Journal of Food Engineering 93 (2009) 134–140

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Journal of Food Engineering

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Modelling of rheological behaviour of pummelo juice concentratesusing master-curve

N.L. Chin a,*, S.M. Chan a, Y.A. Yusof a, T.G. Chuah b, R.A. Talib a

a Department of Process and Food Engineering, Faculty of Engineering, University Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysiab Department of Chemical and Environmental Engineering, Faculty of Engineering, University Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

a r t i c l e i n f o

Article history:Received 8 September 2008Received in revised form 8 January 2009Accepted 9 January 2009Available online 27 January 2009

Keywords:Rheological modelMaster-curveModellingPummelo juice concentratePower law

0260-8774/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.jfoodeng.2009.01.005

* Corresponding author. Tel.: +60 389466353.E-mail addresses: chinnl@eng.upm.edu.my, cnyukl

a b s t r a c t

The rheological behaviour of freeze-dried-concentrated pummelo juice was modelled to investigate theeffects of temperature and concentration on its fluid type and viscosity using a rotational viscometer atshear rates ranging from 1 to 400 s�1. The effect of concentration measured by its total soluble solids con-tent resulted in the juice concentrates behaving towards shear thinning or pseudoplastic behaviour withflow behaviour index values, n < 1. Temperature increase from 6 to 75 �C produced a reversing effect ofthe shear thinning behaviour from the increase of n values at all three investigated concentrations, 20, 30and 50 �Brix. The consistency coefficient decreases with temperature but increases with total solublesolid contents. Modelling the rheological behaviour of pummelo juice concentrates using the master-curve yielded results over a range of temperature to overlap on a single line, which allows generalisationof flow behaviour and characteristics. The master-curve plots confirmed that the juice viscosity andpseudoplasticity increase with concentration with high regression coefficients, R2 > 0.98.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

The processing of commercial fruit juices such as heat steriliza-tion, evaporation or pasteurization is favoured in terms of preserv-ing the juice for a longer period of time. However, vitamin C, awater-soluble antioxidant vitamin which is important in formingcollagen, a protein that gives structure to bones, cartilage, muscle,and blood vessels, is very sensitive to heat and will be easily de-stroyed during heat treatment. The development of concentratedfruit juice in the form of dehydrated fruit juices or frozen concen-trates serves as an alternative method for maintaining more nutri-ents and volatile properties of the fresh fruit. Juices obtained byremoval of a major part of their water content by vacuum evapora-tion of fractional freezing are known as concentrated juice (Lozano,2006).

The processing of commercialised juice is subjected to tightsupervision because its properties, such as viscosity, concentration,and temperature vary during processing. The flow properties andbehaviour of processed juice products are important in determin-ing the power requirements for pumping and sizing of pipes inits processing (Kimball et al., 2004; Sestak et al., 1983; Telis-Romero et al., 1999). In the design and operations, it is importantto determine the type of flow, such as turbulent or laminar in heatexchangers (Gratão et al., 2006). An assumption of simple Newto-

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ing@gmail.com (N.L. Chin).

nian flow can result in error in the estimation of holding time. Thechanges in properties are also important in the selection of equip-ment and type of processing. For example, the film type evapora-tors are generally used in concentrating juices. Due to theimportance of liquid properties during processing, rheologicalmodels are frequently constructed to aid processing. Rheologicalproperties, such as viscosity arise from studies of flow and defor-mation of a matter (Barnes et al., 1993). Besides playing an impor-tant role during processing, such as in plant design, flow processes,quality control, storage, it is also referred for measurement of pro-cessing stability and for predicting texture (Davis, 1973). A param-eter of juice quality which is related to rheology is known as themouthfeel. Matz (1962) defines mouthfeel as the mingled experi-ence deriving from the sensation of the skin of the mouth afteringestion of a food or beverage and that it relates to density, viscos-ity, surface tension and other physical properties of the materialbeing sampled. The physical properties of fruit juices have beginto gain importance as textural dimensions of fruits juices havebeen developed and quantified (Ingate and Christensen, 2007).

Various mathematical models have been used to represent theflow behaviour of non-Newtonian fluids (Rao, 1999). FollowingRao (1999), there are Power law model, Herschel–Bulkley model,Bingham model, Cross-model, Carreau model, Casson model, andthe Heinz Casson model. Crandall et al. (1982) used the Powerlaw model to study concentrated orange juice at 42.5 �Brix whileIbarz et al. (1992) studied clarified peach juice from 40 to 60 �Brix.Although the physical properties such as viscosity, flow behaviour

Nomenclature

C concentration measured in total soluble solids (�Brix)Ea activation energy (J/kg mol)K and K

0consistency coefficient of Power law model (Pa sn)

K0 constant in Arrhenius equation (Pa sn)K1 constant in power equationN and n

0flow behaviour index in Power law model

n1 constant in power equation�n average of flow behaviour index

R universal gas constant 8314.34 (J/kg mol K)R2 coefficient of determinationT temperature (�C)gapp apparent viscosity (Pa s)r shear stress (Pa)_c shear rate (s�1)aT dimensionless shift factor

N.L. Chin et al. / Journal of Food Engineering 93 (2009) 134–140 135

index and density of many tropical fruit juices have been studied,most of the investigations are at few and low concentrations.Among them are fruits juices such as guava juice at 9 and 11 �Brix(Zainal et al., 2000, 2001), guava juice at 10–40 �Brix (Shamsudinet al., 2005), cashew juice at 5.5–25 �Brix (Azoubel et al., 2005),mango juice at 7.6–26 �Brix (Dak et al., 2007), pineapple juice at12–13 �Brix (Shamsudin et al., 2007) and pummelo juice at 8 and10 �Brix (Chuah et al., 2008). Rheological studies on juice concen-trates were mainly on sub-tropical fruits such as clarified applejuice at 12–70 �Brix (Constenla et al., 1989), pear juice at 10–70 �Brix (Ibarz and Miguelsanz, 1989), apple juice at 14–39 �Brix(Bayindirli, 1992), grape juice at 20–80 �Brix (Bayindirli, 1993),peach juice at 40–69 �Brix (Ibarz et al., 1992), cherry juice (Gineret al., 1996) and clarified peach and orange concentrates at 60 �Brix(Ramos and Ibarz, 1998).

The present study uses modelling to investigate the effect tem-perature and juice concentration on the rheological properties andflow characteristics of pummelo juice concentrates. The pummelofruit is gaining popularity since studies showed that it containsantioxidant capacity as extracts of carotenoids, phenolics, vitaminC, lycopene, and anthocyanins were found in them (Tsai et al.,2007; Jayaprakasha et al., 2008). An advantage of using concen-trated pummelo juice sample is that it has a low pH value (Chinet al., 2008) and it is known that a pH value less than 3.7, bacteriawill not multiply and only a short time pasteurization process isnecessary (Arthey and Ashurst, 1996). The rheological propertieswere superposed along the stress axis using shift factors at a cho-sen arbitrary reference temperature in a stress–temperature super-position (Harper and El Sahrigi, 1965; Rao et al., 1981; Vitali andRao, 1984; Speers and Tung, 1986; Steffe, 1996; Udyarajan et al.,2007).

2. Materials and methods

2.1. Preparation of Juice

Fresh harvest of Pummelo fruits, Citrus grandis (L.) Osbeck, wereobtained from the same cultivation batch from a farm as raw mate-rials. The pummelo fruits were stored in a refrigerator at 10 �C for afew days until the peeling process for juice sample extraction. Thethick fruit skin was peeled away after incision of longitudinal cutswith a sharp knife onto the spongy skin to reveal the juicy seg-ments. The fruit was separated into individual segments and theinner skin of each segments was peeled and discarded, includingany seeds found. Most of the bitter component, the naringin andlimonin found in the white membrane were completely removed.Using the cold peel method, the peel was stripped off manuallyto remove both albedo and the outer membrane of each segment(Arthey and Ashurst, 1996). The juice was extracted by using ahome kitchen juice blender (HR2027, Philips, Malaysia) and fil-tered using nylon to remove its pulps from the juice. The phys-ico-chemical compositions of fresh pummelo juice at moisture

content of 85.32 ± 1.52% is at about 10 �Brix (Chin et al., 2008).About 2 l of juice, sampled into 200 ml each, was dry concentratedby using a laboratory vacuum freeze dryer (Model SB4, Pump Mod-el RV8, Edward High Vacuum International, Crawley Sussex, Eng-land) or 24 h with a drying temperature programmed from 25 to�40 �C. During the freeze drying process, the juice was frozenand the frozen solvent was removed by sublimation under vac-uum. The sublimed ice was pulled from the vacuum chamber byvacuum pumps. The freeze-dried concentrated juice was then di-luted to three concentrations, 20, 30 and 50 �Brix with distilledwater for rheological test.

2.2. Rheological measurements

The rheological properties investigation of pummelo juice con-centrates were performed using a computerised rotational viscom-eter (Rotovisco RT 20, Haake, Germany) using the concentriccylinder geometry, Z40 DIN Ti. The sample volume of the geometrysystem is 70 cm3. The viscometer consists of high rotor speeds witha powerful drive motor, enabling it to be operated at a wide shearrate range of 0.1–1000 s�1. The viscometer is equipped with anelectric temperature controlled system (DC 50) to control theexperimental temperature to ±0.1 �C. The system consists of a hy-brid base with an electric heater and connectors for thermal liquidcooling. Data was recorded from the interface software, RheoWinJob Manager. Concentrated pummelo juice samples were mea-sured at six levels of temperatures, i.e., 6, 20, 30, 40, 60 and75 �C for each concentration level of 20, 30 and 50 �Brix from 1to 400 s�1 at a continuous increasing shear rate manner.

2.3. Analysis and modelling

The experiments were conducted in triplicates. Mean and stan-dard deviation were calculated using Microsoft Excel 2003 (XP Edi-tion, Microsoft Corporation, USA). The error bars in the graphs arethe standard deviation of means from three replications. Analysisof variance (ANOVA) at alpha level of 0.05 was performed usingthe statistical tool in Microsoft Excel. Curve fitting was performusing the solver function in Microsoft Excel adopting the general-ised reduced gradient (GRG2) nonlinear optimization code todetermine the rheological parameters, K and n in the Power lawmodel (Eq. (1)). The best fitted line with minimum sum of squareerrors (SSE) was used as the sole criteria during curve fitting. Thegoodness of fit, R2 was calculated as R2 ¼ 1� SSE

SST, where SST is thetotal corrected sum of squares (Walpole et al., 2002). In determin-ing the effects of temperature and concentration on rheologicalparameters, the Arrhenius (Eq. (3)) and a power type equation(Eq. (4)) were linearised by taking the logarithmic terms to obtainthe constants and coefficients.

2.3.1. Modelling of fluid flow behaviour using Power lawThe fluid behaviour of pummelo juice concentrate was the mod-

elled using the Power law:

136 N.L. Chin et al. / Journal of Food Engineering 93 (2009) 134–140

r ¼ K _cn ð1Þ

where r is the shear stress exerted by the fluid (Pa), K is the consis-tency coefficient, _c is the shear rate (s�1) and n is the flow behaviourindex. n does not equal to 1 for non-Newtonian fluids and it deter-mines the type of fluid category it belongs to. For non-Newtonianfluids, the apparent viscosity, gapp is reported as a function of shearrate. For this work, a shear rate of 100 s�1 was chosen because 10–100 s�1 approximates the shear rate of tumbling and pouring while100–1000 s�1 approximates the shear rate of home mixers (Bourne,2002):

gapp ¼ f ð _cÞ ¼ r_c¼ K _cn

_c¼ Kð _cÞn�1 ð2Þ

2.3.2. Effect of temperature on rheological modelThe dependence of consistency coefficient, K, on temperature is

described using the Arrhenius relationship

K ¼ K0 exp�

Ea

RT

�ð3Þ

0

1

2

3

4

5

6

7

0 100 200 300 400 500

0

10

20

30

40

50

60

70

80

90

0 100 200

a

c

Fig. 1. Rheograms showing shear stress versus shear rate plots for pummelo juice conconcentration at (a) 20, (b) 30, and (c) 50 �Brix. Lines are calculated model values using

The data on consistency coefficient from Eq. (1) was used to ob-tain constants, K0 and Ea, known as the frequency factor and acti-vation energy, respectively. Eq. (3) was linearised by taking thelogarithm on each term. The constants, K0 and Ea were obtainedfrom the y-intercept and the slope of the linearised equation.

2.3.3. Effect of concentration on rheological modelThe dependence of consistency coefficient, K, on concentration

is modelled using the power type relationship where both con-stants of the K1 and n1 values were determined from the y-inter-cept and the slope of the linearised equation

K ¼ K1ðCÞn1 ð4Þ

2.3.4. Modelling fluid flow using master-curve equationEq. (5) shows that a rheogram at any temperature in the inter-

ested range can be generated by utilising constant values obtainedfrom Eqs. (1) and (3), such as the average flow behaviour index, �n,frequency factor, K0 and activation energy, Ea. When expressed interms of shear stress, the combined effect of shear rate and tem-perature in a single expression is as follow (Harper and El Sahrigi,1965):

0

2

4

6

8

10

12

14

16

0 100 200 300 400 500

30 400 5000

b

centrates at 6 �C (j), 20 �C (h), 30 �C (�), 40 �C (e), 60 �C (N), and 75 �C (D) forparameters given in Table 1.

N.L. Chin et al. / Journal of Food Engineering 93 (2009) 134–140 137

r ¼ f ðT; _cÞ ¼ K0 expEa

RT

� �ð _cÞ�n ð5Þ

Concurrently, the master-curve was also developed to allowprediction of rheological behaviour that covers the entire rangeof temperature and shear rates. As such, the rheological behaviourof pummelo juice concentrate at six different temperatures wasfurther interpreted using the master-curve technique. The shearrates were horizontally shifted at r = 2.5 Pa using Eq. (1) to obtainthe dimensionless shift factors, aT, defined as the ratio of shiftedshear rates with a selected reference temperature of 20 �C. Themaster-curve was then plotted using original shear stress versus

0.4

0.6

0.8

1.0

1.2

0 20 40 60 80

Temperature (οC)

n

a

Fig. 2. Effect of (a) temperature at 50 �Brix (N), 30 �Brix (h), 20 �Brix (�), and (b) total soluon flow behaviour index (n) of pummelo juice concentrate.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0 20 40 60 80

ba

Temperature (οC)

Fig. 3. Effect of (a) temperature at 50 �Brix (N), 30 �Brix (h), 20 �Brix (�), and (b) total soluon consistency coefficient (k) of pummelo juice concentrate.

original shear rates divided by the dimensionless shift factors.The horizontal shifting causes data to overlap on a singe line. Final-ly the master-curves at various concentrations were fitted to theoriginal Power law equation to present a single description of flowbehaviour in terms of consistency coefficient, K0 and flow behav-iour index, n0.

3. Results and discussion

The rheograms in Fig. 1 shows plots of shear stress versus shearrate of pummelo juice concentrates at three concentration levels

0.4

0.6

0.8

1.0

1.2

15 30 45 60

Total Soluble Solids (οB)

n

b

ble solids content at 6 �C (j), 20 �C (h), 30 �C (�), 40 �C (e), 60 �C (N), and 75 �C (D),

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

15 30 45 60

Total Soluble Solids (οB)

ble solids content at 6 �C (j), 20 �C (h), 30 �C (�), 40 �C (e), 60 �C (N), and 75 �C (D),

Table 2Parameters from Arrhenius equation fitting, K ¼ K0 exp Ea

RT

� �; activation energy, Ea (J/kg mol) and constant, K0 (Pa sn) of pummelo juice concentrates at various concentrations in

�Brix.

Total soluble solids (�Brix) Activation energy, Ea (J/kg mol) Constant in Arrhenius equation, K0 (Pa sn) Coefficient of determination, R2

20 34.02 ± 1.042 3.023E�08 ± 4.311E�10 0.943730 42.06 ± 4.432 9.979E�08 ± 9.486E�09 0.968450 22.12 ± 1.360 3.632E�04 ± 1.534E�05 0.9693

Table 3Parameters from power equation fitting, K ¼ K1ðCÞn1 ; K1 and n1 of pummelo juice concentrates at various temperatures in �C.

Temperature (�C) Constant in power equation, K1 Constant in power equation, n1 Coefficient of determination, R2

6 2.7271E�07 ± 1.3756E�08 4.3066 ± 0.1223 0.976820 1.8578E�07 ± 1.4278E�08 4.4302 ± 0.2507 0.971330 6.3311E�08 ± 6.0751E�09 4.9276 ± 0.4018 0.994740 8.9958E�09 ± 8.2446E�10 5.3856 ± 0.4961 0.993060 4.5857E�10 ± 2.0668E�11 5.5167 ± 0.0928 0.978075 1.7647E�09 ± 1.6099E�10 5.2690 ± 0.2992 0.9826

Table 1Parameters from power law equation fitting, r ¼ K _cn; consistency coefficient, K, and flow behaviour index, n and apparent viscosity, gapp calculated at 100 s�1 of pummelo juiceconcentrates at various concentrations in �Brix and temperatures in �C.

Total soluble solids (�Brix) Temperature (�C) Consistency coefficient, K Flow behaviour index, n Coefficient of determination, R2 Apparent viscosity, gapp

20 6 0.0710 ± 0.0222 0.7412 ± 0.0399 0.9996 0.0215 ± 0.002420 0.0410 ± 0.0225 0.7709 ± 0.0748 1.0000 0.0143 ± 0.002430 0.0221 ± 0.0178 0.8507 ± 0.1069 0.9999 0.0111 ± 0.002240 0.0111 ± 0.0089 0.9478 ± 0.1198 0.9989 0.0088 ± 0.001960 0.0066 ± 0.0007 1.0079 ± 0.0190 0.9996 0.0068 ± 0.000275 0.0042 ± 0.0017 1.0551 ± 0.0643 0.9999 0.0054 ± 0.0004

30 6 0.6621 ± 0.1803 0.5041 ± 0.0493 0.9996 0.0674 ± 0.004720 0.4193 ± 0.0794 0.5301 ± 0.0351 0.9998 0.0482 ± 0.002430 0.2072 ± 0.0523 0.6019 ± 0.0369 0.9999 0.0332 ± 0.002640 0.1284 ± 0.0087 0.6465 ± 0.0049 0.9998 0.0252 ± 0.001260 0.0418 ± 0.0338 0.7431 ± 0.1062 0.9983 0.0128 ± 0.002375 0.0217 ± 0.0119 0.8371 ± 0.0832 0.9972 0.0103 ± 0.0015

50 6 3.7564 ± 0.4065 0.5041 ± 0.0112 0.9998 0.3827 ± 0.021720 2.4023 ± 0.2254 0.5152 ± 0.0063 1.0000 0.2576 ± 0.021830 1.9646 ± 0.0817 0.5136 ± 0.0145 0.9999 0.2091 ± 0.014740 1.5045 ± 0.0864 0.5212 ± 0.0195 1.0000 0.1659 ± 0.013960 0.9900 ± 0.0406 0.5319 ± 0.0235 0.9999 0.1146 ± 0.007875 0.4983 ± 0.0480 0.5663 ± 0.0331 1.0000 0.0676 ± 0.0039

138 N.L. Chin et al. / Journal of Food Engineering 93 (2009) 134–140

measured at temperatures from 6 to 75 �C. The values of consis-tency coefficient, K, and the flow behaviour index, n, were obtainedby curve fitting using least square method and presented in Table 1showing high goodness in fitting with high regression coefficients,R2, from 0.9972 to 1.0000. A close observation on each of the n va-lue shows that pummelo juice concentrates exhibited a shear thin-ning, non-Newtonian behaviour and behaves pseudoplastically(n < 1) at all concentration levels. The pseudoplastic behaviour in-creases with concentration of juice while the effect of temperatureseems to reduce its pseudoplasticity at each concentration level.The juice concentrates at 20 �Brix (double the concentration offresh juice) shows a characteristic approaching Newtonian whenapproaching high temperatures of about 60 �C. Fig. 2 highlightsthat the effect of temperature in reducing pseudoplasticity is moreprominent to juices at lower concentration. Fig. 3 illustrates thatthe consistency coefficient, K, decreases with temperature but in-creases with concentration of pummelo juice concentrates. Thisphenomena of viscosity increase with total soluble solids contentand decrease in viscosity with temperature is consistent withmany other studies, e.g., in guava puree by Vitali and Rao (1982),apricot puree by Duran and Costell (1982), clarified peach juiceby Ibarz et al. (1992), orange juice by Ibarz et al. (1994), clarifiedapple juice by Constenla et al. (1989), and grape juice by Bayindirli

(1993). It was reported that high pulp levels and soluble compo-nents can contribute to the apparent viscosities (Kimball, 1986).The calculated apparent viscosity of pummelo juice concentratesat 100 s�1 as presented in Table 1 showed an agreeing trend tothe consistency coefficient with respect to the effect of tempera-ture and concentration levels. Both analysis on n and K valuesare important in juice processing. For example, the increase in con-sistency coefficient will decrease the flowing rate of juice in thepipe due to more resistance flow (Earle, 1985). This means thatheating or holding time in flow lines during pasteurization at rec-ommended temperature will be longer for juices with higher totalsoluble solids for the same pressure drop.

Table 2 lists the results of constants, K0 and Ea obtained throughlinearization of Eq. (3). The K0 values which are in the order oftenth power of negative 4–8 are in the range of those reportedby Ibarz et al. (1992) on clarified peach juices at 40–69 �Brix withthe range from tenth power of negative 6–11. The maximum acti-vation energy, Ea of 42.06 (kJ/mol) occurred at the concentration of30 �Brix. This activation energy value is in a reasonable range forjuice products (Rao, 1986). There are inconsistent reports aboutchanges of activation energy with concentration as increase withconcentration is reported in Ibarz et al. (1994), Giner et al.(1996), Singh and Eipeson (2000), Kaya and Belibagli (2002), Altan

4.0

4.5

5.0

5.5

6.0

0 2 0 4 0 6 0 8 0

n 1

0

50

100

150

200

250

300

350

0 2 0 4 0 6 0 8 0

K1x1

09

a b

Temperature (οC) Temperature (οC)

Fig. 4. Dependence of (a) constant (K1) and (b) constant (n1) on temperature in �C.

1

10

100

1 10 10 0 100 0T (s

-1)

Shea

r St

ress

(Pa

)

1

10

100

1 10 100 1000

Shea

r St

ress

(Pa

)

20°B

30°B

50°B

1

10

100

1 10 100 1000

Shea

r St

ress

(Pa

)

Fig. 5. Master-curves showing stress–temperature superposition with referencetemperature at 20 �C for pummelo juice concentrates at 6 �C (j), 20 �C (h), 30 �C(�), 40 �C (e), 60 �C (N), and 75 �C (D) at three concentrations, 20, 30 and 50 �Brix.

N.L. Chin et al. / Journal of Food Engineering 93 (2009) 134–140 139

and Maskan (2005) and Belibagli and Dalgic (2007) while a de-crease by Dak et al. (2007). Saravacos (1970) reported that the acti-vation energy decreases with the presence of suspended particlesin the fruit juice.

Table 4Parameters from power equation fitting into master-curve data, r ¼ K 0 _c

aT

� �n0

; K0 and n0 of

Total soluble solids (�Brix) Consistency coefficient, K0 Flow behaviour inde

20 0.0351 0.794930 0.5380 0.483050 2.9774 0.4729

Modelling using Eq. (4) presents the parameters as listed in Ta-ble 3. Constant, K1 decreases but n1 increases with temperature in-crease (Fig. 4). The values of R2 calculated were from 0.9713 to0.9930 suggesting good fitness and accuracy in the constants ob-tained. An observation of the slight decrease of flow behaviour in-dex at the highest temperature of 75 �C could be due to the effectof high heat which may have resulted in biochemical changes ofthe juice concentrate.

In giving an overall picture of the flow behaviour of pummelojuice concentrate, disrespect of its temperature, the master-curvetechnique was used to model the rheological behaviour to obtaina general fluid characterisation. With a reference temperature of20 �C and a 2.5 Pa basis of shear stress, the master-curve wasdeveloped through the determination of shift factor, aT. Fig. 5shows the plot of original shear stress as y-axis while x-axis isthe shifted shear rates divided by the shift factors in logarithmicscales yielding a linear line for each concentration due to the hor-izontal shifting of data which caused an overlap. Table 4 presentsthe results of Power law model fitting of the master-curve data dis-playing K0 values which increases and n0 values which decreaseswith concentration thus confirms the earlier analysis suggestingthat both juice viscosity and pseudoplasticity increase with con-centration. The absolute values of flow behaviour index via thismethod were about 9–25% lower compared to the average flowbehaviour index. Nonetheless, these master-curves are still recom-mended when comparing data from different products of juice andsolving engineering problems such as those requiring prediction offluid velocity profile or pressure drop during fluid flow (Steffe,1996).

pummelo juice concentrates at various temperatures in �C.

x, n0 Coefficient of determination, R2 Average flow behaviour index, �n

0.9932 0.89560.9887 0.64380.9981 0.5254

140 N.L. Chin et al. / Journal of Food Engineering 93 (2009) 134–140

4. Conclusions

Modelling of the rheological behaviour of pummelo juice con-centrates showed that it is non-Newtonian fluid, and that it pos-sesses characteristics which is pseudoplastic or shear thinning.The effect temperature and concentration both are significant to-wards the consistency coefficient and index behaviour such thatviscosity decreases with temperature but increases with total sol-uble solid contents. Modelling the rheological behaviour using themaster-curve also presented an increase of viscosity and pseudo-plasticity with concentration. This technique is useful for reportingthe behaviour with respect to any working temperature hence al-lows convenient comparison of different juice products.

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