheeses with three instrumental methods. However,


instrumental measurements of “mechanical” characteristics, those that are mani-fested by the reaction of the foods to applied stress (Szczesniak, 1963b), have been correlated with sensory attributes fairly well (Szczesniak, 1968). The 10 most fre-quently used texture terms in the United States are: crisp, dry, juicy, soft, creamy, crunchy, chewy, smooth, stringy, and hard (Szczesniak and Kleyn, 1963). Most of these attributes pertain to the mechanical characteristics of foods.

Texture measurement techniques can be grouped as either subjective or instru-mental. The subjective measurements or sensory evaluation are made by the trained taste panel. The instrumental methods can be broadly grouped under the following three categories (Scott-Blair, 1958): empirical, imitative, and fundamental. None of the methods in each of the above categories may be best suited for measurement of food texture adequately. Bourne (1975a) suggested that an ideal texture-measurement test may include some aspect of empirical, imitative, and fundamental methods.

The empirical measurements are those tests that tend to relate a measured variable to a material property without a rigorous scientific basis (Rosenthal, 1999). The penetrometer, puncture test, and ball-compressor tests are good examples of empirical measurements. The imitative methods, which may also be called semifundamentalmethods, include measurement systems that are used to make mechanical measure-ments with little control of experimental variables (e.g., probe type and size, product shape, etc.). They attempt to mechanically mimic the sensory evaluation of human evaluators. In fact, when the instrumental test used mimics the action of the human assessor, more accurate models of food texture attributes could be developed (Szczesniak, 1987; Hort and Grys, 2000). The test results from imitative tests are analyzed and correlated to sensory perceptions of taste panels without valid structural and molecular-level reasoning. Therefore, the test results, at best, serve as relative measures of textural attributes of products tested. Nonetheless, the imitative methods are perhaps the largest group of instrumented texture-measurement methods. The widely adopted texture profile analysis (TPA) belongs to this group.

The fundamental methods employ valid rheological test techniques, and the data are analyzed using well-defined rheological, structural, and molecular theories. The fundamental test methods also yield results that are independent of test instrument. Some fundamental tests that are popularly used for texture evaluation include uni-axial compression, bending, and torsion tests (see Chapter 2). Steady shear viscosity of liquid foods (at a shear rate of 10 s–1) has been correlated well with the sensory thickness (Cutler et al., 1983) and spreadability (Kokini and Dickie, 1982). A word of caution may be in order here with regards to the now-popular dynamic oscillatory shear rheological measurements. Since such measurements employ small strains, it is unlikely that the test results directly relate to product texture, an inherently large strain fracture property. However, some good statistical correlations between dynamic rheological data and textural attributes have been reported (Drake et al., 1999; Wium and Qvist, 1997; Tunick et al., 1990). Bourne (2002) has described many of the empirical, imitative, and fundamental test methods used for food texture evaluation.

For liquid foods there have been some successful correlations of fundamental measurement of rheological properties and sensory perception of viscosity or thick-ness, smoothness, etc. (Sherman, 1977; Kokini, 1987) and even for soft cheeses (Omar et al., 1995; Daubert et al., 1998). However, solid foods such as most cheeses


present an additional challenge because they require work of mastication before their texture can be perceived, and, even worse, the texture of solid foods changes during mastication. Marshall (1990) attempted to obtain psychophysical relationships between measured physical and sensory properties of processed cheese analogs con-taining different types and amounts of fat. He concluded that mouthfeel of cheeses (and fracture stress and toughness) is influenced by the lubricating properties of the fats. Similar observation was made with processed cheese spreads (Muir et al., 1997).

Rosenthal (1999) notes that most texture measurement instruments focus on one physical property at a time. These piecemeal-wise, single-property measurements seriously limit evaluation of texture as an all-encompassing human experience with foods before and during consumption. Likewise, Bourne (1975b) cautioned that rheological measurements, which often focus on a single, large deformation breaking the sample into pieces, are inadequate in describing food texture. Peleg (1980a, 1980b, 1983) pointed out an important drawback in correlating sensory texture evaluation and instrumental texture measurements. The sensory texture evaluation involves an interaction between the food and the soft body tissues of fingers and mouth. In instrumented measurements, only the food material is deformed. This makes the measured responses to be inherently different from those observed sen-sorially, as confirmed by several researchers. Jack et al. (1993) remarked that even though the instrumental and compositional analyses routinely used in the cheese industry provide data related to texture, the correlations between these and the perceptions of texture by untrained consumers are limited. Therefore, instrumented and other techniques are of restricted value in predicting the product characteristics as perceived by the consumers.

TEXTURE PROFILE ANALYSIS

The texture profile analysis (TPA) was originally developed at the General Foods Corporation Technical Center in the early 1960s (Friedman et al., 1963). This was patterned after the Arthur D. Little flavor profile method (Cairncross and Sjostrom, 1950). The original TPA test was performed using the General Foods Texturometer (GFT) that compressed the food sample in two successive deformations by means of a flat plunger. To imitate the grinding action of the jaw, the plunger was driven by an eccentric at constant speed; but the plunger traveled with a sinusoidally varying speed, coming to a momentary stop at both ends of the stroke (Friedman et al., 1963). Brennan et al. (1975) presented an engineering analysis of the action of the GFT. The precursors to GFT are a wedge-fracture machine designed by Volodkevich (1938) to measure chewing resistance or tenderness of foods, and Denture Tendero-meter designed at the Massachusetts Institute of Technology (Proctor et al., 1955). This illustrates the longstanding efforts to instrumentally measure the perceived texture in foods. In fact, in a 1963 review, Szczesniak (1963b) remarked that devices used for objective measurement of food texture are “too numerous to list.” Szczesniak (1963a) classified the textural characteristics of foods as: mechanical, geometrical, and other. The mechanical properties were further grouped as primary (hardness, cohesiveness, viscosity, elasticity, and adhesiveness) and secondary (brittleness, chewiness, and gumminess). The geometrical properties are those related to size and


shape, and the other properties are those pertaining to moisture content and fat content (e.g., oiliness and greasiness) of the product. This classification was intended to be used with both sensory and instrumental measurements of texture to help bridge the gap between them. Brandt et al. (1963) developed a “procedure for evaluating texture” based on the above classification, as presented in Figure 7.4. This procedure follows a three-pronged approach in characterizing food texture as those properties perceived on first bite, during chewing, and during mastication. Szczesniak et al. (1963a) also listed some anchor products to describe a standard hardness scale of 1 through 9. On that scale, cream cheese (at 45 to 55°F) was the anchor for hardness value of 1, and American process cheese (at 50 to 65°F) for hardness value of 4. Cream cheese was also used as a standard for cohesiveness (3 on a scale of 1 through 5).

Bourne (1968) adapted the TPA, performed using the GFT, to more commonly and commercially available universal testing machines (UTM, Figure 2.11). Thus, the current TPA test is essentially a uniaxial compression test. Additional details on compression testing are presented in Chapters 2 and 3. The primary differences between the TPA test and uniaxial compression test are: (a) unlike in compression tests, the TPA test is performed by subjecting a cylindrical specimen to a two-step compression. The first compression step, known as the “first bite,” is followed by a second compression, the “second bite.” This is to simulate the first two bites taken during chewing of the food. The two compression steps may be separated by an optional wait time; and (b) deformation used in the TPA test is often 70% or more. To imitate the chewing action more closely, Bourne (2002) even suggested a 90% compression. The uniaxial compression tests are terminated at or before macroscopic sample failure.

Though a considerable amount of structural breakdown may occur during the first two bites of mastication, Rosenthal (1999) observes that in tests such as the two-bite TPA, other sensory attributes experienced closer to the time of swallowing are not evaluated. Breene (1975) provided a detailed account of the history of

FIGURE 7.4 Original procedure for evaluating food texture. (After Brandt et al., 1963.)


developments and applications of the TPA method. A recent development is the Bi-cyclical Instrument for Texture Evaluation (BITE master) by Meullenet et al. (1997), who adapted the UTM to generate motions that more closely mimicked the three-dimensional chewing action in a device that included a set of artificial dentures.

A typical TPA test performed using a UTM would generate a force–time profile as shown in Figure 7.5. The time scale on the x-axis can be converted into deformation knowing the crosshead (plunger) speed. The many textural parameters determinedfrom the TPA curve are: hardness, cohesiveness, adhesiveness, gumminess, springi-ness, and fracturability. These terms are defined in Table 7.2 along with appropriate dimensions and SI units for each term. These definitions are the same as those of Friedman et al. (1963) except how areas A1 and A2 are calculated. Friedman et al. (1963) used the areas under both compression and withdrawal portions of first- and second-bite force–deformation curves. The areas A1W and A2W, during the withdrawal strokes of the first and second bite, respectively, are shaded in Figure 7.5 and are not included in the calculations proposed by Bourne (1968). This affects the calcula-tions of cohesiveness, chewiness, and gumminess. Peleg (1976) suggested correc-tions to the areas A1 and A2, by subtracting areas A1W and A2W, respectively, owing to the fact that the chart directions are not reversed when the direction of compression is reversed. This correction factor, however, is small if the return (withdrawal) speed of the cross head is much greater than that during its downward movement. Other-wise, the correction factor may be significant, especially for the second bite. Olkku and Rha, (1975) estimated that A2W can be as high as 25 to 41% of A2 for some

FIGURE 7.5 Schematic of a typical two-bite texture profile analysis force–time (or deforma-tion) curve. (A1, A1W and A2, A2W are areas under the compression and withdrawal portions of the first-bite and second-bite curve, respectively; A3, d3 are the negative force area during the first withdrawal and the corresponding crosshead travel distance, respectively; P1, P2 and d1, d2 are peaks of the first and second compressions and the corresponding crosshead travel distance, respectively; F1 is the first significant break in the first compression curve).


products. As an example we have presented the TPA curve of Monterey Jack cheese (Figure 7.6). It also shows that A1W and A2W are significant compared to A1 and A2. Nonetheless, several investigators do not apply any corrections to A1 and A2 (Chen et al., 1979). The definitions for chewiness based on different ways of calculating areas A1 and A2 are summarized in Table 7.3. Bourne (1978) included an additional TPA term, “stringiness.” This is the length of UTM crosshead movement correspond-ing to the negative force area A3 (distance d3 in Figure 7.5). However, no related discussion was presented despite the fact that the same figure was reproduced in his recent book (Bourne, 2002). None of the researchers have since used that term. Stringiness, the ability to form strings when pulled, is an important textural attribute for some cheeses such as Mozzarella cheese and string cheese. In addition, a new term, “resilience” has also been proposed (www.texturetechnologies.com) but is not popularly used. It should be recognized that not all TPA textural terms are suitable

TABLE 7.2TPA Texture Terms and Definitions

TPA Term(SI units)

[dimensions]a Definition

How Measured(see Figure 7.5 forsymbol definitions)

Hardness (N)[MLT–2]

Force necessary to attain a given deformation Force corresponding to P1

Fracturability (N)[MLT–2]

Force at significant break in the curve on the first bite (originally known as “brittleness”)

Force corresponding to F1

Cohesiveness (–)[–]

Strength of the internal bonds making up the body of the product

A2/A1

Adhesiveness (J)[ML2 T–2]

Work necessary to overcome the attractive forces between the surface of the food and surface of other materials with which the food comes in contact

A3

Gumminess (N)[MLT–2]

Energy needed to disintegrate a semisolid food until it is ready for swallowing

Hardness* Cohesiveness

Chewiness (J)[ML2 T–2]

Energy needed to chew a solid food until it is ready for swallowing

Hardness*Cohesiveness *Springiness

Springiness (m)[L]

The distance recovered by the sample during the time between end of first bite and start of second bite (originally known as “elasticity” — rate at which a deformed material goes back to its undeformed condition after the deforming force is removed)

d2

Stringiness (m)[L]

Distance traveled by the plunger during the negative force area A3

d3

Resilienceb (–)[–]

Measure of how well a product “fights to regain its original position”

A1w/A1

a L = length (m); M = mass (kg); T = time (s). Appropriate SI units for the dimensions are given in parenthesis.b Defined by (www.texturetechnologies.com); compression and withdrawal speeds should be the same.

Source: After Friedman et al., 1963; Szczesniak, 1963a; Bourne, 1968.

http://www.texturetechnologies.com/



for all products. For example, gumminess may be a better term than chewiness for cheese and other semisolid foods (Lee et al., 1978). Also, for most cheeses and other soft foods, fracturability is either unidentifiable (Figure 7.6) or not meaningful.

TPA TESTING OF CHEESE

As mentioned earlier, cream cheese and American process cheese have been used as anchors for hardness and cohesiveness scales on the original TPA test described by Szczesniak et al. (1963a). Brennan et al. (1970) were among the first to perform TPA on Cheddar cheese using the GFT. They were able to obtain good correlation with sensory evaluation only for hardness. Later, Brennan et al. (1975) compared the measurements made with the GFT and UTM and reported that the UTM measure-ments were better. The TPA remains to be among the most widely used instrumental

TABLE 7.3Definition of TPA Chewiness Based on How Areas A1, A1W, A2, and A2W Are Accounted for (see Figure 7.5) According to Different Researchers

Definition Ref.

(A2 + A2W)/(A1 + A1W) Friedman et al., 1963A2/A1 Bourne, 1968(A2 – A2W)/(A1 – A1W) Peleg, 1976

FIGURE 7.6 TPA force–time curve for 5-day-old Monterey Jack cheese (A1, A1W and A2,

A2W are areas under the compression and withdrawal portions of the first-bite and second-bite curve, respectively).


measurement for cheese-texture evaluation (Emmons et al., 1980; Tunick et al., 1991; Tunick et al., 1993; Bryant et al., 1995; Yun et al., 1993a, b, c).

Since cheese is a viscoelastic material, the rate of compression and time between first and second bite will affect the test results. This factor is not accounted for in the typical TPA test. Peleg and Normand (1982) remarked that due to the rheological characteristics of foods and their relaxation time and, to a smaller extent, the exact deformation regime, the information obtained in sensory and mechanical testing can be different in both kind and magnitude. Thus, for optimal correlation with sensory data, each food type may have to be tested instrumentally under different conditions (Szczesniak, 1987). The fracture strain of cheeses is in the order of 25 to 60% (50 to 60% for Cheddar cheese, Ak and Gunasekaran, 1992; 25 to 35% for Feta cheese, Wium et al., 1997). However, in typical TPA tests, the cheese is compressed 70% or more of the sample initial height. Thus, the sample is compressed beyond its macroscopic failure. Data collected after this fracture point should be evaluated with this fact in mind. Most users of TPA data are not aware of this.

Imoto et al. (1979) investigated the effect of compression ratio (20 to 80%) on the firmness of different cheeses. They found little effect of the extent of compression on the correlation between cheese firmness determined instrumentally and sensory evaluation. Similar results were reported by Casiraghi et al. (1989). This shows that uniaxial compression method is fairly reliable in estimating cheese firmness. Bourne and Comstock (1981) investigated the effect of degree of compression on TPA data using a range of products, including cream cheese, and concluded that the variations in TPA data due to the extent of deformation requires a standardization of the TPA test protocol.

Also, the deformation rates used during a TPA test are also selected empirically. Creamer and Olson (1982) obtained a linear increase in compression force of Cheddar cheese with deformation rates in the range of 2 to 500 mm/min. Shama and Sherman (1973) also affirmed the effect of compression rate on cheese firmness determination. The deformation rate in the mouth during chewing is estimated to be between 1400 to 1500 mm/min (Zoon, 1991; Langley and Marshall, 1993) and that between fingers during squeezing is 150 mm/min (Voisey and Crete, 1973). The need to match the strain rate used in testing and consumption of foods has been acknowledged by many researchers (Boyd and Sherman, 1975; Wium et al., 1997; Vincent et al., 1991). However, maxima of firmness vs. fracture stress for both oral and nonoral firmness assessment of Feta cheese were not found at their expected deformation rates (Wium et al., 1997). Thus, a wide range of deformation rates above 50 mm/min may be considered suitable for TPA testing of Feta cheeses. It is not clear if such a conclusion can be made for other cheeses If not a standard TPA protocol, at least acceptable ranges of test parameters and sample geometry should be defined for cheese and other foods in order to obtain more reliable and meaningful results and facilitate comparisons of TPA data of different foods obtained in different laboratories.

Chen et al. (1979) compared the TPA parameters on 11 store-bought cheeses of varying levels of different textural attributes (Table 7.4). Based on the combined data for all cheeses, they also developed stepwise regression equations to relate


TPA data to cheese composition. An R2 of 0.92 was obtained for the hardness (measured in kilograms) and cheese composition:

(7.1)

Where, P, W, F, and N are protein, water, fat, and NaCl content in percent, respectively; pH is the cheese pH. Further, they ranked the cheese constituents in the order of their effect on TPA attributes as follows: protein, NaCl, water, pH, and fat. Given the wide range of store-bought cheeses they tested, it is difficult if such a general equation and the ranking of relative importance of different constituents can be made without careful investigation of each factor at various levels.

In general, reduction in fat content results in increase in hardness and springiness, and the increase in moisture content produces the opposite effects (Emmons et al., 1980; Tunick et al., 1993; Bryant et al., 1995). Increase in moisture content also makes cheese more adhesive (Bryant et al., 1995). During storage, cheeses tend to become softer and less springy due to the proteolytic breakdown of casein matrix (Tunick et al., 1993). Effects of several other cheesemaking variables have not resulted in obvious textural changes (Yun et al., 1993a,b,c) either due to negligible effects or due to compounding nature of other related factors.

Some investigators have obtained correlations between TPA texture and cheese functional properties such as meltability. Harvey et al. (1982) obtained a positive

TABLE 7.4Comparative Rankinga of Different (Store-Bought) Cheese Types According to Several TPA Parameters Measured

Cheese Type

TPA Parameter Measured

Hardnessb Cohesivenessb Gumminessb Adhesivenessb Elasticityc Chewinessd

Brick 10 5 9 10 2 9Colby 9 7 11 8 7 8Cheddar 5 11 8 9 9 10Edam 2 8 7 5 6 6Gouda 3 9 6 6 8 7Mozzarella 6 3 3 3 1 2Muenster 8 2 4 7 5 4Parmesan 1 10 1 1 11 1Provolone 7 4 5 4 10 5Swiss 4 6 2 2 3 3Processed Cheddar 11 1 10 11 4 11

a The cheeses were ranked from 1 to 11, 1 being the best. The highest and lowest ranked cheeses in each attribute are bold-faced.b See definition in Table 7.1.c Elasticity = [(original height-deformation)/original height] during first compression.d Chewiness = Hardness*Cohesiveness*Elasticity.

Source: After Chen et al., 1979.

TPA Hardness pH= − + − − − +3 25 0 216 0 558 0 0054 0 665. . . . .P W F N


correlation between process Cheddar cheese meltability (at 139°C) and TPA cohesiveness, which was unexpected. However, Gupta et al. (1984) observe such a correlation between cohesiveness and meltability (at 92°C). These discrepancies and correlations are perhaps due to the empirical nature of both the TPA and the meltability measurements made.

UNIAXIAL TESTS FORCHEESE TEXTURE MEASUREMENT

COMPRESSION TEST

The uniaxial tests other than those following the TPA protocol are also widely used in measuring cheese properties. The commonly available UTM machines are used for testing cheese and other foods. Some general considerations for selecting a suitable UTM for texture analysis of foods are listed in Table 7.5. The uniaxial test

TABLE 7.5Considerations for Selecting a Suitable Uniaxial Testing Machine for Texture Analysis of Foods

Feature Criteria

Force capacity Most texture tests for food products requires less than 500 N (50 kg) of forceForce accuracy ±0.5% full scale Stroke (maximum

deformation) lengthThis is important mainly for tensile testing; generally the longer the better; a minimum of 1 m is recommended.

Position accuracy ±0.02 mm provides accuracy needed for force–deformation calculationsDeformation rate A deformation rate of 1000 mm/min may be necessary to imitate chewingAuto sample height

measurementVery useful feature, because sample deformation can be calculated as a

percentage of the original sample heightTrigger force sensing A user-configurable force trigger mechanism is useful in sensing the

beginning of a test, especially for foods that do not have a uniform sample test surface that comes in initial contact with the compression platens or other probes

Test accessories A wide range of easily mountable probes, grips, anvils, and other fixtures should be available

Data collection Data collection at 500 Hz with 10 Hz bandwidth provides more accurate results than lower rates; brittle foods require faster data acquisition rates to accurately record peak forces

Software The software should be user-friendly; it should allow stand-alone programs to run all standard tests on foods and allow flexibility for changing test and measurement configurations; the software should also allow customizing user-created experiments (e.g., using macros); it should allow changing of measurement units, and plotting option should include transporting the data to a commonly available spreadsheet program

Data handling Consider the need to send ASCII format data to a network and need for Windows OLE information transfer

Source: After McManuis, 2001.


results on cheeses are described in detail in Chapter 3. Here, we limit our discussion to highlight selected test results that correlate measured mechanical properties to some textural attributes of cheeses.

Hort and Grys (2000) tested 17 Cheddar-type cheeses using uniaxial compression test and cutting test. The cutting test was performed by forcing a 1-mm-thick blade at a 66° angle 5 mm through the cheese. The sensory panel scores were used to develop statistical models relating textural parameters and uniaxial test data. The correlation coefficients obtained with different textural attributes are presented in Table 7.6. Among the textural attributes, firmness and springiness correlated well with test data. The firmness is traditionally the highly correlated (with fracture force or stress) texture property for different cheeses (Lee et al., 1978; Vernon-Carter and Sherman, 1978; Green et al., 1985; Qvist, 1987). Firmness is also recognized as one of the most important textural property of cheese (Baron and Scott Blair, 1953; Lee et al., 1978). The cutting force from the blade-cutting test correlated well with all textural properties. One sensory property, creaminess (the extent to which cheese has a velvety mouthfeel), did not correlate well with any of the measured data.

Cohesion of Gruyere-type unripened hard cheese was measured by uniaxial compression, tension, three-point bending, cutting tests, and stress relaxation test (Pesenti and Luginbuhl, 1999). Out of these, uniaxial tension was the best to quantify cohesive properties of hard cheeses.

WEDGE FRACTURE TEST

In this test, a wedge is driven into a specimen until it is fractured by propagation of a crack in a stable manner ahead of the tip of the wedge (Figure 7.7). Vincent et al. (1991) called this test the f-Wedge test to emphasize the fact that the material is fractured in a controlled manner, and to distinguish this test from other wedge tests

TABLE 7.6Pearson’s Correlation Coefficients Between Sensory Textural Attributes and Parameters Measured by Uniaxial Compression or Blade-Cutting Tests

MeasuredParameter

Crumbliness(fingers) Firmness Graininess

Hardness(cutting)

Hardness(first bite) Springiness

Yield strain — –0.77c — –0.68b –0.62b 0.76 c

Yield stress 0.59 b 0.74 c 0.60 b 0.62 b 0.65 b –0.72c

Fracture strain –0.76c –0.84c –0.55a –0.78c –0.63b 0.87 c

Fracture stress — 0.64 b — 0.70 b 0.66 b –0.57a

Toughness –0.75 c –0.76c –0.53a –0.69b –0.54a 0.83 c

Young’s Modulus 0.5 a 0.74 c 0.55 a 0.57 a 0.60 b –0.73c

Cutting force 0.79 c 0.86 c 0.73 b 0.74 b 0.77 c –0.86c

a p ð 0.05.b p ð 0.01.c p ð 0.001.— = not significant.

Source: After Hort and Grys, 2000. With permission.


that simply push a wedge through the sample more like a penetration test (Volod-kevich, 1938). The controlled crack propagation is essential for accurate calculation of fracture energy (Mai and Atkins, 1980). For the f-Wedge test, the fracture energy (R) is calculated as follows:

(7.2)

where, E is the modulus of elasticity, H the half sample width, u the distance between the split ears of the sample where the wedge is forcing them apart, a the length of one split ear.

Vincent et al. (1991) used a 10° Perspex wedge to determine fracture properties of Gouda cheese and related them to sensory panel texture evaluations. Excellent correlations were obtained between fracture energy calculated and panel evaluations, giving the same degree of discriminations between young and old Gouda cheeses. Additional discussion on fracture tests and fracture properties of cheese are presented in Chapter 4.

FIGURE 7.7 Schematic of the wedge test for cheese texture evaluation. (After Vincent et al., 1991.)

REu H

aH

a

=+

0 75

1 0 64

2 3

4 4

. ( )

( . )


TORSION TEST AND VANE RHEOMETRY

TEXTURE MAP

Hamann and MacDonald (1992) described using the torsional test (see Chapter 2) data to create a texture map for different foods. The texture map is a plot of fracture stress vs. fracture strain of a product manufactured or tested at varying conditions (composition, pH, age, etc.). The texture map can be divided into four quadrants to represent various material textures. The products that fall in Quadrant 1, on lower left, are soft and “short” and materials in this quadrant are labeled “mushy.” In Quadrant 2, lower right, the materials are soft but are “long” and are known as “rubbery.” The materials that have high fracture stress and fracture strain are “tough.” These are located in Quadrant 3, on top right. The materials that are firm but have a small fracture strain are “brittle.” These will fall in Quadrant 4, on top left. These textural attributes have been assigned to these four quadrants on the texture map based on the common descriptors consumers likely use to describe gel texture as the stress and strain trend away from the center of the plot to any corner. Of course, it is up to the user to prescribe the dividing boundaries of these quadrants for the particular product concerned, which perhaps can be done with ample experience. However, it must be emphasized that the descriptors are at best used in relative sense when comparing two or more products, as one is “less rubbery” or “more brittle,” etc., than the other. Texture maps have been used successfully to describe the texture changes in seafood gels (Surimi) with regard to manufacturing protocols (Hamann and MacDonald, 1992) and other foods (Peron, 2000). A texture map for some selected cheeses is presented in Figure 7.8. Though data in this figure have been

FIGURE 7.8 Texture map of cheese. Arrows indicate the direction of increase of that textural attribute. (After Lanier, 1998.)

Fracture Strain (-)

Frac

ture

Str

ess

(kP

a)

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.910

50

40

30

20

60

70

Light Sharp Cheddar

Light Mild Cheddar

Light American Process

American Process

Monterey Jack

Mild Cheddar

Medium Cheddar

Light Monterey Jack

Swiss

Mozzarella

Muenster

Sharp Cheddar

TOU

GHB

RIT

TL

E

MU

SH

Y RU

BB

ER

Y


obtained from the torsion test, a similar map may be drawn using the results from other rheological tests, such as the vane rheometry (see Chapter 2).

Daubert et al. (1998) described a procedure similar to that of the texture map to develop a “spreadability map,” a plot of yield stress vs. yield strain measured using a vane rheometer. They followed the model of Kokini and Dickie (1982), who reported that the subjective spreadability of soft foods is proportional to the maxi-mum shear stress on the spreading device (i.e., knife). Based on the spreadability map, Daubert et al. (1998) indicated that in addition to the yield stress, yield strain should be also accounted for in describing the spreadability of foods. Accordingly, texture maps of different cheeses have been developed based on vane rheometry yield stress vs. yield strain data (Truong and Daubert, 2001; Breidinger and Steffe, 2001). Furthermore, the texture maps developed using the data from torsion test and vane rheometery were reportedly similar for some cheeses. Thus, the vane rheometry may be a better choice due to the ease of sample preparation (Truong and Daubert, 2001). The texture map may be used as a tool for evaluating spreadability of cream cheeses (Breidinger and Steffe, 2001) and possibly other soft cheeses.

DYNAMIC TESTS

The dynamic rheological tests (Chapter 5) are performed mostly in the linear visco-elastic range of the material. This is possible by limiting the imposed strain (or stress) to a very small value (i.e., strain ð 5%). Therefore, inherently these tests are suitable for probing structure and structure development as they affect rheology. Since texture is the property of foods generally appreciated during consumption involving large strain and fracture, the dynamic test results are not an obvious choice for studying food texture. Since the material structure is the basis for both rheology and texture, some useful correlations have been obtained between sensory texture and dynamic rheological data. Wium and Qvist (1997) were able to distinguish textures of different Feta cheeses based on complex modulus (G*) and phase angle (δ) measured in strain sweep or frequency sweep tests. Tunick et al. (1990) examined the textural differ-ences between Cheddar and Cheshire cheeses based on dynamic rheological para-meters, storage modulus (G′), loss modulus (G″), and complex viscosity (η*); such a distinction was not possible by other analytical methods. Drake et al. (1999) reported good correlations between hardness and springiness and G′ and G″. How-ever they remarked that empirical methods can provide equally good or better correlations with sensory texture. Therefore, dynamic rheological measurements should be used only as a supplementary test in cases where additional structure information is needed to explain textural differences.

EMPIRICAL TESTS

CRUMBLINESS

Hwang and Gunasekaran (2001) developed an empirical method based on uniaxial compression test to quantify the crumbliness of cheese. The crumbliness is a unique textural property of some cheeses (e.g., Queso Fresco) that are crushed and sprinkled


on foods and then consumed (Figure 7.9). These cheeses maintain their integrity under heat, so they are ideal for casseroles, Mexican specialties such as enchiladas, quesadillas, and tacos, and other dishes that are broiled or baked before serving. Queso Fresco is one of the most common Latin American white cheeses (Geilman and Herfurth-Kennedy, 1992). Because the Queso Fresco-type cheese is crumbled by fingers before serving, a textural attribute describing how easy it is to fragment the cheese may be the best descriptor of crumbliness.

The compression test was performed to 90% deformation at a speed of 1250 mm/min to crumble the cheeses. The crumbled samples were analyzed for their particle size characteristics using a set of nine U.S. Standard sieves with opening sizes ranging from 12.70 to 1.41 mm. A geometric mean diameter, dgm, and total number of particles, Nt, were calculated as follows:

(7.3)

(7.4)

where, Mi is mass (g) retained by ith sieve, and di is geometric mean diameter (mm) on ith sieve; Mt is total mass (g); βv is shape factor for calculating volume of particles (= π/6, assuming spherical shape); ρ is particle density (g/cm3); σln is log-normal geometric standard deviation of parent population by mass in natural logarithm; and dgm is geometric mean particle diameter (mm) by mass. A similar particle size analysis has been used to characterize Cottage cheese by Kosikowski and Mistry (1997).

Statistical analyses of the test results (Table 7.7) indicate that the sensory crumbli-ness perception, the ease of fragmenting cheese into small particles, correlated well with the number of particles determined by particle analysis of compression-fractured

FIGURE 7.9 Mexican White cheese (Queso Fresco) before and after crumbled.

d

M d

Mgm

i i

i

n

i

i

n=

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

− =

=

∑∑

log

( log )1 1

1

NM

dtt

vgm= −

β ρσexp( . ln )ln4 6 32


cheese samples. The r = 0.676, though weak, was the best among other instrumental test (compression test, shear test, and TPA) parameters The number of crumbled particles also related well with average geometric mean diameter, as well as sensory perception of particle size (Table 7.8). Based on these, the number of particles estimated by particle-size analysis was proposed as the single, objective measure of cheese crumbliness. However, the reported correlations are barely acceptable.

TABLE 7.7Correlation Analysis with Sensory Crumbliness Perception

Test Property Correlation Coefficient, r

Sensory test Moistness 0.043Firmness –0.191Size 0.709 a

Uniformity 0.508 a

TPA Hardness –0.039Adhesiveness 0.300Springiness 0.060Cohesiveness –0.021Resilience –0.007

Particle analysis Total number 0.676 a

Shear test Shear strain –0.274Shear stress –0.253Shear modulus –0.004Shear energy –0.339 a

Compression test Compressive Stress –0.359 a

Compressive modulus –0.287 a

a Probability values were found to be less than 0.05 and show significant correlation.

Source: After Hwang and Gunasekaran, 2001.

TABLE 7.8Correlation Analysis of Sensory Perceptions with Total Number of Particles

Sensory Property Correlation Coefficient, r

Moistness –0.114Firmness 0.384Crumbliness 0.676 a

Size 0.681a

Uniformity 0.310

a Probability values were found to be less than 0.05 and show significant correlation.

Source: After Hwang and Gunasekaran, 2001.


Peleg and co-workers (Rohde et al., 1993; Ulbricht et al., 1994) reported evalu-ating crumbliness of “crunchy” foods (e.g., cheese balls) based on the “jaggedness” of the force–deformation curves. However, their results are not applicable to the high-moisture soft foods such as cheese. These results highlight a need for further research to fully understand the rheological basis for describing the cheese crumbli-ness and its objective measurement.

CONE PENETROMETER

Cone penetrometer (CP) is one of the rapid and empirical methods used in the evaluation of consistency of wide variety of solid and semisolid food and nonfood products (Figure 7.10). In rheology, consistency is used as “a general term for the property of a material by which it resists permanent change of shape” (Barnes et al., 1989). CP also allows direct measurement of properties such as hardness “on the spot” (i.e., on the samples in their packaging), which avoids textural damage due to transfer of sample from its original packaging to the measurement cup. Also, the rigidity, plasticity, or firmness of fats, cheese, and gels can be determined.

Three modes of operations are possible with the cone penetrometer: (a) a cone assembly of specific dimensions and weight is allowed to sink into the sample, and the depth of penetration after a fixed time (e.g., 5 s) is measured; (b) a cone assembly of specific dimensions and weight is released into the sample, and the depth of

FIGURE 7.10 Illustration of a constant-weight cone penetrometer test. H = cone height; α = cone angle, h = cone penetration depth.


penetration is measured when it comes to rest due to yield stress of the test material, (c) a cone assembly of specific dimensions and weight is driven at a constant speed into the sample, and the force required for the cone penetration is recorded. For a proper test the surface of the specimen must be smooth and flat.

In the constant weight test the penetration will be quick initially, but will gradually slow down and finally come to rest. The penetration depth at rest (h) is used to calculate an “apparent yield stress,” σapp:

(7.5)

where, M is the cone mass, g the acceleration due to gravity, and α the cone angle. For a given cone of known mass and cone angle, the equation simplifies in terms of just h, i.e., σapp = k/h2, where, k is a constant for the particular cone. Cone probes with various angles (e.g., 20–90°) are available to be used with commercial instruments (www.texturetechnologies.com).

The apparent yield stress determination by cone penetrometer measurements are found to offer a good correlation with the spreadability evaluation by sensory methods. Korolczuk and Mahaut (1988, 1991) used the cone penetrometer to mea-sure texture of acid fresh cheeses of different solids content. They developed a relationship for tangential shear stress, S in terms of the cone penetration depth, h and the corresponding penetration force, F and cone angle α, as given below:

(7.6)

where, the cone constant C = (cos2α/π tanα).Drake et al. (1996a, b) obtained good correlations between firmness measure-

ments of Cheddar-type reduced-fat cheeses using the cone penetrometer (firmness = peak force) and the sensory panel evaluation. Breuil and Meullenet (2001) com-pared the results of cone penetrometer (30° stainless steel cone, driven 10 mm in to the sample at 1 mm/s) with those from a needle puncture test and TPA using 29 cheese types. Different parameters of the cone penetrometer force–deformation test data provided the best correlations with sensory evaluations for hardness (r = 0.87), springiness (r = 0.98), and cohesiveness (r = 0.89) of cheeses compared to the puncture test and TPA data.

STRINGINESS

Stringiness is a textural attribute considered important for Mozzarella cheese and its variant, the string cheese. In case of string cheese, stringiness is related to the ability of the cheese to be peeled of as “cheese strands” by tearing at room tempera-ture (Taneya et al. 1992), and for Mozzarella cheese, stringiness is related to stretchability at elevated temperatures, e.g., pizza. Stringiness is also measured for

σπ αapp

M g

h=

⎛⎝

⎞⎠

2 2

2tan

SCF

h= 2



other foods such as starch pastes, where the ability to form long threads are undesirable (Steeneken and Woortman, 1993). Bourne (1978, 2002) indicated the distance d3, the distance during the negative force area (see Figure 7.5), as the “stringiness” without describing it further. Intuitively, for some materials d3 could represent the length of strings formed during the withdrawal stroke of the plunger during the TPA test. After all, the negative area is due to material stuck to the plunger and the bulk of the product during the withdrawal of the plunger. No such test results have been reported.

Stringiness may also be measured empirically by allowing the material to flow from a spoon or a funnel and determining the length of the thread formed (Wolden-dorp and de Noord, 1966). Steenken and Woortmen (1993) attempted to relate the stringiness of starch pastes to their rheological properties. Fairly good correlation (r = 0.84) was obtained between string length l and ηa/Gb on a double logarithmic scale. Where, η is the shear viscosity and G, the shear modulus; a = 1.2; and b = 0.83. Such measurements of stringiness of melted cheese are complicated by the phase separation of fat. Thus, the stretchability of cheese is measured by the fork method and its instrumented versions. The detailed discussion of cheese stretchability measure-ments is presented in Chapter 9.

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Measuring Cheese Melt and Flow Properties

Cheese is an ingredient in many prepared, ready-to-consume foods such as pizza. In these applications, the cheese-containing foods are prepared at temperatures high enough for the cheese to melt and flow. To a large extent, consumer preference and acceptance of such foods depend on the quality of melted cheese. Thus, characteri-zation of melt and flow properties of cheese is extremely critical for successful use of cheese as an ingredient. This need is becoming increasingly important as more new cheese types and cheese-containing foods are developed.

There are at least two primary issues in studying the behavior of cheese at high temperatures: (a) the physicochemical and technological reasons for cheese behavior at high temperatures is not well understood, and (b) a widely accepted objective method (one that is not affected by test conditions) for quantifying melt or flow of cheeses is not available. As Arnott et al. stated in 1957, “The lack of a suitable method for evaluating melting quality may be responsible for the delay in overcoming causes for poor and irregular melting of cheeses.” Unfortunately, this statement is just as true today. Separation of fat during a melt test is one major stumbling block. As long as it continues to be a problem, as Park et al. (1984) stated, we have to use some of the currently used empirical parameters as relatively crude indicators, which only distinguish large melting differences rather than as quantitative meltability criteria.

MELTABILITY

The melting quality of cheese is commonly referred to in the industry as its “meltability.” Attempts to characterize cheese meltability have been stymied by the lack of a clear definition of this term. Several industry and academic researchers have interpreted the term differently, often to suit a specific need or application. For example, meltability has been considered as the property of cheese shreds to fuse together upon heating. This definition or description is suitable for applications such as pizza but is rather difficult to use as a measurement criterion. From an objective measurement perspective, meltability may be defined as “the ease and extent to which cheese will melt and spread upon heating.” This definition encom-passes two aspects: (a) ease of melting and (b) extent of flow. Ease of melting is most directly related to the heat transfer and thermal phase change properties of the cheese. Extent of flow is related to rheological properties of the cheese at high temperatures, as well as the force necessary to cause the flow. Therefore, a good method to measure cheese meltability should account for both heat transfer and thermal phase changes of the solid cheese and rheological flow properties of the melt (Park et al., 1984).

8


EMPIRICAL TESTS

Perhaps the first reported quantitative method to measure cheese meltability is that of Arnott et al. (1957). It is a departure from the previous practice of visually observing the effect of heating cheese cylinders placed on a heat source for certain duration. Arnott et al. were attempting to correlate the melting quality of process cheese with fat, moisture, pH, and protein hydrolysis of Cheddar cheese. The melt-ability was determined by “exposing a standard cylinder of cheese to 100°C for 15 min. Measurements of cylinder height before and after treatment were used as a basis of comparison.” The height of the center of the cylinder was measured. Following the heat treatment in an oven, samples were allowed to stand at room temperature for 15 min and placed in a refrigerator at 7.2°C (45°F) for 30 min. Then the center of the cylinder was measured again, “regardless of the surface shape or depression.” They repeated the tests on samples exhibiting a marked irregularity in the upper surface, apparently attempting to make a reasonably consistent measure-ment. The meltability was a relative measurement expressed in terms of percent decrease in cylinder height after the heat treatment. The empirical nature of several aspects of this measurement protocol is fairly obvious. The Arnott test is illustrated in Figure 8.1.

In the following year, Olson and Price (1958) reported two potential problems in applying Arnott’s and several other similar methods then in use: (a) film formation on the surface due to exposure to air during heating, and (b) uneven flowing of melted cheese. They also referred to some unreported methods requiring a “rather difficult estimate of areas covered by cheeses before and after some prescribed heat treatment.” Partly because of the softer texture of their product, pasteurized process cheese spread, they proposed what is now known as the “tube method” (Figure 8.2). This method had also been used for testing meltability of natural and process cheeses. A glass tube holds the sample during the test. One end of the tube is closed with a

FIGURE 8.1 Arnott test — sample cheese cylinders heated in oven for measuring change in height.


rubber stopper but is vented by a 1-mm-diameter glass tube. A reference line is etched on the glass 27.5 mm from the opposite end of the melting tube. A measured quantity (15 g) of the sample is placed at this end and closed with a rubber stopper. The tube with the sample is held horizontally in a rack and heated in an oven. The sample is tempered for 30 min at 4.4°C (40°F) and then heated in an oven at 110°C for 6 min. Finally, the rack is tilted to stop further flow of the sample. The distance of flow from the reference line is quickly measured. The tube is reheated for an additional 2 min in the horizontal position, and the distance of flow is measured again. The total distance (in mm) covered by the sample in 6 + 2 min of heating is called the “cheese-flow.” The two-stage heating avoids measuring troubles with samples that might flow excessively in less than 8 min. However, they noted that the heating period “can be varied to suit the particular product being tested.” Though very empirical, as were other methods of that time, the tube method addressed one important problem — film formation and dried surfaces during uncovered heating of cheese in open air, which interferes with, melt and flow behavior of cheeses.

Subsequently, several reports have appeared introducing modifications of the above tests either in terms of sample size or heating conditions (Breene et al., 1964; Keller et al., 1974; Schafer and Olson, 1975; Chang, 1976; Kovacs and Igoe, 1976; Nilson and LaClair, 1976). However, none of these methods gained wide acceptance. Kosikowski (1977) reported a method in his book Cheese and Fermented Milk Foods. This method, known as the Schreiber test, has become the most popular test in the industry for evaluating cheese meltability (Figure 8.3). The test protocol, described as “testing melting quality of process cheese by standard L.D. Schreiber test,” follows.

“Remove two thick or three thin cheese slices from the sliced production run every 10 min and stack them to give a 0.5-cm (3/16-in.) thickness. Then insert a sharp-edged copper cylinder or round cookie cutter with 41-mm (1.6-in.) inside diameter into the slices and push out a sample onto the center of a clean glass Petri dish. Set this thin-

FIGURE 8.2 Tube test — sample cheese cylinder heated in a water bath for measuring distance of flow. A sample is shown inside a vented glass tube before (top) and after heating (bottom).


walled 15- × 100-mm dish with a cover marked with an identification number in a kitchen oven, preferably electric, at 232°C (450°F) for exactly 5 min. Using thermal safety gloves, remove the plates and set them to cool on a flat surface for about 30 min. Then center them over a concentrically numbered target-type graph. Looking through the uncovered glass Petri dish, record numerically the outer edge of the flow line. As the cheese melts uniformly and easily, its diameter and flow line number increase. Cheeses attaining a value of 4 or higher are acceptable. Cheeses with values below 4 are rejected and corrective action is immediately instituted. A dark brown discoloration indicates the presence of sugar or high pH.”

This standard L.D. Schreiber test was apparently developed by the then L.D. Schreiber Company (now known as Schreiber Foods, Inc.) of Green Bay, WI, as

FIGURE 8.3 Schreiber test — a sample cheese cylinder (top) placed on a Petri dish heated in oven (bottom) for measuring the largest diameter of spread. A grid of concentric circles is laid under for measurement.


Kosikowski (1977) lists a personal communication with an L.D. Schreiber Company employee (T. A. Home) in 1975. Kosikowski stated that:

“Melting quality, observed by controlled laboratory heating, is a key to proper formu-lation and fabrication of processed cheese and especially critical for slices. Meltdown must show over a fixed heating period a maximum area spread with an evenness of texture as gauged by a standard test. Otherwise, the processed cheese is deficient in an important functional quality and warrants stoppage of the sliced cheese product line until the fault is remedied.”

It is interesting to note that the original L.D. Schreiber test also called for measuring melted cheese color and texture in addition to flow area.

The empirical and arbitrary nature of several steps in the measurement protocol is obvious. Nonetheless, the Schreiber test is still the most popular test for deter-mining cheese meltability for the following reasons: (a) simplicity both in terms of sample preparation and skills needed by operators; (b) ability to test multiple samples simultaneously; and (c) reasonable correlation with perceived melt quality of several cheeses.

However, the method suffers from three shortcomings.

1. Excessive heat treatment. The 232°C oven temperature specified in the test procedure was apparently the temperature for baking frozen pizza. During pizza baking, evaporative cooling effect due to moisture in the crust and other ingredients keeps the overall cheese temperature well below the oven temperature. Therefore, most cheeses get scorched and show brown or black discoloration especially at the edges when heated at 232°C (Figure 8.4).

2. Uncontrolled heating. The cheeses are heated in an oven during which they undergo nonuniform temperature distribution. As the outer edges begin to flow, this thin layer then gets heated further to even higher temperature, causing both moisture loss and scorching. Moisture loss during heating may adversely affect measurements if the heat and mass transfer properties of the cheeses being tested are different. This condition is further exacerbated by the excessive heating discussed above. Cheeses may also develop a thin surface film due to exposure to air.

3. Measurement of flow line. This is one of the simplifying elements of the Schreiber test. However, the measurement of flow line indicated by the leading edge of the melted cheese flow is appropriate only if the melted cheese spreads evenly into a circular pattern. This occurs with some regular-fat natural cheeses. Many other natural and process cheeses, espe-cially lower-fat types, spread very unevenly when heated. In such cases, the leading edge flow line measurement gives totally misleading data (Figure 8.4).

Citing some of these problems, Muthukumarappan et al. (1999a) proposed a modified Schreiber test to evaluate the meltability of Mozzarella. They conducted the Schreiber test at different oven temperatures (60–232°C) and used different


heating surfaces (Petri dish, aluminum plate, stainless-steel plate). They measured both the cheese flow line per Kosikowski (1977) and the cheese spread area. The spread area was determined by a computer vision method. Different heating surfaces were used to determine if thermal and surface tension properties would have an effect on the extent of flow. Based on this investigation, they proposed that the Schreiber test for Mozzarella should be performed at 90°C for 5 min on an aluminum plate and that the melted spread area should be measured as an indicator of cheese meltability. Tests performed under these conditions using five cheeses of different meltabilities (based on compositional and technological factors) resulted in the five cheeses being grouped into three melt categories. This was the best possible grouping among all the tests performed (Tables 8.1, 8.2, and 8.3). Temperatures above 100°C caused outer edges of the cheese spread to char.

FIGURE 8.4 Excessive oven temperature used in the Schreiber test protocol (232°C) causes scorching of the cheese samples, and lower-fat cheeses do not spread out into a circular pattern.

TABLE 8.1Chemical Composition of Shredded Mozzarella Cheeses

Sample pHFat Moisture Salt

- - - - - - - - - -% - - - - - - - - - -

A 5.16 22.0 46.8 1.44B 4.96 25.0 52.4 1.84C 5.14 24.3 48.2 1.18D 5.11 23.0 48.8 1.60E 5.01 21.5 49.8 1.72

Source: After Muthukumarappan et al., 1999a. With permission.


TABLE 8.2Results of the Schreiber Tests as Measured by the Surface Area (cm2) of Cheese Spread on Stainless Steel (SS), Aluminum Plate (AP), or Petri Dish (PD) at 60, 70, 90, and 232°C

Sample

60°C

Sample

70°C

SS AP PD SS AP PD

A 12.3ab 13.3bc 12.5a A 13.0b 15.3b 12.9b

B 12.5ab 14.1ab 11.9a B 15.2a 16.1ab 14.0a

C 11.6b 12.9c 11.8a C 12.1b 13.0c 12.3b

D 11.7b 12.6c 12.0a D 12.8b 13.9 c 12.8b

E 13.0a 14.4a 12.5a E 14.7a 16.5a 14.3a

90°C 232°C

A 16.5b 17.1b 15.9c A 19.2c 27.4c 22.3c

B 19.3a 20.1a 17.9b B 24.3b 36.5b 25.6b

C 15.9bc 16.9b 14.7c C 22.7 bc 34.0b 25.0b

D 14.9c 15.6c 14.6c D 20.9 bc 24.8c 22.1c

E 18.9a 20.5a 19.7a E 30.9a 42.9a 30.3a

a, b, c, d Within each column, means without a common superscript differ (P < 0.05).


TABLE 8.3Results of the Schreiber Tests as Measured by the Maximum Diameter (cm) Cheese Spread on Stainless Steel (SS), Aluminum Plate (AP), or Petri Dish (PD) at 60, 70, 90, and 232°C

60°C 70°C

Sample SS AP PD Sample SS AP PD

A 2.08b 2.50b 2.25a A 2.08b 2.75b 2.17a

B 2.17b 2.50b 2.00a B 2.92a 3.00a 2.42a

C 2.00b 2.08c 2.00a C 2.08b 2.17d 2.00a

D 2.00b 2.08c 2.17a D 2.25b 2.42c 2.33a

E 2.33a 2.83a 2.00a E 2.75a 3.17a 2.50a

90°C 232°Ce

A 3.08b 3.33b 2.92 bc A 4.42c 5.33c 4.33c

B 4.08a 4.17a 3.33 ab B 5.17b 7.25b 4.92b

C 3.17b 3.25bc 3.00 bc C 4.58c 6.92b 4.83b

D 2.83b 3.08c 2.42c D 4.17c 4.83c 4.25c

E 3.83a 3.92a 3.67a E 6.58a 8.75a 5.83a

a, b, c, d Within each column, means without a common superscript differ (P < 0.05).e Data in PD column were obtained as per the actual Schreiber test protocol



Note that the modified Schreiber test conditions proposed by Muthukumarappan et al. (1999a) were empirically determined and should be considered suitable only for testing regular-fat Mozzarella cheeses. It may be possible to develop similar “optimal” test conditions for other cheeses and perhaps one set of conditions for several cheeses that will overcome some of the shortcomings of the original Schreiber test.

Many researchers routinely use other variations of the Schreiber test protocol, such as testing smaller samples and not waiting for 30 min between heating and taking measurements, different oven temperature and heating times, etc. (Table 8.4). Bogenrief and Olson (1995) reported using a microwave oven for heating the sample (for 45 s) instead of the traditional convection oven. The Schreiber test was also adapted for shredded cheese by measuring out a quantity and forming it into a disk (Muthukumarappan et al., 1999b). In this case, it is important to use same sample forming procedures so that the test results can be compared.

An effort was made to predict cheese meltability as determined by the modified Schreiber test protocol described above. Gunasekaran (1998) obtained the following empirical relationship based on testing of 19 Mozzarella cheese samples manufac-tured with 0 to 2% each of non-fat dry milk (NFDM) and starch.

(8.1)

where F = fat content (%); M = moisture content (%); and pH = pH of the cheese. This equation (r = 0.85) provided statistically valid effects of parameters. The spread area can be determined by knowing only moisture, fat content, and pH of the cheese. The added starch and NFDM do not significantly affect meltability. Fat and moisture and fat and pH have a combined effect, positive for moisture and fat and negative for fat and pH. However, due to the complex interactions among the compositional and technological factors, it is difficult, if not impossible, to arrive at empirical relations that can predict cheese melt spread area.

In another study, Park et al. (1984) compared results of Schreiber and Arnott tests. They performed the tests both in convection and microwave ovens using different cheeses (mild and sharp Cheddar, Mozzarella, process American, and process cheese product). Three to seven manufacturers were represented in each group. After this exhaustive testing, they found a marked lack of correlation between the Schreiber and Arnott results. Given the empirical nature of these tests, it is not surprising that the results did not match. Park et al. (1984) also alluded to the importance of thermal effects, and hence thermal properties, that affect the melt-ability of different cheeses. This partly accounts for the different shapes that cheeses assume during heating (Figure 8.5). They further concluded that Schreiber and Arnott tests do not measure the same rheological attributes even if the effects of other factors (e.g., heat transfer) could be ignored. Similar results from microwave-heated samples led them to remark that “in any meltability evaluation, the rheological and thermal aspects ought to be considered as equally important and no single parameter can meaningfully account for both.”

cheese spread area (mm M F F pH2 ) . . .= − + ∗ ∗( ) − ∗ ∗( )5 321 0 0398 0 208


TABLE 8.4Empirical Cheese Meltability Tests

Cheese type

Sample Size

Measurement

Heatingmedium Temp.

(°C) Heating Time Heater ReferenceDiameter

(mm)Height(mm)

Process Cheddar 17 17 % decrease in height 100 15 min Oven Arnott et al., 1957Cheddar 17 17 Time needed to melt, s 80 — Water bath Weik et al., 1958Cheese spread 30 20 Distance of flow from reference line, mm 110 8 min Forced draft oven Olson & Price, 1958Pizza 15 5 % decrease in height and increase in

diam. penetrometer98 5 min Water bath Breene et al., 1964

Mozzarella 15 5 % decrease in height 98 5 min Water bath Keller et al., 1974Process 19.1 6.4 % increase in diam. 232 3 min Oven Chang, 1976Cheese spread 38.1 4.8 Diam. increase by flow line number 204 5 min Oven Kovacs & Igoe, 1976Process 40.6 4.8 Diam. increase by flow line number 232 5 min Oven Kosikowski, 1977Process 37.5 7.5 % increase in diam. 250 and 100 5 and 15 min Oven Sood & Kosikowski, 1979Caseinate — — Melt area per unit weight, cm2/g — 15 s Microwave oven Hokes et al., 1982Process Cheddar 36 5 Area 139 6 min Oven Harvey et al., 1982Various 17 17 % decrease in height 100 0–1 min Microwave oven Park et al., 1984Various 41 4.8 Diam. increase 232 0–1 min Microwave oven Park et al., 1984Various 30 20 Distance of flow from reference line, mm 92 8 min Water bath Gupta et al., 1984Mozzarella 15 4 % increase in area 100 10 min Oven Fernandez & Kosikowski,

1986Raclette 32 7 % increase in area 140 3 min Oven Schluep & Purhan, 1987Raclette 32 7 % increase in area 140 3 min Oven Eberhard et al., 1986Process 25 25 Distance of flow from reference line, mm 110 50 Oven Kalab et al., 1991Cheddar 30 20 Distance of flow from reference line, mm 95 5, 8, and 12 min Water bath Bogenrief and Olson,

1995


TABLE 8.4 (continued)Empirical Cheese Meltability Tests

Cheese type

Sample Size

Measurement

Heatingmedium Temp.

(°C) Heating Time Heater ReferenceDiameter

(mm)Height(mm)

Cheddar 30 20 Maximum width and width at right angle to the maximum width

95 45 s Microwave oven (set at full power, 600 W)

Bogenrief and Olson, 1995

Mozzarella shreds Spread at 1.73 kg/m2 on polished stainless steel tray

Time needed for shreds to disappear 280 Oven Guinee et al., 1998

Mozzarella 44.5 4 % increase in area 280 4 min Oven Guinee et al., 1998Mozzarella 35 21 Area of spread on aluminum plate 90 5 min Oven Muthukumarappan et al.,

1999bMozzarella 35 25 Distance of flow from bottom of tube,

mm100 30 min Oven Wang et al., 1998

Mozzarella 30 5 % increase in diameter 160 2.5 Oven Madsen and Qvist, 1998Reduced-fat

Process30 Distance of flow from bottom of tube, cm 104 60 min Oven Raval and Mistry, 1999

Mozzarella various various Increase in spread area 130 or 200 10 min Oven Wang & Sun, 2002bMild Cheddar 45 square 3 Ratio of area to spread 70 to 200 12–20 min Oven Wang & Sun, 2001, 2002aVarious 30 5 Melt spread diameter by laser beam 80 Continuous

measurementHot plate Gunasekaran et al., 2002

Various 30 5 Melt spread area by computer vision 80 Continuous measurement

Hot plate Gunasekaran et al., 2002

Source: In part from Ruegg et al., 1991.


The data from differential scanning calorimetry also failed to show any distinct patterns that would indicate differences in meltability of cheeses. They made a very convincing claim that a “well defined meltability criteria ought to be based on a comprehensive rheological analysis presenting the data in terms of temperature and time parameters.”

In a test developed at Utah State University (Oberg et al., 1992), 15 g of shredded cheese is placed at one end of a 30- × 250-mm glass tube. It is tempered for 30 min at 4°C while the tube is held vertically, and then transferred to an oven and held horizontally at 110°C for 60 min. After cooling to room temperature, the distance the cheese has flowed is measured. Guinee et al. (1998) described a procedure in which the time it takes for cheese shreds to disappear and form a molten mass in an oven is considered an indicator of meltability.

In a series of papers, Wang and Sun (2001, 2002a, 2002b) applied a procedure similar to Muthukumarappan et al. (1999a) measuring cheese spread area upon melting using a computer-vision system. They used the ratio of spread area or increase in spread area to represent meltability. The meltability increased with sample size. The melting degree (ratio of cheese area after and before heating) and melting rate (rate of change in melt area during the first minute of heating) were

FIGURE 8.5 Schematic illustration of typical shape changes of cylinders of sharp Cheddar, process American, and Mozzarella cheeses at 5-min intervals (from top to bottom) during heating in an oven at 100°C. (After Park et al., 1984. With permission.)

Sharp Cheddar Process American Mozzarella


calculated. Both sample size and test temperature significantly affected the melt-ability measurements. They reported an optimal temperature range between 140 and 160°C for both Cheddar and Mozzarella cheeses (Figure 8.6).

Recently, Gunasekaran et al. (2002) described additional changes to the Schreiber test protocol. They replaced the convective oven, typically used for the test, by direct conduction heating via the metal plate on which the cheese disk is heated and allowed to flow. Not requiring an oven to perform the melt test also reduced the overall cost and space requirements. In addition, the sample was more easily accessible for spread length and area measurements. The conduction-heating test is faster and allows continuous cheese melt/flow measurement. For example a laser beam or a computer-vision system camera can be used to continually record the cheese spread length or area, respectively, for automatic meltability determination (Figure 8.7). Further, this system can be adapted to make multi-sample measurements (Figure 8.8). These improvements will enable more consistent cheese meltability measurements to be faster and more efficient than the currently available methods. Moreover, compared to Schreiber test, the conduction test accentuated the differences between melt properties of different cheeses (Figure 8.9) even though the tests were conducted at a lower temperature (70°C) that the modified Schreiber test (120°C). Therefore, the conduction test may be able to help distinguish between different cheeses that are similar in their melt/flow characteristics.

Several of the empirical tests used over the years are summarized in Table 8.4. It can be seen that many researchers, and in some cases same researchers, have used different variations of some of the tests described above. Such variations in test protocols make applicability of the test results rather limited. In addition, the varia-tion of cheese thermal properties with respect to composition (Marschoun et al., 2001) also compounds the problems of uncontrolled and arbitrary heating protocols used in the empirical tests.

FIGURE 8.6 Melting degree (MD) and melting rate (MR) of Cheddar and Mozzarella cheeses. (After Wang and Sun, 2002a.)

Temperature (°C)

80 120 160 200

Mel

ting

degr

ee (

%)

80

120

160

200

Mel

ting

rate

(m

m2 /m

in)

0

20

40

60

80

MR

MR

MD

MD

Cheddar

Mozzarella


OBJECTIVE TESTS

Several researchers have proposed different methods to measure cheese meltability objectively. These efforts range from semiempirical methods based on homemade devices to fundamental rheological measurements, using dynamic rheometers.

Flow behavior of materials is characterized by their viscosities. Accordingly, measurement of cheese viscosity was a major focus in an effort to objectively quantify meltability. According to our definition, meltability is related to both ease and extent of flow of melted cheese. Ease of flow can be determined from the stress causing flow, and extent of flow can be related to strain rate. Viscosity, the ratio of

FIGURE 8.7 Schreiber test may be improved by conduction heating and measuring cheese melt spread area by a computer-vision system. The computer interface allows continuous recording of changes in spread area. (After Gunasekaran et al., 2002. With permission.)

FIGURE 8.8 Multi-sample measurement system with conduction heating plate rotating at a slow speed (~1 rpm) under a computer-vision system camera. The cheese samples, heated by the plate, melt and spread on the plate. (After Gunasekaran et al., 2002. With permission.)


stress to strain rate, can help estimate the combined behavior, the meltability. Many of the instrumented cheese meltability tests are summarized in Table 8.5.

STEADY SHEAR VISCOMETRY

Lee et al. (1978) were among the first to attempt to measure cheese viscosity. They used a Brookfield viscometer along with a T-bar spindle. The viscometer reading in relative scale (in %) was measured as a function of cheese temperature. They obtained a characteristic curve for each type of cheese tested (Figure 8.10). Since both the viscometer geometry and speed were arbitrary, and temperature distribution was not uniform, this test is of limited value.

Steady shear viscometry is inherently unsuitable for measuring cheese viscosity due to fat separation (Reugg et al., 1991). As cheese is heated, the fat melts and lubricates the stationary and rotating cylinders (or plates) to such an extent that they slip past each other. The entire molten cheese mass is either left in the middle between the concentric cylinders (or plates) or rotates en masse.

For acid fresh cheeses, such as cottage cheese, fat separation is not an issue. They can be considered as a dispersion of hydrated casein particles in whey. For such fresh and soft cheeses, steady shear viscometry has been applied successfully to characterize their flow properties (Corrieu et al., 1982; Massaguer-Roig et al., 1984; Korolczuk and Mahaut, 1989, 1990; Korolczuk, 1993). In general, power law relationships have been observed between apparent viscosity and shear rate, all

FIGURE 8.9 Comparison of cheese melt spread area of three process cheeses by modified Schreiber test (oven set at 120°C) and conduction heating test (70°C). (After Gunasekaran et al., 2002. With permission.)


exhibiting shear thinning behavior. Korolczuk (1993) also reported observing thixo-tropic behavior of fresh cheeses apparently due to continuous destruction and restoration of casein aggregates.

CAPILLARY RHEOMETRY

Capillary rheometry is widely employed in the polymer industry to determine vis-cosity of molten plastics. It is based on fundamental engineering principles with well-developed test and data analysis procedures (Van Wazer et al., 1967; Okubo and Hori, 1979). Due to apparent similarities between molten plastic and molten cheese, capillary viscometry is a natural choice for cheese viscosity measurement. Smith et al. (1980) employed capillary rheometry to evaluate the flowability of melted Mozzarella, Cheddar, and American process cheeses. The flow curves (shear stress vs. shear rate) and viscosity curves (apparent viscosity vs. shear rate) for Mozzarella determined by a capillary rheometer are presented in Figures 8.11 and 8.12.These figures show that Mozzarella is a Herschel-Bulkley fluid, i.e., a pseudoplastic fluid with a yield stress. The drop in viscosity is more pronounced in the 55 to 70°C range than in the 40 to 55°C range (Figure 8.12). Based on this expected trend, capillary viscometry should be considered a reasonable choice for measuring the viscosity of Mozzarella. However, Smith et al. (1980) also reported serious slippage

TABLE 8.5Summary of Various Instrumented Cheese Meltability Tests

Instrument Measurement Ref.

Brookfield steady shear viscometer with T-bar spindle

Viscometer relative torque reading Lee et al., 1978

Capillary rheometer Apparent viscosity Smith et al, 1980Squeeze-flow rheometry Biaxial elongational viscosity Ak and Gunasekaran, 1992,

1995; Casiraghi et al., 1985; Luyten et al., 1991; Campanella et al., 1987

UW Meltmeter (squeeze flow) Biaxial elongational viscosity Wang et al., 1998UW Meltmeter Sample height after 5 s Kuo et al., 2000UW Meltmeter (creep test) Viscoelasticity index Kuo et al., 2000UW Melt Profiler (squeeze flow) Softening point, average flow rate Muthukumarappan et al., 1999bDynamic rheometer (small strain

oscillatory shear test)Storage and loss moduli crossover Sutheerawattananonda and

Bastian, 1998; Gunasekaran et al., 2002

Helical viscometry (Brookfield viscometer with T-bar spindle and Helipath drive)

Apparent viscosity reading from the instrument

Kindstedt et al., 1989a; Kindstedt and Kiely, 1992; Fife et al., 1996; Guinee and O’Callaghan, 1997; Savage and Mullan, 2000

Modified UW Melt Profiler (squeeze flow under conduction heating)

Softening point, average flow rate Gunasekaran et al., 2002


problems due to fat separation interfering with viscosity measurements of Cheddar and American process cheeses. Among the conditions Van Wazer et al. (1967) listed as requirements for valid measurements using a capillary rheometer are: (a) isothermal flow; (b) negligible radial flow; (c) negligible wall slip; (d) fluid is incompressible; (e) flow is laminar; and (f) minimal end effects. Among these, notable problems in testing cheeses using a capillary rheometer are the presence of viscoelastic effects and end effects. The fat separation further complicates the situation. Therefore, though capillary rheometry appears to have some value for testing the viscosity of Mozzarella, appropriate correction factors must be applied. Determination of such correction factors is time-consuming and tedious, as it requires multiple tests using capillaries of different diameters. These difficulties and the expensive test instrumentation necessary deterred further investigations of cheese using the capillary rheometer.

SQUEEZE-FLOW RHEOMETRY

This is a uniaxial compression test performed by eliminating (or minimizing) friction between the sample-compression platen interfaces. It was first described by Chatraei et al. (1981) for evaluating biaxial extensional behavior of high-viscosity polymers such as polydimethylsiloxane. This method is suitable for cheese meltability evalua-tion for two reasons.

FIGURE 8.10 Schematic viscometer torque reading vs. temperature of two cheeses using a T-bar spindle in a Brookfield rotational viscometer. (After Lee et al., 1978.)

100

75

50

25

0

Vis

com

eter

Rea

ding

(%)

Temperature (C)


1. Melt/flow is a biaxial phenomenon. Therefore, biaxial elongational vis-cosity that can be determined from test data should adequately describe the melt/flow characteristics of the cheese.

2. The presence of slip at sample-platen interfaces caused by fat separation is not only a prerequisite for a proper test but also is incorporated in the calculation of results.

The test procedure is also simple and straightforward — compressing the sample axially between two lubricated plates in a uniaxial instrument such as an Instron (Figure 8.13). Under this configuration, assuming perfect slip, shear stress at sample–platen interfaces is zero (Chatraei et al., 1981; Isayev and Azari, 1986; Wang et al., 1998).

Elongational viscosity of Cheddar (Ak and Gunasekaran, 1992), Mozzarella (Casiraghi et al, 1985; Ak and Gunasekaran, 1995), Gouda (Luyten et al., 1991), American process cheese (Campanella et al., 1987), and process cheese spread (Casiraghi et al., 1985) has been reported. Most of these tests were performed at room temperature, except those by Campanella et al. (1987), who worked in the 36 to 62°C range, and by Ak and Gunasekaran (1995), who worked in the 30 to 60°C range. In all tests, the biaxial elongational viscosity was observed to decrease with

FIGURE 8.11 Flow curves of Mozzarella cheese measured using a capillary rheometer at different temperatures. The shear stress and shear rate have been corrected for viscoelastic and end effects. (After Smith et al., 1980.)

0

3

6

9

12

15

0 1000 2000 3000

Corrected Shear Rate (s−1)

Cor

rect

ed S

hear

Str

ess

(kP

a)

70°C

40°C

55°C


biaxial strain rate (Figure 8.14). This validates the strain–rate thinning behavior of cheeses. Campanella et al. (1987) also reported the expected lower viscosity at higher temperatures. They related the difference in biaxial elongational viscosity between a national brand and a supermarket brand to meltability differences as measured by the Schreiber test.

UW MELTMETER

Gunasekaran’s research team at the University of Wisconsin (UW) designed and developed a device to objectively measure melt/flow behavior of cheeses at different temperatures (Ak, 1993; Wang et al., 1998). This device, named the UW Meltmeter, was configured to perform the lubricated squeeze-flow tests. The details of this device are depicted in Figure 8.15. It is made of aluminum and has a movable outer cylindrical

FIGURE 8.12 Apparent viscosity of Mozzarella cheese measured using a capillary rheometer at different temperatures The shear rate has been corrected for viscoelastic and end effects. (After Smith et al., 1980.)

FIGURE 8.13 Lubricated squeeze flow test — the sample is held between two well-lubricated parallel plates (left) and compressed uniaxially at a constant rate (right).

0

0.5

1

1.5

2

2.5

1.5 2 2.5 3 3.5 4

log Corrected Shear Rate (s−1)

log

App

aren

t Vis

cosi

ty (

Pa.

s) 40°C

55°C

70°C

1


annulus (75-mm outer diameter; 30-mm inner diameter). The annulus can be moved up and down by a lever around a 30-mm diameter stationary center cylinder. The stationary cylinder is equipped with an electric heater operated by a temperature controller. At the start of a test, the lever arm is raised such that the annulus is up, forming a 30-mm-diameter, 7-mm-deep sample well over the stationary cylinder. A sample of the same size as that of the sample well is placed in the well. The top

FIGURE 8.14 Biaxial elongational viscosity of Cheddar cheese as a function of radial biaxial extension rate at different deformation rates. (After Ak and Gunasekaran, 1992. With permission.)

FIGURE 8.15 UW Meltmeter photograph and drawing.

LVDT

Heater

Lever

Bottom plate(flow platform)Sample

Circular top plate

Moveable outerannulus

30 mm Stationary piston

Stationary innercylinder

LVDT rod

To computerdata acquisition

Base Plate

7 mm

Powersupply


of the sample should be flush with the top surface of the annulus, which serves as a platform for the melted cheese to flow and spread. The top of the cheese surface is covered with a 66-mm-diameter lubricated circular plate attached to a linear variable differential transformer (LVDT) rod. The roles of this circular plate are:

1. It effectively seals the plate-cheese interface, preventing any loss of moisture from the sample during heating.

2. It maintains constant contact with the cheese, enabling continuous moni-toring of sample flow.

3. Along with the LVDT rod, it applies the force required during a test to cause the melted cheese to flow.

The LVDT is supported separately and connected to a computer data acquisition system. The sample is heated to the test temperature. A fine thermocouple inserted into the sample before the test monitors cheese temperature within 1°C and controls the heater. Once the sample attains the desired temperature (60°C), the lever arm is lowered to bring the annulus down. Simultaneously, the sample is subjected to lubricated axial compression due to the weight of the circular plate and LVDT core. This causes the cheese to flow. Additional weight may be added or a lighter plate can be used, as required, to change force causing flow. The sample height vs. time of flow data are continuously recorded. The operating sequence of the UW Meltmeter is schematically illustrated in Figure 8.16.

The above procedure employs a constant force. The UW Meltmeter can also be operated under constant deformation rate by removing the LVDT and circular plate and bringing the test platen of a uniaxial testing machine in contact with the sample and flow platform at the beginning of a test. When the sample reaches the test temperature, the lever arm is lowered and crosshead of the uniaxial testing machine is activated simultaneously to deform the sample at a constant rate. A particular advantage of the UW Meltmeter is its ability to perform tests at selected conditions,

FIGURE 8.16 Operating sequence of UW Meltmeter: (a) starting position, sample being heated to test temperature; (b) test commences, outer annulus being lowered by actuating a lever; (c) test progresses, heated cheese flows between two lubricated parallel plates under constant force.

(b) (c)(a)


e.g., at low rates similar to those experienced by melting cheese in foods such as pizza. This is easily done by adjusting the deformation rate in the constant rate. However, the constant force mode is simpler and easier to perform than the constant rate mode, and the strain rate is adjusted by varying the applied force.

As described previously, shear-free conditions are essential at the sample-test surface interfaces. This was guaranteed by lubricating all surfaces (sample well, flow platform, and bottom of the circular plate) with a dry-film lubricant and then covering them with mineral oil. Using a marker technique of Isayev and Azari (1986), the Meltmeter was verified to operate under practically shear-free conditions. There-fore, data analysis can be performed according to established procedures (Chatraei et al., 1981; Campanella et al., 1987).

Typical sample height vs. time data obtained using the UW Meltmeter are presented in Figure 8.17. These data can be recalculated and plotted as biaxial extensional strain rate vs. time (Figure 8.18), and further as biaxial stress growth coefficient (akin to biaxial elongational viscosity) vs. biaxial extensional strain rate (Figure 8.19). The strain-rate thinning behavior of cheese melt is evident from Figure 8.19, along with the expected trends of decreasing viscosity with increased temper-ature and fat content. Similar results are also obtained in the controlled deformation rate test. The results presented in Figure 8.19 indicate that higher-fat Mozzarella and Cheddar cheeses have a lower biaxial stress growth coefficient (i.e., they flow more easily). Also, the Mozzarella cheeses had lower biaxial stress growth coeffi-cient and higher biaxial elongation strain rate at 60°C than at 40°C. The effect of higher temperature lowering product viscosity is well known. In cheese, it is influ-enced largely by the state of fat globules. The ratio of solid to liquid fat, the major factor determining the melting properties of fat, decreases with increasing temper-ature (Prentice, 1987).

FIGURE 8.17 Mozzarella cheese sample height vs. time data obtained using UW Meltmeter for two fat levels and test temperatures. (After Wang et al., 1998. With permission.)

Time (s)

0 10 15 20 25 30

Sam

ple

heig

ht (

mm

)

0

1

2

3

4

5

6

7

8

(14%, 40°C)

(43%, 40°C)

(14%, 60°C)

(43%, 60°C)

5


An interesting trend can be observed in results obtained under constant force (Figure 8.19). The viscosity curves for all samples are approximately parallel and aligned within a diagonal narrow band. Within this region, the top left corner represents very high viscosity and virtually no flow (extremely low strain rate). The viscosity curve of cheese with poor meltability will be close to this region. The bottom right corner represents the opposite condition — very low viscosity and very high flow. The viscosity curve of a cheese with good meltability will be close to this region. Accordingly, this narrow band may be divided into three or four smaller zones, signifying different meltabilities, such as very high, high, good, low, and very low. Given the complex interactions of various compositional and technological factors, this suggestion may be more reasonable than trying to assign a unique melt index for each cheese that is tested. Of course, the end use application of the cheese should also be taken into account in establishing a melt index.

The relative meltability of the samples can be compared using any of the above three representations. Depending on sample and test operating conditions, Figures 8.17to 8.19 are informative when comparing tests performed using different sample sizes and forces. The entire curve or the biaxial stress growth coefficient value (or simply the reciprocal of sample height) shortly after flow has commenced (1–5 s) may be useful in comparing meltability of different cheeses.

The results of the UW Meltmeter test at 60°C compared well with those of the Schreiber test (Table 8.6). The advantage of using the Meltmeter is evidenced by significantly smaller standard deviation and coefficient of variation among the three replicates. The five commercial cheese samples used can only be grouped into three statistically different groups based on the Schreiber test due to high data dispersion. Based on results from the UW Meltmeter, however, all cheeses were identified to be different from one another. The convenience of automatic data acquisition and analysis should be considered an added advantage.

FIGURE 8.18 Cheese sample strain rate vs. time data obtained using UW Meltmeter for two fat levels and test temperatures. (After Wang et al., 1998. With permission.)

Time (s)0 5 10 15

Bia

xial

ext

ensi

onal

str

ain

rate

(s−1

)

0.00

0.050.10

0.15

0.20

0.25

14%, 40°C 43%, 40°C14%, 60°C43%, 60°C


The UW Meltmeter test is different in the following ways that eliminate much of the empiricism in the Schreiber test protocol.

1. Controlled heating. The sample is heated to a point higher than the melt temperature (60 or 65°C), which eliminates sample scorching at the edges.

2. Uniform temperature. The sample is not allowed to flow until the entire mass is at a uniform temperature. This prevents uneven temperature distribution during heating in the oven and the concomitant nonuniform flow pattern.

FIGURE 8.19 Biaxial stress growth coefficient (BSGC) vs. strain rate data obtained using UW Meltmeter. Top: Mozzarella cheese at two levels of fat, test temperatures, and applied forces. Bottom: Cheddar cheese at three levels of fat. (After Wang et al., 1998. With permission.)

Biaxial extensional strain rate (s−1)

10−4 10−3 10−2 10−1 10°

Bia

xial

str

ess

grow

th c

oeffi

cien

t (P

a.s)

102

103

104

105

106

107

14%, 40°C, 0.7 N14%, 40°C, 0.9 N14%, 60°C, 0.7 N14%, 60°C, 0.9 N43%, 40°C, 0.7 N43%, 40°C, 0.9 N43%, 60°C, 0.7 N43%, 60°C, 0.9 N

Mozzarella Cheese

103

104

105

106

Bia

xial

str

ess

grow

th c

oeffi

cien

t (P

a.s)

10−4 10−3 10−2 10−1

21%

27%

34%

Cheddar Cheese

Biaxial extensional strain rate (s−1)


3. Prevention of moisture loss. Since the sample is tightly covered during heating and a layer of oil is applied in the UW Meltmeter, there is no moisture loss, which improves the consistency and accuracy of melt-ability data.

4. Continuous monitoring of flow. The LVDT and circular disk maintain continuous contact with the sample during flow, allowing calculation of flow rate. In the Schreiber test, only the end of the flow is measured.

The UW Meltmeter is one of the first instrumented methods to be made available in a long time (introduced almost 20 years after the Schreiber test). Therefore, it elicited some attention, from both industry and academia. Nonetheless, the Melt-meter is not without problems.

1. Each measurement takes too long, chiefly due to time-consuming sample and test surface preparation. This is unacceptable for routine testing in the industry.

2. Multiple tests cannot be performed simultaneously, which compounds the excessive time factor. With the Schreiber test, tens of samples can be tested at the same time.

3. Moving parts get clogged. Fat melts from samples and gets into crevices and clogs the Meltmeter’s moving annulus. The device becomes inoperable unless it is dismantled and cleaned, which can take as much as 30 min.

The UW Meltmeter design was improved to address some of these drawbacks. The new design includes a dual unit (Figure 8.20) so one sample well can be prepared while the other is in use for a test, thus reducing total test time to about 10 min per test. The annulus design was modified with a scraper ring that scrapes off accumu-lating fat each time the lever arm is actuated. Though these changes are substantial, they have not led to a device suitable for routine industrial use. However, the UW Meltmeter remains an objective cheese meltability test device suitable for research and development.

VISCOELASTICITY INDEX FOR CHEESE MELTABILITY

The typical UW Meltmeter test result is a curve (see Figures 8.16 to 8.18), which is difficult to use in assigning a melt index for different cheeses. Therefore, the current procedure is to use a single point value as an indicator of meltability. For example, the sample height or biaxial stress growth coefficient value at any time between 1 to 5 s after the start of the test may be taken to represent meltability (Table 8.6). Such a measurement is suitable for comparing relative changes in meltabilities between cheeses.

To utilize the entire data set obtained during a melt test, Kuo et al. (2000) modified the UW Meltmeter and data analysis based on fundamental rheological procedures. The Meltmeter was modified to operate in a constant stress mode instead of the previously described constant force mode. The only modification necessary was making the diameter of the circular plate connected to the LVDT the same as


the diameter of the sample at the beginning of the test. (Figure 8.21). By so doing, the UW Meltmeter test readily becomes a creep test — apply an instantaneous and constant stress and record the strain with time. In order to stay within the linear viscoelastic range, however, the test temperature of 40°C and a constant stress of 1119.5 Pa were selected. The generalized Kelvin* model was considered for repre-senting creep data. The mathematical representation of the time-dependent compli-ance of the generalized Kelvin Model is:

(8.2)

(8.3)

FIGURE 8.20 UW Meltmeter dual unit (top) and one of the sample wells being prepared for a test (bottom).

* Also called Kelvin-Voigt model (see Chapter 2).

J t J J tt

i ivi

N

( ) = + − −( )[ ] +=

∑0

1

1 exp τη

τη

ii

iE=


(8.4)

where: J(t) is the total shear creep compliance at time t; J0 (1/E0) is the instan-taneous rigidity compliance; Ji (1/Ei) are the retarded compliances; τi (ηi /Ei) are the retardation times; ηi are the retarded viscosities; Ei are the elastic moduli of springs; and ηv is the Newtonian viscosity. The tensile creep compliance function D(t) is equal to one-third of J(t).

Since the biological materials typically have more than one retardation time, the behavior of such materials cannot be represented by a single Kelvin model or by a four-element Burger model. A six-element Kelvin model (Figure 8.22) was found to provide the best fit in describing the experimental creep data, according to Equation 8.2. Accordingly, the following equation represents the cheese flow data.

TABLE 8.6Comparison of the Meltability Evaluations of Five Commercial Cheeses by the Schreiber and UW Meltmeter Tests (Based on Three Replications Each)

Sample

Schreiber Test UW Meltmeter Test1

Average2 Std. Dev. CV3,% Average Std. Dev. CV,%

1 2.92a 0.12 4.1 0.45a 0.005 1.12 3.33b 0.24 7.2 0.60b 0.010 1.73 3.00bcd 0.41 13.7 0.40c 0.011 2.84 2.42e 0.12 5.0 0.35d 0.009 2.65 3.67bc 0.47 12.8 0.64e 0.009 1.4

Mean CV,% 8.6 1.9

1 Reciprocal of sample height 5 s after the cheese was allowed to flow at 60°C.2 Superscripts of same letters are statistically not different at the 5% level of significance.3 CV = Coefficient of Variation (= Average * 100/Std. Dev.).

FIGURE 8.21 Creep-test geometry in UW Meltmeter is the same as in Figure 8.16, except the diameter of the top plate and the sample are the same at the beginning of the test.

(b) (c)(a)

D tt

J t( ) = ( ) = + ( )εσ0

13


(8.5)

where: J(t) is the total creep compliance at time t; J0 is the instantaneous rigidity compliance; J1 and J2 are the retarded compliances; τ1 and τ2 are the retardation times; and ηv is the Newtonian viscosity. In Figure 8.23, the fitted value overlaid with the observed data indicates an excellent fit of the model.

The values of the viscoelastic parameters calculated for both full- and reduced-fat cheeses are given in Table 8.7. The higher instantaneous compliance reflects a high degree of nonretarded Hookean-type deformation, indicating that the polypep-tide strands in the network are relatively free to rearrange between crosslinks.

FIGURE 8.22 Generalized six-element Kelvin model used to fit the creep data of cheese. (After Kuo et al., 2000. With permission.)

FIGURE 8.23 Prediction of creep compliance of Cheddar cheese by six-element Kelvin model. (After Kuo et al., 2000. With permission.)

0

0.2

0.4

0.6

0.8

1

Cre

ep c

ompl

ianc

e (1

/kP

a)

0 20 40 60 80 100 120 140 160

Time (s)

Predicted

Experimental

J t J J t J tt

v

( ) = + − −( )[ ] + − −( )[ ] +0 1 1 2 21 1exp expτ τη


Reduced-fat cheese had a lower instantaneous compliance J0 than full-fat cheese. This suggests that a reduction in fat results in an increase in protein content, and thus an increase in the elastic (or solid-like) character of the reduced-fat cheese. The higher Newtonian viscosity ηv of reduced-fat cheese suggests a greater resistance to flow at longer time. Thus, reduced-fat cheese would seem to retain more of its solid-like viscoelastic structure than full-fat cheese.

A typical creep curve and corresponding mechanical model (six-element Kelvin model) are shown in Figure 8.24. The curve has three segments corresponding to the Hookean, Voigt, and viscous elements. The retarded compliances J1 and J2

represent the principal components of the viscoelastic behavior of Cheddar cheeses. This reflects a high degree of retarded Voigt-type deformation in Cheddar under external loading.

The instantaneous slope of the creep curve can be calculated by taking the first derivative of Equation 8.5 at time zero. This instantaneous slope is defined as the viscoelasticity index VI, which is computed as:

(8.6)

In terms of Equation 8.6, the VI accounts for the constants J1, J2, τ1 , τ2, and ην .Both meltability and creep test provide consistent and reproducible results when

sample temperature and dimensions are controlled. A reasonably strong linear rela-tionship (R2 = 0.81) was obtained between VI and meltability of Cheddar cheese (Figure 8.25). The general trend is that the higher the VI, the better the meltability. The effect of fat reduction and ripening in Cheddar cheese was also accounted for by changes in the VI.

TABLE 8.7Viscoelastic Parameters for Six-Element Kelvin Model in Creep Test for Different Fat Levels in Cheddar Cheeses

Six-Element Kelvin ModelParameters

Cheddar

Full-fat Reduced-fat

J0 (1/kPa), instantaneous compliance 0.14a 0.11 a

J1 (1/kPa), retarded compliance 0.27 a 0.19 a

J2 (1/kPa), retardation compliance 0.55 a 0.46 a

τ1 (s), retardation time 3.35 a 3.25 a

τ2 (s), retardation time 28.046 a 23.89 b

ηv (kPa•s), Newtonian viscosity 137.9 a 149.6b

a,b Within each row, means without a common superscript differ (P < 0.05).

Source: After Kuo et al., 2000. With permission.

VIdJ

dt

J J

t v

= = + +=0

1

1

2

2

1τ τ η


DYNAMIC SHEAR RHEOMETRY

The dynamic shear rheometry or the small amplitude oscillatory shear (SAOS) test has become a popular test for characterizing rheological properties of foods. How-ever, applying this technique for cheese meltability evaluation has the problem of excessive slippage due to fat melting at elevated temperature.

The problem has been addressed by using serrated plates or plates with a fine grade of sandpaper glued on, or by bonding samples directly onto a plate using a

FIGURE 8.24 Illustration of typical creep curve showing correspondence to mechanical elements in the six-element Kelvin model. (After Kuo et al., 2000. With permission.)

FIGURE 8.25 Linear relationship between the viscoelastic index and meltability determined by UW Meltmeter test at 60°C (represented as change in sample height at 1 s after start of flow) for Cheddar cheese. (After Kuo et al., 2000. With permission.)

R2 = 0.81

0

1

2

3

4

5

0.00 0.05 0.10 0.15 0.20 0.25

Viscoelasticity Index (1/kPa.s)

Mel

tabi

lity

(mm

)


commercial adhesive such as cyanoacrylate ester (Nolan et al., 1989; Yun et al., 1994; Subramanian and Gunasekaran, 1997; Sutheerawattananonda and Bastian, 1998).

Another problem experienced during SAOS study of cheeses is moisture loss, especially at high temperatures and during tests that take a long time. This can be overcome by applying a mineral oil or similar coating to the samples (Subramanian and Gunasekaran, 1997; Sutheerawattananonda and Bastian, 1998).

SAOS tests have been widely used in determining the gel point of gelling systems such as polysaccharides and proteins. In these, the moment at which the system begins to change from a viscous liquid (sol) to an elastic solid (gel) during the course of the gelation process is known as the gel point. Among the many rheological means to detect gel point is when G′ becomes just greater than G′′ (Konuklar and Gunasekaran, 2002). This is known as the “cross-over” method. During heating of some gels, the G′–G′′ cross-over can also be used to identify gel melting transitions (Gunasekaran and Ak, 2000).

Sutheerawattananonda and Bastian (1998) examined the meltability of process Cheddar cheese based on the cross-over temperature (Figure 8.26). They investigated the effect of emulsifying salts trisodium citrate (TSC) and disodium phosphate (DSP) and moisture content. The cross-over temperatures for process cheeses made with TSC was lower than those made with DSP (56.5°C compared to 64.6°C). This finding was substantiated by similar results reported earlier using the tube method (Savello et al., 1989). In addition, Arrhenius rate constant (slope of complex viscosity η* vs. inverse of absolute temperature plot) was higher for the TSC cheese than for the DSP cheese. Though this is not a rigorous study, it supports the notion that the crossover point can be used to identify the solid-like to liquid-like phase transitions the cheese undergoes during melting.

FIGURE 8.26 Storage (G′ ) and loss (G″ ) moduli vs. temperature for process cheese made with disodium phosphate (DSP) and trisodium citrate (TSC). (After Sutheerawattananonda and Bastian, 1998.)

20 40 60 80 100101

102

103

104

105

G′ o

r G

′′ (P

a)

Temperature (°C)

DSP

TSC

G′ G′′


In a purely empirical exercise, Ustunol et al. (1994) established a linear relation between meltability as measured by the Arnott test and the complex modulus G*for Cheddar cheeses made with 0 to 34.3% fat content (Figure 8.27). The large data scatter and low R2 value (0.64) make their claim suspect unless further rigorous test results are available. No scientific reasons were suggested for such observed corre-lation, and perhaps none is possible. In fact, Sutheerawattananonda and Bastian (1998), in their study with process Cheddar cheese, could not substantiate the results of Ustunol et al (1994).

HELICAL VISCOMETRY

Kindstedt et al. (1989a) proposed an instrumented method to measure meltability of Mozzarella cheese. In this method, known as helical viscometry, a rotational viscometer (e.g., Brookfield) is used. A T-bar spindle is attached to the rotating part instead of a cylindrical spindle as used in a typical rotational viscometry. The T-bar is lowered inside a ground mass of Mozzarella held (at 60°C) in a glass beaker. The torque to rotate the spindle at a certain speed (1 rpm) as the T-bar spindle is raised through the melted cheese is recorded. This is a variation of the cheese viscosity measurement by Lee et al. (1978) using a T-bar spindle without raising the T-bar during the measurement. The peak torque recorded and expressed in relative units of the full-scale response of the viscometer is used as an index of meltability. The viscometer displays an apparent viscosity value in centipoise. Thus, it is very much an empirical measurement mode using a standard laboratory viscometer. The helical viscometry measurement is illustrated in Figure 8.28. Though this method was reported to provide useful measurements (Kindstedt et al., 1989b), the protocol was revised due to problems with measurements made on Mozzarella cheeses of different compositions and ages. The lack of sufficient free oil in some Mozzarella cheeses was thought to interfere with the helical viscometry measurements. Hypothesizing

FIGURE 8.27 Meltability measured by Arnott test vs. complex modulus. (After Ustunol et al., 1994. With permission.)

6

5

4

3

2

1 1.5 2 2.5 3

Mel

tabi

lity

by A

rnot

t tes

t (cm

)

log G* (Pa)

Meltability = 4.45–0.52 log G* (R2 = 0.64)


that the natural formation of free oil in Mozzarella cheese during melting may improve the helical viscometer measurement by minimizing artifacts from heat and moisture loss, Kindstedt and Kiely (1992) proposed using exogenous butter oil on the samples. For this, unsalted butter was melted at 60°C and centrifuged for 5 min. After decanting off the oil phase, it was added to the samples halfway through the 60 min of sample melting period. The addition of 25 mL of butter oil to a 150-g sample was reported to improve the consistency of test results judged by the smaller coefficient of variation compared to the results obtained without using butter oil.

Savage and Mullan (2000) reported a very large coefficient of variation even in maximum torque measurement (21–50%) with butter oil added. They concluded that helical viscometry is not suitable for assessing the functional properties of unripened Mozzarella. This should only highlight the sensitivity of semiempirical tests, such as the helical viscometry test and others to moisture loss and uncontrolled heating. For lack of a better method and due to its apparent objectivity by using a commonly available viscometer, several researchers have since used this method for reporting meltability of Mozzarella and related cheeses. Some have further modified the procedure (Fife et al., 1996).

CHEESE MELT PROFILE MEASUREMENT

During heating cheese undergoes a phase change from solid to liquid. This transition, plotted as “cheese flow vs. heating time,” is known as the cheese melt profile. A typical cheese melt profile is shown in Figure 8.29. It depicts the transition of cheese flow from the “flow initiation zone” to “flow termination zone” via “rapid flow zone,” where most of the flow occurs. The cheese temperature vs. heating time may also be plotted along with the melt profile to assist in graphical determination

FIGURE 8.28 Helical viscometry. A T-bar spindle is immersed in melted cheese and raised as it is being rotated by means of a Helipath drive. The Brookfield viscometer gives a reading proportional to torque. (After Kindstedt et al., 1989a.)

Water bath

Melted cheese

T-bar spindle

Brookfiledviscometer

Helipath drive


of cheese melt/flow parameters. Also, the cheese sample height may be normalized with respect to the initial sample height.

The major advantage of the cheese melt profile measurement is that it facilitates determining several parameters, in addition to cheese meltability, that are relevant to end-use applications of cheese. Some of the parameters that can be determined from the melt profile are as follows:

1. Softening point (TSP) — temperature at which the cheese flow transitions from flow initiation zone to rapid flow zone (i.e., temperature of cheese at which the cheese changes from a semisolid to an almost free-flowing liquid)

2. End point (TEP) — temperature at which the cheese flow transitions from rapid flow zone to flow termination zone

3. Softening time (tSP) — heating time from beginning until TSP

4. End time (tEP) — heating time from beginning until TEP

5. Rapid flow time (tRF) — heating time between TSP and TEP

6. Flow completion time (tFC) — heating time from beginning until end of flow (i.e., no further measurable cheese flow) or end of test

7. Inflection point (IFP) — point at which the slope of the melt profile is maximum

8. Maximum flow rate (MFR) — slope at IFP9. Average flow rate (AFR) — slope of the line connecting TSP and TEP. The

AFR is the estimate of cheese meltability in this test

In addition, knowing the mass and thermal properties of cheese, one can calculate thermal energies involved in different flow ranges.

The concept of softening point temperature can be used advantageously by cheese manufacturers for tailor-making cheeses that will soften but may not flow for certain applications (e.g., when used on a hamburger). The AFR measurement

FIGURE 8.29 Schematic of the cheese melt profile (cheese sample height vs. time) along with cheese temperature vs. time curve. (After Gunasekaran et al., 2002. With permission.)

Time (s)

Che

ese

sam

ple

heig

ht (

mm

)

Che

ese

sam

ple

tem

pera

ture

(°C

)

TSP

tSP tEP tFC

Flow initiation zone Rapid flow zone Flow termination zone

AFR

TEP

IFP

MFR

tRF


is the equivalent of cheese meltability measurement. For most cheeses, TSP and AFR trends follow each other. But they can vary independently.

UW MELT PROFILER

The UW Meltmeter can be used to obtain the cheese melt profile. Since, the UW Meltmeter test is performed at a constant temperature, a series of tests at different temperatures should be performed. Such a procedure is rather time consuming. Therefore, Muthukumarappan et al. (1999a) adapted the UW Meltmeter to perform a transient temperature test. The squeeze-flow measurement platform, along with the LVDT deformation sensor, is placed inside an oven. The cheese sample height is recorded continuously as the sample is heated by the oven set at a constant tempera-ture. A thermocouple inserted at the sample center is used to record the cheese temperature simultaneously. This apparatus is similar to the UW Meltmeter without the sample heating and moving cylinder sections, and is called the UW Melt Profiler (Figure 8.30). The sample used in both tests is a 30-mm-diameter, 7-mm-thick disk.The transient temperature test is performed in the oven set at a temperature in the range of 60 to 80°C. Different sample sizes and test temperature may be used for sample-to-sample comparisons.

DETERMINATION OF MELT PROFILE PARAMETERS

GRAPHICAL METHOD

As illustrated in Figure 8.29, the graphical method involves constructing tangents to the curves in different flow zones. The temperature corresponding to the inter-section of tangents of the flow initiation zone and rapid flow zone is TSP. Similarly, the temperature at the intersection of tangents of the rapid flow zone and flow termination zone is the TEP. Once these points are identified, then other parameters are easily read off the plot or calculated. The tangents can either be drawn manually or with a graphical program. Though this method is very easy to apply, it is prone to error, as the tangents are easily manipulated by considering different data ranges.

MODELING MELT PROFILE

CONSTANT TEMPERATURE TEST

Due to the highly nonlinear and asymmetrical nature of the melt profile, attempts to develop simple models whose coefficients can be related to melt/flow parameters were rather difficult. A fourth-order polynomial gives a good fit between logarithm of biaxial elongational viscosity (ηB) of the cheese and temperature (T):

(8.7)

where, a0, a1, a2, a3, and a4 are constants. The second differential of the above equation exhibited the maxima of the [log(ηB) vs. T] curve (Figure 8.31a, b). The exact transition point was determined from the third differential as explained below:

log ηB a a T a T a T a T( ) = + + + +0 1 22

33

44


(8.8)

FIGURE 8.30 UW Melt Profiler device. Schematic drawing (top) and picture when used inside an oven (bottom).

d

dTa a T

settingd

dT

T Ta

a

B

B

SP

3

3 3 4

3

3

3

4

6 24

0

4

η

η

= +

=

= =−


TRANSIENT TEMPERATURE TEST

In this case, we fit the sample height (h) vs. heating time (t) data to a fourth-order polynomial and softening time (tSP) is determined by setting d3h/dt3 = 0. The softening point (TSP) is calculated by substituting the tSP for t in the T vs. t regression model.

The melt profile obtained by the transient temperature test using the same cheese as in Figure 8.31 is shown in Figure 8.32. As can be observed, regardless of the test method, the TSP determined is about the same. However, the transient temperature takes considerably less time (about 15 min per sample). Since, test duration is a critical issue, especially for routine testing in the industry, the transient test is recommended.

FIGURE 8.31 Biaxial elongational viscosity (ηB) vs. Cheddar cheese temperature obtained using UW Meltmeter. Softening point (TSP) is determined by constructing tangents (top) and by determining maxima of the curve (bottom). (After Muthukumarappan et al., 1999b. With permission.)

Cheese temperature (°C)

30 40 50 60 70

η+ B (P

a.s)

102

103

104

105

106

tSP = 48°C


30 35 40 45 50 55 60 65 70−0.006

−0.004

−0.002

0.000

0.002

0.004

0.006

TSP = 48°C

d2 log

(ηB)/

dT2


The transient test cheese flow data may also be plotted as sample height vs.cheese temperature (Figure 8.33a, b). This plot shows only two zones, unlike the three distinct zones in the melt profile. The first is the heating zone, where the sample temperature changes more than its height; and the second is the melt/flow zone, where most of the flow occurs. The temperature at the transition from the heating to flow zone is the TSP, which can be determined by constructing tangents or by other computational methods described earlier. The slope of the straight-line portion of the flow region, the flow rate, is a measure of cheese meltability (similar to AFR). For a given sample, TSP determined is not affected by how the data are plotted (Figure 8.33). However, the flow rate calculated in the height vs. temperature curve is smaller than AFR, as it includes the flow termination zone observed in the melt profile. The difficulty in observing the flow termination zone is the major drawback in the cheese height vs. temperature plot. Therefore, the melt profile is evaluated using the cheese height vs. heating time plot in conjunction with the cheese temperature vs. heating time curve.

Though the polynomial curve fitting procedure is a valid method for parameter estimation, it has some drawbacks. The data range included in the polynomial models have an effect on the parameters determined, and the R2 value cannot be the sole judge of the goodness of fit of the data (Figure 8.34). Small deviations at critical regions have a large effect on the parameters. To avoid these, and to speed up the parameter determination, Venkatesan et al. (2000) developed a LabVIEW (National Instruments Corp., Austin, TX) program used with a computer data acquisition system to capture and analyze the melt profile obtained from the UW Melt Profiler almost in real time. In this method, the melt profile is divided in half at the IFP and then, using a coordinate-shift algorithm, the TSP and TEP are determined. The program can also evaluate the data and terminate the test as prescribed by the user. Since this method is programmed using LabVIEW, it is simple and fast. Figure 8.35 shows a computer screen the

FIGURE 8.32 Melt profile of Cheddar cheese obtained by transient temperature test in UW Melt Profiler. Softening point (TSP) is determined by constructing tangents. (After Muthukuma-rappan et al., 1999b. With permission.)


LabVIEW program outputs displaying the cheese melt profile, cheese and oven temperature curves, and some of the melt/flow parameters determined.

Just as in the case of meltability measurements (Wang and Sun, 2002a, b), the melt/flow parameters determined from cheese melt profile are also affected by experimental conditions — sample size, test temperature, surface over which the melt flows, force causing flow, etc. Therefore, the results from this test do not represent a “property” of the cheese, but rather an estimate. The results can be used for sample-to-sample comparison only when they were determined under the same experimental protocol.

FIGURE 8.33 Melt profile of reduced-fat Cheddar cheese (top) and the same data plotted as cheese height vs. temperature (bottom). Both plots give same softening point (TSP). The end point (TEP) is not observable in the bottom plot. The average flow rate (AFR) measured from the top plot is larger than the flow rate measured from the bottom plot.

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200

Heating time (s)

Nor

mal

ized

che

ese

heig

ht

0

10

20

30

40

50

60

70

Che

ese

tem

pera

ture

(°C

)

TEP

TSP = 46°C

tEPtSP = 380 s

Slope = AFR

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

10 20 30 40 50 60 70


Nor

mal

ized

che

ese

heig

ht

0

200

400

600

800

1000

1200

Hea

ting

time

(s)

TSP = 46°C tSP = 380 s

Slope = Flow rate


CONDUCTION HEATING

The UW Melt Profiler was designed to be used inside a convection oven. Due to poor convective heat transfer in the oven, this procedure requires more than 15 min per test. Gunasekaran et al. (2002) described modifications to the UW Melt Profiler

FIGURE 8.34 A fourth-order polynomial gives a good fit to cheese melt profile as noted by high R2 value. But deviations at transition regions can cause large errors in melt/flow parameter determination.

FIGURE 8.35 Computer screen displaying the melt profile and cheese and heating source temperature vs. time traces. Some melt/flow parameters automatically determined instanta-neously upon test completion. (After Gunasekaran et al., 2002. With permission.)

(R2 = 0.9958)

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200Heating time (s)

Nor

mal

ized

che

ese

heig

ht

4th-order polynomial fith(t) = 3E–13t4 + 1E–09t3–2E–06t2 + 0.0006t + 0.9622


by eliminating the convection oven as the heat source. Instead, they heated the cheese sample by conduction via foil heaters embedded inside the top and bottom metal plates (Figure 8.36). These aluminum plates (4-mm thick; 90-mm diameter) are in constant thermal contact with cheese sample. This allows the sample to be heated quickly. Thermocouples are used to continuously monitor and control the tempera-ture of sample and heating plates to ensure that the sample is not scorched. To minimize any possible convective cooling to the surrounding, an optional air shield is installed around the sample. Not requiring an oven to perform the melt test also reduces the overall cost and space requirements. In addition, the sample is easily accessible for temperature sensing and visual observation as needed.

The melt profiles obtained using this conduction test (at 70°C) is similar to that of the typical melt profile (obtained by convection heating in the oven) (Figure 8.37).

FIGURE 8.36 Modified UW Melt Profiler. The convective oven is replaced by direct con-duction heating via foil heaters embedded in the top and bottom plates. (After Gunasekaran et al., 2002. With permission.)

FIGURE 8.37 Melt profiles of high melt (Hi-melt) and medium melt (Med-melt) and restricted melt process cheeses obtained by the modified UW Melt Profiler. (After Gunaseka-ran et al., 2002. With permission.)

Foil Heaters

Bottom heating plate

Thermocouple

Optionalair shield

LVDT

To data acquisition

To heater controller

Top heating plate

Cheese sample(5-mm thick)


In the case of the restricted melt cheese, the melt profile was atypical because the cheese virtually did not melt at the test temperature. The conduction test takes less time (about 3 min) than the convection test, as measured by TEP, especially at low test temperatures. As mentioned previously, the softening point temperatures signify the transition of cheese from being a solid to almost free-flowing liquid. In an SAOS test, this will correspond to the crossover temperature (i.e., tan δ = 1). The softening point temperatures obtained for different cheeses in the UW Melt Profiler test (at 70°C) and the modified UW Melt Profiler test (at 70°C) are compared with the SAOS crossover temperatures (obtained in temperature sweep test, cheese heated to 80°C at 5°C/min) in Figure 8.38. The softening points determined in the modified UW Melt Profiler test match more closely the crossover temperatures than those obtained in the UW Melt Profiler test. Due to highly nonmelting characteristic of the restricted melt process cheese, the softening point and crossover temperature comparisons for that cheese are not valid.

For the same cheese and at same test temperature, the TSP and AFR were higher in the conduction test compared to the convection test (Figure 8.39). Moreover, the AFR seems to plateau after 60°C test temperature in the conduction test indicating lower test temperature may be sufficient. This further illustrates that not only the temperature (Muthukumarappan et al., 1999b; Wang and Sun, 2002a; 2002b) but also the rate of heating has an effect on the melt-related transitions in the cheese. It is interesting to notice that the high-melt process cheese

FIGURE 8.38 Comparison of softening point temperatures from UW Melt Profiler (open bars) and modified UW Melt Profiler (bars with hatch marks) with cross over temperatures obtained in SAOS tests (filled bars) for process (high melt, medium melt, and restricted melt) and natural (Monterey Jack and Mozzarella) cheeses. Melt Profiler testes were performed at 70°C; SAOS test was performed by temperature sweep to 80°C at 5°C/min. Restricted melt process cheese did not yield valid softening points due to virtually no melting.


had a higher average flow rate but a lower softening point than the medium-melt process cheese. This is an example that the softening point may vary independently of meltability of cheese.

REFERENCES

Ak, M.M. 1993. Rheological Measurements on Mozzarella Cheese. Ph.D. Thesis, University of Wisconsin-Madison.

FIGURE 8.39 Softening point (top) and average flow rate (bottom) of high melt (Hi-melt) and medium melt (Med-melt) process cheeses measured by the UW Melt Profiler (CV test) and modified UW Melt Profiler (CD test) at different test temperatures. (After Gunasekaran et al., 2002. With permission.)


Ak, M.M. and S. Gunasekaran. 1992. Stress–strain curve analysis of Cheddar cheese under uniaxial compression. Journal of Food Science 57(5):1078–1081.

Ak, M.M. and S. Gunasekaran. 1995. Evaluating rheological properties of Mozzarella cheese by the squeeze flow method. Journal of Texture Studies 26:695–711.

Arnott, D.R., H.A. Morris, and W.B. Combs. 1957. Effect of certain chemical factors on the melting quality of process cheese. Journal of Dairy Science 40:957–963.

Bogenrief, D.D. and N.F. Olson. 1995. Hydrolysis of β-casein increases Cheddar cheese meltability. Milchwissenschaft 50(12): 678–682.

Breene, W.M., W.V. Price, and C.A. Ernstrom. 1964. Manufacture of pizza cheese without starter. Journal of Dairy Science 47:1173.

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Fife, R.L., D.J. McMahon, and C.J. Oberg. 1996. Functionality of low-fat Mozzarella cheese. Journal of Dairy Science 79:1903–1910.

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Measuring Cheese Stretchability

Stretchability is unique to Mozzarella and other pasta filata style cheeses. It is the property that allows Mozzarella cheese to form fibrous strands when heated and stretched. More than any other property, the fact that Mozzarella cheese forms strings when stretched is its most distinguishable characteristic. Almost all pizza packaging and commercials show a pizza slice lifted off the pan with strands of melted Mozzarella cheese stretching out from the slice to the pan (Figure 9.1). Apparently, this stretchy quality enhances consumer appeal for pizza and other prepared foods containing Mozzarella cheese. Stretchability of Cheddar type hard and semihard cheeses are also occasionally reported as a way of comparing the effect of manufacturing variables among cheeses. As in the case of cheese meltability (and other functional properties), there is no formal definition for stretchability. Only empirical methods are still being used widely to measure Mozzarella stretchability. We define stretchability as “the ease and extent to which melted Mozzarella can be drawn to form strings.” Some empirical and instrumented methods developed for measuring this attribute are described below.

EMPIRICAL METHODS

One of the oldest methods to test stretchability is with the help of a fork. The “fork test,” as it is called, is performed by picking up a lump of melted cheese vertically with a fork until the bulk of the cheese strands break (Figure 9.2). The length of the strands at failure is taken to indicate stretchability. The test is usually performed on Mozzarella melted on a pizza crust containing pizza sauce. The type and size of crust, amount of sauce, oven used, and baking conditions are determined by the user. McMahon (1996) listed some additional details such as: crust size (8 to 14 in; 20 to 36 cm in diameter), amount of pizza sauce (2 to 5 oz; 60 to 150 g), amount of cheese (8 to 12 oz; 240 to 360 g), baking time (4 to 6 min), and oven temperature (400 to 550°F, 104 to 188°C or higher). He also stated that a typical test would be performed using a 12-in (30-cm) diameter crust, 4 oz (120 g) of sauce, and 10 oz (300 g) of shredded cheese. The pizza should be baked for 4 to 6 min at 500°F (160°C) and allowed to sit for 30 to 60 s before the fork is inserted to stretch the melted cheese. Despite these guidelines, the fork test is performed very differently in practice, especially in an industrial setting. The uncontrolled thermal (cheese temperature at time of stretching), rheological (direction and speed of stretching), and physical (sample size) variables make test results subjective even if some or all of the guidelines above are followed. Therefore, results of a fork test are only suitable for sample-to-sample comparison at the same location. When performed with care and replicated sufficiently, experienced operators can control some of the data variability and produce reasonably reliable results. This, and the fact that it is such an easy test to perform, contributes to its popularity and wide use by the industry.

9


INSTRUMENTED METHODS

Rheologically speaking, stretchability is a uniaxial property (compared to meltabil-ity, a biaxial property). Based on our definition of the “ease and extent” of stretch, an objective test should account for the applied force or stress (the ease of stretch) and the failure deformation or strain (the extent of stretch). This is easier said than done. A prerequisite for a proper tensile test is a proper grip on the sample. For food and biological materials, a good grip is not easily achieved. Such materials are often soft. Therefore, they tend to deform at the grips, and the stress concentration around the grip areas also leads to failure at the grips. This complicates data analysis. In the case of cheese, the additional problems are due to high test temperature and the difficulty in measuring the applied stress. Since the fibrous strands that form continuously yet randomly will thin out and break, typical stress profiles are very jagged. Therefore, most tests focus mainly on characterizing failure strain as an indicator of stretchability. Many of the tests described in this section are indeed empirical in nature and imitative at best.

FIGURE 9.1 A pizza slice lifted off the pan to show stretchy strands of melted Mozza-rella cheese.

FIGURE 9.2 The fork test is still the most commonly used in industry to test for cheese stretchability. (After NZDRI, 1997.With permission.)


VERTICAL ELONGATION

Tensile tests that vertically strain a cheese sample until failure reflect how we intuitively perceive the stretch, in effect mimicking the fork test. It is the most popular tensile test configuration. In one such test (Pena et al., 1996), a fork of different design is mounted on the moving crosshead of the uniaxial test device (e.g., Texture Analyzer).Among the probes used (3.8-cm × 2.0-cm fork prongs, 3.2-cm × 0.8-cm solid rect-angle, and 3.2-cm × 1.9-cm open-wire rectangle) at various test speeds using different cheeses, the best agreement with instrumented data and sensory panel scores was obtained with the open-wire rectangle probe operated at 1 mm/s.

Gunasekaran and Ak (1997) described a stretch test in which a T-bar is used in place of a fork to hold and lift the cheese using the crosshead of an Instron. In this T-bar stretch test, the sample is held in a temperature-controlled Petri dish (Figure 9.3). The T-bar stays immersed during melting of the cheese shreds. As the T-bar is raised, strands are formed and stretched at a constant deformation rate. The resultant force–deformation curve is termed the “stretch profile.” The stretch profile

FIGURE 9.3 Vertical elongation stretch with a T-bar. (After Gunasekaran and Ak, 1997.)

100-gLoad Cell

Instron Crosshead

Cheese shreds

Water in

Water outPetri dish

T-bar

Stainless steelRecirculatingwater tank

Latch to hold Petri dish

200 mm

255 mm

Constant deformation rate stretching

Thermocouple

To data logger

180 mm

48.2 mm

Diameter1.57 mm


is analyzed to determine the peak force (a measure of ease of stretch) and failure strain (a measure of extent of stretch). In addition, toughness (area under the force–time — deformation — curve) can also be measured to represent the combined effect of peak force and stretch length (Table 9.1).

A typical stretch profile is shown in Figure 9.4, along with cheese temperature during stretching. Some features are obvious from this. After reaching a peak, the force decreases steadily. Breakage of cheese strands and eventual failure of the entire stretch are also discernable. The stretch profiles obtained for Mozzarella, pizza, and Cheddar cheeses are shown in Figure 9.5. The stretch profiles of Cheddar and pizza cheeses are similar, though the stretch length of the pizza cheese is higher than that

TABLE 9.1T-Bar Stretch Test Data for Mozzarella Cheesea

Measureof Stretchability

Speed of Stretch(cm/min) Age (d)

20 50 40 54

Peak stretch force (N) 0.39±0.031a 0.61±0.029b 0.51±0.028a 0.49±0.032a

Stretch length (cm) 17.7±1.55a 18.6±1.47a 20.0±1.4a 16.3±1.62b

Toughness (N.m) 2.3±0.24a 2.6±0.23a 3.0±0.22a 1.9±0.25b

a Mean ± standard deviation are listed; data in each row followed by same letter superscripts are not statistically different.

Source: After Gunasekaran and Ak, 1997.

FIGURE 9.4 Typical cheese stretch profile determined in the T-bar stretch test: A — peak stretch force; B — breaking of cheese strands; C — breaking of entire cheese stretch. Simul-taneous measurement of cheese temperature is also shown. (After Gunasekaran and Ak, 1997.)

Time (s)

806040200 100

For

ce (

g) o

r T

empe

ratu

re (

°C)

0

10

20

30

40

50

60Crosshead speed: 20 cm/min

A

B

B

C

Stretch length

Force

Cheese Temperature

Peakforce


of Cheddar. This figure clearly shows that Mozzarella cheese generally stretches better than pizza and Cheddar cheeses. The requisite failure strain was not attained, as some strands were still there even after the instrument crosshead travel limit has been reached. It can also be observed that the strands are also fairly strong. Of these three cheeses, only Mozzarella has the oriented protein fiber network in its micro-structure. The pizza cheese is a nonpasta filata Mozzarella cheese that is manufac-tured following make procedures similar to that of Mozzarella, but without the crucial mixing and molding step which imparts Mozzarella cheese its characteristic oriented strands (Chen and Johnson, 1999).

Common problems associated with uniaxial stretch tests, such as the one described above, are the effect of deformation rate (i.e., crosshead speed) and temperature change during the test. The cheese strands can cool rapidly because they are exposed to room temperature and, more importantly, are thinning out. In Figure 9.4 the cheese temperature decreases almost linearly at about 20°C/min. Such cooling can harden the strands with concomitant increase in force (Figure 9.5), and may shorten the stretch length.

The effect of deformation rate on viscoelastic materials is well known. At higher deformation rates, either in compression or tension, the material force (or stress) response is higher. This is evident in the tests performed at deformation rates of 20 cm/min and 50 cm/min (Table 9.1). However, stretch length and toughness were not significantly different. The age effects are significant in terms of stretch length and toughness.

A variation of the tensile test was developed at the Utah State University (Fife et al., 2002). Besides using a different probe to draw a sample (at the deformation rate of 1.7 cm/s) from melted cheese (Figure 9.6), they evaluated three parameters from the stretch profile, the load vs. time curve obtained during the tensile test. They

FIGURE 9.5 Comparison of stretch profiles of Mozzarella, pizza, and Cheddar cheeses. (After Gunasekaran and Ak, 1997.)

0

20

40

60

80

100

120

0 5 10 15 20 25

Time (s)

For

ce (

g)

65 70 75

MozzarellaPizzaCheddar

End of crosshead travel limit.Some Strands still intact.

Crosshead speed: 50 cm/minTest temperature: 55°C


are: melt strength — the peak load; stretch length — maximum length of cheese strands until failure (or until maximum stroke length of the test device is reached); and stretch quality — a measure of the ability of the cheese strand(s) to remain together as a cohesive mass while being stretched. Stretch quality is calculated as the mean value of the load exerted as the strands elongate from 5 to 20 cm. These are illustrated in Figure 9.7. Typical data obtained from this test are summarized in Table 9.2 for low-fat Cheddar and part-skim and low-fat Mozzarella cheeses.

Low-fat Mozzarella does not stretch well, as indicated by the poor stretch length and stretch quality data. Surprisingly, low-fat Cheddar was better than low-fat Mozzarella in all measured parameters.

Another imitative tensile test was proposed by Apostolopoulos (1994). He used a 165-mm-diameter Perspex plate in which a 60-mm-diameter center piece was cut and a vertical rod attached (Figure 9.8). A pizza crust is similarly cut with a hole at the center to accommodate the vertical rod. The pizza base is placed over the Perspex plate and sprinkled with a measured quantity of shredded cheese. This entire

FIGURE 9.6 Three-pronged hook used in the Utah State University (USU) stretch test. All dimensions are in mm. (After Fife et al., 2002.)

81.00

11.00

4.38

7.00

25.50

2.62

26.00

f10.00f2.00 f3.50

12.75


arrangement is heated in a microwave oven for 15 s. Then the vertical rod is attached to the crosshead of a uniaxial testing machine, and the center piece is pulled up vertically at 25 mm/s. Stretchability is measured as the distance through which the center piece could be lifted until all the strands failed.

FIGURE 9.7 Stretch profile obtained in Utah State University (USU) stretch test to measure melt strength, stretch length, and stretch quality of low-moisture, part-skim Mozzarella cheese at different temperatures. (After Fife et al., 2002.)

TABLE 9.2Stretch Profile Data Determined by the Utah State University Stretch Test at 70°C

CheeseAge(d)

Melt Strength(g)

Stretch Length(cm)

Stretch Quality(g)

Low-fat Cheddar 400 143 31 10Part-skim Mozzarella 26 191 31 21Low-fat Mozzarella 38 127 5 1

Source: After Fife et al., 2002.

Stretch Length

Stretch Quality

Melt Strength

250

200

150

100

50

0

50

0

50

0

50

00 5 10 15 20 25 30

60C

70C

80C

90C

Length (cm)

Load

(g)


Ak and Gunasekaran (1995) reported a significant variation in tensile testing of Mozzarella. Unlike other tensile tests, their test did not require the use of a materials testing machine either to stretch the cheese or to record the force and time data. It was based on the technique used by Tschoegl et al. (1970) for determining large deformation and rupture properties of wheat flour dough in simple tension.

The test is performed in a specially designed apparatus (Figure 9.9). A dumbbell-shaped cheese sample is allowed to stretch by its own weight while suspended in hot oil (60°C). At the end of the test, the sample is removed by means of a strainer located at the bottom. The test section of the sample is 6 mm thick, 7 mm wide, and 60 mm long. An optical sensor records the downward movement of the sample by counting the number of holes on a wheel the descending cheese turns. This information is used to calculate the strain rate. The sample is suspended by a load cell, and the data from which are used to calculate the stress. Using the stress and strain rate values, elongational viscosity is calculated. This viscosity is more accu-rately termed “transient elongational viscosity” because the strain rate is not constant during the test (Figure 9.10). The pulling weight can be increased by adding external weights to the sample. The calculations are made using the following equations:

(9.1)

(9.2)

FIGURE 9.8 Imitative tensile stretch test of Mozzarella cheese on a pizza. (After Apostolo-poulos, 1994. With permission.)

Hencky strain : εH

L t

L=

⎛

⎝⎜⎞

⎠⎟ln

( )

0

True stress : σ =− −

⎛⎝⎜

⎞⎠⎟

m gd L t

dF

A LL t

B

2

2

0 0

( )

( )


(9.3)

where:

L(t) = momentary length at time tL0 = original length at time t = 0m = mass of sample (plus any added)g = acceleration due to gravityFB = buoyant forceAo = original sample cross-section area of sample at time t = 0

FIGURE 9.9 Vertical elongation stretch test apparatus schematic drawing (top) and photo-graph (bottom) along with the dumbbell-shaped cheese sample used. (After Ak and Gunasekaran, 1995. With permission.)

Wheel

Optical sensor

Hot water out

Thread

Hot water in

Strainer

Insulation

Hot oil bath

Optional weight

Dumbell-shapedcheese sample

Sample grip

Load cell

Transient elongational viscosity : η σ σε

+ =E

H

t( , )˙


The strain rate is calculated as:

(9.4)

where,

(9.5)

Equation 9.5 is a popular form to describe the stress-relaxation data (Peleg, 1980). The constants k1 and k2 are obtained by fitting the length vs. time of elongation curve (Figure 9.10) to Equation 9.5.

The ability to closely control test parameters and to make uniaxial elongation viscosity measurements makes this a fundamental test. Other advantages include use of hot oil as the heating medium, as compared to hot air in most other tests. The oil supports the cheese to some extent, keeping it from collapsing, and prevents moisture loss during the test. Moisture loss during a stretch test is significant because of high temperatures and large surface areas as the cheese strands thin out. However, the use of hot oil introduced an attendant problem of a messy work place. The transient elongational viscosity vs. strain rate plot (Figure 9.11) shows the strain-weakening nature of the cheese at high temperature. This is similar to the results of Smith et al. (1980) in capillary rheometry. However, Apostolopoulos (1994) reported that the elongational viscosity increased with biaxial strain rate at a constant temperature in biaxial compressive elongation tests. However, tests with 7- to 28-day-old Mozzarella indicated that transient elongational viscosity was not significantly affected by aging. This is contrary to the widely accepted notion that

FIGURE 9.10 Stretch length changes nonlinearly during the vertical elongation test as cheese temperature increases with time. (After Ak and Gunasekaran, 1995. With permission.)

0 10 20 30 40 50 60 700.05

0.1

0.15

0.2

0.25

0.3

R2 = 0.95

Time (s)

Leng

th (

m)

˙( )

εH L t

dL

dt= 1

L t Lk k t

( ) = −+

⎛

⎝⎜⎞

⎠⎟01 2

11


proteolysis during storage breaks down αs1-casein which renders cheese softer and improves melt/flow and stretch properties. Perhaps this method is not sensitive enough to distinguish age-related stetchability variations in Mozzarella.

HORIZONTAL EXTENSION

Ak et al. (1993) developed another fundamental method in which the cheese is stretched horizontally even though the test device operates as if it were a tensile test. For tensile tests, the sample is normally held vertical, as described previously. The problem of sample sagging under gravity, which might occur in both configu-rations, is generally overcome by surrounding samples with a density-matching medium. This also serves to maintain temperature uniformity and to prevent food samples from drying out (Tschoegl et al., 1970; Vinogradov et al., 1992). In addition, they devised a method to clamp the samples during the test. The main experimental difficulty in tensile tests is to ensure that the specimen does not break at the clamps. This problem has been overcome by adapting approaches used in testing engineering materials (Luyten, 1988) and gellan gels (Lelievre et al., 1992).

A schematic of the uniaxial horizontal extension apparatus is presented in Figure 9.12. It is operated in conjunction with a materials testing machine and consists of a double-walled steel sample chamber. The sample chamber is filled with mineral oil and maintained at a constant temperature to ensure uniform sample temperature and to prevent moisture loss. A dumbbell-shaped cheese sample is held between a stationary clamp and a moving clamp. The entire sample and clamp module is immersed in the oil bath. During testing, the downward movement of the universal testing machine is translated to the moving clamp via a set of pulleys and cord into

FIGURE 9.11 Transient elongational viscosity vs. strain rate of Mozzarella cheese at 60°C in the vertical elongation test. (After Ak and Gunasekaran, 1995. With permission.)

0.001 0.01 0.1 1

106

105

104

103

Strain rate (s−1)

Tra

nsie

nt e

long

atio

nal v

isco

sity

(P

a.s)


a horizontal movement. The oil bath is held at a constant temperature by circulating hot water through the chamber’s hollow wall. Temperatures above 40°C may cause samples to sag during stretching in the sample chamber.

Assuming the cheese is incompressible, the momentary cross-sectional area of the sample is computed knowing the sample length at any instant. Using this, the true stress values and Hencky strain values are determined (Figure 9.13). Fracture stress, fracture strain, and the modulus are used to evaluate stretchability character-istics of the cheese. The results are generally consistent with expected trends (Figure 9.14). As temperature increased, fracture stress and deformability modulus decreased, but fracture strain increased. These trends are generally opposite with increasing deformation rate. Kuo and Gunasekaran (2002) modified this horizontal

FIGURE 9.12 Uniaxial horizontal extension apparatus. (After Ak et al., 1993. With permission.)

FIGURE 9.13 True stress vs. Hencky strain replicate curves of horizontal extension test for Mozzarella cheese. (After Ak et al., 1993. With permission.)

Fixed holderMoving holder

Dumb bell-shapedCheese sample

Cord

Sample chamber

InstronFrame

Load cell

Crosshead

To dataacquisition

Waterout

Water in

Hencky strain

0.1 0.2 0.3 0.4 0.5 0.60

Tru

e st

ress

(kP

a)

20

40

60

80

100

0Slack

Mozzarella cheese at 40C Deformation rate 50 mm/min


tensile test by introducing new grips to hold a rectangular slab of cheese (38 × 20 × 6 mm) and substituting electrical heating for hot oil bath. This simplified the rather messy test protocol and cleanup needed in the original test. Nonetheless, the cheeses stretch fairly well, and satisfactory data can be obtained (Figure 9.15). The maximum force to stretch (at a deformation rate of 127 cm/min, 55°C) and fracture strain are recorded. The reciprocal of peak force is used as a measure of stretchability.

Guinee and O’Callaghan (1997) described a similar but more of an empirical test. A pizza base is cut in half but not separated. Shredded cheese is sprinkled (0.35 g/cm2) over this and heated for 4 min at 280°C. After this, one pizza half is held in place, and the other is moved away at a constant velocity (3.3 to 10 cm/s) until the strands fail completely (Figure 9.16). The distance between the halves is taken as an index of cheese stretchability. A slightly modified version was reported by Guinee et al. (1999).

COMPRESSION TESTS

Compression is a rather unconventional testing mode to investigate stretchability. However, Apostolopoulos (1994) suggested using what he called a “compressive-elongation test.” The configuration and protocol for this test are similar to the

FIGURE 9.14 Effect of test temperature and deformation rate in horizontal extension test. Mean and 95% confidence interval are plotted. (After Ak et al., 1993. With permission.)

5 10 15 20 25 30 35

Temperature (°C)

0.31

0.41

0.51

0.61

0.71

0.81

23334353637383

040

80120

160200240

0.40

0.44

0.48

0.52

0.56

0.60

26

36

46

56

66

60

80

100

120

140

Deformation rate (mm/min)

0 100 200 300 400 500 600

Def

orm

abili

ty m

odul

us (

kPa)

Frac

ture

str

ess

(kP

a)Fr

actu

re s

trai

n

Def

orm

abili

ty m

odul

us (

kPa)

Frac

ture

str

ess

(kP

a)Fr

actu

re s

trai

n


lubricated squeeze flow test described previously as a test for cheese meltability. His premise was:

The entanglement and crosslink formation of the protein molecules is a phenomenon that assures the integrity of the strings of cheese when pulled apart. Since the resistance to flow is directly related to the degree of entanglement, the value of the elongational viscosity should characterize the degree of molecular entanglement and, therefore, the ability of the cheese to form strings. Thus the greater the elongational viscosity, the more stretchy the cheese would be.

FIGURE 9.15 Modified sample gripping for the horizontal extension test schematic (top) and photograph (bottom) before (A) and after (B) stretching. (After Kuo and Gunasekaran, 2002.)

FIGURE 9.16 Empirical horizontal extension test. (After Guinee and O’Callaghan, 1997.)

Fixed sampleholder

Moving sampleholder

Cheese sample

Stretching

Travel direction

A B

Stretchedcheese strands

Cheese massPizza basePull string attachedto pizza base anddrive motor

Direction of stretchSupport


Though it is true that elongational viscosity can be related to stretchability, a uniaxial test is more suitable because the compressive-elongation test measures a biaxial prop-erty. Furthermore, the viscosity will only provide information on “resistance to flow.” The more important “extent of stretch” cannot be obtained from this type of test.

HELICAL VISCOMETRY

This semiempirical method was described already in Chapter 8, Measuring Cheese Melt and Flow Properties. The standard Brookfield viscometer is used in conjunction with the Brookfield Helipath™ stand. This stand is designed to raise and lower a Brookfield viscometer slowly so that its rotating shearing element describes a helical path through a test sample. According to the manufacturer, “the attachment allows always cutting into fresh material, the problem of channeling or separating is elimi-nated, and meaningful viscosity/consistency measurements can be made.” However, it is doubtful that this claim is valid for cheese, given its unique nature. Based on the resistance to the rotating shearing element, the instrument supplies an apparent viscosity value. This apparent viscosity value, obtained using a T-bar spindle as the rotating shearing element, has been correlated with cheese meltability (Kindstedt et al., 1989). Some researchers attempted to also correlate the apparent viscosity value and the data obtained after the T-bar spindle leaves the mass of melted cheese to stretchability (Oberg et al., 1991; Yun et al., 1995; Fife et al., 1996). This is questionable because the Brookfield viscometer reading is proportional to the torque or resistance experienced by the rotating shearing element. This, of course, is depen-dent on the mass of the material still left on the T-bar spindle. Therefore, data obtained after the T-bar spindle leaves the cheese mass can only be related to how much cheese is carried with the spindle. Unless steps are taken to ensure that the same mass of cheese is carried with the spindle, any successful correlation between the empirical interpretation of the data and stretch characteristics of Mozzarella cheese should be considered merely coincidental.

FIBER-SPINNING TECHNIQUE

Cavella et al. (1992) reported using a fiber-spinning technique originally developed by Petrie (1979) for assessing the spinnability of polymeric melts. Their instrumen-tation is schematically depicted in Figure 9.17. It consists of a piston-type capillary rheometer. As melted cheese is extruded as a thin string through the capillary, it is taken up by a pick-up system equipped with a force transducer that measures the strength of the melt. At the start of a test, the extrusion speed and pick-up speed are kept equal to avoid any elongation of the thread of melted cheese. After the experi-ment has started, the pick-up speed is increased linearly at a preset rate, and the extruded thread is stretched until it breaks. The best operating conditions for Mozzarella cheese are an extrusion speed of 1.24 cm/s and a rate of increase in pick-up speed of 38.5 cm/s.

Based on the ultimate strength of the cheese thread, they determined an experi-mental temperature range of 57 to 83°C. The failure stress and strain values deter-mined for Mozzarella are presented in Figure 9.18. Maximum failure stress and


strain were obtained at about 63 and 72°C, respectively. This temperature approxi-mates the temperature at which Mozzarella cheese curd is processed. This method thus provides both the failure stress and strain values directly corresponding to the “ease and extent” of stretch preferable to describe stretchability. As objective as this test may be, it is rather difficult to adopt. It has not gained the attention it deserves, and further investigations have not been reported.

THE WEISSENBERG EFFECT

If a vertical rod, partly immersed in a viscoelastic fluid, is rotated about its axis, the fluid tends to climb up the rod and is eventually thrown off by centrifugal action. This phenomenon, well known in polymer rheology, is called the Weissenberg effect

FIGURE 9.17 Fiber-spinning system with a capillary rheometer. (After Cavella et al., 1992.)

FIGURE 9.18 Failure stress and strain as a function of Mozzarella cheese temperature deter-mined in fiber-spinning experiment. (After Cavella et al., 1992.)

To force transducer

Pick-up system

Piston

Cheesesample

Cheesestring

Capillary

Temperaturecontrolled chamber

0

100

200

300

400

500

600

55 60 65 70 75 80 85Temperature (°C)

Fai

lure

str

ess

(Pa)

0

50

100

150

200

250

300

Fai

lure

str

ain

(%)


or the rod-climbing phenomenon. It is the direct consequence of the normal stress, which acts like a hoop stress around the rod. The normal stress causes the liquid to “strangle” the rod and hence move along it (Barnes et al., 1993). Olson and Nelson (1980) proposed a method based on the Weissenberg effect to measure the stretch-ability of Mozzarella cheese. The test device they used is schematically represented in Figure 9.19. A 1.9-cm-diameter, 13-cm-high aluminum rod is partially immersed in a pan containing shredded Mozzarella cheese melted at 63°C. The rod is wrapped in filter paper to overcome slippage caused by fat melting. The free oil reduced adherence of the cheese to the rotating rod. A metal screen is placed on the inside pan walls to create a rough surface so the cheese would not rotate en masse. The rod is rotated at 10 rpm, and the cheese climbed the rod. The maximum height to which the cheese climbed is measured. They also observed that the softened cheese tended to wind around the rod and form strands as it climbed the rod. The strands fractured when the cheese climbed to maximum height. Therefore, in addition to measuring the maximum height attained, they measured the time required to fracture the cheese, the place of fracture of the cheese mass in the pan, and the texture of the cheese as it climbed the rod. They assigned some empirical criteria for these measurements, as indicated in Table 9.3. Based on test results with Mozzarella and imitation Mozzarella cheeses and on subjective evaluation of the cheeses on a pizza, they concluded that the Weissenberg effect could predict the performance of cheeses on pizzas.

Nonetheless, the method never became popular, probably because of the complex measurement protocol used and the empirical nature of the measurements made.

The various instrumented methods of cheese stretchability proposed are sum-marized in Table 9.4.

The extensional rheometry is considered relatively young even in polymer research (Schweizer, 2000). Nonetheless, it is fairly well developed in testing of polymer melts, compared to testing of cheese melts and other foods where elonga-tional properties are of practical importance (e.g., dough). The extensional properties

FIGURE 9.19 Cheese stretch test proposed based on the Weissenberg effect (also known as rod-climbing effect) of viscoelastic materials. (After Olson and Nelson, 1980.)


of polymeric melts are determined in uniaxial tests using one of the two popular rheometers: (a) Munstedt Tensile Rheometer (MTR) and (b) Rheometric Scientific RME (RME). The MTR rheometer is based on the work of Munstedt (1975, 1979) in which a cylindrical sample is suspended in hot oil and the extension of the constant volume sample is measured as a function of time. The cheese stretchability method described previously (Ak and Gunasekaran, 1995) was in fact based on this principle. The sample can be stretched either at constant rate or under constant stress. For this technique to be successful it is important to properly prepare the sample, i.e., without

TABLE 9.3Measurements and Observations from the Weissenberg Test Used to Place Cheese in Four Elasticity Categories

SampleHeight Climbed

(cm)Fracture Time

(min) Place of Fracture Texture

No elasticity 0 0 rod extremely smoothLittle elasticity < 2 > 4 intermediate extremely smoothGood elasticity > 2 2–4 edge smoothPronounced elasticity > 2 < 2 edge not smooth

Source: After Olson and Nelson, 1980.

TABLE 9.4Summary of Various Methods for Measuring Cheese Stretchability

Method Measurement Made Ref.

Rod-climbing Height cheese climbed on a rod Olson and Nelson, 1980

Helical viscometer Apparent viscosity value Kindstedt et al., 1989

Fiber spinning (with capillary rheometer)

Failure stress and strain of cheese drawn as thin fibers

Cavella et al., 1992

Horizontal extension Fracture strain, stress, and deformability modulus

Ak et al., 1993

Tensile test Length of stretched cheese strings Apostolopoulos, 1994

Compression test Biaxial elongational viscosity Apostolopoulos, 1994

Vertical elongation by sample weight

Transient elongational viscosity Ak and Gunasekaran, 1995

Vertical elongation Length of stretched cheese strings Pena et al., 1996

Tensile test on a pizza Length of cheese strings stretched between two pizza halves

Guinee and O’Callaghan, 1997

Tensile test with a T-bar Stretch profile data (peak force and deformation)

Gunasekaran and Ak, 1997

Horizontal extension Inverse of peak force Kuo and Gunasekaran, 2002

Tensile test with a three-pronged hook

Stretch profile data (melt strength, stretch quality, stretch length)

Fife et al., 2002


any inhomogeneities and closely match the densities of the oil and sample (Baird, 1999). The RME is currently marketed by Rheometric Scientific Inc. This is based on the design of Meissner and Hostettler (1994). In this, instead of hot oil, the sample is surrounded by an air table. The air table suspends the sample from sagging while it is melted and stretched by counter-rotating belts that operate at constant velocity (Figure 9.20). Due to this, the sample length, rather than its volume, remains constant during the test. Though the strain rate is limited to 1 s–1, the main advantage of this technique is that extension as high as 7 Hencky strain units can be applied, which may be advantageous in the case of testing Mozzarella cheese under certain condi-tions. In addition, by surrounding the sample with nitrogen, temperatures as high as 350°C can be used. The lack of oil bath makes RME testing easier compared to the MTR, similar to the changes made by Kuo and Gunasekaran (2002) to the test protocol of Ak and Gunasekaran (1995). Both MTR and RME allow calculating the extensional viscosity. It is not clear to what extent the RME is suitable for measuring cheese stretchability. The problems that continue to daunt cheese rheologists, phase separation of fat at high temperatures and sample drying out, will still have to be dealt with. Even if that were addressed, by surrounding the cheese melt with another suitable medium, other problems remain. They are the ability to calculate tensile stress and strain correctly (Schweizer, 2000). The experimental difficulties with the extensional testing have led to wide variation of data obtained with RME in a multi-laboratory round robin tests on polymer melts (Schulze et al., 2001). Special particle tracking procedures have been proposed to account for ever-changing sample cross-section during the test (Rohr, 1996; Wassner, 1999). These and other inherent practical difficulties of the uniaxial extensional test procedures compounded with the unique and complex nature of cheese melt render the goal for developing an objective cheese stretchability measurement a challenge for a long time to come.

REFERENCES

Ak, M.M. et al. 1993. Rheological evaluation of Mozzarella cheese by uniaxial horizontal extension. Journal of Texture Studies 24:437–453

Ak, M.M. and S. Gunasekaran. 1995. Measuring elongational properties of Mozzarella cheese. Journal of Texture Studies 26(2):147–160.

FIGURE 9.20 Schematic of the RME extensional rheometer. The sample is suspended over an air table while it is melted and stretched by the counter-rotating belts. (After Schulze et al., 2001. With permission.)

Direction of beltmovement

Air Table

2 mm

SampleBelt treadPin


Apostolopoulos, C. 1994. Simple empirical and fundamental methods to determine objectively the stretchability of Mozzarella cheese. Journal of Dairy Research 61:405–413.

Baird, D.G. 1999. The role of extensional rheology in polymer processing. Korea-Australia Rheology Journal 11(4):305–311.

Barnes, H.A., J. F. Hutton, and K. Walters. 1993. An Introduction to Rheology. Amsterdam, The Netherlands: Elsevier.

Cavella, S., S. Chemin, and P. Masi. 1992. Objective measurement of the stretchability of Mozzarella cheese. Journal of Texture Studies 23:185–194.

Chen, C. and M.E. Johnson. 1999. Pasta filata-simulative cheese product and method of making same. U.S. Patent. No. 5,942,263.

Fife, R.L., D.J. McMahon, and C.J. Oberg. 1996. Functionality of low fat Mozzarella cheese. Journal of Dairy Science 79:1903–1910.

Fife, R.L., D.J. McMahon, and C.J. Oberg. 2002. Test for measuring the stretchability of melted cheese. Journal of Dairy Science 85:3549–3556.

Guinee, T.P. and D.J. O’Callaghan. 1997. The use of a simple empirical method for objective quantification of the stretchability of cheese on cooked pizza pies. Journal of Food Engineering 31(2):147–161.

Guinee, T.P., D.J. O’Callaghan, and H.J. O’Donnell. 1999. Stretching the limits of cheese testing. European Dairy Magazine No. 4:28–30.

Gunasekaran, S. and M.M. Ak. 1997. Measuring physical and functional properties of cheese. National Cheese Technology Forum, Dec. 9–10, Chicago, IL.

Kindstedt, P.S., J. K. Rippe, and C.M. Duthie., 1989. Measurement of Mozzarella cheese melting properties by helical viscometry. Journal of Dairy Science 72:3117.

Kuo, M.-I and S. Gunasekaran. 2002. Effect of frozen storage on physical properties of pasta filata and non-pasta filata Mozzarella cheeses. Journal of Dairy Science (submitted).

Lelievre, J., I.A. Mirza, and M.A. Tung. 1992. Failure testing of gellan gels. Journal of Food Engineering 16:25–37.

Luyten, H. 1988. The Rheological and Fracture Properties of Gouda Cheese. Wageningen Agricultural University. The Netherlands.

McMahon, D.J. 1996. Measuring stretch of Mozzarella cheese. Proceedings of 12th Biennial Cheese Industry Conference, Utah State University, Logan, UT.

Meissner, J. and J. Hostettler. 1994. A new elongational rheometer for polymer melts and other highly viscoelastic liquids. Rheologica Acta 33:1–21.

Munstedt, H. 1975. Viscoelasticity of polystyrene melts in tensile creep experiments. Rheologica Acta 14:1077–1088.

Munstedt, H. 1979. New universal extensional rheometer for polymer melts — measurements on a polystyrene sample. Journal of Rheology 23(4):421–436.

NZDRI, 1997. Creating the opportunities, Innovation, Speed, Quality. Annual Report. Palmerston North, New Zealand.

Oberg, C.J. et al. 1991. Effects on proteolytic activity of thermolactic cultures on physical properties of Mozzarella cheese. Journal of Dairy Science 74:389.

Olson, N.F. and D.L. Nelson. 1980. A new method to test the stretchability of Mozzarella cheese on pizza. Proceedings of the 17th Marschall Italian and Specialty Cheese Seminars, Madison, WI.

Peleg, M. 1980. Linearization of relaxation and creep curves of solid biological materials. Journal of Rheology 24:451–463.

Pena, J. L. et al. 1996. A probe for measuring stretchability (string) of melted cheese by instrumented means. IFT Annual Meeting Book of Abstracts. Chicago, IL: Institute of Food Technologists, No. 80-B15.


Petrie, C.J.S. 1979. Elongational Flow: Aspects of the Behaviour of Model Elasticoviscous Fluids. London: Pitman.

Rohr, D. 1996. Manual for the true elongational strain rate software for the RME. Swiss federal Institute, Zurich, Switzerland.

Schulze J.S. et al. 2001. A comparison of extensional viscosity measurements from various RME rheometers. Rheologica Acta 40:457–466.

Schweizer, T. 2000. The uniaxial elongational rheometer RME — six years of experience. Rheologica Acta 39:428–443.

Smith, C.E., J. Rosenau, and M. Peleg. 1980. Evaluation of the flowability of melted Mozzarella cheese by capillary rheometry. Journal of Food Science 45:1142–1145.

Tschoegl, N.W., J. A. Rinde, and T.L. Smith. 1970. Rheological properties of wheat flour doughs. I. Method for determining the large deformation and rupture properties in simple tension. Journal of Science Food Agriculture. 21:65–70.

Vinogradov, G.V., V.D. Fikhman, and B.V. Radushkevich. 1992. Uniaxial extension of poly-styrene at true constant stress. Rheological Acta 11:286–291.

Wassner, E. 1999. Determination of true elongational viscosities with a Meissner-type rheo-meter (RME). Proceedings of the Polymer Processing Society 15th Annual Meeting. Hertogenbosch, The Netherlands, pp 66.

Yun, J. J. et al. 1995. Mozzarella cheese. Impact of rod: coccus on composition, proteolysis, and functional properties. Journal of Dairy Science 78:751.


Factors Affecting Functional Properties of Cheese

Rheological and textural properties of cheese are affected by numerous factors. Many such effects are fairly well documented, and yet others are still the subject of continued research. Several factors that affect rheological and textural properties of cheeses also have an effect on flavor, appearance, and other attributes important to consumers. The emphasis in this chapter is only on those factors that have a significant effect on the mechanical or physical properties of unmelted and melted cheese and some appearance factors that can be collectively termed as functional or end-use properties. Some of these functional properties are meltability, stretchability, shredability, free-oil forma-tion, and browning. Meltability, stretchability, and shredability have been discussed previously in other chapters. Free-oil formation is the process of fat globules melting and leaving the protein matrix structure. It is also referred to as “oiling-off” or “fat leakage.” Browning is the discoloration that develops when cheese is heated. While free-oil formation and browning of cheese is expected and even desirable during heating of cheese, excessive oiling-off and browning are undesirable. Different empiri-cal tests have been developed to quantify free-oil formation in cheese (Kindstedt and Rippe, 1990; Kindstedt and Fox, 1991; Wang and Sun, 2002c). The browning of cheese is the result of typical Maillard browning reaction that occurs between the reducing sugars lactose and galactose and amino acids (Kosikowski and Mistry, 1997). The degree of discoloration is evaluated either visually or using some color measurement instruments (Bley et al., 1985; McMahon et al., 1993; Matzdorf et al., 1994; Wang and Sun, 2002a; 2002b). Some recent reviews on cheese functional properties include those of Kindstedt (1993), McMahon et al. (1993), and Rowney et al. (1999).

It is rather a challenging task to describe the effects of various factors on the functional properties of cheese due to the complex and interacting effects of the factors involved. An example of this has already been presented in Chapter 1 (Tables 1.7athrough 1.7d) for one cheese type. The task is even more daunting if the numerous cheese types were considered. Therefore, the primary focus of this chapter is some selected hard or semihard cheeses (e.g., Cheddar, Gouda, and Mozzarella cheeses). The various factors that affect their functional properties have been grouped under the following broad categories: (a) properties of milk, (b) cheesemaking procedures, (c) cheese composition, and (d) postmanufacturing processes.

PROPERTIES OF MILK

As the primary raw material, the quality and properties of milk have a direct effect on cheese functional properties. Such factors as the breed of cattle, stage of lactation,

10


milking season, and feeding affect milk composition and buffering capacity, and thus the cheese properties (Guinee et al., 1998; Lucey et al., 1992). For example, Mozzarella cheese made from late-lactation milk is softer and exhibits lower appar-ent viscosity than that made from mid-lactation milk (Lucey et al., 1992). Milk is normally standardized to minimize some of the variations e.g., due to composition. The standardization is performed with a target casein-to-fat ratio. When the casein-to-fat ratio is not properly controlled, the cheese may be either too soft or too hard, unless adjustments are made to change water content in the curd (Scott et al., 1998). The milk fat melting point has been shown to change seasonally (Papalois et al., 1996). Fat melting is directly related to cheese melting, stretching, and related properties of cheese at elevated temperatures. Thus, seasonal variations may affect cheese properties even if the milk is standardized.

The buffering capacity of milk is primarily due to colloidal calcium phosphate (Lawrence et al., 1987). Soluble phosphate, citrate, bicarbonate, and casein are other main buffering components in milk (Lucey et al., 1993). Depending on milk pH and temperature, about two-thirds of the calcium is colloidal and the rest is in solution. The proportion of colloidal calcium phosphate retained in the curd and curd pH together affect the stretchability of Mozzarella cheese. The buffering capacity of cheese milk has been shown to affect the extent of curd demineralization and eventually the stretchability (Fernandez and Kosikowski, 1986; Kosikowski, 1951). The pH of milk at coagulation affects melting properties of direct-acidified Mozza-rella cheese due to its effect on cheese mineral content. Keller et al. (1974) showed that calcium and phosphorus levels decrease with decreasing coagulation pH, leading to improved cheese meltability. The fat content, composition, and nature of fat also affect cheese properties.

Homogenization of milk prior to cheesemaking is not very common. But use of homogenized milk can increase cheese yield. Homogenization of milk or cream reduces fat globule size and alters the fat globule membrane (Darling and Butcher, 1977). It is also believed to create a new fat-water interface predominantly containing caseins that can make fat globules more stable (Rowney et al., 1999; Cano-Ruiz and Richter, 1997; Sharma and Dalgleish, 1993). The size of fat globules and their distribution in the casein matrix influence meltability and free-oil formation (Jana and Upadhyay, 1992; Rowney et al., 1998; Tunick, 1994). Tunick (1994) reported that the insulating effect of small fat globules in casein matrix prevents fat from melting easily. Physical changes in cheese structure because of a reduction in fat-particle size improve the appearance (whiteness) of unmelted Mozzarella cheese (Rudan et al., 1998a). Some researchers reported adverse effects of homogenization, such as poor body, texture, and, in the case of Mozzarella, reduced stretchability and meltability (Tunick et al., 1993a; Tunick, 1994). Lelievre et al. (1990) determined that homogenization at high pressures (~6.7 MPa) adversely affects melt and stretch characteristics of Mozzarella cheese. However, no such adverse effects were observed when the milk was homogenized at lower pressures (~400 kPa). In addition, homoge-nizing milk and cream at low pressures can reduce free-oil formation (Tunick, 1994; Lelievre et al., 1990). Nair et al. (2000) reported improved meltability and decreased free-oil formation in Cheddar cheese over limited aging when manufactured with homogenized milk. Rudan et al. (1998a) reported that homogenization of cream


instead of milk improves the cheesemaking performance by reducing the amount of curd shattering and fines, and by reducing the amount of fat lost during cheesemaking.

Milk proteins are mostly either colloidal caseins or whey proteins that are available in serum solution. The caseins are primarily α-casein (~40%), β-casein (~35%), and κ-casein (~15%). The α-casein is composed of smaller units, αs1, αs2, αs3, αs4, and αs5. Among these, αs1-casein is the major component. The hydrolysis of αs1-casein and β-casein affects cheese functional properties during maturation, as discussed later in this chapter.

CHEESEMAKING PROCEDURES

ADDITION OF STARTER CULTURE AND COAGULANTS

The main purpose of adding starter is for acid production. Other major effects are proteolytic activity and utilization of sugars (e.g., galactose, glucose, lactose). The rate of acid production is critical in carefully controlling cheese composition and meltability (McMahon et al., 1993; Kindstedt et al., 1989). The proteolytic activity of the starter culture affects rheological and textural properties of cheese through slow but progressive breakdown of caseins during storage (Lawrence et al., 1987). Different starter cultures have varying effects. For example, the meltability and stretchability of Mozzarella cheese made with Lactobacillus bulgaricus, a protein-ase-negative culture, differs from that of cheese made with a proteinase-positive strain (Oberg et al., 1991a; 1991b). The inability of some starter-culture bacteria to ferment galactose contributes to Maillard browning of cheese during cooking (Matzdorf et al., 1994; Oberg et al., 1991a; Johnson and Olson, 1985). Certain cultures and combinations of cultures have been reported to reduce the extent of browning (Mukherjee and Hutkins, 1994; McMahon et al., 1993; Hickey et al., 1986).

Scott et al. (1998) reported that about 6% of the coagulant added to milk is active in the cheese curd. The primary proteolysis, the initial breakdown of the caseins into peptides, generally results from the action of the residual coagulant (Barbano et al., 1993). This initial breakdown is followed by secondary proteolysis of the peptides by the starter culture enzymes into smaller peptides and free amino acids. Such activity is lower for Mozzarella than for Cheddar cheese due to the heat treatment during the mixing and molding step in Mozzarella cheese manufacture (Yun et al., 1993a; Farkye, et al., 1991; Mathesson, 1981; Creamer, 1976). Creamer (1976) suggested that αs1-casein is important in providing Mozzarella cheese with its distinguishing properties, based on his observation that degradation of αs1-casein is higher in Cheddar cheese than in Mozzarella cheese. Different enzymes break down caseins in cheese to varying extent. For example, Chymosin breaks down αs1-casein more than the rennet from Mucor miehei. But these enzymes have the opposite effect on β-casein (Oberg et al., 1992a). Hydrolysis of αs1-casein and β-caseinhas been related to changes in melt and softening qualities of Cheddar cheese (Kim, 1999). Stretching properties of Mozzarella may be related to its high content of intact casein and large peptides (McMahon et al., 1993).

Direct acidification of milk also has been found to influence the functional properties of cheese depending on the type of acid used and pH (Keller et al., 1974).


As the data in Table 10.1 indicate, cheese viscosity generally decreases with decreasing pH. Pizza cheese is firmer when phosphoric and hydrochloric acids are used compared to when lactic acid is used (Shehata et al., 1967). Mozzarella cheese made using direct acidification generally has a softer body and better melting quality than cheese of similar age made with starter culture (Kindstedt and Guo, 1997a). Acids that are strong calcium chelators such as citric acid cause greater curd demineralization than nonchelating acids such as acetic acid (Keller et al., 1974; Shehata et al., 1967).

CURD HANDLING

The coagulum or curd is cut and “cooked” (i.e., scalded) to enhance syneresis. The temperature at which the curd is cooked in the whey has been shown to affect rheological properties to some extent, through control of moisture and fat content and acid development (Ghosh et al., 1990). A higher cooking temperature normally results in a lower moisture content cheese due to curd shrinkage. High scalding temperature also enhances the metabolic activity of bacteria in the curd, which increases lactic acid production and thus lowers pH, which further helps to contract the curd, expelling more whey. This renders cheese acidic, hard, crumbly, and dry (Scott et al., 1998). High cooking temperatures may also affect cheese properties by decreasing the residual proteolytic activity of the coagulant and starter culture. While Tunick et al. (1993b) reported a decrease in meltability and increase in hardness of Mozzarella cheese in the temperature range of 32 to 46°C, no significant

TABLE 10.1Effect of Acid Used for Acidification of Milk and pH at Coagulation on Viscosity of Mozzarella Cheese

Acid used pHViscosity × 10–6

(Pa.s)a

Malic 5.2 0.351a

Acetic 5.2 0.696a

Citric 5.2 0.706a

Citric 5.6 0.793a

Acetic 5.4 1.076ab

Hydrochloric 5.2 1.350abc

Hydrochloric 5.4 1.449abcd

Malic 5.6 2.044bcd

Acetic 5.6 2.053bcd

Phosphoric 5.4 2.520cd

Hydrochloric 5.6 2.730d

Phosphoric 5.6 3.238d

a The values designated by same letter(s) are not statistically different (P = 0.01).

Source: After Keller et al., 1974.


changes in Mozzarella cheese meltability and free-oil formation were observed over the 38 to 41°C range, even though the moisture content decreased significantly with temperature (Yun et al., 1993c).

Acid development (or pH) of whey at drainage is the primary factor in deter-mining the extent of curd demineralization — i.e., loss of calcium and phosphate to whey (Kiely et al., 1992a). Therefore, pH at whey draining critically affects the functional stability of the curd for mixing/stretching and the eventual functional properties of the Mozzarella cheese (Kindstedt, 1985; Keller et al., 1974). The pH at whey drainage also affects the amount of lactose in the cheese curd, and hence the rate of acid development during cheddaring or dry stirring (Kindstedt, 1993; McMahon et al., 1993). However, pH at milling in the range of 5.1 to 5.4 does not significantly affect the texture and meltability of Mozzarella cheese (Yun et al., 1993a). Therefore, pH at whey drainage is considered more important than at milling. When the curd is milled at higher pH, the cheese tends to contain higher calcium and moisture content (Yun et al, 1993b). The stretchability of Mozzarella cheese is related to curd pH and the amount of colloidal calcium phosphate retained in the curd (Lawrence et al., 1987). The demineralization of curd caused by acidification plays an important role in the initial onset of stretching properties (Kosikowski, 1951).

The curd is salted and pressed to form the eventual cheese block. The pressing step, though poorly understood, is important in giving some cheeses their character-istic textures. In the case of Cheddar cheese, applying high pressure promotes matting of the curd particles into a contiguous, firm mass. On the other hand, in case of the Cheshire cheese, the pressing step is performed to prevent curd particles from matting so that an open texture results. An open texture is also desirable in blue-veined cheeses, as it facilitates oxygen to penetrate and promote mold growth throughout the curd.

COOKING, STRETCHING, AND COOLING

The cooking and stretching step is unique to the pasta filata family of cheeses, such as Mozzarella cheese. In this step, both pH and temperature affect cheese properties. Mozzarella cheese curd is normally cooked at 40°C or higher (Kosikowski and Mistry, 1997) which removes moisture from cheese and causes some inactivation of chymosin and starter culture microorganism (Kindstedt, 1993). Higher cooking temperature lowers cheese moisture content and rate of proteolysis, and hence lowers cheese meltability and stretchability (Yun et al., 1993d). When cook temperature is reduced to 35°C, the curd retains more moisture, which results in a softer cheese and a higher level of proteolysis after the cheese is made (Tunick et al., 1991, 1993a). The breakdown of αs1-casein that takes place during extended storage weakens the cheese further and eliminates textural and melting problems often experienced with reduced-fat Mozzarella.

At a pH of 5.2 to 5.4, di-calcium paracaseinate is converted into mono-calcium paracaseinate by the action of lactic acid and imparts cheese a stringy texture and sheen. At a pH greater than 5.4, curd will not stretch; at a pH less than 5.2, excessive fat losses occur, and the cheese becomes too tough (Ghosh et al., 1990). Curd stretched at pH 5.3 has a more structured texture and takes longer to age. Yun et al.


(1993b) reported that curd stretched at pH 5.3 exhibited higher apparent viscosity immediately after manufacture and during aging compared to Mozzarella cheese made from curd stretched at pH 5.0.

For optimal stretching, there is an optimal combination of curd pH and stretch-ing temperature. Scott et al. (1998) indicated that curd at pH 5.1–5.4 should be placed in hot water at 70 to 82°C for stretching. The curd temperature is normally about 55 to 60°C (Webb et al., 1983). Mulvaney et al. (1997) reported a reduction in elastic properties of Mozzarella when the stretching temperature of the curd was increased from 57 to 75°C. Another effect of higher stretching temperature is increased inactivation of proteolytic organisms and residual enzymes and a con-comitant reduction in primary and secondary proteolysis during aging (Yun et al., 1994; McMahon et al., 1993). The method of curd stretching also seems to affect cheese properties. Apostolopoulos et al. (1994) compared Mozzarella cheese made with a conventional cooker/stretcher to that made using a high-pressure, twin-screw extruder. The extruder stretching resulted in a cheese with lower meltability and no detectable free oil.

Stretched curd is cooled in chilled water-cooling towers or by other means while the Mozzarella cheese is still in molds. This is performed at a high rate to limit growth of certain undesirable microorganisms, such as L. caseii, which may lead to soft-body texture defect and gas holes (Hull et al., 1983). Soft-body defect renders cheese soft and pasty with poor shredding qualities and excessive meltability (Kind-stedt, 1991). Cooling continues to occur when Mozzarella cheese is placed in brine for salting. At this stage, a nonuniform salt and moisture gradient is established in the cheese block (Turhan and Gunasekaran, 1999; Kindstedt, 2001) and eventually leads to variations in cheese meltability, stretchability, free-oil formation, etc., at different locations within the block (Kindstedt et al., 1988; Kindstedt et al., 1992).

CHEESE COMPOSITION

Typical composition of several cheese types is presented in Table 1.6. The major and minor constituents of cheeses have varying effects on the end-use functional properties. In addition, consumer preference for some functional-property levels vary with several socio-economic, ethnic, and geographic factors. Therefore, it is often difficult to describe an optimal composition for cheeses. As an example, composi-tional factors for premium-quality Cheddar cheese determined by different research-ers are listed in Table 10.2. Needless to say, these recommendations vary. However, the table lists, in addition to age, the major compositional factors that affect cheese properties. They are moisture content, fat content, salt content, and pH.

MOISTURE CONTENT

Moisture is a major constituent of cheese. It comprises more than one-third (and as high as one-half) of the cheese mass. The moisture content may be represented in wet basis as percent of total cheese mass or as percent moisture in the nonfat portion (MNFP) of the cheese. The MNFP is considered to have a more direct relationship to cheese properties than moisture content, per se. Lelievre and Gilles (1982), after


studying the quality-composition relationships of numerous cheeses manufactured in New Zealand, stated that MNFP is the most important factor affecting cheese quality.

The moisture content in cheese is affected by various factors such as cooking temperature, salt content, etc. (Yun et al., 1993a; Kindstedt et al., 1992). In the case of Mozzarella cheese, its moisture content is also affected by screw speed in the mixer/stretcher. The longer manufacturing time, due to slow acid production, results in lower moisture content cheese (Renda et al., 1997). Kindstedt and Guo (1997b) and McMahon et al. (1999) reported that the state of the water in the cheese-protein matrix that affects the water-holding capacity of Mozzarella is partly responsible for its functional properties. A dynamic relationship exists between the casein matrix and the serum phase in the young Mozzarella and pizza cheeses. Kuo et al. (2001a) determined, via Nuclear Magnetic Resonance (NMR) analysis, that there is a redis-tribution of quantity and mobility between the initially more-mobile to less-mobile fraction of water in Mozzarella cheese during the first 10 days after manufacture. However, an increase of mobility in both fractions of water molecules was observed. The chemical and physical environments that change due to the structure rearrange-ment of the protein matrix is believed to contribute to the increase of water mobility during aging. Therefore, the effect of moisture content on properties of cheese is due to both the quantity of water available and the state of the water in the cheese.

It is generally established that the greater the moisture content, the softer the cheese and the better its meltability. However, high-moisture cheese has poor shre-dability. Tunick et al. (1991) reported that as the moisture content of Mozzarella cheese increased from 47 to 52%, the cheese became softer with significantly increased meltability. Based on a survey of 50 low-moisture Mozzarella cheeses and low-moisture part-skim Mozzarella cheeses from two manufacturers over 10 weeks, Kindstedt et al. (1988) reported that apparent viscosity of cheeses aged for 12 days at 4°C was inversely related to moisture content. Low apparent viscosity should be construed as good cheese meltability (see Chapter 8). Wang and Sun (2002a) compared the meltabilities of Cheddar cheese (32.3% fat, 32.8% moisture) and Mozzarella cheese (18% fat, 46.9% moisture) at different temperatures. The Cheddar cheese melted considerably more than the Mozzarella cheese at all temperatures, not only because of its higher fat content, but also due to its higher “active water”

TABLE 10.2Compositional Factors for Premium-Quality Cheddar Cheese Suggested by Different Researchers

pH

Fat in theDry Matter,FDM (%)

Moisture inNon-fat Portion,

MNFP (%)Salt-in-Moisture,

S/M (%)Age

(week) References

4.95–5.10 52–55 52–56 4–6 2 Gilles and Lawrence, 1973

<5.4 — <38 >1.4 10 Fox, 1975

4.95–5.15 — 52–54 4.2–5.2 2 Pearce and Gilley, 1979

a Moisture in the nonfat portion.


content, the water entrapped by the protein matrix (McMahon and Oberg, 1998). The expressible serum level in Mozzarella cheese is higher, which relates to the lower water-binding capacity of Mozzarella cheese compared to Cheddar cheese (Guinee et al., 2000a). This is likely the reason for lower meltability of Mozzarella cheese despite its higher water content than Cheddar cheese.

FAT CONTENT

Fat content in most semihard and hard cheeses varies from about 20 to 33%. Fat in cheese is present as globules contained within the protein matrix network. Therefore, they can be considered as “fillers” that influence the rheological and functional properties of cheese (Desai and Nolting, 1994). Fat content in the cheese is respon-sible for its many desirable functional, textural, and sensory properties. The fat content in the cheese may be expressed in percent fat in wet basis or as percent FDM (fat-in-the-dry-matter) in dry basis, or as casein-to-fat ratio. The required regulatory limits of fat level for different labeling, e.g., low-fat, fat-free, etc., are listed in Tables 5.6 and 5.7.

The size and distribution of fat globules and the nature of proteinaceous stabili-zing species adsorbed at the fat globule/water interface have an effect on the prop-erties of cheese (van Vliet and Dentener-Kikkert, 1982; Xiong and Kinsella, 1991). The average fat-globule size varies from about 1.5 µm to 4 µm, at various stages of Cheddar cheesemaking (Everett et al., 1995). Three-dimensional evaluation of in situ fat globules in Cheddar cheese (Ding and Gunasekaran, 1998; Gunasekaran and Ding, 1999) indicate that the higher the fat content, the higher the number of large fat globules and the higher the average fat-globule size. The fat globules in cheese are far from being spherical (sphericity ≅ 0.2), and the sphericity is not affected by the fat content. When cheese milk is homogenized, the fat globules become part of the protein matrix due to incorporation of casein submicelle into a new fat globule membrane (Lelievre et al., 1990). Fat present in cheese curd acts as a plasticizer and inhibits the formation of cross links between the casein chains (Johnston, 1984). The weaker and more porous the protein network, the more readily the fat is lost from the network.

Higher fat content allows cheeses to melt better, but it may be more difficult to shred (Masi and Addeo, 1986) and produces higher free-oil (Kindstedt and Rippe, 1990). Figures 10.1A and 10.1B show the change in meltability of Cheddar and Mozzarella cheeses of different fat levels as a function of ripening time. Ruegg et al. (1991) reported that fat content does not always relate to cheese meltability since its effect is confounded by the effect of other constituents. Olson and Bogenrief (1995) reported that change in FDM from 18 to 45% had little effect on meltability, but at FDM levels above 45%, meltability increased substantially (Figure 10.2). The stretch-ability of Cheddar cheese also increases with fat level up to 30 days of ripening.

Numerous studies have focused on the effect of fat content (or its reduction) in the cheese due to the consumer interest in a low-fat diet. Fat reduction brings about concomitant changes in other cheese constituents (Guinee et al., 2000b; Rudan et al., 1999; Gilles and Lawrence, 1985). Guinee et al. (2000b) reported significant increases in moisture, protein, and ash content and decreases in MNFP, FDM, and


salt (S/M) as the fat level is reduced in Cheddar cheese. They also observed an increase in total calcium and phosphorous with reduction in fat content. However, fat content did not affect the calcium-to-protein ratio in cheese. In low-fat cheeses, for example, MNFP levels are maintained about the same as in their regular-fat counterparts (Mistry and Anderson, 1993; Mistry, 2001). Therefore, the salt-in-moisture level goes down. Such a change is considered responsible for many adverse

FIGURE 10.1A Effect of fat content and ripening time on Cheddar cheese meltability mea-sured as percent increase in diameter of cheese disk heated at 280°C for 4 min. (After Guinee et al., 2000b. With permission.)

FIGURE 10.1B Effect of fat content and ripening time on Mozzarella cheese meltability measured according to modified Schreiber test. (After Rudan et al., 1999.)

Ripening time (days)

0 10 20 30 40 5038

42

46

50

54

Mel

tabi

lity

(mm

)

5%

10%

15%

25%


functional property changes in cheese (Banks et al., 1993; Bryant et al., 1995). The functionality of low-fat cheese may improve due to the additional moisture present (Fife et al., 1996). Hence, increasing the moisture content is generally recommended to improve the quality of lower-fat cheeses. Bryant et al. (1995) observed the microstructure of reduced-fat Cheddar cheese and remarked that the nature of pro-tein-matrix structure affects cheese properties more than the moisture content. Thus, an increase in moisture content alone cannot improve properties of lower-fat cheeses.

As the fat content decreases, changes in physical properties and flavor lower the cheese quality (Emmons et al., 1980; McMahon et al., 1993; Mistry, 2001; Olson and Johnson, 1990). The change in functional properties are presumably due to loss of plasticizing action of the fat and increased cross-linking within the curd and hence in the cheese. A relatively low number of fat globules in reduced-fat cheese results in a denser structural matrix leading to a firm and dry cheese that melts poorly (Emmons et al., 1980). Cheese becomes softer when the amount of liquid fat, the fat that is not bound to the protein matrix, increases (Green et al., 1985). For example, Cheddar cheese with less than 48% FDM is more firm and less meltable (Lawrence and Gilles, 1980; Emmons et al., 1980) than the higher-fat cheeses. Though lower-fat Mozzarella cheese exudes limited free oil, it becomes excessively brown when baked or otherwise heated (Rudan et al., 1998a). Low-fat cheese also tends to form a dry film or “skin” on the surface during heating, which limits cheese meltability

FIGURE 10.2 Meltability of Cheddar cheese as a function of fat-in-the-dry matter (FDM). Meltability was determined as flow distance in a tube test. (After Olson et al., 1995.)

FDM (%)

Mel

tabi

lity

(mm

)

10 20 30 40 50 600

20

40

60

80


(Figure 10.3). The dry surface skin formation may be alleviated by applying a hydrophobic coating (e.g., vegetable oil) on the surface of low-fat Mozzarella cheese before the cheese is heated (Rudan and Barbano, 1998). When such a hydrophobic coating is applied on fat-free (<0.25% fat) or lower-fat (6 to 9% fat) Mozzarella cheeses, their melting and browning qualities are similar to full-fat (21% fat) Mozzarella cheese. Based on this, Rudan and Barbano (1998) hypothesized that fat within the interior microstructure of the cheese is not necessary to achieve proper functionality. Lefevere et al. (2000) reported better correlation between fat content and cheese meltability (R2 = 0.90) than between FDM and meltability (R2 = 0.61), which indicated that moisture content is also a major factor affecting cheese melt-ability in addition to fat content.

Several technological changes have been proposed, including use of fat replace-ments, to improve functional properties of low-fat cheeses (Mistry, 2001; Rudan et al., 1998b; Tunick et al., 1993b). These changes have met with only limited success. For example, substituting up to 70% of whole cow’s milk with reconstituted skim milk results in a natural part-skim, Mozzarella-type cheese that has acceptable shredding characteristics, good stretchability, and moderate to mild melting proper-ties without any oiling off (Davide et al., 1993). Nonetheless, consumer acceptance of lower-fat cheeses has only been tepid. Therefore, some hard-cheese plants are adding extra cream to make higher-fat cheeses that offer improved functional proper-ties (Honer and Ruland, 1995).

SALT CONTENT

Salt is a minor constituent of cheese, but can have a major effect on properties of both unmelted and melted cheese. In addition to enhancing cheese taste, salt in cheese controls moisture content, growth of undesirable microorganisms, and acidity development by controlling the growth of lactic-acid organisms.

In the case of Cheddar cheese, direct addition of salt is very common. The Mozzarella cheese is salted by placing the cheese in brine after the mixing and molding step. During this step, cheese is also simultaneously cooled. Salt may affect properties of Mozzarella cheese by exchanging with calcium, thus enhancing the emulsification of fat within the protein matrix and giving it a firmer texture (Kindstedt et al., 1992). This effect is considered independent of moisture content (McMahon et al., 1993). In general, cheese with a high salt content (~2%) melts poorly (Olson, 1982).

FIGURE 10.3 Low-fat cheeses form a dry film or “skin” when heated, which limits their meltability.


Salt content also affects the changes in cheese properties during aging. Lower-salt Mozzarella softens more rapidly during storage (Cervantes et al., 1983; Olson, 1982). Olson (1982) reported that Mozzarella cheese with a high salt content of 1.78% is less meltable and less stringy than cheese of equal age with a lower salt content of 1.06%. Insufficient proteolysis due to high salt content can cause a “curdy” texture.

Salt content also affects the free oil in cheese. The exchange between sodium in brine (used for salting) with calcium in the casein matrix enhances the ability of casein to emulsify fat, thus lowering free-oil formation but firming the cheese texture (Kindstedt et al., 1992). Accordingly, Mozzarella cheese with a high (3%) salt content exudes less free oil than samples with a low (0.4%) salt content. The effect of salt on the functionality of cheese is also related to the changes in water-binding capacity (Kindstedt and Guo, 1997a, 1997b). Unsalted fat-free Mozzarella cheese contains pockets of free serum compared to a more uniform casein matrix in the salted cheese. Therefore, unsalted cheese gives off higher expressible serum and melts less easily (Paulson et al., 1998). A low salt level and high moisture content can make cheese pasty and off-flavored (Fox, 1975).

PH

A change in pH affects cheese functional properties profoundly (Visser, 1991; Lawrence et al., 1987; Noel and Lefier, 1991). Dramatic changes in the properties of cheeses occur as the pH is reduced from 5.4 to 4.9 that result from several factors, including solubilization of most of the colloidal calcium phosphate (Roefs et al., 1985; Rowney et al., 1999), alteration in cheese microstructure with reduction in protein aggregate size (Lawrence et al., 1993), and alterations in bonding between and within the cheese protein network (Luyten et al., 1991). Perhaps the most obvious effect of pH in hard cheese is the brittleness of cheese when pH is less than 5.0. For example, the fracture strain of cheeses is substantially lower at lower pH (and at longer aging) compared to at higher pH (Figure 10.4). Other properties such as softness in semisoft or soft cheese and meltability of all cheese types are also affected by pH (Noel and Lefier, 1991).

Yun et al. (1993b) investigated the effects of pH at milling on the composition and functional properties of Mozzarella cheese. Milling cheese curd at pH 5.10, 5.25, or 5.40 did not affect meltability or textural properties of cheese, but the apparent viscosity of melted cheese increased (implying decreased meltability) as pH increased. The effect of pH and temperature of Mozzarella curd at stretching has been discussed previously. The pH of cheese is not the singular dominant factor affecting meltability of Cheddar cheese (Olson and Bogenrief, 1995). However, pH is a major factor along with FDM in affecting Cheddar cheese meltability (Olson et al., 1996).

POST-MANUFACTURING PROCESSES

AGING/RIPENING

Aging or ripening of many hard and semihard cheeses is essential for the cheeses to develop their characteristic functional properties and flavor. In the case of Cheddar


cheese, it must undergo an aging or ripening stage, from three months to as much as 24 months. The recommended maturation period for Mozzarella cheese is shorter, in the order of few weeks. The proteolytic hydrolysis of intact caseins into peptides and free amino acids is one of the driving forces for changes in functional charac-teristics of cheeses during aging. Enzymes from several sources contribute to proteo-lysis. These sources are: milk (plasmin), coagulant (rennet, chymosin, etc.), starter, secondary starter, and nonstarter microorganisms (Fox et al., 1994). Barbano et al. (1993) reported that initial proteolysis is generally due to the residual coagulant present in the cheese and is known as primary proteolysis. This is followed by secondary proteolysis, the breakdown of peptides into smaller peptides and free amino acids that occurs because of the action of the starter culture enzymes (Rowney et al., 1999). Proteolysis is also affected by a number of other factors such as pH, moisture content, and salt content of the cheese. Sousa et al. (2001) describe the complex series of biochemical and some chemical events that occur during proteo-lysis of different cheeses in much detail.

Breakdown of caseins during proteolysis leads to reorganization and weakening of the protein matrix and enables the fat globules enmeshed within the matrix to be released such that they coalesce when cheese is heated, thus increasing meltability (Figures 10.1A and 10.1B) and free-oil formation (Kiely et al., 1993; Tunick et al., 1993a; Tunick, 1994). During cheese maturation, β-casein is also hydrolyzed, albeit slower than αs1-casein. The half-life of αs1-casein is two weeks and that of β-casein is 37 weeks (Basch et al., 1989). However, microbial enzyme from Cryphonectria(Endothia) parasitica can hydrolyze β-casein more so than rennet, and the hydrolysis of β-casein, rather than αs1-casein, has been reported to improve Cheddar cheese meltability (Bogenrief and Olson, 1995).

Mozzarella cheese is considered an unripened cheese. The high-temperature mixing-molding step during its manufacture partly inactivates the coagulant

FIGURE 10.4 Effect of pH and ripening time on fracture strain of Gouda cheese. (After Visser, 1991.)


(Creamer, 1976). However, significant and characteristic changes in functional properties of Mozzarella cheese take place during the first few weeks after manu-facture (Kindstedt, 1993; Kiely et al., 1993; Tunick et al., 1993a). Mozzarella cheese manufactured by ultrafiltration has poor meltability due to the incorporation of whey proteins, which are not hydrolyzed by rennet, plasmin, or other enzymes from starter bacteria. However, when proteolysis of ultrafiltered Mozzarella cheese is accelerated by enzyme addition, the meltability improves due to increased casein degradation (Madsen and Qvist, 1998). Browning of Mozzarella is also affected by aging. Alvarez (1986) reported that the tendency for browning of fresh Mozzarella cheese decreased dramatically during the first two weeks postmanufacture. This was followed by a gradual increase in tendency for browning with aging. Oberg et al. (1992a) observed a more complex relationship between cheese aging and browning.

Several researchers have reported on the degree to which the proteolytic action of a particular coagulant affects cheese functionalities (Kindstedt et al., 1991; Yun et al., 1993c, d; Oberg et al., 1992a). The extent, rate, and specificity of proteolysis of caseins in Mozzarella cheese can be significantly influenced by the type of coagulant used, and different coagulant can be influenced differently by different cheesemaking factors (Yun et al., 1993d). Oberg et al. (1992a) showed that the type of milk-clotting enzyme used played a significant role in determining physical properties of Mozzarella cheese. The meltability was affected by choice of enzyme and duration of storage. Increase in meltability of the cheese made with calf chymosin was the largest during 28-day ripening. Mozzarella made with coagulant from E. parasitica protease was more meltable and had less free-oil release on melting than other cheeses. Cheeses made with Chymosin and Mucor mieheiproteases were similar in functional characteristics. Stretchability is significantly affected by the enzyme used and storage time. Cheese made with porcine pepsin had the greatest stretch between day 7 and day 28.

Kindstedt et al. (1995) studied the effect of the amount of residual coagulant on functional properties of Mozzarella cheese during storage. They found that reducing the coagulant concentration from 0.1 to 0.06 mL/kg significantly decreased free-oil formation. The effect of coagulant concentration on meltability was not significant.

The specific mix of starter cultures used in cheesemaking may affect cheese functionality. Oberg et al. (1991a, 1991b) investigated the influence of starter culture on physical properties of Mozzarella cheese over time. Proteolytic activities of starters of L. delbrueckii varied widely, and different strains had a significant effect on the functionality of Mozzarella (Oberg et al., 1991a). Oberg et al. (1991b) reported no difference in melt and stretch based on culture types, but both melt and stretch were significantly affected by storage time.

It has been determined that the selection of Lactobacillus culture strains for Mozzarella cheesemaking influenced functional properties. Yun et al. (1995) studied the effect of rod-to-coccus ratio on cheese functionality during storage. They suggested that the amount of starter used might have more impact on functional properties of Mozzarella cheese than the rod-to-coccus ratio. In addition to proteo-lysis, the concomitant increase in water-holding capacity of Mozzarella cheese during storage may improve its functional behavior. McMahon et al. (1999) determined the changes of water in Mozzarella cheeses during storage and related those changes


to cheese microstructure and functionality. Based on the changes observed in expressible serum and the microstructure of Mozzarella, they concluded that the expansion of the protein matrix occurred over the same time span as the decrease in expressible water and indicated that the protein matrix is adsorbing water origi-nally located in fat-serum channels. In addition, meltability of Mozzarella increased during storage while the percentage of entrapped water increased, suggesting that the improvement in the meltability occurs concomitantly with the protein matrix becoming more hydrated.

FREEZING AND FROZEN STORAGE

Freezing of foods helps to preserve their shelf-life, color, flavor, and nutritive value. However, freezing also brings about certain physical and organoleptic changes which may not be desirable. Commercially, cheeses are frozen and stored to stop ripening and to prolong shelf-life during marketing. A recent practice is to distribute fresh pizza in a frozen state, which is then thawed at retail outlets and sold as a refrigerated product (Anonymous, 1996). Initial studies of freezing of cheese were to evaluate the potential damage from freezing during transit. (McDowall, 1938; Sommer, 1928). Freezing Cheddar cheese at –18°C was reported to cause the cheese to become crumbly, but the texture was recovered after thawing at normal storage temperatures. In subsequent years, interest in freezing cheese increased as a means of prolonging desirable cheese properties. Morris and Combs (1955) reported that Cheddar cheese could be satisfactorily frozen if cut into one-pound or smaller pieces and wrapped in foil. Shannon (1974) observed that frozen Cheddar cheese had a crumbly body and mealy texture but did not see any significant difference in firmness as measured by a shear test. Luck (1977) noted that high fat content helped cheese to withstand structural changes during frozen storage.

Cervantes et al. (1983) found that there were no statistically significant effects or consistent trends in textural and sensory attributes of Mozzarella cheese with respect to freezing. Dahlstrom (1978) reported that frozen-thawed cheese evaluated immediately after thawing exhibited an acid flavor, free surface moisture, and poor cohesiveness as compared to the unfrozen cheese. However, the cheese regained its normal characteristics after the thawed cheese was aged for one week to three weeks. Kasprzak (1992) reported that there were no statistically significant effects in texture, flavor, and meltability of Cheddar with respect to freezing and thawing. Oberg et al. (1992b) reported that freezing, thawing, and shredding of low-moisture, part-skim (LMPS) Mozzarella cheese significantly affected cheese stretchability and meltability. They showed that shredded cheese frozen at –196°C (and stored at –70°C for 21 days) stretched the best. However, block cheese frozen and stored at –20°C melted the best. Muthukumarappan and Gunasekaran (1994) evaluated the physical properties of Cheddar and Mozzarella cheeses exposed to different freeze-thaw protocols. The cheeses became softer and generally melted better after freezing and thawing compared to the controls.

Diefes et al. (1993) investigated the rheological behavior of frozen and thawed LMPS Mozzarella cheese. Their study showed that the frozen and thawed Mozzarella tested at 20°C became harder and more elastic with storage time, while samples


stored in a refrigerator became softer and more elasticoviscous with time. Upon melting, both 90-day frozen and 90-day refrigerated cheeses were less elastic and viscous than 14-day refrigerated samples.

Tunick et al. (1991) froze Mozzarella cheese, stored it at –20°C for eight weeks, and tempered it at 4°C for three more weeks. They observed that frozen cheeses melted better than unfrozen controls. Oberg et al. (1992b) studied the effect of freezing, thawing, and shredding of LMPS Mozzarella cheese on its physical prop-erties. They found that block cheese frozen at –20°C melted more after frozen storage than the cheese samples frozen at –196°C and stored at –70°C. Shredded cheese frozen at –196°C stretched the best. However, stretching was not affected by freezing temperature. Bertola et al. (1996a) evaluated the effects of aging, ripening before or after freezing, and freezing rate on the physical properties of low-moisture Moz-zarella cheese. From extensive statistical analyses, they concluded that low-moisture Mozzarella could be frozen and then stored at –20°C without loss of quality when aged from 14 to 21 days at 4°C before consumption.

The industry practice is to freeze young Mozzarella soon after shredding. How-ever, it is not clear if the timing of freezing currently used in industry is optimal to ensure desirable physical properties of the cheese. Therefore, Kuo and Gunasekaran (2002) studied the effects of frozen storage, tempering, and aging on physical properties of pasta filata and nonpasta filata Mozzarella cheese to determine an optimal frozen storage, tempering, and aging combination for these cheeses. The composition of these cheeses are listed in Table 10.3. The effects of frozen storage and tempering on the physical properties of LMPS pasta filata and nonpasta filata Mozzarella cheeses (Chen and Johnson, 1999) of three aging periods before frozen storage are shown in Figure 10.5. Frozen-stored pasta filata and nonpasta filata Mozzarella cheeses melted more but stretched less than the refrigerated control cheese. These significant differences in physical properties are due to the effect of frozen storage on cheese microstructure (Kuo, 2001; Kuo and Gunasekaran, 2002).

Harvey et al. (1982) stated that meltability may be related to the state of casein in cheese and extent of proteolysis. Diefes et al. (1993) mentioned that local dehydration of proteins causes breaks in protein structure as cheese freezes. Bertola

TABLE 10.3Composition of Pasta Filata and Nonpasta Filata Mozzarella Cheeses Used for Studying the Effect of Freezing and Frozen Storage (see Figure 10.5)

Cheese MNFPa FDMb

Salt(%) Protein pH

LMPS Pasta Filata Mozzarella 60.00 41.00 1.32 24.87 5.37LMPS Nonpasta Filata Mozzarella 60.63 43.02 1.88 24.56 5.02

b Fat in the dry matter.

Source: After Kuo and Gunasekaran, 2002.


et al. (1996b) reported that the protein network in cheese weakened by freezing is more susceptible to proteolysis. Fontecha et al. (1993; 1996) reported an increase in the unordered structure resulting from conversion of α-helix and β-structures (sheet or strand) of casein in frozen sheep’s milk cheese, especially in slowly frozen samples, consistent with greater damage to microstructure observed by scanning electron microscopy and greater proteolysis.

Local dehydration of proteins and formation of ice crystals in cheese during freezing and frozen storage might damage the protein structure. Extended frozen storage could result in extensive breakdown of cheese structure due to recrystalli-zation of ice crystals. Upon tempering, the proteins are unable to fully rebind water (Diefes et al., 1993). Thus, the pools of unbound water in frozen-stored cheese could lead to a more porous matrix. Extended frozen storage critically damages the cheese

FIGURE 10.5 Effect of frozen storage, aging, (before frozen storage), and tempering (after frozen storage) on the meltability and stretchability of pasta filata and nonpasta filata Mozzarellacheeses. (A = two-dimensional aging and 1-wk frozen storage; B = two-dimensional aging and 4-wk frozen storage; C = 7-d aging and 1-wk frozen storage; D = 7-d aging and 4-wk frozen storage; E = 14-d aging and 1-wk frozen storage; F = 14-d aging and 4-wk frozen storage). The 5% LSD (least significant difference) is indicated on top of the bars. (After Kuo and Gunasekaran, 2002.)

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matrix of nonpasta filata Mozzarella cheese, leading to increased meltability. Partial rehydration of the protein matrix in frozen-stored samples during tempering may cause a decrease in stretchability of nonpasta filata Mozzarella. The effect was more pronounced for the four-week frozen-stored sample.

The results of Kuo (2001) suggest that pasta filata Mozzarella should be aged one week at 7°C before freezing and could be stored for four weeks at –20°C without quality loss as long as the final product was tempered for seven days before con-sumption. The nonpasta filata Mozzarella could be stored up to four weeks at –20°C as long as the product is aged at 7°C for a total (before and after frozen storage) of 9 to 16 days. Kuo et al. (2001b) reported that the water-holding capacity of pasta-filataMozzarella increased from day two to day 10. Water in pasta-filata Mozzarella exists in the fat-serum channel and is absorbed into the protein matrix during early stages of maturation. Combining these observations, it may be presumed that a considerable number of water molecules in seven-day aged cheese are in the protein matrix. Thus, protein fibers suffer minor damage due to small ice crystals in the cheese matrix. During tempering, the rest of the water molecules in cavities continuously migrate into the protein matrix as evidenced by the formation of a reticular structure (Kuo, 2001). Minor damage on the protein matrix would not change the physical properties to an extent that would make the cheese unacceptable to consumers.

HEAT PROCESSING

It is well known that temperature has a profound effect on meltability and stretch-ability of cheese. Usually, high temperature improves these functional properties. The meltability of Cheddar cheese measured at 70 to 200°C is shown in Figure 10.6 (Wang and Sun, 2002a). Similar results are also reported for Mozzarella cheese. These results show that meltability increased with temperature from 70 to 130°C. Beyond that, increased temperature lowered cheese meltability due to loss of fat and moisture from the cheese matrix.

The heating temperature (70 to 200°C) has a near linear relationship with intensity of browning in Cheddar cheese (measured by the relative gray scale value of the cheese surface color before and after heating) (Wang and Sun, 2002a). The browning is more a function of heating temperature than heating duration. At low temperature, prolonged heating (70°C for 20 min) did not brown the cheese, but even brief exposure to high temperature (1 to 3 min at 200°C) resulted in substantial browning. This is typical of the Maillard reaction. Rudan and Barbano (1998) limited moisture loss and skin formation during baking of fat-free (<0.25% fat) and lower-fat (6 to 9% fat) Mozzarella cheeses by a hydrophobic surface coating of cheese to reduce the browning intensity and improve meltability.

The temperature history during heating also affects melting characteristics of the cheese. Harvey et al. (1982) observed that the meltability of processed cheeses decreased as the duration of heating at 74°C increased. Kim (1999) reported a significant change in viscosity of melted Cheddar cheese held at 60°C before it was allowed to flow compared to cheeses that were allowed to flow without the “holding time.” The change in viscosity of melted cheese depends on the duration the cheese is held at 60°C. One reason for increased viscosity during heating is thought to be


the protein aggregation by hydrophobic interactions among the caseins. The relation-ship between melting and protein degradation in cheese has long been known (Arnott et al., 1957).

Kuo et al. (2001b) investigated the effect of holding times of 0, 10, and 20 min at 60°C, composition and age (1, 3, 6, and 12 weeks after production date) on the meltability of Cheddar cheese and compared the effect of heat treatments on the meltability of Cheddar and brine-salted, LMPS Mozzarella cheeses. The effects of holding time and aging on the meltability at 60°C of Cheddar cheeses different in FDM are shown in Figure 10.7. At 1 week and 3 weeks, the meltability of the traditional Cheddar cheese decreased with increasing holding time, but the change was significant for only the 3-week-old cheese of normal fat content. At 6 and 12 weeks, both cheeses, heated to 60°C for 20 min showed a significant (p < 0.05) decrease in meltability.

As cheese is heated, the protein matrix adsorbs energy that influences the interactions that maintain the protein structure (Meyers, 1990). Interactions under entropic control (e.g., hydrophobic interactions) are strengthened, while those under enthalpic control (i.e., electrostatic and van der Walls’ interactions and hydrogen bonds) are weakened. As a result of the opposing temperature dependencies, proteins unfold in the 60 to 80°C range. When proper hydrophobic sites are exposed due to

FIGURE 10.6 Meltability of Cheddar cheese (relative increase in area of melted cheese spread compared to area unmelted cheese sample, 45 mm square and 3 mm thick) as a function of heating time at different temperatures in a convection oven. (After Wang and Sun, 2002a. With permission.)


unfolding, hydrophobic interactions are excited among the exposed hydrophobic sites, resulting in aggregation of protein molecules (Nakai, 1983). Accordingly, when the cheeses are held long enough at an appropriate temperature (60°C), the caseins aggregate and there is lower cheese meltability.

Kim (1999) reported that increase in surface hydrophobicity and decrease in solubility during heating of Cheddar cheese decreases its meltability. The effects of holding time and aging on the meltability of low-fat Cheddar cheeses of three MNFP levels are shown in Figure 10.8. The very low meltability of low MNFP cheese probably resulted due to a combination of high protein content and low MNFP content. It seems possible that prolonged heating of Cheddar cheeses up to 20 min at 60°C induced exposure of previously buried hydrophobic groups in the protein matrix, resulting in enhanced hydrophobic interactions. Accumulated protein aggre-gations in the casein matrix during heating changes the moisture distribution within the protein matrix. Local hardness and uneven distribution of moisture in the protein matrix decreases cheese meltability.

The effect of holding time on cheese meltability is the same whether the FDM or MNFP values of the cheeses were low or high. The effect of holding time on meltability is more pronounced at 6 weeks and 12 weeks of aging. Since the casein

FIGURE 10.7 Effect of holding time at 60°C and age on the meltability of Cheddar cheese of two FDM levels, (A) 52% FDM; (B) 36% FDM. The standard deviation is indicated on top of the bars. a,b,c Different letters indicate significance (P < 0.05) between the mean meltability values within each age. (After Kuo et al., 2001b. With permission.)

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aggregates of young cheese cross-link throughout the cheese structure (Creamer et al., 1982), the hydrophobic groups are not readily exposed during heating, and thus hydrophobic interactions are rather limited. However, due to proteolysis that breaks these network linkages, the protein matrix in mature cheese (at least 6 weeks old) is fairly open. This allows hydrophobic bonding to form more readily as holding time is prolonged at high temperature. The meltability of LMPS Mozzarella cheese is affected significantly by the holding time, consistent with the similar effect on Cheddar cheese (Kuo et al., 2001b).

OTHER FACTORS

Functional properties of cheeses are affected if they are blended with other cheeses (Kiely et al., 1992b) or when cheese is in contact with other ingredients such as tomato sauce in the case of pizza (Wang et al., 1998). Properties such as free-oil

FIGURE 10.8 Effect of holding time at 60°C and age on the meltability of Cheddar cheese of three MNFP levels, (A) 46% MNFP; (B) 54% MNFP; (C) 57% MNFP. The standard deviation is indicated on top of the bars. a,b,c Different letters indicate significance (P < 0.05) between the mean meltability values within each age. (After Kuo et al., 2001b. With permission.)

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and apparent viscosity (measured by helical viscometer; see Chapter 8) of low-moisture Mozzarella and LMPS Mozzarella are strongly affected by the blended cheese. Figure 10.9 presents the effect on free-oil formation of blending different levels of Cheddar, Provolone, and Muenster cheeses with low-moisture and LMPS Mozzarella cheese. Since the free-oil in Cheddar and Provolone is substantially higher than in Mozzarella, they affect the overall free oil even when added at a 25% level.

The interaction between pizza sauce and Mozzarella cheese significantly decreased the cheese pH and NaCl and Ca content and increased its moisture content. These effects are normally expected to increase meltability. However, a decrease of about 50% in meltability within 12 days of refrigerated storage (Figure 10.10) was observed when the cheese was in contact with pizza sauce.

There have been recent reports of ultra-high pressure (200 to 400 MPa) treatment of milk for durations ranging from 1 to 15 min (Molina et al., 2000; Kheadr et al., 2002). Besides improving the microbial quality, the high-pressure treatment of milk reduces the size of casein micelles and fat globules. This may lead to increased casein–casein and casein–fat interactions (Kheadr et al., 2002). Molina et al. (2000) reported that high-pressure treated milk coagulated faster and produced firmer curds, and the resultant reduced-fat cheese had improved texture and overall acceptability. Messens et al. (2000) high-pressure treated the Gouda cheese at 50 to 400 MPa for one hour. They reported that hydrophobic interactions were weakened by pressure treatment, which may have led to structural changes of the paracasein network, thus affecting rheological properties of the cheese.

FIGURE 10.9 Relative change in free-oil formation compared to 100% Mozzarella cheese in blends of low-moisture, part-skim (LMPS) Mozzarella cheese (filled symbols) and low-moisture Mozzarella cheese (open symbols) with Cheddar (C), Provolone (P), and Munster (M) cheeses. (After Kiely et al., 1992b.)

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