This article was downloaded by: [University of Nebraska, Lincoln]On: 09 October 2014, At: 12:49Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

International Journal of Food PropertiesPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/ljfp20

STRESS RELAXATION CHARACTERISTICS OF CHEDDARCHEESEV. Venugopal a & K. Muthukumarappan aa Department of Agricultural and Biosystems Engineering , South Dakota State University ,P.O. Box 2120, Brookings, SD, 57007, U.S.A.Published online: 17 Aug 2006.

To cite this article: V. Venugopal & K. Muthukumarappan (2001) STRESS RELAXATION CHARACTERISTICS OF CHEDDAR CHEESE,International Journal of Food Properties, 4:3, 469-484, DOI: 10.1081/JFP-100108649

To link to this article: http://dx.doi.org/10.1081/JFP-100108649

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use ofthe Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

STRESS RELAXATION CHARACTERISTICS

OF CHEDDAR CHEESE

V. Venugopal and K. Muthukumarappan*

Department of Agricultural and Biosystems Engineering,SouthDakota StateUniversity, P.O. Box 2120, Brookings, SD 57007

ABSTRACT

Stress relaxation experiments were conducted by heating a cheese sample(22mm diameter and 17.5mm height) at 40, 50 and 60�C in an aluminumcup whose inner diameter and depth were 22mm and 17.5mm, respec-tively. A plunger of 18mm diameter, which was attached to an Instrontype machine, was allowed to compress the cheese instantaneously to10% deformation. The relaxation of stress was recorded as a function oftime. Cheddar cheeses with four different fat content (15.3, 22.8, 37.3 and45.6% fat dry matter7FDM) and two different moisture content (58.1and 62.4% moisture in non fat portion7MNFP) at 2, 4, 12 and 24 weekswere used in this study. Generalized Maxwell and empirical Peleg modelswere used to characterize the stress relaxation behavior of melted cheese.The effect of fat content, moisture content, and age of cheese on stressrelaxation behavior was studied. Peleg model well described the stressrelaxation behavior of melted cheese (cheeses above 50�C) and eightelement Maxwell model predicted better than three element Maxwell andsix element Maxwell models. The stress relaxation experiment differ-entiated the viscoelastic nature of different cheeses due to reduction of fatcontent, increase in moisture, increase in melting temperature and age ofcheese. Stress relaxation test can be used as a tool to systematically studycheese functionality.

*Corresponding author. Fax: 605-688-6764; E-mail: muthukum@sdstate.edu

469

INTERNATIONAL JOURNAL OF FOOD PROPERTIES, 4(3), 469–484 (2001)

Copyright # 2001 by Marcel Dekker, Inc. www.dekker.com

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014

INTRODUCTION

Use of cheese as an ingredient in prepared foods is increasing. Cheeseplays an increasingly important role in adding taste, texture and nutritionalqualities to several prepared foods. Recent survey showed that 421 newcheeses were introduced in 1996, up 70% from 1995 [1]. The world cheeseproduction increased by 9% between 1987 and 1996 with production inNorth America increasing by 25%. Concomitant with this is an increasedneed for characterizing the behavior of cheeses at elevated temperatures.Functional properties of cheese, namely softening, melting and flowing, andviscoelasticity are extremely important of successful use of cheese as a foodingredient.

Large deformation studies include stress relaxation and creep tests toaccess structural behavior. Researchers used the stress relaxation test tocharacterize the rheological properties of cheeses [275]. Lu and Puri [6]characterized the relaxation behavior of apple flesh using confined uniaxialstress relaxation test, by making the lateral deformation of the specimen tozero. This methodology can be used to evaluate stress relaxation behavior ofmelted cheese.

Yun et al. [7] showed that hypothetical equilibrium stress in the stress-relaxation test was higher at a draw pH of 6.40 than 6.10 and alsodecreased with storage, suggesting cleavage of structural cross-links causedby the coagulant. Korolczuk [3] evaluated the stress relaxation data’s ofCheddar cheese using four different models and showed that Avrami’sequation is a best fit for Cheddar cheese with a coefficient of variabilityof 1%.

The primary objectives of this study were to provide a better under-standing the functionality of cheese as a function of cheese composition,maturation and temperature; and to understand the interactions betweendifferent processing parameters. Studying the effect of temperature on thefunctional properties of cheeses is not only of practical importance, but alsoof intrinsic scientific importance. Investigating the rheological and functionalproperties of the cheeses could help in predicting cheese behavior in manyfood applications.

The specific objectives of this study were to:

1. characterize the stress relaxation behavior of melted cheese using amechanical model (Generalized Maxwell) and an empirical model(Peleg model),

2. study the effect of fat content, moisture content, cheesemelting temperature, and age of cheese on the stress relaxationbehavior.

470 VENUGOPAL AND MUTHUKUMARAPPAN

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014

MATERIALS AND METHODS

Chemical Analysis of Cheese

Fat content was determined using the Modified Mojonnier EtherExtraction Method as described in the Association of Official AnalyticalChemists [8]. Protein concentration was determined by the Kjeldahl method,as described in the Association of Official Analytical Chemists [8]. Moisturecontent of the cheese was determined with a moisture balance (ModelMB200; Ohaus Corp., Florham Park, NJ) as described by Crosser andMistry [9]. Ash was determined by heating in a muffle furnace at 535�C asoutlined by Association of Official Analytical Chemists [8]. Soluble proteinwas measured by the Kjeldahl method [10]. The salt content [11] of the cheesewas determined using a sodium electrode attached to an ion analyzer (Model150, Corning Medical, Medfield, MA).

Sample Preparation

Cheese blocks were cut into cylindrical sample of 22mm diameter usinga cork-borer and 17.5mm height using a knife. The cheese samples were putinto plastic bags and placed in the refrigerator (476�C) for about 30minbefore testing in order to avoid loss of moisture before testing.

The apparatus consists of an aluminum body with a well at the topcenter whose diameter and depth were 22 and 17.5mm, respectively. Thisaluminum body was attached to a heater and a temperature controller unit(CN 44000, Omega Engineering, Inc., Stanford, CT) to control the heater.A plunger with 18mm diameter was attached to the sensor of Sintechmachine (2=D-4000=min, MTS System Corp., Research Triangle park, NC) tomonitor the stress relaxation of the cheese. A personal computer and soft-ware (Testwork Version 3.10, MTS System Corp., Eden Prairie, MN) wereused for data collection and analysis.

Stress Relaxation Experiment

Tests were performed by placing the cheese specimen (�22mm dia and17.5mm thick) into the sample well. The temperature of the aluminum bodywas set before the specimen was placed. The cheese sample was covered withaluminum foil in order to prevent loss of moisture during heating. Tem-perature of cheese in the sample well was monitored using a thermocoupleinserted into the specimen. The time of heating the sample varied for different

STRESS RELAXATION AND CHEDDAR CHEESE 471

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014

cheeses. For high fat cheese, the heating time was about 10min to reach thetest temperature where as for low fat cheese it was about 15min. Once thesample attained the test temperature, the aluminum cover was removed fromthe top of the cheese and cheese was cut with the knife to the surface of thealuminum body so that any projection over cheese if present was removed.Then, the plunger of the testing machine was allowed to touch above thesurface of the cheese so that the stress applied was zero. The plunger wasset to motion and the sample was compressed instantaneously to 10% defor-mation whereupon the crosshead was stopped and the sample was held in itscompressed position such that the strain of 10% was constant throughout theduration of the experiment. The lateral stress developed by the heated cheesedue to compression was confined within the boundary of the aluminum bodyand this tests were similar to those conducted by Lu and Puri [6].

Based on the preliminary results, three different temperatures 40�C,50�C and 60�C were chosen to study the stress relaxation effect on themeltability of cheeses. Tests were carried out on cheese samples at 2, 4, 12,and 24 weeks after production of cheese.

Data Analysis

The stress relaxation was recorded as a function of time. The stress isconverted into modulus of elasticity by dividing it by constant strain. Toobserve the time effect on the mechanical properties of a material, threeelement Maxwell model and empirical Peleg model were used. Three elementMaxwell model consist of a Maxwell body connected in parallel with aspring, and equation is represented by,

EðtÞ ¼ E1 � exp�t

t

� �þ E2 ð1Þ

where EðtÞ is the modulus of elasticity for the entire three-element body atany time t; E1 is the modulus of elasticity of the first element of the Maxwellbody, E2 is the modulus of elasticity of second element in this case a spring,and t is the relaxation time of the Maxwell element of the body. Therelaxation time is the time required for the stress on the Maxwell body todecay to a valve that is 37% of the total stress of that body. The coefficient ofviscosity for the Maxwell body was determined using Z ¼ t� E1.

The Peleg model used in the study, whose time dependent elasticmodulus can be represented as [3, 4, 12]:

SðtÞ ¼ Si � ðSi � SeÞ½t=ðtþ BÞ� ð2Þwhere SðtÞ is the modulus of elasticity for the entire Peleg model at any timet; Si is the initial modulus of elasticity, Se is the equilibrium modulus ofelasticity at infinite time, B¼ time necessary for (Sl � SiÞ=ðSi � Se) to becomeequal to 0.5.

472 VENUGOPAL AND MUTHUKUMARAPPAN

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014

In general, stress-relaxation model is composed of one or more Maxwellbodies (2) arranged in parallel. Six element and eight element Maxwell modelwere analyzed using a non-linear regression by a statistical software [13]. Thefollowing equation represents six-element Maxwell model:

EðtÞ ¼ E1 � exp�t

t1

� �þ E2 � exp

�t

t2

� �þ E3 � exp

�t

t3

� �ð3Þ

where EðtÞ is the modulus of elasticity for the entire three-element body atany time t; E1; E2, and E3 are the elastic modulus of springs; t1 ¼ 1; t2 ¼ 10and t1 ¼ 100 are the relaxation times.

The following equation represents an eight-element model:

EðtÞ ¼ E1 � exp�t

t1

� �þ E2 � exp

�t

t2

� �þ E3 � exp

�t

t3

� �þ E4 � exp

�t

t4

� �

ð4Þwhere EðtÞ is the modulus of elasticity for the entire three-element body atany time t; E1; E2; E3 and E4 are the elastic modulus of springs; t1 ¼ 0:1,t2 ¼ 1, t3 ¼ 10 and t4 ¼ 100 are the relaxation times.

Statistical Analysis

Mean square values of viscoelastic parameters of stress relaxation testswere determined using the General Linear Model procedure on the SASStatistical software package (Version 6.12, SAS Institute, Inc., Cary, NC).An interaction is described to be significant only when p< 0.05. The data wasanalyzed by factorial analysis of variance to examine the effects of interac-tions of fat, heating temperature, aging of Cheddar cheese; of moisturecontent, heating temperature, and aging of Cheddar cheese.

RESULTS AND DISCUSSION

Cheese Composition

Mean values of the composition analysis of four different fat Cheddarcheeses are shown in Table I. The moisture, salt and protein content of cheeseincreased with decreased fat content. It is very difficult to study the individualfactors such as fat and moisture level on the physical properties of cheese,since changes in one automatically change the values of the other compo-nents. The moisture in non-fat portion (MNFP) remains almost same fordifferent fat content cheeses, where as the fat in dry matter (FDM) tends todecrease as fat content decreased. This MNFP and FDM variation for dif-ferent cheeses is termed as effect of reduction in fat content of cheese. Whenthese factors on their own have an opposite effect on cheese physical

STRESS RELAXATION AND CHEDDAR CHEESE 473

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014

properties the combined influence may lead to conflicting results. Meanvalues of Cheddar cheeses with different moisture contents are shown inTable I. The MNFP increased as moisture content increased but FDMremained the same. This MNFP and FDM variation for different cheese istermed as effect of increase in moisture content of cheese. However, the salt,protein and pH of cheese decreased with increased moisture content.

Solubility Test

The percentage of soluble protein during aging of four different fatCheddar cheeses is shown in Figure 1. The percentage of soluble proteinformed increased with increased aging and varied for different fat Cheddarcheeses. The increase for low fat cheese was higher compared to high fatcheese. The percentage of soluble protein during aging for two moisture levelCheddar cheeses is shown in Figure 2. The soluble protein formed for thesetwo cheeses during aging were similar.

Model Fitting

Changes in elastic modulus of 45.6% FDM Cheddar cheese with time at40�C is shown in Figure 3. Peleg model predicted the experimental databetter than three element Maxwell model. The correlation coefficient g ofthree element model varied from 0.81 to 0.85 for cheeses at 40�C where as at60�C the g value varied from 0.91 to 0.95. Peleg model showed g varying from0.92 to 0.96 at 40�C where as at 50�C and 60�C, g> 0.98 were observed.These results indicated that the Peleg model is more appropriate for cheese

Table I. Chemical Composition of Cheeses Used in This Study

Fat

(%)

Moisture

(%)

MNFP1

(%)

FDM2

(%)

Protein

(%)

Salt

(%)

S=M3

(%)

Initial pH

(%)

Cheddar cheeses with varying fat content28.4 37.7 52.6 45.6 24.6 1.8 4.8 5.522.8 38.9 50.4 37.3 28.4 2.1 5.3 5.5

16.6 41.8 50.1 28.4 31.7 2.2 5.2 5.68.2 46.6 50.4 15.3 36.6 2.5 5.3 5.7

Cheddar cheeses of varying moisture content31.2 39.9 58.1 51.9 24.6 1.3 3.25 5.0928.8 44.4 62.4 51.8 22.4 1.15 2.59 4.94

1Moisture-in-the-nonfat portion.2Fat in the dry matter.3Salt in moisture.

474 VENUGOPAL AND MUTHUKUMARAPPAN

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014

that is more viscoelastic liquid in nature at 50 and 60�C rather than visco-elastic solid at 40�C.

Comparing the experimental stress relaxation curves and the theoreticalstress relaxation curves of the proposed models (Figures 3 and 4), an

Figure 1. Percentage of soluble protein during aging for four different fat Cheddar cheeses.

Figure 2. Percentage of soluble protein during aging for two different moisture Cheddarcheeses.

STRESS RELAXATION AND CHEDDAR CHEESE 475

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014

eight-element model can be regarded as the appropriate model for char-acterizing the Cheddar cheese. Since bonds do not break and reform at thesame rate [14], biological materials typically have more than one relaxationtime [15]. Thus a three-element Maxwell model or a Peleg model cannotrepresent the viscoelastic behavior of such material, but Peleg model may be

Figure 3. Prediction of elastic modulus of 45.6% FDM Cheddar cheese by three-element

Maxwell and Peleg model at 40�C.

Figure 4. Prediction of elastic modulus of 45.6% FDM Cheddar cheese by eight-element

Maxwell model at 40 �C.

476 VENUGOPAL AND MUTHUKUMARAPPAN

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014

more appropriate for material, which is more viscoelastic liquid in nature(cheeses above 50�C).

Effect of Fat

Modulus of elasticity is defined as amount of stress required to deforma substance per unit strain. Thus the cheese sample with higher modulus ofelasticity indicates that cheese became harder with increasing fat content(Figure 5).

Initial modulus of elasticity or stress (S1, Peleg model) which may berelated to the strength of cheese, increased with decrease in fat content ofCheddar cheese (Table II). Thus cheese with low fat content showed higherS1 value. The value of B was not significantly different with different fatcontent of cheese. This indicated that the time taken by any cheese samples todissipate the stress to a value of 50% of the initial amount of stress remainssame. The residual elastic modulus (S2) can be considered as a factor thatdetermines the viscoelastic nature of the substance. Higher the value of S2

means the material behaves more like viscoelastic solid in nature. Forexample, 15.3% FDM Cheddar cheese at 40�C (Table II) has S2 of1193.1 kPa where as for high fat cheese (45.6% FDM) the value of S2 was43.8 kPa indicating that former was more viscoelastic solid in nature thanthat of later. We can note that as value of S2 increased, the mean correlationcoefficient g for the model obtained decreased (for example low fat cheesethat has high S2 at 40

�C has g¼ 0.92 where as for high fat cheese that has low

Figure 5. Effect of fat level on the elastic modulus of different fat Cheddar cheese at 40�C.

STRESS RELAXATION AND CHEDDAR CHEESE 477

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014

S2 at 40�C has g¼ 0.96 and at 60�C has g¼ 0.99). This indicates that theresidual factor S2 alone cannot determine the viscoelastic nature of cheesebut we may need to consider the time duration of the experiment. At infinitetime, the value of S2 may attain zero but it doesn’t means that the material isviscoelastic liquid in nature. Value of both B and S2 together can characterizethe viscoelastic nature of material.

The calculated parameter of the eight-element Maxwell model mayrepresent functional variability of the cheese, since the parameters obtainedrefers to the same fixed relaxation times and its parameter are function oftime, temperature and storage period [16]. The value of E1 (at t ¼ 0:1) maybe correlated to the hardness of the cheese. Thus, decrease in fat contentleads to increase in E1 value, which we observed from our experiment(Table III). Elastic modulus E2; E3 and E4 may constitute residual modulusof elasticity and hence higher their values indicate more viscoelastic solid innature. Thus low fat cheese posses more viscoelastic solid nature than thathigh fat cheese. If the number of elements in the Maxwell model is increased,the prediction of data may be accurate but at the same time the interpretationof such data precisely would be much difficult.

Effect of Moisture

As the moisture content of the Cheddar cheese increased, the modulusof elasticity of cheese decreased significantly (Figure 6). The value of S1

Table II. Viscoelastic Parameters of Peleg Model in Stress Relaxation Tests of Cheddar

Cheeses with Different Fat Cheddar Cheese at Different Temperatures

% FDM

Temperature (�C) Parameters 45.6 37.3 28.4 15.3

40 S1 (kPa) 1120.3 1918.5 5640.4 13409.0

S2 (kPa) 43.8 96.7 340.1 1193.1B 0.28 0.27 0.30 0.30g 0.96 0.94 0.93 0.92

50 S1 (kPa) 862.5 1888.6 2694.6 7027.0

S2 (kPa) 1.4 35.3 50.6 65.8B 0.27 0.29 0.30 0.26g 0.98 0.98 0.98 0.98

60 S1 (kPa) 461.7 1084.9 1540.1 3203.2S2 (kPa) 0.2 6.3 2.6 45.8

B 0.22 0.26 0.28 0.29g 0.98 0.99 0.99 0.98

478 VENUGOPAL AND MUTHUKUMARAPPAN

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014

decreased significantly with increase in moisture content (Table IV) indicatingthat increasing moisture content of the cheese decreases the hardness orstrength of the cheese. The elastic modulus S2 of 62.4% MNFP Cheddarcheese at 40�C was 0 kPa compared to 36.9 kPa of 58.1% MNFP Cheddarcheese at same temperature. This indicates that high moisture cheese is more

Table III. Viscoelastic Parameters of Eight-Element Maxwell Model in Stress Relaxation

Tests of Cheddar Cheeses with Different Fat Cheddar Cheese at Different Temperatures

Temperature Parameters% FDM

(�C) (kPa) 45.6 37.3 28.4 15.3

40 E1 2.626108 4.416108 1.296109 3.726109

E2 1597.7 2589.1 6845.4 16800.7E3 169.2 315.3 972.5 2144.2E4 83.5 173.5 589.2 2079.6

50 E1 2.326108 4.696108 6.786108 2.186109

E2 1215.6 2949.5 4628.6 10298.6

E3 79.4 259.5 395.7 909.6E4 10.7 79.2 122.5 200.6

60 E1 1.506108 2.836108 3.816108 8.836108

E2 675.0 1789.7 2586.5 4992.2E3 26.6 107.2 130.7 362.6

E4 1.7 20.6 15.1 93.1

Figure 6. Relationship between moisture content of cheese and elastic modulus at 40�C.

STRESS RELAXATION AND CHEDDAR CHEESE 479

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014

viscoelastic liquid in nature. At 50�C the value of S2 was almost zero andcomparing the B value indicates that high moisture cheese relax faster(B ¼ 0:21 s at 50�C) compared to normal cheese (B ¼ 0:29 s at 50�C). Hencehigh moisture cheese possessed more viscoelastic liquid in nature.

Increase of moisture content in Cheddar cheese lead to decrease in E1

values (Table IV), which indicates 62.4% MNFP moisture cheese was softerthan 58.1%MNFP moisture cheese. E2, E3 and E4 of high moisture were lowcompared to normal cheese indicating that high moisture cheeses possesmore viscoelastic liquid in nature than normal moisture cheese.

Effect of Temperature

Increase in temperature resulted in decrease in elastic properties of allthe cheeses. A typical example is shown in Figure 7. This indicated that dueto melting of fat globules in cheese the elastic property decreases. Thevalues of the viscoelastic parameters at different temperature of different fatcontent Cheddar cheese calculated from Peleg and eight-element Maxwellmodels are shown in Table II through IV. Elastic modulus S1 decreased,as cheese temperature was increased. From S2 value of 45.6% FDM cheese,it can be noted that the cheese is more viscoelastic liquid in nature atztemperature greater than 50�C. But when B of 50�C was compared with60�C, the value of B decreased drastically, which indicated that cheese at60�C was more viscoelastic liquid in nature and hence relaxed faster.

Table IV. Viscoelastic Parameters in Stress Relaxation Tests of Different Moisture Cheddar

Cheeses

Percentage MNFP

40�C 50�C 60�C

Parameters 58.1 62.4 58.1 62.4 58.1 62.4

Peleg model

S1 (kPa) 1258.9 711.0 650.0 332.4 452.3 222.0S2 (kPa) 36.9 0.0 0.0 0.9 0.0 1.8B (sec) 0.43 0.24 0.29 0.21 0.25 0.18g 0.96 0.98 0.99 0.98 0.99 0.95

Eight-element Maxwell

E1 (kPa) 2.246108 1.936108 1.626108 1.296108 1.276108 1.196108

E2 (kPa) 1994.4 1015.5 1191.8 380.7 794.8 195.9E3 (kPa) 289.8 108.2 59.1 0.0 21.4 11.6

E4 (kPa) 84.4 2.4 2.5 0.0 0.0 0.0

480 VENUGOPAL AND MUTHUKUMARAPPAN

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014

Figure 7. Relationship between melting temperature and elastic modulus of 45.6%- MNFPCheddar cheese.

Table V. Viscoelastic Parameters of Peleg Model in Stress Relaxation Tests at 40�C During

Aging of 45.6%, 37.3%, 28.4%, and 15.3% Cheddar Cheese

Aging

% FDM Parameters 2-Week 4-Week 12-Week 24-Week

45.6 S1 (kPa) 1120.3 870.9 1013.9 1062.1S2 (kPa) 43.8 19.7 48.1 41.1B 0.28 0.33 0.30 0.24g 0.96 0.97 0.96 0.96

37.3 S1 (kPa) 1918.5 2093.7 1787.7 1537.1

S2 (kPa) 96.7 74.0 85.5 35.6B 0.27 0.32 0.28 0.27g 0.94 0.96 0.96 0.96

28.4 S1 (kPa) 5640.4 3726.1 3784.7 2185.4S2 (kPa) 340.1 244.9 125.4 112.8

B 0.30 0.29 0.25 0.25g 0.93 0.89 0.95 0.96

15.3 S1 (kPa) 13409.0 8535.2 6772.8 4721.4S2 (kPa) 1193.1 456.2 323.5 329.8

B 0.30 0.27 0.25 0.26g 0.93 0.95 0.96 0.95

STRESS RELAXATION AND CHEDDAR CHEESE 481

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014

Similar trend was observed for other Cheddar cheeses of different fatcontent, but B was not significantly different indicating the presence ofresidual stresses. The viscoelastic parameters of different moisture Cheddarcheese showed a similar trend at different temperature. Visser [17] suggestedthat stiffness of cheese could be related to its fat content and that at hightemperature stiffness of cheese decreased with amount of fat due to meltingof milk fat.

Effect of Aging

Viscoelastic parameters of different Cheddar Cheeses during agingcalculated using Peleg model (S1; S2 and B) and eight-element Maxwellmodel (E1; E2; E3 and E4) are shown in Tables V and VI. The % solubleprotein formed due to aging increased significantly regardless of the fat levelsas shown in Figure 2. The value of S1 decreased during aging of cheese. Thiseffect was profound for reduced fat cheese (37.3, 28.4 and 15.3% fat cheese)at 40�C. The value of S1 for 45.6% FDM Cheddar cheeses due to aging wasnot significant at this temperature. At 60�C, all level of fat content cheesesshowed significant decrease in S1 value and this effect was profound for low

Table VI. Viscoelastic Parameters of Peleg Model in Stress Relaxation Tests at 60�C During

Aging of 45.6%, 37.3%, 28.4%, and 15.3% FDM Cheddar Cheese

Aging

% FDM Parameters 2-Week 4-Week 12-Week 24-Week

45.6 S1 (kPa) 461.7 413.5 235.7 277.7

S2 (kPa) 0.2 0.0 0.6 2.1B 0.22 0.19 0.22 0.22g 0.98 0.98 0.96 0.96

37.3 S1 (kPa) 1084.9 1086.2 451.6 383.9

S2 (kPa) 6.3 0.0 0.0 0.3B 0.26 0.25 0.21 0.20g 0.99 0.98 0.97 0.95

28.4 S1 (kPa) 1540.1 1674.4 687.9 436.2S2 (kPa) 2.6 4.4 0.0 0.1

B 0.28 0.26 0.21 0.22g 0.99 0.98 0.96 0.97

15.3 S1 (kPa) 3203.2 2867.2 1196.9 1139.1S2 (kPa) 45.8 21.2 0.0 0.1B 0.29 0.28 0.23 0.23

g 0.98 0.98 0.97 0.98

482 VENUGOPAL AND MUTHUKUMARAPPAN

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014

fat cheese (Table VII). The value of S2 decreased significantly in low fatcheeses (28.4 and 15.3%-fat) at all the temperature indicating that theybecome more viscoelastic liquid in nature due to aging. During aging, E1

value decreased which means that hardness or strength of cheese decreasesdue to aging of cheese. E2; E3 and E4 values indicates that cheese becomemore viscoelastic liquid in nature due to aging of cheese. Different moisturecheeses showed similar trend due to aging. This represents weakening ofprotein matrix due to aging.

CONCLUSIONS

1. Peleg and eight element Maxwell model predicted the stressrelaxation behavior of cheeses better than the three element Max-well model and six element Maxwell model.

2. Elastic modulus of Cheddar cheeses decreased with increase in fatcontent, test temperature and moisture content.

3. The elastic modulus of all cheeses reduced significantly due to aging(2 to 24 weeks).

Table VII. Viscoelastic Parameters of Eight-Element Maxwell Model in Stress Relaxation

Tests at 60�C During Aging of 45.6%, 37.3%, 28.4%, and 15.3% FDM Cheddar Cheese

ParametersAging

% FDM (kPa) 2-Week 4-Week 12-Week 24-Week

45.6 E1 1.506108 1.536108 8.466107 9.526107

E2 675.0 516.1 234.5 289.3E3 26.6 17.6 16.2 25.0E4 1.7 2.4 4.1 8.1

37.3 E1 2.836108 3.646108 1.586108 1.396108

E2 1789.7 1760.9 626.2 454.3

E3 107.2 94.3 8.6 15.3E4 20.6 5.4 1.9 4.9

28.4 E1 3.816108 3.806108 2.686108 2.056108

E2 2586.5 2214.0 1255.4 597.2E3 130.7 82.3 17.1 4.5

E4 15.1 4.2 0.2 1.1

15.3 E1 8.836108 6.926108 3.856108 3.736108

E2 4992.2 4886.3 1894.5 1698.5E3 362.6 331.7 3.9 48.4

E4 93.1 60.6 3.3 3.4

STRESS RELAXATION AND CHEDDAR CHEESE 483

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014

REFERENCES

1. Friedman, M. Deluge of Dairy Foods. In. Prepared Foods, New Food Pro-ducts Annual 1997, 165 (5), 65766.

2. Konstance, R.P.; Holsinger, V.H. Development of Rheological Test Methodsfor Cheese. 1992, 46 (1), 1057109.

3. Korolczuk, J. Rheological Properties of Fresh Cheeses by Compression-relaxa-tion Method. II. Stress Evolution During Relaxation Period. Milchwissen-schaft 1996, 51 (3), 1487150.

4. Nolan, E.J.; Holsinger, V.H.; Shieh, J.J. Dynamic Rheological Properties ofNatural and Imitation Mozzarella Cheese. J. Texture Studies 1989, 20,1797189.

5. Rao, M.A.; Steffe, J.F. V|scoelasticity of Foods; Elsevier Applied Science:New York, 1992.

6. Lu, R.; Puri, V.M. Characterization of Nonlinear Behavior of Apple FleshUnder Stress Relaxation. J. Rheol. 1992, 36 (2).

7. Yun, J.J.; Hsieh, Y.L.; Barbano, D.M.; Kindstedt, P.S. Draw pH and StorageAffect Rheological Properties of Mozzarella Cheese. J. Food Sci. 1994, 59 (6),130271304.

8. Association of Official Analytical Chemists. Official Methods of Analysis.AOAC Int., Arlington, VA, 1995, 16th ed.

9. Crosser, A.E.; Mistry V.V. Use of a Moisture Balance to Determine Moistureof Cheese. J. Dairy Sci. 1991, 74, 126.

10. Kosikowski, F.V. CheeseandFermentedMilkFoods, 2nd Ed.; Edwards Brother,Inc.: Ann Arbor, MI, 1997, 4057406.

11. Kindstedt, P.S.; Kosikowski, F.V. Measurement of Sodium Chloride in Cheeseby a Simple Sodium Ion Electrode Method. J. Dairy Sci. 1984, 67, 8797883.

12. Peleg, M. Characterization of the Stress Relaxation Curves of Solid Foods.J. Food Sci. 1979, 44, 277.

13. SAS1 User’s Guide: Statistics, Version 6.08 Edition. 1991. SAS Inst., Cary,NC.

14. Shama, F.; Sherman, P. Stress Relaxation During Force Compression Studieson Foods with the Instron Universal Testing Machine and its Implications.J. Texture Studies 1973, 4, 353.

15. Sherman, P. The Texture of Ice Cream. 3. Rheological Properties of Mix andMelted Ice Cream. J. Food Sci. 1966, 31, 7077716.

16. Miller, B.D.R.; Peleg, M.; Normand, M.D.; Gonter, R.H.; Klein, E. A Com-puter Aided Model for the Rheological Characterization and Classificationof Solid Food Materials. J. Food Sci. 1986, 51 (1), 1237124.

17. Visser, J. Factors Affecting the Rheological and Fracture Properties of Hardand Semi Hard Cheese. Bulletin of the International Diary Federation 1992,268, 49761.

Received October 10, 2000Revised February 19, 2001Accepted February 26, 2001

484 VENUGOPAL AND MUTHUKUMARAPPAN

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

12:

49 0

9 O

ctob

er 2

014