International Dairy Journal 17 (2007) 1063–1072 Rheology of mozzarella cheese Edward B. Muliawan, Savvas G. Hatzikiriakos Department of Chemical and Biological Engineering, The University of British Columbia, 2360 East Mall, Vancouver, BC, Canada V6T-1Z3 Received 23 March 2006; accepted 12 January 2007 Abstract The rheological properties of mozzarella cheese were studied by using a parallel plate, a sliding plate, an extensional and a capillary rheometer over a temperature range of 25–60 1C. While mozzarella cheese behaves as a semisolid at room temperature, it behaves mostly as a liquid at higher temperatures (typically greater than 40 1C). The rheological data obtained from the various pieces of rheometers were compared. Differences among the various data sets were observed and these were demonstrated to be due to the inherent changes to the material structure during testing and to the changes in the physical properties of the cheese at different temperatures. Mozzarella cheese is a viscoelastoplastic material at room temperature, which becomes viscoelastic at about 60 1C. Its yield stress gradually decreases with increase of temperature pointing to structural changes that occur at elevated temperatures. A Herchel–Buckley viscoplastic rheological model was found to describe adequately its rheology. r 2007 Elsevier Ltd. All rights reserved. Keywords: Cheese; Mozzarella; Cheese extrusion; Cheese rheology 1. Introduction Rheology can be used as a quality control tool in processing, as it has been closely correlated with the overall texture, sensory attributes of the food products and microstructural changes during processing (Drake, Gerard, Truong, & Daubert, 1999; Karoui, Laguet, & Dufour, 2003; Truong, Daubert, Drake, & Baxter, 2002). The most common method to determine the rheological properties of food materials (in our case a specific type of mozzarella cheese) is through small amplitude oscillatory shear (SAOS). Nolan, Holsinger, and Shieh (1989) determined the rheological differences between natural and imitation mozzarella cheese. Ak and Gunasekaran (1996) used SAOS tests to investigate the effect of refrigerated storage on low- moisture, part-skim mozzarella cheese. In later reports, Subramanian and Gunasekaran (1997a, 1997b) also perfor- med SAOS experiments to determine the effect of tempera- ture and refrigerated storage on the linear viscoelasticity of different types of mozzarella cheese. The results obtained over a temperature range of 10–70 1C; thermorheological simplicity was reported by successfully applying the time– temperature superposition principle. However, since moz- zarella cheese changes nature from 10 to 70 1C, the origin of the thermorheological simplicity is not well understood. In a more recent study, Venugopal and Muthukumarappan (2003) used SAOS to determine the rheological properties of cheddar cheese with different moisture and fat contents and aging period during heating and cooling. Other reports on SAOS experiments include those by Tunick et al. (1990), Joshi, Muthukumarappan, and Dave (2004), Ma, Drake, Barbosa-Canovas, and Swanson (1996), and Gravies, Zaritzky, and Califano (2004). Another type of deformation that has been used to characterize cheese is extensional. Campanella, Popplewell, Rosenau, and Peleg (1987) performed compression tests to achieve elongational deformation in order to measure the elongational viscosity of melted American process cheese. It was found that the temperature dependence of elonga- tional viscosity cannot be described by the Arrhenius or the Williams–Landel–Ferry (WLF) models. Similar experi- mental set ups have also been performed by Casiraghi, Bagley, and Christianson (1985) and Ak and Gunasekaran (1995). Ak, Bogenrief, Gunasekaran, and Olson (1993) investigated the effect of storage time and temperature on ARTICLE IN PRESS www.elsevier.com/locate/idairyj 0958-6946/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.idairyj.2007.01.003 Corresponding author. E-mail address: [email protected] (S.G. Hatzikiriakos).
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ARTICLE IN PRESS
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doi:10.1016/j.id
�CorrespondE-mail addr
International Dairy Journal 17 (2007) 1063–1072
www.elsevier.com/locate/idairyj
Rheology of mozzarella cheese
Edward B. Muliawan, Savvas G. Hatzikiriakos�
Department of Chemical and Biological Engineering, The University of British Columbia, 2360 East Mall, Vancouver, BC, Canada V6T-1Z3
Received 23 March 2006; accepted 12 January 2007
Abstract
The rheological properties of mozzarella cheese were studied by using a parallel plate, a sliding plate, an extensional and a capillary
rheometer over a temperature range of 25–60 1C. While mozzarella cheese behaves as a semisolid at room temperature, it behaves mostly
as a liquid at higher temperatures (typically greater than 40 1C). The rheological data obtained from the various pieces of rheometers
were compared. Differences among the various data sets were observed and these were demonstrated to be due to the inherent changes to
the material structure during testing and to the changes in the physical properties of the cheese at different temperatures. Mozzarella
cheese is a viscoelastoplastic material at room temperature, which becomes viscoelastic at about 60 1C. Its yield stress gradually decreases
with increase of temperature pointing to structural changes that occur at elevated temperatures. A Herchel–Buckley viscoplastic
rheological model was found to describe adequately its rheology.
Rheology can be used as a quality control tool inprocessing, as it has been closely correlated with the overalltexture, sensory attributes of the food products andmicrostructural changes during processing (Drake, Gerard,Truong, & Daubert, 1999; Karoui, Laguet, & Dufour,2003; Truong, Daubert, Drake, & Baxter, 2002). The mostcommon method to determine the rheological properties offood materials (in our case a specific type of mozzarellacheese) is through small amplitude oscillatory shear(SAOS). Nolan, Holsinger, and Shieh (1989) determinedthe rheological differences between natural and imitationmozzarella cheese. Ak and Gunasekaran (1996) used SAOStests to investigate the effect of refrigerated storage on low-moisture, part-skim mozzarella cheese. In later reports,Subramanian and Gunasekaran (1997a, 1997b) also perfor-med SAOS experiments to determine the effect of tempera-ture and refrigerated storage on the linear viscoelasticity ofdifferent types of mozzarella cheese. The results obtainedover a temperature range of 10–70 1C; thermorheological
e front matter r 2007 Elsevier Ltd. All rights reserved.
simplicity was reported by successfully applying the time–temperature superposition principle. However, since moz-zarella cheese changes nature from 10 to 70 1C, the origin ofthe thermorheological simplicity is not well understood. In amore recent study, Venugopal and Muthukumarappan(2003) used SAOS to determine the rheological propertiesof cheddar cheese with different moisture and fat contentsand aging period during heating and cooling. Other reportson SAOS experiments include those by Tunick et al. (1990),Joshi, Muthukumarappan, and Dave (2004), Ma, Drake,Barbosa-Canovas, and Swanson (1996), and Gravies,Zaritzky, and Califano (2004).Another type of deformation that has been used to
characterize cheese is extensional. Campanella, Popplewell,Rosenau, and Peleg (1987) performed compression tests toachieve elongational deformation in order to measure theelongational viscosity of melted American process cheese.It was found that the temperature dependence of elonga-tional viscosity cannot be described by the Arrhenius or theWilliams–Landel–Ferry (WLF) models. Similar experi-mental set ups have also been performed by Casiraghi,Bagley, and Christianson (1985) and Ak and Gunasekaran(1995). Ak, Bogenrief, Gunasekaran, and Olson (1993)investigated the effect of storage time and temperature on
ARTICLE IN PRESSE.B. Muliawan, S.G. Hatzikiriakos / International Dairy Journal 17 (2007) 1063–10721064
the extensional rheological properties of mozzarella cheese.Ak and Gunasekaran (1997) and Cervantes, Lund, andOlson (1983) examined the effect of anisotropy ofmozzarella cheese on compression deformation.
However, a study on the comparison of rheologicalproperties obtained from the different deformations isscarce; as will be seen in this work such a comparison turnsout to be extremely useful in order to obtain consistentrheological data, which in turn can be used by themanufacturers as a quality control tool. Therefore, themain objective of the present work was to carry out arheological characterization of mozzarella cheese usingdifferent modes/scales of deformations and check theconsistency of the rheological data by comparison. First,linear and nonlinear rheological results obtained from fourdifferent shear and extensional rheometers are presented;the results are compared and differences are explained onscientific ground. Finally, the rheological data are used topropose a rheological model that could be useful in processsimulation studies in the future.
2. Experimental
2.1. Materials
Best Buy Mozzarella cheese manufactured by LucerneFoods (Calgary, AB Canada) available at local grocerystores was used as the main material for this study. Itsmoisture content was determined by drying, using avacuum oven at 100 1C until constant weight was measured.The average of quadruplicate measurements indicated thatthe cheese contains approximately 4575wt% moisture.Samples obtained every several months (�2 months) apartwere tested for their linear viscoelastic properties. Differ-ences on the linear viscoelastic properties of these samplesof the order of 710% were observed. Thus, it was deducedthat this particular mozzarella cheese shows enoughconsistency in its properties and therefore was suitable forthis work.
2.2. Equipment and methodology
Dynamic oscillatory measurements were performedusing a stress controlled parallel plate rheometer (BohlinC-VOR manufactured by Malvern Instruments, Worces-tershire, UK). In using the rheometer, sample preparationis very crucial, since samples need to be in contact withboth the upper and lower plates. At the same time, thesamples cannot be overcompressed in order to avoidliquid/fat migration and prestressing effects. Thin slices(2–3mm) were cut cleanly and easily from a block at a lowtemperature (�4 1C). Sand paper was used to eliminate slipbetween the sample and the plates (25mm parallel plates)and mineral oil was used to coat the outer circumferentialarea of the sample in order to minimize moisture loss.However, it was determined from time sweep experimentsthat significant increase in dynamic moduli occurs after
certain period of time, which was attributed to the loss ofmoisture. To minimize this effect, all dynamic oscillatoryexperiments were completed before significant increase inthe moduli (increase by 5%) was observed.The Bohlin C-VOR rheometer (Malvern Instruments)
was also used to measure the yield stress of the mozzarellacheese. The rheometer was operated under the stress rampmode. In this method, stress was applied onto the sampleand the viscosity of the sample was measured. The level ofapplied stress was gradually increased, which caused theviscosity to increase gradually. At a certain stress, theviscosity started to decrease, which was essentially taken asthe yield stress (Cheng, 1986). The stress ramp rates used todetermine the yield stresses at 25, 40, and 50 1C were 8.25,2.54, and 0.05 Pa s�1, respectively.An Interlaken sliding plate rheometer incorporating a
shear stress transducer (Interlaken Technology, Chaska,MN, USA) was used to obtain nonlinear rheologicalresults. Such a rheometer has been used in the past to studythe nonlinear viscoelastic properties of a variety of cheesesin terms of large amplitude oscillatory shear (Tariq,Giacomin & Gunasekaran, 1998). More details on theprinciples of operation of this rheometer can be found inGiacomin, Samurkas, and Dealy (1989).A constant-speed Instron capillary rheometer (Instron,
Norwood, MA, USA) was used to determine the viscosityof cheese at high shear rates. The cross head that drives theplunger is capable of traveling at a maximum speed of85mm s�1. A 890N load cell was used to measure theextrusion load. A barrel with a diameter of 9.525mm wasused and it was equipped with PID-controlled heaters thatcontrol the temperature within 70.1 1C. The effectivelength of the barrel is approximately 305mm. Capillarydies of various diameters, entrance angles and lengths wereused, necessary to determine all the corrections associatedwith analysis of capillary rheological data (Dealy &Wissbrun, 1990).The Sentmanat Extensional Rheometer (SER, Xpansion
Instruments, Akron, OH, USA) was used to carry outextensional experiments (Fig. 1). This rheometer isdesigned to be fitted into a strain-controlled rheometer(Bohlin VOR rheometer with a 86 gcm load transducer). Itsunique design allows the rotational motion of the BohlinVOR motor to counter-rotate the two drums (connected byintermeshing gears) on which a sample is attached. As thedrums rotate in opposite directions, the sample is stretcheduniformly from both sides. The material fails always in themiddle section of the sample, an indication of the uniformextensional deformation. Since SER is designed to fit intothe chamber of the convective oven of the Bohlin VORrheometer, experiments can be carried out at hightemperatures. Thin samples of about 0.8mm in thicknesswere used, which were cut from a cheese block at a lowtemperature of about 4 1C as before. More details on theperformance of this rheometer as well as the raw dataanalysis can be found elsewhere (Sentmanat, Muliawan, &Hatzikiriakos, 2004).
ARTICLE IN PRESS
Torque Response
Housing
Drive Shaft Rotation
Intermeshing Gears
Stretching ForceExerted By Sampling
Windup drums
Sample
Fig. 1. A schematic of the Sentmanat Extensional Rheometer (SER) used
in this work.
Table 1
Discrete Maxwell relaxation spectra of mozzarella cheese at 60 1C
Relaxation time li (s) Relaxation modulus Gi (Pa)
4.37E�04 6953
4.64E�03 3919
4.62E�02 1127
0.3216 242.4
4.904 47.73
Shear stress (Pa)
10-2 10-1 100 101 102 103 104 105
Com
ple
x m
odulu
s,
G*
(Pa)
100
101
102
103
104
105
106
Str
ain
10-5
10-4
10-3
10-2
10-1
100
101
102
25°C
40°C
50°C
60°C
Mozzarella cheeseFrequency = 1.5 Hz Filled symbol - Strain
Open symbol - Modulus
Fig. 2. Stress sweeps of mozzarella cheese at a frequency of 1.5Hz and at
different temperatures (25–60 1C). Open and filled symbols represent the
effect of shear stress on the complex modulus G* and strain, respectively.
The extensional results are reported in terms of thetensile stress growth coefficient, ZþE , as a function ofHencky strain, eH or time, for various values of the Henckystrain rates, _�H. The linear viscoelastic envelope was alsocalculated and plotted together with the extensional resultsas a way of checking the consistency of the results (Dealy &Wissbrun, 1990). This is essentially obtained by using thelinear viscoelastic moduli to determine the relaxationspectrum in terms of a discrete spectrum of Maxwellrelaxation times (Dealy & Wissbrun, 1990). The storageand loss moduli in terms of the discrete Maxwellianspectrum can be expressed as
G0 ¼X
i
Gi
ðoliÞ2
ðoliÞ2, (1a)
G00ðoÞ ¼X
i
Gi
oli
1þ ðoliÞ2, (1b)
where o is the frequency of oscillation and Gi and li are thegeneralized Maxwell model parameters. The parameters(Gi, li) of Eqs. (1a) and (1b) were determined using anonlinear optimization program following the algorithmdeveloped by Baumgartel and Winter (1989). The programresults in the least number of (Gi, li) parameters(Parsimonious spectra). Table 1 lists the representativevalues of these parameters for mozzarella cheese at 60 1C.These parameters were then used to calculate, ZþE accordingto the following expression:
ZþE ¼ TZþS ¼ TX
i
Gi
li
1� exp ð�t=liÞ� �
, (2)
where T is the Trouton’s ratio taken equal to 3 forincompressible homogeneous materials (Bird, Armstrong,& Hassager, 1977).
3. Experimental results
3.1. Linear viscoelastic measurements
Stress sweeps were performed on the cheese samples todetermine the region of linear viscoelasticity. The resultsare plotted in Fig. 2. The complex modulus, G* (leftvertical axis) and the strain (right vertical axis) are plottedas functions of applied stress at the frequency of 1.5Hz. Itcan be seen that the region of linear viscoelasticity dependson the temperature. A smaller strain or stress should beused to obtain linear viscoelastic measurement withincrease of temperature. For example, the maximum strainto ensure linear viscoelasticity at 601C is only 1%. This is inagreement with the work published by Nolan et al. (1989),Ak and Gunasekaran (1996) and Subramanian andGunasekaran (1997a).Time-sweep experiments were performed in order to
check the stability of the materials at various temperatures.The results are shown in Fig. 3. At room temperature, itseemed that the sample was quite stable up to 30min. Onthe other hand, at 60 1C, the complex modulus started toincrease quite sharply after about 100 s. This was due to theloss of moisture despite the fact that mineral oil was used tocoat the exposed area of the sample. The loss of moisturecauses the cheese to harden which increases its dynamicmoduli. As stated earlier, all small amplitude oscillatory
ARTICLE IN PRESSE.B. Muliawan, S.G. Hatzikiriakos / International Dairy Journal 17 (2007) 1063–10721066
experiments were completed before significant increase inthe moduli was observed. For example, for the experimentsperformed at 60 1C, tests were completed within 100 s.
Frequency sweep experiments were performed at 25, 40,50, and 60 1C. The results are plotted in Fig. 4. It can beseen that at 25 1C, G0 is always higher than G00 over thewhole frequency range. This is typical behavior of aviscoelastic solid, also reported by Subramanian andGunasekaran (1997b), Nolan et al. (1989) and Diefes,Rizvi, and Bartsch (1993). As the temperature was
100 101 102 103 104
Com
ple
x m
odulu
s,
G*
(Pa)
102
103
104
105
106Mozzarella cheese
Frequency = 1.5 Hz
25°C
40°C
50°C
60°C
Time (s)
Fig. 3. Effect of time on the complex modulus G* of mozzarella cheese at
a frequency of 1.5Hz and at different temperatures (25–60 1C).
10-2 10-1 100 101 102
Dynam
ic m
oduli,
G',
G"
(Pa)
103
104
105
106
Com
ple
x v
iscosity,η
* (P
as)
102
103
104
105
106
107Mozzarella cheese
Temperature = 25°CShear Stress = 1000 Pa G'
G"
η*
10-2 10-1 100 101 102
Dynam
ic m
oduli,
G',
G"
(Pa)
102
103
104
105
Com
ple
x v
iscosity,η
* (P
as)
101
102
103
104
105Mozzarella cheese
Temperature = 50°CShear Stress = 10 Pa
G'
G"
η*
Frequency (Hz)
Frequency (Hz)
Fig. 4. Linear viscoelastic data (G0, G00 and Z*) of mozz
increased, the sample started exhibiting liquid-like beha-vior due to the melting of the fat and increased proteinmobilization. Furthermore, at 601C, loss modulus starts todominate the linear viscoelastic properties of the sampleand the behavior resembles that of a viscoelastic fluid i.e.similar to that of a molten polymer (Dealy & Wissbrun,1990).This transition (from a solidlike to a fluidlike behavior)
can be seen more clearly from a temperature-sweepexperiment (see Fig. 5). The phase angle, d�tan�1(G0/G00),is relatively constant at a temperature below 40 1C (solid-like behavior). As the temperature is increased beyond
10-2 10-1 100 101 102
Dyna
mic
moduli,
G',
G"(
Pa)
102
103
104
105
Com
ple
x v
iscosity,η
* (P
as)
101
102
103
104
105
106Mozzarella cheese
Temperature = 40°CShear Stress = 100 Pa
G'
G"
η*
10-2 10-1 100 101 102
Dynam
ic m
oduli,
G',
G"
(Pa)
101
102
103
104
Com
ple
x v
iscosity,η
* (P
as)
101
102
103Mozzarella cheese
Temperature = 60°CShear Stress = 1 Pa
G'
G"
η*
Frequency (Hz)
Frequency (Hz)
arella cheese at (a) 25, (b) 40, (c) 50, and (d) 60 1C.
20 30 40 50 60 70 80 90 100
Com
ple
x m
odulu
s,
G*
(Pa)
0
10x103
20x103
30x103
40x103
50x103
60x103
Phase a
ngle
, δ (
°)
10
20
30
40
50
60
70
δ
G*
Mozzarella cheeseFrequency = 1.5 HzShear Stress = 1 Pa
Temperature (°C)
Fig. 5. Effect of temperature on the complex modulus G* and phase angle
d of mozzarella cheese at a frequency of 1.5Hz and shear stress of 1 Pa.
ARTICLE IN PRESSE.B. Muliawan, S.G. Hatzikiriakos / International Dairy Journal 17 (2007) 1063–1072 1067
40 1C, d increases gradually, indicating the increasingdominance of the viscous properties of the cheese.
To obtain master curves, the time–temperature super-position principle was applied on the linear viscoelasticdata plotted in Fig. 4. The reference temperature wasselected to be 60 1C. The horizontal shift factors, aT werefound to follow the Arrhenius equation
aT ¼ expEa
R
1
T�
1
T ref
� �� �, (3)
where Ea is the energy of activation in calmol�1, R is thegas constant (1.987 calmol�1K�1), and Tref the referencetemperature in K. In this case, Ea was found to be4.11E04 kcal kmol�1. It is noted that the data obtained at25 1C cannot be superposed satisfactorily to the dataobtained at 40, 50, and 60 1C (shown in Fig. 6). This agreeswith the results plotted in Fig. 5, where it is found that at atemperature below 40 1C, the cheese behaves as a solid. Asthe temperature exceeds 40 1C, the cheese started melting,undergoing structural changes. These (structural changes)include increased separation of fat from the protein matrix(Guinee & Fox, 2001), increased ratio of liquid to solid fat(Prentice, 1987), increased mobility of the protein phase(Wettton & Marsh (1990)), and loss of moisture. Thismeans that essentially, the data obtained at highertemperatures (440 1C) corresponds to a physically differ-ent material. This is supported from the works done byMavridis and Shroff (1992) and Van Gurp and Palmen(1998) who attribute the failure of time–temperaturesuperposition as an indication of the presence of relaxationtime (or moduli) having nonuniform temperature depen-dence such as those exhibited by multiphase systems orthose that undergo physical changes during the rheologicalmeasurements. As illustrated earlier, cheese can beclassified as a multiphase system that exhibits a solid-likebehavior, which gradually changes to a liquid-like behavior
10-2 10-1 100 101 102 103 104
Co
mp
lex v
isco
sity,
η*/a
T(P
a s
)
100
101
102
103
Dyn
am
ic m
od
uli,
G', G
" (P
a)
100
101
102
103
104
105
Mozzarella cheese
Tref = 60°C
G'
G"
η*Maxwell model prediction
40°C50°C60°C
Shifted frequency, ω/aT (Hz)
Fig. 6. Time–temperature superposition of mozzarella cheese linear
viscoelastic data (G0, G00 and Z*) obtained at 40, 50, and 60 1C at the
reference temperature of 60 1C. Solid line represents the Maxwell model
prediction of the data.
as the temperature is increased. Thus, it is not surprisingthat only the data obtained at the melt state (440 1C)could be superposed.
3.2. Extensional rheology
The extensional properties of the cheese sample weredetermined by using the SER at 25, 40, 50 and 60 1C. At25 1C, extensional tests were performed on samples cut inthree different directions; perpendicular, parallel and intransverse directions to check for anisotropy. It was foundthat the mozzarella cheese used in this work is isotropic.On the other hand, Ak and Gunasekaran (1997) reportedanisotropy, which might be due to the method used toproduce the cheese. Extensional results at differenttemperatures are shown in Fig. 7 in terms of stress growthcoefficient, ZþE � sE=_�H as a function of time for variousHencky strain rates, _�H, where sE is the tensile stress.Plotted also is the linear viscoelastic envelope predictedfrom the generalized Maxwell model fit to the oscillatorydata as discussed before. The disagreements between shearand extensional data in the figure will be discussed in detaillater.From Fig. 7, at 25 1C, a rapid increase in the tensile
stress growth can be observed that is followed by a suddendecrease. The later decrease is consistent with a brittle-typefailure of a solid-like material. Note the excellent super-position of the various curves corresponding to thedifferent Hencky strain rates at small times. This showsthat slip of cheese on the drums has been eliminated. As thetemperature was increased, a gradual change in the type ofcheese failure (from brittle to ductile) was observed. At60 1C, a plateau in the tensile stress growth was obtained asthe cheese exhibited significant strain softening and ductilefailure.
3.3. Yield stress measurements
A typical shear stress ramp test used to determine theyield stress at 25 1C with a stress ramp rate of 8.25 Pa s�1 isshown in Fig. 8. From the analysis of the stress rampmeasurements, it was found that the mozzarella cheesetested in this work has a yield stress of 1620793 Pa at25 1C. Yield stress values were also determined at 40 1C(216719 Pa) and 50 1C (1.470.3 Pa). At 60 1C, however, itwas not possible to determine a yield stress value. It seemedthat the structure has been broken completely due tocomplete fat melting and protein mobilization.
4. Comparison of rheological data
4.1. Comparison of shear with extensional rheology
Comparison of the oscillatory shear with the extensionalrheological data is typically done by comparing the linearviscoelastic envelope with the extensional stress growthcurves, ZþE (Eq. (2) with T ¼ 3 assumed for a homogeneous
ARTICLE IN PRESS
Time (s)
0.01 0.1 1 10 100103
104
105
106
107S
tres
s gr
owth
coe
ffici
ent,
η+ (P
a.s) Mozzarella cheese
T = 25°C
Mozzarella cheeseT = 50°C
Mozzarella cheeseT = 60°C
LVE Maxwell model fit - 3*ηs+
LVE Maxwell model fit - 3*ηs+
LVE Maxwell model fit - 3*ηs+
LVE Maxwell model fit - 3*ηs+
1.13 s-1
0.714 s-10.45 s-1
0.226 s-1
0.113 s-10.045 s-1
Sliding Plate, � = 0.08 s-1
Time (s)
0.01 0.1 1 10103
104
105
Str
ess
grow
th c
oeffi
cien
t, η+
(Pa.
s) Mozzarella cheeseT = 40°C
0.45 s-1
0.226 s-1
0.714 s-1
1.13 s-1
0.01 0.1 1 10103
104
105
Str
ess
grow
th c
oeffi
cien
t, η+
(Pa.
s)
1.13 s-1
0.714 s-10.45 s-1
0.01 0.1 1 10102
103
104
105
Str
ess
grow
th c
oeffi
cien
t, η+
(Pa.
s)0.714 s-1
0.45 s-10.226 s-1
EEE
Time (s)
E
Time (s)
�H = 4.50s-1.�H = 4.50 s-1.
�H = 4.50 s-1.
�H = 4.50 s-1.
.
0.226 s-1
1.13 s-1
Fig. 7. Tensile stress growth coefficients of mozzarella cheese at (a) 25, (b) 40, (c) 50, and (d) 60 1C obtained from extensional experiments. The dashed
lines represent the Maxwell model predictions of the tensile stress growth coefficients based on the oscillatory shear data for comparison purposes.
Shear stress (Pa)
0 1000 2000 3000 4000
Insta
nta
neous v
iscosity (
Pas)
0.0
500.0x103
1.0x106
1.5x106
2.0x106
2.5x106
3.0x106
Mozzarella cheese
T = 25°C
Run 1
Run 2
Fig. 8. The measured instantaneous viscosity of mozzarella cheese in
response to a shear stress ramp at 25 1C. The inflexion point of the curves
is the point when the mozzarella cheese starts to flow and therefore
incompressible material). Alternatively, the linear visco-elastic envelope can be obtained from a startup of steadyshear test at a very low shear rate, i.e., typically 0.05 s�1,using a sliding plate rheometer. In the present work, thedynamic moduli were used to generate the discrete
relaxation spectrum, which was then used to predict thetransient shear stress growth as discussed earlier.The comparison of the various curves is shown in Fig. 7.
It can be seen that there is lack of agreement between thetwo sets of shear and extensional data as noticed before. Ata temperature higher than 25 1C, the Maxwell model fitsare well below extensional ones. As the temperatureincreases, the disagreement between the two sets of data(shear vs. extensional) seems to be more pronounced. Thisdiscrepancy is mainly due to moisture loss that is morepronounced at elevated temperatures. In performing theextensional tests, a very small amount (�1 g) was usedhaving a relatively high surface-to-volume ratio(�1600m�1). For comparison, an oscillatory test sampleusually had a surface area to volume ratio of approxi-mately 0.16m�1. Although the extensional tests typicallylasted less than 2min including equilibration time, theminute amount of sample used (notably thin) wassignificantly affected within this period of time. As thesample is heated up in the oven prior to and during testing,significant loss of moisture occurs, which definitely affectsthe extensional measurements. For comparison, it waspresented earlier that even for samples used in dynamicoscillatory tests, significant changes can occur in as little as
ARTICLE IN PRESS
10-2 10-1 100 101102
103
104
105
106
Str
ess g
row
th c
oe
ffic
ien
t, η
+ (
Pa
.s)
Mozzarella cheese
�H = 0.226 s-1
LVE Maxwell model fit:
0 rest time
10 min rest time at 50°C30 min rest time at 50°C60 min resttime at 50°C
Time (s)
E
T = 50°C
.
�H = 1.13 s-1.
�H = 4.50 s-1.
�H = 0.714 s-1.�H = 0.450 s-1.
Fig. 10. Comparison of the stress growth coefficient of mozzarella cheese
100 s at the temperature of 60 1C. At 25 1C, where moistureloss is insignificant as can be seen from the time sweepexperiment, there is a very good agreement between theshear data obtained from the sliding plate rheometer andthe extensional data.
To quantify the moisture loss, a simple mass balanceexperiment was conducted. Cheese samples were cut intotypical testing dimensions and they were placed into theoven for a certain period of time. The mass of the samplebefore and after being placed into the oven was measured.The difference in mass was taken to be the moisture lossfrom the cheese. The initial moisture level was determinedto be 45% of the initial total mass of the sample. A plotthat summarizes the result is shown in Fig. 9. It can be seenthat during the extensional tests (SER), moisture loss issignificant. For example, for the extensional sample toachieve a 5% loss of moisture is only 0.6min compared
0 10 20 30 40 50 60 70
Mo
istu
re lo
ss (
% o
fin
itia
l va
lue
)
0
2
4
6
8
10
12Mozzarella cheese
SER sample
0 1000 2000 3000 4000
Mo
istu
re lo
ss (
% o
f in
itia
l va
lue
)
0
2
4
6
8
10
12
14
16
18Mozzarella cheese
Oscillatory sample
Time (s)
Time (s)
a
b
Fig. 9. The effect of rest time at 50 1C on the moisture loss of mozzarella
cheese of (a) SER sample and (b) oscillatory sample. The lines shown are
the best fit using linear regression of the data (R2¼ 1.00 for (a) and
obtained from the extensional rheometer (SER) with those obtained from
the Maxwell model fit. Dashed lines represent the Maxwell model
predictions of cheese samples which have been preheated at 50 1C at
different equilibration times (0–60min).
with about 20min for the oscillatory test sample. This ratioof about 33 is quite high.Samples which had been placed into the oven at 50 1C
for various rest times before testing were tested for theirlinear viscoelastic properties. The obtained data weresubsequently analyzed in terms of the relaxation spectrumand Eq. (2) was used to predict the transient shear stressgrowth as explained earlier. The results are plotted inFig. 10. Satisfactory agreement between shear and exten-sional data was achieved if the oscillatory sample was leftin the oven for about 30min. Referring back to Fig. 9, itcan be seen that after this period of time, there is about a6% loss of moisture in the sample used for the oscillatorytest. This corresponds to about 42 s in the extensional test.This value compares very well with the equilibration timeof the sample loaded into the SER in extensional tests. Thisexperiment demonstrated that moisture loss (due toincreased temperature) is a crucial factor that cansignificantly affect the rheological properties of cheese,especially for samples having a relatively high surface-to-volume ratio. Obviously other structural changes such asdegradation, increased separation of fat from the proteinmatrix, increased ratio of liquid to solid fat and increasedmobility of the protein phase with exposure time cannot beexcluded.
4.2. Comparison between SAOS and capillary rheometry
Plots that depict a comparison between the dynamic andabsolute viscosities in shear are shown in Fig. 11. Viscositydata obtained from the sliding plate rheometer at 25 1C arealso plotted. Very good agreement can be seen between theviscosity determined from the sliding plate and capillaryrheometers. On the other hand, the dynamic and steadyviscosities are different at 25, 40 and 50 1C. First of all,
ARTICLE IN PRESS
10-2 10-1 100 101 102 103 104
η, η
* (P
a s)
100
101
102
103
104
105
η, η
* (P
a s)
100
101
102
103
104
105
106
107
CapillaryOscillatorySliding Plate
CapillaryOscillatory
CapillaryOscillatory
CapillaryOscillatory
Mozzarella CheeseT = 25°C
�A (s-1), ω (rad s-1)
10-2 10-1 100 101 102 103 104
�A (s-1), ω (rad s-1)
10-2 10-1 100 101 102 103
�A (s-1), ω (rad s-1)
η, η
* (P
a s)
100
101
102
103η,
η*
(Pa
s)
100
101
102
103
104
105
10-2 10-1 100 101 102 103
�A (s-1), ω (rad s-1)
Mozzarella CheeseT = 40°C
Mozzarella CheeseT = 50°C
Mozzarella CheeseT = 60°C
Fig. 11. Comparison of rheological properties of mozzarella cheese obtained from capillary, sliding plate and parallel plate rheometers at (a) 25, (b) 40,
it should be stressed that this disagreement is not due tomoisture loss as the samples in these tests were exposedminimally and structural changes occurred much slowercompared with extensional tests. The lack of agreementshows that cheese does not follow the classical Cox–Merzrule that typically applies to simple polymer melts at leastover a range of shear rates. Bistany and Kokini (1983)reported similar result for various types of food materialssuch as butter, ketchup, margarine and cream cheese. Theysuggested that the dynamic and steady shear data can besuperposed by shifting the dynamic data; no scientificreason was given for the necessity to this shift. Similarobservations have also been reported by Doraiswamy et al.(1991) for concentrated suspension systems and Yu andGunasekaran (2001) for different types of food such asketchup, yogurt, mayonnaise, and mozzarella cheese.These systems including mozzarella cheese possess struc-ture and therefore yield stress. In SAOS experiments, thestructure is preserved as only small strains are applied inthe measurements. In sliding plate and capillary rheometry,samples experience large strain and stresses and as a resulttheir structure breaks and the material exhibits its fluid-likecharacter. At higher temperatures where cheese melts and
loses its solid-like character, agreement between oscillatoryand capillary data was obtained (see Fig. 11(d)).
5. A rheological model for mozzarella cheese
Fig. 12 depicts the shear rheological data obtained fromthe sliding plate and capillary rheometers. It can be seenthat a very good agreement between the two sets of dataexist, as also discussed above. This set of data can bedescribed by a Herschel–Bulkley model as follows(continuous line in Fig. 12):
s ¼ sy þ K _gn, (4)
where sy is the yield stress, K and n are the consistency andpower law indexes, respectively, yielded sy ¼ 1930 Pa,K ¼ 3.34 Pa s, and n ¼ 0.28.The value of 1930 Pa resulting from the fitting compares
well to the yield stress obtained from the ramp method. Aninteresting point to note is also the fact that this stressvalue is in close proximity to the limit of linearviscoelasticity which is about 1500 Pa (see Fig. 2).Based on the yield stress analysis, the discrepancy
between the dynamic and steady shear viscosity data
ARTICLE IN PRESS
10-2 10-1 100 101 102 103 104100
101
102Mozzarella cheese
T = 25°CDie: 2 =180°
Capillary
Sliding Plate
Wall
shear
str
ess,
σ w (
KP
a)
Apparent shear rate, �A (s-1).
Fig. 12. A Herschel–Bulkley model fits well with the true flow curve of
mozzarella cheese at 25 1C, resulting a yield stress value that agrees well
plotted in Fig. 11 can be further explained. At 25 1C, thedynamic oscillatory data were collected using a very smallstress well below the yield stress. This caused no destruc-tion of the structure. On the other hand, in capillaryextrusion and sliding plate experiments, the deformationswere nonlinear and resulted in stresses well beyond theyield stress. This essentially broke the structure of thematerial. This observation has also been reported by Yuand Gunasekaran (2001) on their work on yogurt andmozzarella cheese. They attributed the discrepancy to thepresence of a weak gel structure that is broken in the large-scale deformation but stays intact during SAOS experi-ments. Similarly, at 40 and 50 1C, the fact that yield stressexists at these temperatures show that the cheese stillmaintains the structure of the protein matrix to a certainextent as the protein has not been totally softened. Again,extrusions at these temperatures involved large straindeformations that essentially damaged the structure ofthe cheese. SAOS experiments, on the other hand, wereperformed at deformations that were small enough topreserve structures and this caused the disagreementbetween the capillary and oscillatory rheological dataplotted in Figs. 11(a)–(c).
At 60 1C, there seem to be no structure as most of theprotein achieves total mobilization. Thus, at 60 1C,dynamic oscillatory tests were performed at a deformationwhich caused the cheese sample to actually flow. Thus, theagreement between the dynamic and steady shear data isnot surprising.
6. Conclusions
In this study, a rheological characterization of a specifictype of commercial mozzarella cheese using oscillatoryshear and extensional rheometers was performed. Based onthe results presented, it is evident that significant structuralchanges of the cheese occur with time, temperature and
mode/scale of deformations. With time and temperature,moisture plays a significant effect on the consistency of therheological properties of mozzarella cheese. The differentscale of deformations in oscillatory shear and extensionalexperiments also leads to the inconsistency of the dataobtained from these different experiments as illustratedfrom experiments at room temperature. These differencesprovided the means of concluding the rheological behaviorof mozzarella cheese. In addition, based on the yield stressmeasurement, it was determined that mozzarella cheesepreserves its structure and behaves as a viscoelastoplasticmaterial at temperatures below 60 1C. At 60 1C, mozzarellacheese is completely melted, its structure is completelybroken down and the cheese behaves as a viscoelastic fluid.The yield stress measurements provided an insight on thedisagreements of oscillatory shear and steady shear data atlow temperatures and agreement at 60 1C where mozzarellacheese exhibits no yield effects. Finally, it was found thatthe viscous behavior of mozzarella cheese can be describedadequately well by a Herschel–Bulkley viscoplastic model.If short-time effects become important a viscoelastic modelcan be developed based on the relaxation spectrum analysispresented in this work.
Acknowledgments
The authors wish to thank the National Sciences andEngineering Research Council of Canada (NSERC) andthe Killam Trusts for their financial assistance.
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