Fe-501 physical properties of food Materials

FE-501PHYSICAL PROPERTIES OFPHYSICAL PROPERTIES OF

FOOD MATERIALSFOOD MATERIALSASSOC PROF. DR. YUS ANIZA YUSOFDEPARTMENT OF PROCESS & FOOD ENGINEERING

FACULTY OF ENGINEERINGUNIVERSITI PUTRA MALAYSIA

INTRODUCTION• Foods are characterized by their physical properties.

INTRODUCTIONy p y p p

• Physical properties intensely affect the quality of foods and can be used to classify/identify foods.

• Formerly, the quality of a food was given by its geometric characteristics.

• Now quality of food evaluate as total quality and takes• Now, quality of food evaluate as total quality and takes into account the entire spectrum of physical properties of foods.

• Physical properties should be able to be measured objectively, quickly, individually, at a low cost and in a manner that will not destroy the foodsmanner that will not destroy the foods.

SIZE, SHAPE, VOLUME ANDSIZE, SHAPE, VOLUME AND RELATED PHYSICAL

ATTRIBUTESATTRIBUTES

INTRODUCTION

• Size and shape are important physicalattributes of foods that are used in screening,grading and quality control of foods.

• They are also important in fluid flow and heatand mass transfer calculations.

SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES

SIZE• Size is an important attribute of foods used in

SIZEp

screening solids to separate foreign materials, gradingof fruits and vegetables, and evaluating the quality offood materialsfood materials.

• In fluid flow, and heat and mass transfer calculations, itis necessary to know the size of the sample.y p

• Size of the particulate foods is also critical. Forexample, particle size of powdered milk must be largeenough to prevent agglomeration but small enough toenough to prevent agglomeration, but small enough toallow rapid dissolution during reconstitution.


SIZE

l f d b l l

SIZE

• Particle size was found to be inversely proportional to dispersion of powder and water holding capacity of whey protein powders (Resch & Daubert, 2001). p p ( )

• Decrease in particle size also increased the steady shear and complex viscosity of the reconstituted powder.

• The importance of particle size measurement has been widely recognized, especially in the beverage industry, as the distribution and concentration ratio of particulates present in p pbeverages greatly affect their flavor.

• It is easy to specify size for regular particles, but for irregular ti l th t i t b bit il ifi dparticles the term size must be arbitrarily specified.


SIZE

l d d ff d d

SIZE

• Particle sizes are expressed in different units depending on the size range involved.

• Coarse particles are measured in millimeters, fine particles inCoarse particles are measured in millimeters, fine particles in terms of screen size, and very fine particles in micrometers or nanometers.

• Ultrafine particles are sometimes described in terms of their surface area per unit mass, usually in square meters per gram (McCabe, Smith & Harriot, 1993).( , , )


SIZE

b d d h d h d

SIZE

• Size can be determined using the projected area method. Inthis method, three characteristic dimensions are defined:

1. Major diameter, which is the longest dimension of the1. Major diameter, which is the longest dimension of themaximum projected area;

2. Intermediate diameter, which is the minimumdiameter of the maximum projected area or themaximum diameter of the minimum projected area;

3 Minor diameter which is the shortest dimension of the3. Minor diameter, which is the shortest dimension of theminimum projected area.


SIZE• Length, width, and thickness terms are commonly used that

d j i di d i di

SIZE

correspond to major, intermediate, and minor diameters,respectively.

• The dimensions can be measured using a micrometer orThe dimensions can be measured using a micrometer orcaliper (Fig. 1). The micrometer is a simple instrument used tomeasure distances between surfaces. Most micrometers havea frame anvil spindle sleeve thimble and ratchet stop Theya frame, anvil, spindle, sleeve, thimble, and ratchet stop. Theyare used to measure the outside diameters, inside diameters,the distance between parallel surfaces, and the depth ofholes.


Fig.1

SIZE• Particle size of particulate foods can be determined by sieve

l i (Fi 2) h h l i ll h d

SIZE

analysis (Fig.2), passage through an electrically chargedorifice, and settling rate methods.

• Particle size distribution analyzers (Fig.3), which determineParticle size distribution analyzers (Fig.3), which determineboth the size of particles and their state of distribution, areused for production control of powders.

Fig.3


Fig.2

SHAPE• Shape is also important in heat and mass transfer

SHAPEShape is also important in heat and mass transfercalculations, screening solids to separate foreignmaterials, grading of fruits and vegetables, and, g g g ,evaluating the quality of food materials.

• The shape of a food material is usually expressedThe shape of a food material is usually expressedin terms of its sphericity and aspect ratio.

• Sphericity is an important parameter used in fluidSphericity is an important parameter used in fluidflow and heat and mass transfer calculations.


SHAPE• According to the most commonly used

SHAPEAccording to the most commonly useddefinition, sphericity is the ratio of volume ofsolid to the volume of a sphere that has asolid to the volume of a sphere that has adiameter equal to the major diameter of theobject so that it can circumscribe the solidobject so that it can circumscribe the solidsample. For a spherical particle of diameterDp sphericity is equal to 1 (Mohsenin 1970)Dp, sphericity is equal to 1 (Mohsenin, 1970).


SHAPESHAPE

• Assuming that the volume of the solid sampleg pis equal to the volume of the triaxial ellipsoidwhich has diameters equivalent to those ofthe sample, then:


SHAPE• In a triaxial ellipsoid, all three perpendicular

SHAPEp , p p

sections are ellipses (Fig. 4). If the major,intermediate, and minor diameters are 2a, 2b,, , ,and 2c, respectively, volume of the triaxialellipsoid can be determined from thepfollowing equation:

• Then, sphericity is


SHAPESHAPE

Fig.4 Triaxial ellipsoid


SHAPE• Sphericity is also defined as the ratio of

SHAPEp ysurface area of a sphere having the samevolume as the object to the actual surfacejarea of the object (McCabe, Smith, & Harriot,1993):)

wherewhere,


SHAPE• The equivalent diameter is sometimes defined as

h d f h h h l

SHAPE

the diameter of a sphere having the same volumeas the particle.

• However for fine granular materials it is difficult• However, for fine granular materials, it is difficultto determine the exact volume and surface areaof a particle.

• Therefore, equivalent diameter is usually taken tobe the nominal size based on screen analysis ormicroscopic examination in granular materialsmicroscopic examination in granular materials.

• The surface area is found from adsorptionmeasurements or from the pressure drop in abed of particles.


SHAPE• In general, diameters may be specified for any

SHAPEg , y p y

equidimensional particle.

• Particles that are not equidimensional that isParticles that are not equidimensional, that is,longer in one direction than in others, areoften characterized by the second longestoften characterized by the second longestmajor dimension.

• For example for needlelike particles• For example, for needlelike particles,equivalent diameter refers to the thickness ofthe particles not their lengththe particles, not their length.


SHAPE• In a sample of uniform particles of diameter

SHAPEp p

Dp, the number of particles in the sample is:

where

• Total surface area of particles;


SHAPE• Another definition of sphericity is the ratio of

SHAPEp y

the diameter of the largest inscribed circle (di ) to the diameter of the smallest circumscribed circle (dc) (Mohsenin, 1970):

• Recently, Bayram (2005) proposed another equation to calculate sphericity as:equation to calculate sphericity as:


SHAPE• Where

SHAPE

• According to this formula, equivalent diameter for irregularshape material is accepted as the average dimension.

• Differences between average diameter and measured• Differences between average diameter and measureddimensions are determined by the sum of square ofdifferences.

• When this difference is divided by the square of product of• When this difference is divided by the square of product ofthe average diameter and number of measurements, itgives a fraction for the approach of the slope to anequivalent sphere which is sphericityequivalent sphere, which is sphericity.


SHAPE• According to Eq. (1.9), if the sample sphericity value is close to

zero it can be considered as spherical

SHAPEzero it can be considered as spherical.

• The aspect ratio (Ra) is another term used to express theshape of a material. It is calculated using the length (a) andthe width (b) of the sample as (Maduako & Faborode, 1990):

f h d f• Certain parameters are important for the design of conveyorsfor particulate foods, such as radius of curvature, roundness,and angle of repose. Radius of curvature is important tog p pdetermine how easily the object will roll. The more sharplyrounded the surface of contact, the greater will be thestresses developedstresses developed.


SHAPEWhere

SHAPE

• The minimum and the maximum radii of curvature for larger• The minimum and the maximum radii of curvature for largerobjects such as apples are calculated using the larger andsmaller dial indicator readings, respectively.

• For smaller objects of relatively uniform shape, the radius ofcurvature can be calculated using the major diameter andeither the minor or intermediate diameter.either the minor or intermediate diameter.


SHAPE• Where

SHAPE

• Roundness is a measure of the sharpness of the corners ofthe solid. Several methods are available for estimatingroundness. The most commonly used ones are given below(Mohsenin, 1970):

where


SHAPESHAPE

Fig. 5 Roundness definitions.

• Roundness can also be estimated from Eq. (1.15):

where


SHAPE• Angle of repose is another important physical property used

SHAPEg p p p y p p y

in particulate foods such as seeds, grains, and fruits.

• When granular solids are piled on a flat surface, the sides ofth il t d fi it d ibl l ith ththe pile are at a definite reproducible angle with thehorizontal.

• This angle is called the angle of repose of the material. Theg g pangle of repose is important for the design of processing,storage, and conveying systems of particulate material.

Wh h i h d d d h l f• When the grains are smooth and rounded, the angle ofrepose is low. For very fine and sticky materials the angle ofrepose is high.


PARTICLE SIZE DISTRIBUTION• The range of particle size in foods depends on the cell

PARTICLE SIZE DISTRIBUTIONg p p

structure and the degree of processing.

• The hardness of grain is a significant factor in the particle sizedi t ib ti f fl Th ti l i di t ib ti f fl idistribution of flour. The particle size distribution of flour isknown to play an important role in its functional propertiesand the quality of end products.

• The relationship between the physicochemical properties ofrice grains and particle size distributions of rice flours fromdifferent rice cultivars were examined (Chen Lii & Lu 2004)different rice cultivars were examined (Chen, Lii, & Lu, 2004).

• It was found that physical characteristics of rice grain were themajor factors but chemical compositions were also importantin affecting the particle size distribution of rice flour.


PARTICLE SIZE DISTRIBUTION• Particles can be separated into fractions by using one of the

PARTICLE SIZE DISTRIBUTIONp y g

following methods:1. Air elutriation method: In this method, the velocity of an airstream is adjusted so that particles measuring less than a givenstream is adjusted so that particles measuring less than a givendiameter are suspended. After the particles within the size rangeare collected, the air velocity is increased and the new fraction ofparticles is collected The process continues until the particulateparticles is collected. The process continues until the particulatefood is separated into different fractions.


Air classifier

PARTICLE SIZE DISTRIBUTION2. Settling, sedimentation, and centrifugation method: In settling and

PARTICLE SIZE DISTRIBUTION

sedimentation, the particles are separated from the fluid by gravitationalforces acting on the particles. The particles can be solid particles or liquiddrops. Settling and sedimentation are used to remove the particles fromthe fluid. It is also possible to separate the particles into fractions ofdifferent size or density. Particles that will not settle by gravitational forcecan be separated by centrifugal force. If the purpose is to separate the

ti l i t f ti f diff t i ti l f if d it b tparticles into fractions of different sizes, particles of uniform density butdifferent sizes are suspended in a liquid and settle at different rates.Particles that settle in given time intervals are collected and weighed.


Centrifuge

PARTICLE SIZE DISTRIBUTION3. Screening: This is a unit operation in which various sizes of

PARTICLE SIZE DISTRIBUTIONg p

solid particles are separated into two or more fractions bypassing over screen(s). A dispersing agent may be added toimprove sieving characteristics Screen is the surfaceimprove sieving characteristics. Screen is the surfacecontaining a number of equally sized openings. The openingsare square. Each screen is identified in meshes per inch.Mesh is defined as open spaces in a network. The smallestmesh means largest clear opening.


PARTICLE SIZE DISTRIBUTION• A set of standard screens is stacked one upon the other with

PARTICLE SIZE DISTRIBUTIONp

the smallest opening at the bottom and the largest at the topplaced on an automatic shaker for screen analysis (sieveanalysis) In screen analysis the sample is placed on the topanalysis). In screen analysis, the sample is placed on the topscreen and the stack is shaken mechanically for a definitetime. The particles retained on each screen are removed andweighed. Then, the mass fractions of particles separated arecalculated. Any particles that pass through the finest screenare collected in a pan at the bottom of the stack.p



l l b d d ff


• Particle size analysis can be done in two different ways:– differential analysis

– cumulative analysis.y

• In differential analysis, mass or number fraction in each size increment is plotted as a function of average particle size or

ti l i Th lt ft t dparticle size range. The results are often presented as a histogram as shown in Fig. 6 with a continuous curve to approximate the distribution. If the particle size ranges are all equal as in this figure, the data can be plotted directly.


PARTICLE SIZE DISTRIBUTIONPARTICLE SIZE DISTRIBUTION

Fig. 6 Particle size distribution using

• However it gives a false impression if the covered range of particle

gdifferential analysis.

• However, it gives a false impression if the covered range of particle sizes differs from increment to increment. Less material is retained in an increment when the particle size range is narrow than when it is wide Therefore average particle size or size range versusis wide. Therefore, average particle size or size range versusshould be plotted, where is the mass fraction and is the particle size range in increment i (McCabe et al., 1993).


PARTICLE SIZE DISTRIBUTION• Cumulative analysis is obtained by adding consecutively the

PARTICLE SIZE DISTRIBUTION• Cumulative analysis is obtained by adding, consecutively, the

individual increments, starting with that containing thesmallest particles and plotting the cumulative sums againstthe maximum particle diameter in the increment. In acumulative analysis, the data may appropriately berepresented by a continuous curve.p y

• Table 1 shows a typical screen analysis. Cumulative plots aremade using the second and fifth columns of Table 1 (Fig. 7)


PARTICLE SIZE DISTRIBUTIONPARTICLE SIZE DISTRIBUTION


Fig. 7 Particle size distribution using cumulative analysis

PARTICLE SIZE DISTRIBUTION• Calculations of average particle size, specific surface area, or

PARTICLE SIZE DISTRIBUTIONg p , p ,

particle population of a mixture may be based on either adifferential or a cumulative analysis. In cumulative analysis,the assumption of “all particles in a single fraction are equal inthe assumption of all particles in a single fraction are equal insize” is not required. Therefore, methods based on thecumulative analysis are more precise than those based ondifferential analysis.


PARTICLE SIZE DISTRIBUTION• The specific surface area is defined as the total surface area of


a unit mass of particles.

• For constant density (ρp) and sphericity , specific surface(A ) f th i t iarea (Aw ) of the mixture is:

wherewhere


PARTICLE SIZE DISTRIBUTION• If the cumulative analysis is used, specific surface area of the

PARTICLE SIZE DISTRIBUTIONy , p

mixture is found by integrating with respect to mass fractionbetween the limits of 0 to 1 (McCabe & Smith, 1976):

• Average particle diameter of a mixture can be calculated inAverage particle diameter of a mixture can be calculated in different ways. The most commonly used one is the volume surface mean diameter (Sauter mean diameter). It is used if h f i f i l i h f i i k Fthe mass fraction of particles in each fraction is known. For differential analysis:


PARTICLE SIZE DISTRIBUTION• For cumulative analysis:

PARTICLE SIZE DISTRIBUTIONy

• Mass mean diameter can also be calculated if the massfractions of particles in each fraction are known Forfractions of particles in each fraction are known. Fordifferential analysis:

• For cumulative analysis:


PARTICLE SIZE DISTRIBUTION• If the number of particles in each fraction is known,

PARTICLE SIZE DISTRIBUTIONp ,

arithmetic mean diameter is used. For differential analysis:

where

• For cumulative analysis:For cumulative analysis:


PARTICLE SIZE DISTRIBUTION• The number of particles in the mixture can be calculated from


either differential or cumulative analysis using Eqs. (1.25) and (1.26), respectively:

• where is the volume shape factor, which is defined by the p , yratio of volume of a particle (Vp) to its cubic diameter:


PARTICLE SIZE DISTRIBUTION• Dividing the total volume of the sample by the number of

PARTICLE SIZE DISTRIBUTIONg p y

particles in the mixture gives the average volume of a particle. The diameter of such a particle is the volume mean diameter, which is found from:which is found from:

For the cumulative analysis, volume mean diameter is determined by integrating with respect to mass fraction between the limits of 0 and 1:


VOLUME• Volume is defined as the amount of three‐dimensional space

VOLUMEp

occupied by an object, usually expressed in units that are thecubes of length units, such as cubic inches and cubiccentimeters or in units of liquid measure such as gallons andcentimeters, or in units of liquid measure, such as gallons andliters.

• In the SI system, the unit of volume is m3.

• Volume is an important quality attribute in the food industry.

• It appeals to the eye, and is related to other qualityF i i i i l l d i hparameters. For instance, it is inversely correlated with

texture.


VOLUME• Volume of solids can be determined by using the following

VOLUMEy g g

methods:

1. Volume can be calculated from the characteristic di i i th f bj t ith l hdimensions in the case of objects with regular shape.

2. Volumes of solids can be determined experimentally by liquid, gas, or solid displacement methods.y q , g , p

3. Volume can be measured by the image processing method. An image processing method has been recently d l d l f lli id l i l ldeveloped to measure volume of ellipsoidal agricultural products such as eggs, lemons, limes, and peaches (Sabliov, Boldor, Keener, & Farkas, 2002).


VOLUME

• If the solid sample does not absorb liquid very fast the liquid

VOLUMELiquid Displacement Method

• If the solid sample does not absorb liquid very fast, the liquid displacement method can be used to measure its volume.

• In this method, volume of food materials can be measured by ypycnometers (specific gravity bottles) or graduated cylinders.

• The pycnometer has a small hole in the lid that allows liquid to escape as the lid is fitted into the neck of the bottle (Fig 8)to escape as the lid is fitted into the neck of the bottle (Fig. 8).


Fig. 8 Pycnometer (specific gravity bottle)

VOLUME

• The bottle is precisely weighed and filled with a liquid of


• The bottle is precisely weighed and filled with a liquid of known density.

• The lid is placed on the bottle so that the liquid is forced out p qof the capillary.

• Liquid that has been forced out of the capillary is wiped from the bottle and the bottle is weighed againthe bottle and the bottle is weighed again.

• After the bottle is emptied and dried, solid particles are placed in the bottle and the bottle is weighed again. p g g

• The bottle is completely filled with liquid so that liquid is forced from the hole when the lid is replaced.


VOLUME

• The bottle is reweighed and the volume of solid particles can


• The bottle is reweighed and the volume of solid particles can be determined from the following formula:

where


VOLUME

• The volume of a sample can be measured by direct measurement


• The volume of a sample can be measured by direct measurementof volume of the liquid displaced by using a graduated cylinder orburette.

• The difference between the initial volume of liquid in a graduatedThe difference between the initial volume of liquid in a graduatedcylinder and the volume of liquid with immersed material gives usthe volume of the material.

• That is the increase in volume after addition of solid sample isThat is, the increase in volume after addition of solid sample isequal to the solid volume.

• In the liquid displacement method, liquids used should have a low surface tension and should be absorbed very slowly by thesurface tension and should be absorbed very slowly by the particles.

• Most commonly used fluids are water, alcohol, toluene, and tetrachloroethylene For displacement it is better to use atetrachloroethylene. For displacement, it is better to use a nonwetting fluid such as mercury.


VOLUME

• For larger objects a platform scale can be used (Mohsenin


• For larger objects, a platform scale can be used (Mohsenin,1970) (Fig. 9). The sample is completely submerged in liquidsuch that it does not make contact with the sides or bottom ofthe beaker. Weight of the liquid displaced by the solid sample isdivided by its density. The method is based on the Archimedesprinciple, which states that a body immersed in a fluid willp p , yexperience a weight loss in an amount equal to the weight ofthe fluid it displaces. That is, the upward buoyancy forceexerted on a body immersed in a liquid is equal to the weight ofexerted on a body immersed in a liquid is equal to the weight ofthe displaced liquid.

Fig. 9 Platform scale for


measurement of volume of large objects.

VOLUMEVOLUMELiquid Displacement Method

where


VOLUMEVOLUMELiquid Displacement Method

• Liquids having a density lower than that of sample should beused if partial floating of the sample is observed. The sampleis forced into the liquid by means of a sinker rod if it is lighteris forced into the liquid by means of a sinker rod if it is lighteror it is suspended with a string if it is heavier than the liquid. Ifthe sample is forced into the fluid using a sinker rod, it shouldbe taken into account in the measurement as:


VOLUME

• Volumes of particulate solids and materials with irregular

VOLUMEGas Displacement Method

• Volumes of particulate solids and materials with irregularshape can be determined by displacement of gas or air inpycnometer (Karathanos & Saravacos, 1993).

• The most commonly used gases are helium and nitrogen.

• The pycnometer consists of two airtight chambers of nearlyequal volumes V and V that are connected with smallequal volumes, V1 and V2,that are connected with small‐diameter tubing (Fig. 10).

Fig. 10 Gas comparison


pycnometer.

VOLUME

• The material to be measured is placed in the second chamber


• The material to be measured is placed in the second chamber.

• The exhaust valve (valve 3) and the valve between the twochambers (valve 2) are closed.( )

• The inlet valve (valve 1) is opened and the gas is supplied tothe first chamber until the gauge pressure is increased up to asuitable value (e g 700 1000 Pa)suitable value (e.g., 700–1000 Pa).

• Then, the inlet valve is closed and the equilibrium pressure isrecorded. Assuming that the gas behaves ideally:g g y


VOLUME

where


where

• After the equilibrium pressure is recorded the valve between• After the equilibrium pressure is recorded, the valve betweenthe two chambers is opened (valve 2) and the gas within thefirst chamber is allowed to fill the empty spaces (pores) in the

d h bsecond chamber.• The new pressure (P2) is recorded. When valve 2 is opened,

total mass of gas (m) is divided into two, one of which fills thefirst tank (m1) and the other fills the pore space of the secondtank (m2).


VOLUMEVOLUMEGas Displacement Method

• Assuming that the system is isothermal:

• where Va2 is the volume of the empty spaces within thesecond chamber and can be expressed as:

h V i h l f h lid ( 3) d b l l d• where Vs is the volume of the solid (m3) and can be calculatedfrom the following equation:


VOLUMEVOLUMEGas Displacement Method

• The errors in this method may come from not taking intoaccount the volumes of the tubing connecting the chambers.\

M l h h h l l i id l h• Moreover, although the calculation assumes an ideal gas, theair does not exactly follow the ideal gas law.

• In addition, the equalization in pressures between the twoIn addition, the equalization in pressures between the twochambers is not isothermal.

• To eliminate these errors, the instrument should be calibratedb i bj f i l k lby using an object of precisely known volume.


VOLUME

• The volume of irregular solids can also be measured by sand

VOLUMESolid Displacement Method

• The volume of irregular solids can also be measured by sand,glass bead, or seed displacement method.

• Rapeseeds are commonly used for determination of volumep yof baked products such as bread.

• In the rapeseed method, first the bulk density of rapeseeds isdetermined by filling a glass container of known volumedetermined by filling a glass container of known volumeuniformly with rapeseeds through tapping and smoothing thesurface with a ruler.

• All measurements are done until the constant weight isreached between the consecutive measurements.

Th d iti f th d l l t d f th d• The densities of the seeds are calculated from the measuredweight of the seeds and volume of the container.


VOLUME

• The sample and rapeseeds are placed together in the

VOLUMESolid Displacement Method

• The sample and rapeseeds are placed together in thecontainer. The container is tapped and the surface issmoothed with a ruler. Tapping and smoothing are continueduntil a constant weight is reached between three consecutivemeasurements. The volume of the sample is calculated asfollows:

where


VOLUME

• Volume can be expressed in different forms The form of the

VOLUMEExpressions of Volume

• Volume can be expressed in different forms. The form of thevolume must be well defined before the data are presented. Themost commonly used definitions are:– Solid volume (V ) is the volume of the solid material (including water)Solid volume (Vs ) is the volume of the solid material (including water)

excluding any interior pores that are filled with air. It can be determinedby the gas displacement method in which the gas is capable of penetratingall open pores up to the diameter of the gas molecule.A l (V ) i h l f b i l di ll– Apparent volume (Vapp) is the volume of a substance including all poreswithin the material (internal pores). Apparent volume of regulargeometries can be calculated using the characteristic dimensions.Apparent volume of irregularly shaped samples may be determined bysolid or liquid displacement methods.

– Bulk volume (Vbulk) is the volume of a material when packed or stacked inbulk. It includes all the pores enclosed within the material (internal pores)and also the void volume outside the boundary of individual particlesand also the void volume outside the boundary of individual particleswhen stacked in bulk (external pores).


• Porosity is an important physical property characterizing the

POROSITY

• Porosity is an important physical property characterizing thetexture and the quality of dry and intermediate moisturefoods.

• Porosity data is required in modeling and design of variousheat and mass transfer processes such as drying, frying,baking heating cooling and extrusionbaking, heating, cooling, and extrusion.

• It is an important parameter in predicting diffusionalproperties of cellular foods.

• Porosity (ε) is defined as the volume fraction of the air or thevoid fraction in the sample and expressed as:


POROSITY


• There are different methods for determination ofi hi h b i d f ll

POROSITY

porosity, which can be summarized as follows:1. Direct method: In this method, porosity is determined from the

difference of bulk volume of a piece of porous material and its volume after destruction of all voids by means of compressionvolume after destruction of all voids by means of compression. This method can be applied if the material is very soft and no attractive or repulsive force is present between the particles of solid.

2. Optical method: In this method, porosity is determined from the microscopic view of a section of the porous medium. This method is suitable if the porosity is uniform throughout the sample, that is, the sectional porosity represents the porosity of whole , p y p p ysample. Pore size distribution can be determined if a suitable software is used to analyze images.

3. Density method: In this method, porosity is calculated from the measured densities:measured densities:


POROSITY

• Porosity due to the enclosed air space within the particles

POROSITYDENSITY METHOD

• Porosity due to the enclosed air space within the particlesis named apparent porosity (εapp) and defined as the ratio oftotal enclosed air space or voids volume to the total volume.It can also be named internal porosity. Apparentporosity is calculated from the measured solid (ρx) andapparent density (ρapp)data as:pp y (ρapp)

• or from the specific solid and apparent volumes as:


POROSITY

• Bulk porosity (ε ) which can also be called external or


• Bulk porosity (εbulk), which can also be called external or interparticle porosity, includes the void volume outside the boundary of individual particles when stacked as bulk and calculated using bulk and apparent densities as:

• or from the specific bulk and apparent• or from the specific bulk and apparent volumes as:

• Then, total porosity when material is packed or stacked as bulk is:


POROSITY

• Pores within the food materials (internal pores) can be


• Pores within the food materials (internal pores) can bedivided into three groups: closed pores that are closed fromall sides, blind pores that have one end closed, and open orflow‐ through pores where the flow typically takes place (Fig.1.11).

Fig. 11 Different kinds of pores.


POROSITY

• Since the apparent porosity is due to the enclosed air space


• Since the apparent porosity is due to the enclosed air spacewithin the particles and there are three different forms ofpores within the particles, it can be written as:

where

• Then total porosity can also be written as:• Then, total porosity can also be written as:


POROSITY

4 Gas pycnometer method: Porosity can be measured

POROSITYGAS PYCNOMETER METHOD

4. Gas pycnometer method: Porosity can be measureddirectly by measuring the volume fraction of air using theair comparison pycnometer. Remembering Eq. (1.49):

Porosity can be calculated from Eq. (1.49) as:

5 Using porosimeters: Porosity and pore size5. Using porosimeters: Porosity and pore sizedistribution can be determined using porosimeters,which are the instruments based on the principle ofi h li id i i i li id ieither liquid intrusion into pores or liquid extrusionfrom the pores.


POROSITY

• For extrusion porosimetry, wetting liquids are used to fill the pores in


the porous materials. Liquid is displaced from the pores by applyingdifferential pressure on the sample and volume of extruded liquid ismeasured.

• Extrusion methods can be categorized as capillary flow porosimetryand liquid extrusion porosimetry. Capillary flow porosimetry is a liquid extrusion method in which the differential gas pressure and flow rates g pthrough wet and dry samples are measured (Fig. 12). Capillary flow porosimetry can measure pore size between 0.013 and 500 μm (Jena & Gupta, 2002).

Fig. 12 Principle of capillary flow


capillary flow porosimetry

POROSITY

• For large pore sizes, liquid extrusion porosimetry is preferred.


g p , q p y pLiquid extrusion porosimetry can be used for pore sizes of 0.06 to 1000 μm.

Fig. 13 Principle of liquid extrusion prosimetry


POROSITY

• In intrusion porosimetry, as intrusion liquid mercury, oil, or


water is used.• In intrusion porosimetry, liquid is forced into pores under

pressure and intrusion volume and pressure are measured.• Mercury intrusion porosimetry can measure pores in the

size range of 0.03 to 200 μm while nonmercury intrusionporosimetry can measure pores in the size range of 0.001to 20 μm.

• This method can detect pore volume, pore diameter, andsurface area of through and blind pores.g p

• Since very high pressures are required in mercuryintrusion, the pore structure of the samples can bedistorted.


POROSITY• Porosity may show a maximum or minimum as a function of

POROSITYy y

moisture content.

• It may also decrease or increase exponentially during dryingith t h i ti i twithout showing an optimum point.

• The porosity of the apple rings increased linearly whenmoisture content decreased during drying and then reached ag y gconstant value (Bai, Rahman, Perera, Smith, & Melton, 2002).

• A linear increase in the bulk porosity was also observed duringd i f h h l (M i & S 1990)drying of the starch samples (Marousis & Saravacos, 1990).


POROSITY• The drying method is also important in affecting porosity.

POROSITYy g p g p y

• Freeze drying was found to produce the highest porosity,whereas in conventional air drying the lowest porosity wasb d d t i d tiobserved as compared to vacuum, microwave, and osmotic

drying of bananas, apples, carrots, and potatoes (Krokida &Maroulis, 1997).

• Rahman (2003) developed a theoretical model to predictporosity in foods during drying assuming that volume of poresformed is equal to the volume of water removed duringformed is equal to the volume of water removed duringdrying.


• The presence of pores and degree of porosity affect the

POROSITYp p g p y

mechanical properties of food materials.

• It has been shown that mechanical properties of extrudedf d d t ff t d b it (G & T l dfood products are affected by porosity (Guraya & Toledo,1996).

• Mandala and Sotirakoglou (2005) mentioned that crumb andg ( )crust texture of breads could be related to porosity.


POROSITY• Porosity is also important in frying, since it affects oil uptake

POROSITYy p y g, p

of the product.

• A linear relationship was found between oil uptake during f i d it i t f i (Pi th W i b & Sfrying and porosity prior to frying (Pinthus,Weinberg, & Saguy, 1995).

• Porosity increased during frying of restructured potato y g y g pproduct and after a short initial period, it was found to be linearly correlated with oil uptake.


DETERMINATION OF VOLUME OFDETERMINATION OF VOLUME OF DIFFERENT KINDS OF PORES

• Total specific pore volume within the material can be calculated if the specific volume of all kinds of pores—closed pores blind pores and flow through porespores , blind pores, ,and flow‐through pores are known:

• Total specific pore volume within the material can be calculated by measuring specific bulk and the specific solid volume determined after compacting the sample tosolid volume determined after compacting the sample to exclude all the pores :



• The difference between the specific solid volume determined by gas pycnometer and specific solid volume after compacting the sample gives the volume of closed porescompacting the sample , gives the volume of closed pores since in a gas pycnometer, gas enters into the open and blind pores but not the closed ones. From these results, the specific volume of closed pores can be calculated:

• Volume of flow through or open pores of the sample• Volume of flow through or open pores of the sample, , can be measured directly using liquid extrusion porosimetry.From Eq. (1.51), the specific volume of the blind pores is:



• Substituting Eqs. (1.52) and (1.53) into Eq. (1.54):

• The fraction of open, closed, or blind pores can be calculated by dividing the specified pore volume by total pore volume.


SHRINKAGE• Shrinkage is the decrease in volume of the food

SHRINKAGES age s t e dec ease o u e o t e oodduring processing such as drying.

• When moisture is removed from food duringgdrying, there is a pressure imbalance betweeninside and outside of the food.

• This generates contracting stresses leading tomaterial shrinkage or collapse (Mayor & Sereno,2004)2004).

• Shrinkage affects the diffusion coefficient of thematerial and therefore has an effect on the dryingmaterial and therefore has an effect on the dryingrate.


SHRINKAGESHRINKAGE


SHRINKAGE• Apparent shrinkage is defined as the ratio of

SHRINKAGEApparent shrinkage is defined as the ratio of the apparent volume at a given moisture content to the initial apparent volume ofcontent to the initial apparent volume of materials before processing:

when


SHRINKAGE• Shrinkage is also defined as the percent

SHRINKAGEShrinkage is also defined as the percentchange from the initial apparent volume.

• Two types of shrinkage are usually observed in• Two types of shrinkage are usually observed infood materials. If there is a uniform shrinkagein all dimensions of the material it is calledin all dimensions of the material, it is calledisotropic shrinkage.

Th if h i k i diff• The nonuniform shrinkage in differentdimensions, on the other hand, is called

i i h i kanisotropic shrinkage.SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES

REFERENCES1. Bayram, M. (2005). Determination of the sphericity of granular food

materials. Journal of Food Engineering, 68, 385–390.2. Karathanos,V.T.,&Saravacos, G.D. (1993). Porosity and pore size

distribution of starch materials Journal of Food Engineering 18 259–distribution of starch materials. Journal of Food Engineering, 18, 259280.

3. McCabe, W.L, Smith, J.C., & Harriot, P. (1993). Unit Operations of Chemical Engineering, 5th ed. Singapore: McGraw‐Hill.

h ( ) h l f l d l4. Mohsenin, N.N. (1970). Physical Properties of Plant and Animal Materials. New York: Gordon and Breach.

5. Maduako, J.N.,&Faborode, M.O. (1990). Some physical properties of cocoa pods in relation to primary processing. Ife Journal of Technology, 2, p p y p g f f gy, ,1–7.

6. Sabliov, C.M., Boldor, D.,Keener, K.M.,&Farkas, B.E. (2002). Image processing method to determine surface area and volume of axi‐symmetric agricultural products International Journal of Foodsymmetric agricultural products. International Journal of Food Properties, 5, 641–653.


THANK YOU


MASS AND DENSITY

MASS• Mass is a measure for inertia and heaviness of a body.

H i i d b h E h’ i i l i f

MASS

Heaviness is caused by the Earth’s gravitational attraction fora body. The force between the body of interest and the planetEarth is called the weight force of the body. Mathematically,this force can be expressed as the product of the body’s massand the Earth’s acceleration due to gravity, as shown byequation (3 1)equation (3.1).

• where

(3.1)

MASS & DENSITY

MASS• The density of planet Earth varies with location and the planet

is slightly pear shaped and not in the shape of a perfect

MASS

is slightly pear‐shaped and not in the shape of a perfectsphere, the value of gravitational acceleration differs slightlywith location on the Earth’s surface. Considering the rotationof the planet a body resting at the equator will have a greaterof the planet, a body resting at the equator will have a greatertangential speed and centrifugal force than in regions farnorth or south of the equator.h l f h’ l l h• The value of Earth’s gravitational acceleration in Zurich,Switzerland is used as a standard for calculations, and is calledstandard gravitational acceleration having the value g =

29.80665m∙ s−2.When a balance which was adjusted in Zurich,is taken to another place on the Earth, but is not corrected forthe local gravitational acceleration, the displayed weight maybe in error.

MASS & DENSITY

MASS• Table 3.1 illustrates this concept for a body having a mass of

1k T id i h f hi

MASS

1kg. To avoid erroneous weight measurements of this type, a balance has to be recalibrated at the location in which it will be used. For this purpose, commercial mass standards are produced with the help of national standards organizations around the world.

Table 3.1 Weighing a 1 kg mass in different place

MASS & DENSITY

• A balance is an instrument measuring the weighing force of a

WEIGHING AND ATMOSPHERIC BUOYANCY

g g gbody. However, it usually does not display a force signal (e.g.newtons), but a mass signal (e.g. kilograms).This is due to theprinciple of calibration used for balances: A mass standard isprinciple of calibration used for balances: A mass standard isplaced on the balance that causes a deformation, which canbe read as an angle, a distance or an electric voltage,depending on the type of balance.

• A calibration has to be performed for every type ofsensing/measuring instrument For this purpose appropriatesensing/measuring instrument. For this purpose, appropriaterespective standard materials and procedures are needed,that make it possible to perform calibration of an instrumenti l b tin any laboratory.

MASS & DENSITY

• From a scientific point of view the calibration procedure described


for a balance is basically to use the instrument as a “force meter,”then divide the force G measured by the value of the localgravitational acceleration g, and display the result (equation volumef h d t i 3)of hydrometer in m3).

(3.2)

• Since the middle ages the weight of a body has been a manifold ofa reference weight. So weighing is simply a comparison to a givenmass standard. From this point of view weighing is dividing theweight force of the given body and weight force of a mass standardand the result is a dimensionless number. That is the principle of allmechanical and electronic balances up to today, and a consequenceof lacking an expression for mass with fundamental naturalof lacking an expression for mass with fundamental naturalconstants.

MASS & DENSITY


(3.3)

• where

MASS & DENSITY

• Most weight measurements are carried out with body and balance


surrounded by atmospheric air, which is a gaseous fluid possessingdensity. Only bodies of material with density greater thanatmospheric air at the Earth’s surface can impart a force whenp pplaced upon a balance.

• For example a rubber balloon filled with helium gas (less dense thanair) possesses mass but it will not rest on a balance It will riseair) possesses mass, but it will not rest on a balance. It will riseupward into the atmosphere in search of an altitude at which thedensity of the atmosphere is in equilibrium with itself. His upwardforce caused the density of the Earth’s atmosphere is known asforce caused the density of the Earth s atmosphere is known asbuoyancy. This atmospheric buoyancy causes a body resting on abalance when surrounded by atmospheric air to exhibit a slightlysmaller weight measurement than if it were in a vacuum (Figuresmaller weight measurement than if it were in a vacuum (Figure3.1).

MASS & DENSITY


Figure 3.1 A balance is adjusted to zero weight (picture I). A mass of 1 kg is weight in atmosphere (picture II) and in vacuum (picture III)

MASS & DENSITY

• The calculation needed to correct for this buoyancy effect in


y yorder to yield the true mass of a body is called atmosphericbuoyancy correction. The true mass of a body mK is theproduct of the displayed massm* and a correctional factor Kproduct of the displayed massm K and a correctional factor K.The value of the correctional factor K depends on the densityof the air surrounding the balance. Because weightmeasurement is a comparison of a body of interest and amass standard, the densities of both materials also influencethe correctional factor (equations (3.4) to (3.6):( q ( ) ( )

(3.4)

MASS & DENSITY


(3.5)

Wh(3.6)

• Where

MASS & DENSITY

• The density of air depends on its pressure, temperature,


y p p , p ,humidity and its concentration of CO2.

• For practical purposes, the density of atmospheric air atl t t d l l ( t d d diti )normal room temperature and sea level (standard conditions)

can be taken to be approximately 1.2 kg ∙ m−3. A simpleapproach to calculate the density of air more precisely is givenby equation (3.7):

(3.7)

• where

MASS & DENSITY

• In contrast to air, the density of water is 1000 times greater


, y g(1000 kg ∙ m−3). Therefore, the density range of most food,agricultural and biological materials is in the same order ofmagnitude as that of water about 1200 ± 300 kg ∙ m−3 Themagnitude as that of water, about 1200 ± 300 kg ∙ m 3. Thedensities of materials with high water content are in a rangemore closely to that of water (between 1000 and 1100 kg ∙

3)m−3) while dry materials like agricultural grains, seeds and drybeans consisting of proteins, carbohydrates, starch orcellulose are often in the range 1400–1600 kg ∙m−3.g g

MASS & DENSITY

• The density of a substance is the quotient of mass over

DENSITYy q

volume. The standard international (SI) units for expressingdensity are kg ∙ m−3.The same definition is valid for solid,liquid gaseous and disperse systems like foams bulk goods orliquid, gaseous and disperse systems like foams, bulk goods orpowders.

• The reciprocal of density is called specific volume and theunits are m3 ∙ kg−1 (equations (3.8) and (3.9).

(3.8)

(3.9)

MASS & DENSITY

• where

DENSITY

MASS & DENSITY

DENSITYDENSITYTEMPERATURE DEPENDENCY OF DENSITY

• Many materials undergo thermal expansion when heated,meaning they increase in volume without any change in mass.For this reason, the density of a given material often dependsFor this reason, the density of a given material often dependson temperature. Since the volume of a material normallyincreases with temperature, the density usually decreasesith t t Thi ff t i h l iwith temperature. This effect is much larger in gaseous

systems than in liquid or solid systems.

MASS & DENSITY

DENSITY

• For many engineering applications air can be assumed to

DENSITYTEMPERATURE DEPENDENCY OF DENSITY – IDEAL GAS

• For many engineering applications air can be assumed to behave as an ideal gas, meaning that the ideal gas law can be used for calculating the density of air as a function of temperature and pressure (equations (3.10) and (3.11).

(3.10)

• where

(3.11)

where

MASS & DENSITY

DENSITYDENSITYTEMPERATURE DEPENDENCY OF DENSITY – IDEAL GAS

• In case of low temperatures and humid air the ideal gas lawloses accuracy, and will lead to error. To calculate the densityof air more precisely as a function of water vapor partialof air more precisely as a function of water vapor partialpressure and atmospheric pressure, equation (3.7) can beused.

MASS & DENSITY

DENSITYDENSITYTEMPERATURE DEPENDENCY OF DENSITY – SOLID AND LIQUIDS

• The density of liquids and solids is a function of temperature.Small changes in volume caused by temperature change canbe calculated with the aid of the thermal expansionbe calculated with the aid of the thermal expansioncoefficient:

(3.12)

• where

MASS & DENSITY


• Water shows abnormal behavior in a narrow range oftemperature near its freezing point at atmospheric pressure.When lowering the temperature of water from 4 ◦C and 0◦C,When lowering the temperature of water from 4 C and 0 C,the density of water actually decreases rather than increases.This abnormal behavior of water (see Figure 3.2 and Figure3 3 i t k i t t ithi th l i l f ti f3.3 is taken into account within the polynomial function ofBertsch (1983) for calculation of the density of liquid water(equation (3.13):

(3.13)

MASS & DENSITY


Fig 3 2 Normal (N) and abnormal (H O) Fig. 3.3 Abnormality of water (H2O):

MASS & DENSITY

Fig. 3.2 Normal (N) and abnormal (H2O) thermal expansion (schematic)

g y ( 2 )Temperature dependency of densitycompared to normal behavior (N)


• A further abnormality of water is that the solid phase (ice) hasa lower density than the liquid phase at the sametemperature. This behavior has important consequences fortemperature. This behavior has important consequences forthe biosphere. Because of this temperature dependency ofdensity, control or measurement and recording oft t i h d it i d ftemperature is necessary when density is measured forprocess control and quality control purposes.

MASS & DENSITY

DENSITYDENSITYPRESSURE DEPENDENCY OF DENSITY

• Materials are compressible. On application of pressure theirvolume decreases, causing the density to be a function ofpressure as well as temperature. Gases are far morepressure as well as temperature. Gases are far morecompressible than liquids and solids. Over a normaltemperature range many gases can be assumed to behave likeid lideal gases.

MASS & DENSITY

DENSITYDENSITYPRESSURE DEPENDENCY OF DENSITY – IDEAL GAS

• For ideal gases the density is directly proportional to thepressure:

(3.14)( )

(3.15)

(3.16)

• so the density of the ideal gas is(3.17)

MASS & DENSITY


• The negative slope of the volume–pressure curve divided bythe initial volume is called the compressibility . It is theinverse compression modulus K of a material.inverse compression modulus K of a material.

(3.18)

(3.19)

MASS & DENSITY

DENSITYDENSITYPRESSURE DEPENDENCY OF DENSITY – LIQUIDS AND SOLIDS

• Ideal liquids and solids show an elastic behavior. That meanstheir volume can decrease by a certain amount when apressure is applied, but that it will fully recover to the initialpressure is applied, but that it will fully recover to the initialvolume when the pressure is restored. For this type ofmaterial the change in volume on increasing the pressure canb l l t d b d ti (3 20)be calculated based on equation (3.20):

(3.20)

• with (2.8) and because ofm = const the relative density is:

MASS & DENSITY

(3.21)


• where

MASS & DENSITY


• Liquids and solids with very low compressibility show a verysmall volume reduction and often are treated in practice asincompressible materials. Water has very low compressibilityincompressible materials. Water has very low compressibilitywith a value of ≈ 5x10−10 Pa−1. So, up to pressures in the orderof 10 MPa (100 bar), the reduction of the volume in water is

ll th t it b l t d Alth h i hi hso small that it can be neglected. Although in high pressureprocessing of food, where the pressure will range to some100MPa, the compressibility of water cannot be neglected.

MASS & DENSITY

DENSITYDENSITYSPECIFIC GRAVITY (RELATIVE DENSITY)

• The ratio of the absolute density of a material to the densityof a reference material is called relative density d. Water at 4°C or 20°C is most often used as the reference material forC or 20 C is most often used as the reference material forthis purpose. In the USA and Canada, when water is used asthe reference standard, the term“ relative density” is not

d d i l d b th t “ ifi it ” Siused, and is replaced by the term“ specific gravity.” Sincewater is nearly always chosen as the reference standardworld‐wide, for practical purposes the terms “relativedensity” and “specific gravity” may be considered assynonymous.

(3 22)

MASS & DENSITY

(3.22)


• Where

• It is important to note that both density and specific gravity(relative density) relate to the same physical property. However,d i b d i di i l i f idensity must be reported in dimensional units of mass per unitvolume (e.g. g ∙ cm−3 or kg ∙ m−3), while specific gravity (relativedensity) is a ratio of densities, and is always a dimensionlessnumber. In the case where density is being reported in dimensionalunits of g ∙cm−3 and with the density of the reference material being1 g ∙ cm−3 or nearly 1 g ∙ cm−3 it is interesting to note that numericalvalues of both density and specific gravity (relative density)will bethe same, respectively.

MASS & DENSITY

DENSITYDENSITYMETHODS FOR LABORATORY MEASUREMENT OF DENSITY

• Table 3.2 shows examples of different methods used for densitymeasurement.

MASS & DENSITY


PYCNOMETRIC MEASUREMENT

• By weighing a known volume of a liquid, the density of thatliquid can be measured in a simple way Glass bulbs withliquid can be measured in a simple way. Glass bulbs withprecisely known volume that are used for this purpose arecalled pycnometers. A pycnometer can also be any otheri d i d f h h hinstrument designed for the same purpose that may havesample chambers of precisely known volume, but made ofother materials (not glass bulbs). The glass bulb or samplechamber will have a marker to which the liquid sample mustbe carefully filled. Then the density of the fluid can becalculated by:calculated by:

MASS & DENSITY

(3.23)



• Because of thermal expansion of the glass, the pycnometervolume is known for the temperature at which it wasvolume is known for the temperature at which it wascalibrated, only. So, for measurement of the absolute density,pycnometers should be used at the same temperature athi h h lib dwhich they were calibrated.

• Another way is to measure the relative density (specificgravity) rather than the absolute density. For this purpose, thegravity) rather than the absolute density. For this purpose, thepycnometer is weighed with the sample liquid and againweighed with the reference liquid (often water).The ratio ofboth weights gives the relative density d or specific gravity ofboth weights gives the relative density d, or specific gravity ofthe sample.

MASS & DENSITY



(3 24)

where

(3.24)

MASS & DENSITY



• Once the relative density d, or specific gravity, of the sample isknown and the density of the reference material is knownknown, and the density of the reference material is knownfrom the literature, the absolute density of the sample can becalculated:

(3.25)

MASS & DENSITY



• Fig. 3.4 and 3.5 show different designs of glass pycnometers

MASS & DENSITY

Fig. 3.4 Pycnometer designs: (a) Reischauer, (b) Bingham, (c) Gay‐Lussac, (d) Sprengel,(e) Lipkin, (f) Hubbard



MASS & DENSITY

Fig. 3.5 Examples of pycnometers . The right one is for viscous samples and powders


HYDROSTATIC BALANCES (BUOYANCY WEIGHING)

• The principle of a hydrostatic balance is based on Archimedeslaw of buoyancy If a body is submersed in a fluid its weightlaw of buoyancy. If a body is submersed in a fluid its weightwill be lowered because of the buoyancy force. The buoyancyforce is directly proportional to the volume of the submersedb d d th d it f th fl id B t f thbody and the density of the fluid. By measurement of thebuoyancy force with the balance, the volume of the body canbe determined quite accurately, and together with themeasured mass of the body, the density is obtained.

MASS & DENSITY



• A simple technique for making this type of measurement is toplace a beaker partially filled with water on top of a top‐place a beaker partially filled with water on top of a toploading balance, with the weight of beaker and water tared‐out to read zero on the display. Then, fully submerge the solidb d b th th t f t ki th t it ithbody beneath the water surface, taking care that it neithertouches the bottom nor the sides of the beaker. The weightreading shown on the display of the balance will be theweight of the volume of water displaced by the solid body.Since density of water is known, the precise volume of thesolid body is determined.solid body is determined.

MASS & DENSITY



(3.8)

• with ∆m as the difference in weight (in kg) of the body before

(3.26)

and after submersion:(3.27)

(3 28)(3.28)

(3.29)

MASS & DENSITY

(3.30)



• where

S th d it f b d b bt i d b t ki fi t th• So the density of a body can be obtained by taking first the weight prior to submersion (that means weighing in air) and its weight when submersed in a fluid with a known density F using equation (3.30).

MASS & DENSITY



• With the ratio

(3 31)

• the relative density d (specific gravity) of the body is

(3.31)

the relative density d (specific gravity) of the body is

(3.32)

(3.33)

• That means d can be calculated very quickly after two readings from the balance.

MASS & DENSITY



• If the weight in air mL is not corrected for atmosphericbuoyancy the density obtained by hydrostatic weighing canbuoyancy, the density obtained by hydrostatic weighing canbe called apparent density of the body. If that correctionmade, then mL and K will be slightly higher, and can be calledt d t d ittrue mass and true density.

• On the other hand when a body of known volume issubmersed in a fluid, the difference in weight of the body in, g yair and the weight of fluid displaced by the body can be usedto determine the density of the fluid, and can be calculatedwith equation (3 34):with equation (3.34):

MASS & DENSITY

(3.34)



• Figure 3.6 shows a special design of hydrostatic balance that is suitable for measuring the density of a solid or the density ofsuitable for measuring the density of a solid or the density of the liquid in the reservoir when used with a solid body of precisely known volume.

Fig. 3.6 Hydrostatic balance design.1: balance, 2: platform, 3: smallbeaker 4: large beaker 5: support

MASS & DENSITY

beaker, 4: large beaker, 5: supportbracket, 6: pan, 7: thermometer


HYDROSTATIC BALANCES (BUOYANCY WEIGHING)• To obtain the density of a solid, the sample is weighed first in air, and

then it is submersed and the weight is taken again. As can be seen inFigure 3.6 there is a small pan mounted on the weighing plate of thebalance. A small beaker on a cable is suspended within a larger beakercontaining the fluid of interest. The large beaker is resting on a raisedplatform so its weight is not transmitted to the balance.

• To obtain the fluid density in the large beaker, a test body with knownvolume is first placed on the pan and its weight in air is measured.p p gThen the test body is placed into the small beaker, submersed in thefluid and weighed once again. Then the density of the liquid iscalculated using equation (3.34). It should be remembered that theg q ( )density of the fluid is dependent on temperature so the temperaturemust be controlled and recorded.

MASS & DENSITY


MOHR‐WESTPHAL BALANCE

• The Mohr–Westphal balance (see Figure 3.7) is another type of hydrostatic balance It is designed as a nonsymmetric beamof hydrostatic balance. It is designed as a nonsymmetric beam balance for measuring the density of liquids.

Fig. 3.7 Mohr‐Westphal balance 1: beam 2: weights 3: buoyancy body 4:

MASS & DENSITY

beam, 2: weights, 3: buoyancy body, 4: liquid sample



• At the free end of the arm of the balance a “buoyancy body”is suspended in air The buoyancy body is normally made ofis suspended in air. The buoyancy body is normally made ofglass and can have a built‐in thermometer. Then the buoyancybody is submersed into the liquid of interest.

• Because of the effect of buoyancy, the weight of thesubmersed glass body will appear lower than it was in air, andwill bring the balance out of zero.g

• The buoyancy force can be measured by successively addingsmall weights to the arm until the balance is restored to zero.Th t i th t d ith t fThe measurement is then repeated with water as a referenceliquid.

MASS & DENSITY



• The ratio of both readings provides the relative density or specific gravity of the liquid as can be shown below With thespecific gravity of the liquid as can be shown below. With the buoyancy force

(3.40)

• With the fluid of interest(3.41)

• With water as reference material(3.42)

(3 43)

MASS & DENSITY

(3.43)



• So the ratio is

• Because the volume of the glass body is the same for both readings,

(3.44)

then

(3.45)

• So the specific gravity is simply

(3 46)

MASS & DENSITY

(3.46)



• where

MASS & DENSITY



• The result should be recorded along with the temperature of the measurement Often both readings are taken at 20 ◦C andthe measurement. Often both readings are taken at 20 C and the result is written as d20/20. The quantity d20/4 would mean that the density of the liquid was compared to the density of

t t 4°Cwater at 4°C:

MASS & DENSITY



• The Mohr–Westphal balance can also be used to measure thedensity of a solid sample which is submersed in a fluid withdensity of a solid sample which is submersed in a fluid withknown density. For this purpose, equation (3.37) would beused to calculate the volume of the sample.

MASS & DENSITY


HYDROMETER

• Hydrometers (Fig 3.8) are hollow glass bodies with the shapeof a buoyof a buoy.

• Hydrometers are designed with a volume to mass ratio in sucha way that the glass body will float at a certain depth in theliquid under investigation.

• Depending upon the density of that liquid the hydrometer willfloat at a higher or lower position The upper part of thefloat at a higher or lower position. The upper part of thehydrometer has a scale for reading the nonsubmersed part hof the floating glass body.

MASS & DENSITY


HYDROMETER

• The nonsubmersed length of the hydrometer can be read withthe aid of a scale on the upper part of the hydrometerthe aid of a scale on the upper part of the hydrometer.

• A weight at the bottom of the hydrometer acts like the keel ofa sailboat to ensure that it will float in the liquid in a verticalorientation.

• The scale can be calibrated directly in units of density or, e.g.in concentration units (Fig 3 9)in concentration units (Fig 3.9).

MASS & DENSITY


HYDROMETER

MASS & DENSITY

Fig. 3.8 Hydrometer. 1:scale, 2: body (with and without thermometer), 3: keel Fig. 3.9 Reading of a hydrometer scale at

the liquid surface (example)


HYDROMETER

• The floating depth position of the hydrometer depends on weight force and interfacial force (force due to surfaceweight force and interfacial force (force due to surface tension). It is

(3.47)

• Which means:

(3.48)

• so

(3.49)

MASS & DENSITY


HYDROMETER

• The nonsubmersed part of the hydrometer has the length

• Which means

(3.50)

Which means

• Sometimes the combination of two physical properties will

(3.51)

give the information needed about a process or a product. Forexample, by knowing both the density and refractive index ofbeer wort, the alcohol content can be calculated, and by this,beer wort, the alcohol content can be calculated, and by this,the progress of fermentation

MASS & DENSITY


HYDROMETER

MASS & DENSITY


HYDROMETER

• Without consideration of interfacial tension effects the hydrometer equation simplifies tohydrometer equation simplifies to

(3.52)

• There are hydrometers available which are corrected for interfacial tension offered in different range categories called

L (l 15 35 N 1)– L (low, 15–35mN ∙m−1),

– M(medium, 35–65 mN ∙ m−1) and

– H (high, for higher values).

MASS & DENSITY


SUBMERSION TECHNIQUE

• Pycnometers and hydrometers do not work very well withliquids of high viscosityliquids of high viscosity.

• For highly viscous liquids, measurement of density can beperformed with the submersion technique (see Fig 3.10).

• A beaker with the viscous liquid sample is put on a balance.The display value is recorded, or the display may be set tozero (tare)zero (tare).

• Then a test body with known volume is pressed into thesample.

MASS & DENSITY



Fig. 3.10 Submersion technique for density measurement. 1: depth mark, 2: liquid sample, 3: buoyancy body of known volume

MASS & DENSITY



• The buoyancy force caused by the submerged test body istransferred to the balance and appears on the display as antransferred to the balance and appears on the display as anapparent increased weightm.

• This increased weight force is the buoyancy force, and is theweight of the displaced liquid, which is equal in volume to thevolume of the submersed solid body:

(3.53)

• and

(3.53)

(3.54)

MASS & DENSITY



• So

• where

(3.55)

where

MASS & DENSITY



• For precision measurement, the buoyancy body can be ahollow metal sphere with calibrated volume To avoid errorshollow metal sphere with calibrated volume. To avoid errorsfrom buoyancy of the mounting rod there is normally a depthmark on the rod which indicates the right depth position fori i th t th b d ti f d i t dimmersion so that the submerged section of rod is accountedfor in the calibrated volume.

MASS & DENSITY


DENSITY OF SOLIDS

• Many agricultural materials and food and feed ingredients arein the form of granular materials (grains meals and powders)in the form of granular materials (grains, meals and powders),which are bulk solids made up of small particles.

• The weight or size of the individual particles within any ofthese types of materials may vary over a large range e.g. fromfrozen diced vegetables to corn cornels to fine powderparticles.p

• The term “solid density” means the density of the solidmaterial of which a particle is made, no matter what type offl id th t i l i t b t th ti lfluid or other material may exist between the particles.

MASS & DENSITY


DENSITY OF SOLIDS

• Solid particles contain pores or hollow cavities filled withgases or liquids this contributes to the density of the solidgases or liquids, this contributes to the density of the solid.

• When pores or cavities occur, it is important to state whetherthey are closed or open. If they are closed, meaning they arelocated completely within the solid particle, they belong tothe solid. If they are open to the surroundings at the particlesurface, e.g. the atmosphere, they do not belong to the solid, g p , y gbody.

• To avoid communication errors the density of solids should bei ith t lik “i l di l ” “ ith tgiven with a note like “including pore volume” or “withoutpore volume.”

MASS & DENSITY


DENSITY OF SOLIDS

• This can be accomplished by how the system boundaries are defined and can be calculated as follows:defined, and can be calculated as follows:

(3.8)

• where

MASS & DENSITY


DENSITY OF SOLIDS

• To measure the density of a solid particle often simply means to measure its volume because its mass is known uponto measure its volume, because its mass is known upon weighing.

• To get the volume of the solid sample without its open pores, a pycnometer technique with an appropriate liquid can be used.

• The liquid must not alter or dissolve the sample For thisThe liquid must not alter or dissolve the sample. For this purpose, a sequence of weighings is conducted as indicated in Figure 3.11.

MASS & DENSITY


DENSITY OF SOLIDS

• After weighing the empty pycnometerm0 the pycnometer is weighed with the samplemPweighed with the sample mP.

• Then the pycnometer is filled up to a designated mark with an appropriate reference liquid of known density and weighed again mP,F.

• Finally, the pycnometer is weighed when filled to the same mark with only the reference liquidm :mark with only the reference liquid mF:

MASS & DENSITY


DENSITY OF SOLIDS

Fig. 3.11 Pycnometer measurement of the density of a solid granular material, e.g. a powder

MASS & DENSITY


DENSITY OF SOLIDS

• The density of the solid material then is

(3.8)

(3.56)

(3.57)

(3 58)(3.58)

MASS & DENSITY


DENSITY OF SOLIDS

(3.59)

(3.60)

(3.61)

MASS & DENSITY


DENSITY OF SOLIDS(3.62)

(3.63)

• where

MASS & DENSITY


BULK DENSITY

• Powders and bulk goods contain hollow spaces or voids filledwith gas normally air The density of that type of bulkwith gas, normally air. The density of that type of bulkmaterial, including the void spaces, is called bulk density.

• Using equation (3.8) the bulk density can be calculated byweighing a sample of the bulk material and measurement ofits volume.

• The volume of the whole bulk material must be taken “as is ”The volume of the whole bulk material must be taken as is.To measure this volume, the sample material can be pouredinto a beaker or cylinder up to a known volumetric mark.

MASS & DENSITY


BULK DENSITY

• Different technique in filling the beaker or cylinder may leadto different distributions of solid particles and hollow spacesto different distributions of solid particles and hollow spaces.So, to get repeatable results the technique of filling has to bestandardized.

• To overcome problems with repeatable filling technique, thebulk material can be tapped before reading of the volume. Bytapping the material, the solid particles will “settle” into thepp g , pmost stable situation they can reach. The void spaces will getsmaller as the solid particles settle step by step into a spatialsituation where the bulk density will reach a maximum Thesituation where the bulk density will reach a maximum. Thetime needed to reach this maximum depends on tappingspeed and tapping amplitude. MASS & DENSITY


BULK DENSITY

Figure 3.12. Device for tapping of bulK goods: 1: rotating cam, 2: housing, 3: powder sample, 4: cylinder, 5: overring

MASS & DENSITY

y g


BULK DENSITY

• Figure 3.12 shows an example of a device which can be usedto measure bulk density and tapped bulk densityto measure bulk density and tapped bulk densitysubsequently.

• First the bulk material is filled into a 1000 cm3 cylinder until itis overflowing under repeatable technique conditions. Thenwith aid of a flat spatula, the excess overflow of samplematerial is scraped away from the top of the cylinder to leavep y p ythe sample perfectly level at the top, and the 1000 cm3

sample is weighed to get the bulk density.

MASS & DENSITY


BULK DENSITY

• Now a cylindrical extension overring is slipped onto the 1000cm3 cylinder and more sample material is filled in Thecm3 cylinder and more sample material is filled in. Thecylinder is mounted on the tapping device and moved for afixed number of tappings. In German testing standards a

b f 2500 ith f f 250 1 i ifi dnumber of 2500 with a frequency of 250 s−1 is specified.

• After this the sample material is adjusted to 1000 cm3 againand weighed. The tapped bulk density should be recordedg pp ywith the parameters of its measurement.

MASS & DENSITY


BULK DENSITY

• The difference between bulk density and maximum tappedbulk density provides information about the ability of the bulkbulk density provides information about the ability of the bulkmaterial to be compressed by gravity or pressure. Powderscan be characterized for this property by the Hausner ratio,hi h i th ti t f t d b lk d it t dwhich is the quotient of tapped bulk density over untapped

bulk density (see Table 3.3).

Table 2.7. Characterization of

MASS & DENSITY

Characterization of powder flowabilityby Hausner ratio


POROSITY

• Also the volume of the hollow void space (pores) can becalculated The ratio of the volume of the void space (pores)calculated. The ratio of the volume of the void space (pores)and the total volume of the bulk is called porosity ɛ:

(3 64)(3.64)

(3.65)

• becausemB ≈mS =m

MASS & DENSITY

(3.66)


POROSITY

• So(3.67)

• With ɛ as the relative volume of the hollow pore space, and αas the relative volume of the solid particle space it is evident

( )

that:

(3.68)

MASS & DENSITY


POROSITY

• where

MASS & DENSITY

THE ENDTHE END

RHEOLOGICAL PROPERTIES OF FOODS

MASS AND DENSITY

MASS• Mass is a measure for inertia and heaviness of a body.

H i i d b h E h’ i i l i f

MASS

Heaviness is caused by the Earth’s gravitational attraction fora body. The force between the body of interest and the planetEarth is called the weight force of the body. Mathematically,this force can be expressed as the product of the body’s massand the Earth’s acceleration due to gravity, as shown byequation (3 1)equation (3.1).

• where

(3.1)

MASS & DENSITY

MASS• The density of planet Earth varies with location and the planet

is slightly pear shaped and not in the shape of a perfect

MASS

is slightly pear‐shaped and not in the shape of a perfectsphere, the value of gravitational acceleration differs slightlywith location on the Earth’s surface. Considering the rotationof the planet a body resting at the equator will have a greaterof the planet, a body resting at the equator will have a greatertangential speed and centrifugal force than in regions farnorth or south of the equator.h l f h’ l l h• The value of Earth’s gravitational acceleration in Zurich,Switzerland is used as a standard for calculations, and is calledstandard gravitational acceleration having the value g =

29.80665m∙ s−2.When a balance which was adjusted in Zurich,is taken to another place on the Earth, but is not corrected forthe local gravitational acceleration, the displayed weight maybe in error.

MASS & DENSITY

MASS• Table 3.1 illustrates this concept for a body having a mass of

1k T id i h f hi

MASS

1kg. To avoid erroneous weight measurements of this type, a balance has to be recalibrated at the location in which it will be used. For this purpose, commercial mass standards are produced with the help of national standards organizations around the world.

Table 3.1 Weighing a 1 kg mass in different place

MASS & DENSITY

• A balance is an instrument measuring the weighing force of a


g g gbody. However, it usually does not display a force signal (e.g.newtons), but a mass signal (e.g. kilograms).This is due to theprinciple of calibration used for balances: A mass standard isprinciple of calibration used for balances: A mass standard isplaced on the balance that causes a deformation, which canbe read as an angle, a distance or an electric voltage,depending on the type of balance.

• A calibration has to be performed for every type ofsensing/measuring instrument For this purpose appropriatesensing/measuring instrument. For this purpose, appropriaterespective standard materials and procedures are needed,that make it possible to perform calibration of an instrumenti l b tin any laboratory.

MASS & DENSITY

• From a scientific point of view the calibration procedure described


for a balance is basically to use the instrument as a “force meter,”then divide the force G measured by the value of the localgravitational acceleration g, and display the result (equation volumef h d t i 3)of hydrometer in m3).

(3.2)

• Since the middle ages the weight of a body has been a manifold ofa reference weight. So weighing is simply a comparison to a givenmass standard. From this point of view weighing is dividing theweight force of the given body and weight force of a mass standardand the result is a dimensionless number. That is the principle of allmechanical and electronic balances up to today, and a consequenceof lacking an expression for mass with fundamental naturalof lacking an expression for mass with fundamental naturalconstants.

MASS & DENSITY


(3.3)

• where

MASS & DENSITY

• Most weight measurements are carried out with body and balance


surrounded by atmospheric air, which is a gaseous fluid possessingdensity. Only bodies of material with density greater thanatmospheric air at the Earth’s surface can impart a force whenp pplaced upon a balance.

• For example a rubber balloon filled with helium gas (less dense thanair) possesses mass but it will not rest on a balance It will riseair) possesses mass, but it will not rest on a balance. It will riseupward into the atmosphere in search of an altitude at which thedensity of the atmosphere is in equilibrium with itself. His upwardforce caused the density of the Earth’s atmosphere is known asforce caused the density of the Earth s atmosphere is known asbuoyancy. This atmospheric buoyancy causes a body resting on abalance when surrounded by atmospheric air to exhibit a slightlysmaller weight measurement than if it were in a vacuum (Figuresmaller weight measurement than if it were in a vacuum (Figure3.1).

MASS & DENSITY


Figure 3.1 A balance is adjusted to zero weight (picture I). A mass of 1 kg is weight in atmosphere (picture II) and in vacuum (picture III)

MASS & DENSITY

• The calculation needed to correct for this buoyancy effect in


y yorder to yield the true mass of a body is called atmosphericbuoyancy correction. The true mass of a body mK is theproduct of the displayed massm* and a correctional factor Kproduct of the displayed massm K and a correctional factor K.The value of the correctional factor K depends on the densityof the air surrounding the balance. Because weightmeasurement is a comparison of a body of interest and amass standard, the densities of both materials also influencethe correctional factor (equations (3.4) to (3.6):( q ( ) ( )

(3.4)

MASS & DENSITY


(3.5)

Wh(3.6)

• Where

MASS & DENSITY

• The density of air depends on its pressure, temperature,


y p p , p ,humidity and its concentration of CO2.

• For practical purposes, the density of atmospheric air atl t t d l l ( t d d diti )normal room temperature and sea level (standard conditions)

can be taken to be approximately 1.2 kg ∙ m−3. A simpleapproach to calculate the density of air more precisely is givenby equation (3.7):

(3.7)

• where

MASS & DENSITY

• In contrast to air, the density of water is 1000 times greater


, y g(1000 kg ∙ m−3). Therefore, the density range of most food,agricultural and biological materials is in the same order ofmagnitude as that of water about 1200 ± 300 kg ∙ m−3 Themagnitude as that of water, about 1200 ± 300 kg ∙ m 3. Thedensities of materials with high water content are in a rangemore closely to that of water (between 1000 and 1100 kg ∙

3)m−3) while dry materials like agricultural grains, seeds and drybeans consisting of proteins, carbohydrates, starch orcellulose are often in the range 1400–1600 kg ∙m−3.g g

MASS & DENSITY

• The density of a substance is the quotient of mass over

DENSITYy q

volume. The standard international (SI) units for expressingdensity are kg ∙ m−3.The same definition is valid for solid,liquid gaseous and disperse systems like foams bulk goods orliquid, gaseous and disperse systems like foams, bulk goods orpowders.

• The reciprocal of density is called specific volume and theunits are m3 ∙ kg−1 (equations (3.8) and (3.9).

(3.8)

(3.9)

MASS & DENSITY

• where

DENSITY

MASS & DENSITY

DENSITYDENSITYTEMPERATURE DEPENDENCY OF DENSITY

• Many materials undergo thermal expansion when heated,meaning they increase in volume without any change in mass.For this reason, the density of a given material often dependsFor this reason, the density of a given material often dependson temperature. Since the volume of a material normallyincreases with temperature, the density usually decreasesith t t Thi ff t i h l iwith temperature. This effect is much larger in gaseous

systems than in liquid or solid systems.

MASS & DENSITY

DENSITY

• For many engineering applications air can be assumed to

DENSITYTEMPERATURE DEPENDENCY OF DENSITY – IDEAL GAS

• For many engineering applications air can be assumed to behave as an ideal gas, meaning that the ideal gas law can be used for calculating the density of air as a function of temperature and pressure (equations (3.10) and (3.11).

(3.10)

• where

(3.11)

where

MASS & DENSITY

DENSITYDENSITYTEMPERATURE DEPENDENCY OF DENSITY – IDEAL GAS

• In case of low temperatures and humid air the ideal gas lawloses accuracy, and will lead to error. To calculate the densityof air more precisely as a function of water vapor partialof air more precisely as a function of water vapor partialpressure and atmospheric pressure, equation (3.7) can beused.

MASS & DENSITY


• The density of liquids and solids is a function of temperature.Small changes in volume caused by temperature change canbe calculated with the aid of the thermal expansionbe calculated with the aid of the thermal expansioncoefficient:

(3.12)

• where

MASS & DENSITY


• Water shows abnormal behavior in a narrow range oftemperature near its freezing point at atmospheric pressure.When lowering the temperature of water from 4 ◦C and 0◦C,When lowering the temperature of water from 4 C and 0 C,the density of water actually decreases rather than increases.This abnormal behavior of water (see Figure 3.2 and Figure3 3 i t k i t t ithi th l i l f ti f3.3 is taken into account within the polynomial function ofBertsch (1983) for calculation of the density of liquid water(equation (3.13):

(3.13)

MASS & DENSITY


Fig 3 2 Normal (N) and abnormal (H O) Fig. 3.3 Abnormality of water (H2O):

MASS & DENSITY

Fig. 3.2 Normal (N) and abnormal (H2O) thermal expansion (schematic)

g y ( 2 )Temperature dependency of densitycompared to normal behavior (N)


• A further abnormality of water is that the solid phase (ice) hasa lower density than the liquid phase at the sametemperature. This behavior has important consequences fortemperature. This behavior has important consequences forthe biosphere. Because of this temperature dependency ofdensity, control or measurement and recording oft t i h d it i d ftemperature is necessary when density is measured forprocess control and quality control purposes.

MASS & DENSITY

DENSITYDENSITYPRESSURE DEPENDENCY OF DENSITY

• Materials are compressible. On application of pressure theirvolume decreases, causing the density to be a function ofpressure as well as temperature. Gases are far morepressure as well as temperature. Gases are far morecompressible than liquids and solids. Over a normaltemperature range many gases can be assumed to behave likeid lideal gases.

MASS & DENSITY


• For ideal gases the density is directly proportional to thepressure:

(3.14)( )

(3.15)

(3.16)

• so the density of the ideal gas is(3.17)

MASS & DENSITY


• The negative slope of the volume–pressure curve divided bythe initial volume is called the compressibility . It is theinverse compression modulus K of a material.inverse compression modulus K of a material.

(3.18)

(3.19)

MASS & DENSITY


• Ideal liquids and solids show an elastic behavior. That meanstheir volume can decrease by a certain amount when apressure is applied, but that it will fully recover to the initialpressure is applied, but that it will fully recover to the initialvolume when the pressure is restored. For this type ofmaterial the change in volume on increasing the pressure canb l l t d b d ti (3 20)be calculated based on equation (3.20):

(3.20)

• with (2.8) and because ofm = const the relative density is:

MASS & DENSITY

(3.21)


• where

MASS & DENSITY


• Liquids and solids with very low compressibility show a verysmall volume reduction and often are treated in practice asincompressible materials. Water has very low compressibilityincompressible materials. Water has very low compressibilitywith a value of ≈ 5x10−10 Pa−1. So, up to pressures in the orderof 10 MPa (100 bar), the reduction of the volume in water is

ll th t it b l t d Alth h i hi hso small that it can be neglected. Although in high pressureprocessing of food, where the pressure will range to some100MPa, the compressibility of water cannot be neglected.

MASS & DENSITY


• The ratio of the absolute density of a material to the densityof a reference material is called relative density d. Water at 4°C or 20°C is most often used as the reference material forC or 20 C is most often used as the reference material forthis purpose. In the USA and Canada, when water is used asthe reference standard, the term“ relative density” is not

d d i l d b th t “ ifi it ” Siused, and is replaced by the term“ specific gravity.” Sincewater is nearly always chosen as the reference standardworld‐wide, for practical purposes the terms “relativedensity” and “specific gravity” may be considered assynonymous.

(3 22)

MASS & DENSITY

(3.22)


• Where

• It is important to note that both density and specific gravity(relative density) relate to the same physical property. However,d i b d i di i l i f idensity must be reported in dimensional units of mass per unitvolume (e.g. g ∙ cm−3 or kg ∙ m−3), while specific gravity (relativedensity) is a ratio of densities, and is always a dimensionlessnumber. In the case where density is being reported in dimensionalunits of g ∙cm−3 and with the density of the reference material being1 g ∙ cm−3 or nearly 1 g ∙ cm−3 it is interesting to note that numericalvalues of both density and specific gravity (relative density)will bethe same, respectively.

MASS & DENSITY


• Table 3.2 shows examples of different methods used for densitymeasurement.

MASS & DENSITY



• By weighing a known volume of a liquid, the density of thatliquid can be measured in a simple way Glass bulbs withliquid can be measured in a simple way. Glass bulbs withprecisely known volume that are used for this purpose arecalled pycnometers. A pycnometer can also be any otheri d i d f h h hinstrument designed for the same purpose that may havesample chambers of precisely known volume, but made ofother materials (not glass bulbs). The glass bulb or samplechamber will have a marker to which the liquid sample mustbe carefully filled. Then the density of the fluid can becalculated by:calculated by:

MASS & DENSITY

(3.23)



• Because of thermal expansion of the glass, the pycnometervolume is known for the temperature at which it wasvolume is known for the temperature at which it wascalibrated, only. So, for measurement of the absolute density,pycnometers should be used at the same temperature athi h h lib dwhich they were calibrated.

• Another way is to measure the relative density (specificgravity) rather than the absolute density. For this purpose, thegravity) rather than the absolute density. For this purpose, thepycnometer is weighed with the sample liquid and againweighed with the reference liquid (often water).The ratio ofboth weights gives the relative density d or specific gravity ofboth weights gives the relative density d, or specific gravity ofthe sample.

MASS & DENSITY



(3 24)

where

(3.24)

MASS & DENSITY



• Once the relative density d, or specific gravity, of the sample isknown and the density of the reference material is knownknown, and the density of the reference material is knownfrom the literature, the absolute density of the sample can becalculated:

(3.25)

MASS & DENSITY



• Fig. 3.4 and 3.5 show different designs of glass pycnometers

MASS & DENSITY

Fig. 3.4 Pycnometer designs: (a) Reischauer, (b) Bingham, (c) Gay‐Lussac, (d) Sprengel,(e) Lipkin, (f) Hubbard



MASS & DENSITY

Fig. 3.5 Examples of pycnometers . The right one is for viscous samples and powders



• The principle of a hydrostatic balance is based on Archimedeslaw of buoyancy If a body is submersed in a fluid its weightlaw of buoyancy. If a body is submersed in a fluid its weightwill be lowered because of the buoyancy force. The buoyancyforce is directly proportional to the volume of the submersedb d d th d it f th fl id B t f thbody and the density of the fluid. By measurement of thebuoyancy force with the balance, the volume of the body canbe determined quite accurately, and together with themeasured mass of the body, the density is obtained.

MASS & DENSITY



• A simple technique for making this type of measurement is toplace a beaker partially filled with water on top of a top‐place a beaker partially filled with water on top of a toploading balance, with the weight of beaker and water tared‐out to read zero on the display. Then, fully submerge the solidb d b th th t f t ki th t it ithbody beneath the water surface, taking care that it neithertouches the bottom nor the sides of the beaker. The weightreading shown on the display of the balance will be theweight of the volume of water displaced by the solid body.Since density of water is known, the precise volume of thesolid body is determined.solid body is determined.

MASS & DENSITY



(3.8)

• with ∆m as the difference in weight (in kg) of the body before

(3.26)

and after submersion:(3.27)

(3 28)(3.28)

(3.29)

MASS & DENSITY

(3.30)



• where

S th d it f b d b bt i d b t ki fi t th• So the density of a body can be obtained by taking first the weight prior to submersion (that means weighing in air) and its weight when submersed in a fluid with a known density F using equation (3.30).

MASS & DENSITY



• With the ratio

(3 31)

• the relative density d (specific gravity) of the body is

(3.31)

the relative density d (specific gravity) of the body is

(3.32)

(3.33)

• That means d can be calculated very quickly after two readings from the balance.

MASS & DENSITY



• If the weight in air mL is not corrected for atmosphericbuoyancy the density obtained by hydrostatic weighing canbuoyancy, the density obtained by hydrostatic weighing canbe called apparent density of the body. If that correctionmade, then mL and K will be slightly higher, and can be calledt d t d ittrue mass and true density.

• On the other hand when a body of known volume issubmersed in a fluid, the difference in weight of the body in, g yair and the weight of fluid displaced by the body can be usedto determine the density of the fluid, and can be calculatedwith equation (3 34):with equation (3.34):

MASS & DENSITY

(3.34)



• Figure 3.6 shows a special design of hydrostatic balance that is suitable for measuring the density of a solid or the density ofsuitable for measuring the density of a solid or the density of the liquid in the reservoir when used with a solid body of precisely known volume.

Fig. 3.6 Hydrostatic balance design.1: balance, 2: platform, 3: smallbeaker 4: large beaker 5: support

MASS & DENSITY

beaker, 4: large beaker, 5: supportbracket, 6: pan, 7: thermometer


HYDROSTATIC BALANCES (BUOYANCY WEIGHING)• To obtain the density of a solid, the sample is weighed first in air, and

then it is submersed and the weight is taken again. As can be seen inFigure 3.6 there is a small pan mounted on the weighing plate of thebalance. A small beaker on a cable is suspended within a larger beakercontaining the fluid of interest. The large beaker is resting on a raisedplatform so its weight is not transmitted to the balance.

• To obtain the fluid density in the large beaker, a test body with knownvolume is first placed on the pan and its weight in air is measured.p p gThen the test body is placed into the small beaker, submersed in thefluid and weighed once again. Then the density of the liquid iscalculated using equation (3.34). It should be remembered that theg q ( )density of the fluid is dependent on temperature so the temperaturemust be controlled and recorded.

MASS & DENSITY



• The Mohr–Westphal balance (see Figure 3.7) is another type of hydrostatic balance It is designed as a nonsymmetric beamof hydrostatic balance. It is designed as a nonsymmetric beam balance for measuring the density of liquids.

Fig. 3.7 Mohr‐Westphal balance 1: beam 2: weights 3: buoyancy body 4:

MASS & DENSITY

beam, 2: weights, 3: buoyancy body, 4: liquid sample



• At the free end of the arm of the balance a “buoyancy body”is suspended in air The buoyancy body is normally made ofis suspended in air. The buoyancy body is normally made ofglass and can have a built‐in thermometer. Then the buoyancybody is submersed into the liquid of interest.

• Because of the effect of buoyancy, the weight of thesubmersed glass body will appear lower than it was in air, andwill bring the balance out of zero.g

• The buoyancy force can be measured by successively addingsmall weights to the arm until the balance is restored to zero.Th t i th t d ith t fThe measurement is then repeated with water as a referenceliquid.

MASS & DENSITY



• The ratio of both readings provides the relative density or specific gravity of the liquid as can be shown below With thespecific gravity of the liquid as can be shown below. With the buoyancy force

(3.40)

• With the fluid of interest(3.41)

• With water as reference material(3.42)

(3 43)

MASS & DENSITY

(3.43)



• So the ratio is

• Because the volume of the glass body is the same for both readings,

(3.44)

then

(3.45)

• So the specific gravity is simply

(3 46)

MASS & DENSITY

(3.46)



• where

MASS & DENSITY



• The result should be recorded along with the temperature of the measurement Often both readings are taken at 20 ◦C andthe measurement. Often both readings are taken at 20 C and the result is written as d20/20. The quantity d20/4 would mean that the density of the liquid was compared to the density of

t t 4°Cwater at 4°C:

MASS & DENSITY



• The Mohr–Westphal balance can also be used to measure thedensity of a solid sample which is submersed in a fluid withdensity of a solid sample which is submersed in a fluid withknown density. For this purpose, equation (3.37) would beused to calculate the volume of the sample.

MASS & DENSITY


HYDROMETER

• Hydrometers (Fig 3.8) are hollow glass bodies with the shapeof a buoyof a buoy.

• Hydrometers are designed with a volume to mass ratio in sucha way that the glass body will float at a certain depth in theliquid under investigation.

• Depending upon the density of that liquid the hydrometer willfloat at a higher or lower position The upper part of thefloat at a higher or lower position. The upper part of thehydrometer has a scale for reading the nonsubmersed part hof the floating glass body.

MASS & DENSITY


HYDROMETER

• The nonsubmersed length of the hydrometer can be read withthe aid of a scale on the upper part of the hydrometerthe aid of a scale on the upper part of the hydrometer.

• A weight at the bottom of the hydrometer acts like the keel ofa sailboat to ensure that it will float in the liquid in a verticalorientation.

• The scale can be calibrated directly in units of density or, e.g.in concentration units (Fig 3 9)in concentration units (Fig 3.9).

MASS & DENSITY


HYDROMETER

MASS & DENSITY

Fig. 3.8 Hydrometer. 1:scale, 2: body (with and without thermometer), 3: keel Fig. 3.9 Reading of a hydrometer scale at

the liquid surface (example)


HYDROMETER

• The floating depth position of the hydrometer depends on weight force and interfacial force (force due to surfaceweight force and interfacial force (force due to surface tension). It is

(3.47)

• Which means:

(3.48)

• so

(3.49)

MASS & DENSITY


HYDROMETER

• The nonsubmersed part of the hydrometer has the length

• Which means

(3.50)

Which means

• Sometimes the combination of two physical properties will

(3.51)

give the information needed about a process or a product. Forexample, by knowing both the density and refractive index ofbeer wort, the alcohol content can be calculated, and by this,beer wort, the alcohol content can be calculated, and by this,the progress of fermentation

MASS & DENSITY


HYDROMETER

MASS & DENSITY


HYDROMETER

• Without consideration of interfacial tension effects the hydrometer equation simplifies tohydrometer equation simplifies to

(3.52)

• There are hydrometers available which are corrected for interfacial tension offered in different range categories called

L (l 15 35 N 1)– L (low, 15–35mN ∙m−1),

– M(medium, 35–65 mN ∙ m−1) and

– H (high, for higher values).

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• Pycnometers and hydrometers do not work very well withliquids of high viscosityliquids of high viscosity.

• For highly viscous liquids, measurement of density can beperformed with the submersion technique (see Fig 3.10).

• A beaker with the viscous liquid sample is put on a balance.The display value is recorded, or the display may be set tozero (tare)zero (tare).

• Then a test body with known volume is pressed into thesample.

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Fig. 3.10 Submersion technique for density measurement. 1: depth mark, 2: liquid sample, 3: buoyancy body of known volume

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• The buoyancy force caused by the submerged test body istransferred to the balance and appears on the display as antransferred to the balance and appears on the display as anapparent increased weightm.

• This increased weight force is the buoyancy force, and is theweight of the displaced liquid, which is equal in volume to thevolume of the submersed solid body:

(3.53)

• and

(3.53)

(3.54)

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• So

• where

(3.55)

where

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• For precision measurement, the buoyancy body can be ahollow metal sphere with calibrated volume To avoid errorshollow metal sphere with calibrated volume. To avoid errorsfrom buoyancy of the mounting rod there is normally a depthmark on the rod which indicates the right depth position fori i th t th b d ti f d i t dimmersion so that the submerged section of rod is accountedfor in the calibrated volume.

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DENSITY OF SOLIDS

• Many agricultural materials and food and feed ingredients arein the form of granular materials (grains meals and powders)in the form of granular materials (grains, meals and powders),which are bulk solids made up of small particles.

• The weight or size of the individual particles within any ofthese types of materials may vary over a large range e.g. fromfrozen diced vegetables to corn cornels to fine powderparticles.p

• The term “solid density” means the density of the solidmaterial of which a particle is made, no matter what type offl id th t i l i t b t th ti lfluid or other material may exist between the particles.

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DENSITY OF SOLIDS

• Solid particles contain pores or hollow cavities filled withgases or liquids this contributes to the density of the solidgases or liquids, this contributes to the density of the solid.

• When pores or cavities occur, it is important to state whetherthey are closed or open. If they are closed, meaning they arelocated completely within the solid particle, they belong tothe solid. If they are open to the surroundings at the particlesurface, e.g. the atmosphere, they do not belong to the solid, g p , y gbody.

• To avoid communication errors the density of solids should bei ith t lik “i l di l ” “ ith tgiven with a note like “including pore volume” or “withoutpore volume.”

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DENSITY OF SOLIDS

• This can be accomplished by how the system boundaries are defined and can be calculated as follows:defined, and can be calculated as follows:

(3.8)

• where

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DENSITY OF SOLIDS

• To measure the density of a solid particle often simply means to measure its volume because its mass is known uponto measure its volume, because its mass is known upon weighing.

• To get the volume of the solid sample without its open pores, a pycnometer technique with an appropriate liquid can be used.

• The liquid must not alter or dissolve the sample For thisThe liquid must not alter or dissolve the sample. For this purpose, a sequence of weighings is conducted as indicated in Figure 3.11.

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DENSITY OF SOLIDS

• After weighing the empty pycnometerm0 the pycnometer is weighed with the samplemPweighed with the sample mP.

• Then the pycnometer is filled up to a designated mark with an appropriate reference liquid of known density and weighed again mP,F.

• Finally, the pycnometer is weighed when filled to the same mark with only the reference liquidm :mark with only the reference liquid mF:

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DENSITY OF SOLIDS

Fig. 3.11 Pycnometer measurement of the density of a solid granular material, e.g. a powder

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DENSITY OF SOLIDS

• The density of the solid material then is

(3.8)

(3.56)

(3.57)

(3 58)(3.58)

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DENSITY OF SOLIDS

(3.59)

(3.60)

(3.61)

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DENSITY OF SOLIDS(3.62)

(3.63)

• where

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BULK DENSITY

• Powders and bulk goods contain hollow spaces or voids filledwith gas normally air The density of that type of bulkwith gas, normally air. The density of that type of bulkmaterial, including the void spaces, is called bulk density.

• Using equation (3.8) the bulk density can be calculated byweighing a sample of the bulk material and measurement ofits volume.

• The volume of the whole bulk material must be taken “as is ”The volume of the whole bulk material must be taken as is.To measure this volume, the sample material can be pouredinto a beaker or cylinder up to a known volumetric mark.

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BULK DENSITY

• Different technique in filling the beaker or cylinder may leadto different distributions of solid particles and hollow spacesto different distributions of solid particles and hollow spaces.So, to get repeatable results the technique of filling has to bestandardized.

• To overcome problems with repeatable filling technique, thebulk material can be tapped before reading of the volume. Bytapping the material, the solid particles will “settle” into thepp g , pmost stable situation they can reach. The void spaces will getsmaller as the solid particles settle step by step into a spatialsituation where the bulk density will reach a maximum Thesituation where the bulk density will reach a maximum. Thetime needed to reach this maximum depends on tappingspeed and tapping amplitude. MASS & DENSITY


BULK DENSITY

Figure 3.12. Device for tapping of bulK goods: 1: rotating cam, 2: housing, 3: powder sample, 4: cylinder, 5: overring

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y g


BULK DENSITY

• Figure 3.12 shows an example of a device which can be usedto measure bulk density and tapped bulk densityto measure bulk density and tapped bulk densitysubsequently.

• First the bulk material is filled into a 1000 cm3 cylinder until itis overflowing under repeatable technique conditions. Thenwith aid of a flat spatula, the excess overflow of samplematerial is scraped away from the top of the cylinder to leavep y p ythe sample perfectly level at the top, and the 1000 cm3

sample is weighed to get the bulk density.

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BULK DENSITY

• Now a cylindrical extension overring is slipped onto the 1000cm3 cylinder and more sample material is filled in Thecm3 cylinder and more sample material is filled in. Thecylinder is mounted on the tapping device and moved for afixed number of tappings. In German testing standards a

b f 2500 ith f f 250 1 i ifi dnumber of 2500 with a frequency of 250 s−1 is specified.

• After this the sample material is adjusted to 1000 cm3 againand weighed. The tapped bulk density should be recordedg pp ywith the parameters of its measurement.

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BULK DENSITY

• The difference between bulk density and maximum tappedbulk density provides information about the ability of the bulkbulk density provides information about the ability of the bulkmaterial to be compressed by gravity or pressure. Powderscan be characterized for this property by the Hausner ratio,hi h i th ti t f t d b lk d it t dwhich is the quotient of tapped bulk density over untapped

bulk density (see Table 3.3).

Table 2.7. Characterization of

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Characterization of powder flowabilityby Hausner ratio


POROSITY

• Also the volume of the hollow void space (pores) can becalculated The ratio of the volume of the void space (pores)calculated. The ratio of the volume of the void space (pores)and the total volume of the bulk is called porosity ɛ:

(3 64)(3.64)

(3.65)

• becausemB ≈mS =m

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(3.66)


POROSITY

• So(3.67)

• With ɛ as the relative volume of the hollow pore space, and αas the relative volume of the solid particle space it is evident

( )

that:

(3.68)

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POROSITY

• where

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THE ENDTHE END

RHEOLOGICAL PROPERTIES OF FOODS