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Rheological behaviour of low-fat and full-fat stirred yoghurt
Int. Dairy Journal 5 (1995) 661-671 Q 1995 Elsevier Science Limted Printed in Ireland. AI1 rights reserved 09%6946/95/$9.50 ELSEVIER
0958-6946(95)00047-6
Rheological Behaviour of Low-fat and Full-fat Stirred Yoghurt
L. De Lorenzi, Department
S. Pricl & G. Torriano
of Chemical, Environmental and Raw Materials Engineering, Trieste, Piazzale Europa 1, 1-34127 Trieste, ltaly
University of
(Received January 3 1 1994: revised version accepted November 5 1994)
ABSTRACT The rheological properties of a low-j& and a full-fat yoghurt were investigated under continuous and oscillatory flow conditions with a rotational coaxial-cylinder viscometer at dtfferent temperatures. In continuous shearjlohj tests, flow instability phenomena were detected below a critical shear rate value. Flow curves were correlated with the three parameter De Kee-Turcotte model, and the temperature dependence of the relevant parameters was demonstrated. The non-linear viscoelastic properties of both types of yoghurt were described, at first approximation, in terms of the complex modulus G* and phase lag 6. The efiects of temperature on weakening of the yoghurt structure was illustrated.
INTRODUCTION Yoghurt is a material with non-Newtonian flow properties and with strong timedependence of both the thixotropic and viscoelastic types. The flow curve shows yield value at zero shear. This plastic material is characterized by the presence of a labile structure, which is broken down under shear and slowly and only partially builds up in rest conditions or in conditions of lower shear. Flow properties are temperature dependent. The flow properties of yoghurt have been the subject of investigations by several authors. Approaches to the rheological characterization of yoghurt may be quite different, depending on the aim of the research, the experimental techniques adopted or the experimental data treatment. The microstructure of yoghurt is the main subject of papers, where the flow, properties play only a secondary role (Kalab & Emmons, 1974; Teggatz & Morris, 1990). In other works, the flow properties were correlated with the parameters of the manufacturing process (Labropoulos et al., 1981; Labropoulos et al., 1984; Olson & Bottazzi, 1977; Schmidt et al., 1980); addi661
662
L. De Lorenzi et al.
tion of texture modifiers, like pectin or fruits (Ramaswamy & Basak, 1992); sensory properties (Biliaderis et al., 1992; Rohm, 1989) or composition (O’Neil et al., 1990; Windhab, 1991). Some kinetic aspects of the coagulation time were investigated in connection with the flow properties (Sharma et al., 1989; Dannenberg & Kessler, 1988). The logarithmic time model of Weltman (1943) and the Herschel-Bulkley model (1926) were applied in recent investigations, aimed at a general characterization of yoghurt rheology from steady flow tests (Ramaswamy & Basak, 199la, Ramaswamy & Basak, 1991b). A flow characterization was also attempted by means of oscillatory flow tests (Zoon et al., 1988; Zoon et al. 1989; Steventon et al., 1991; Bohlin et af., 1984) whereas the works of De KCe & Turcotte (1983) and De KCe & Turcotte (1990) and of Benezech & Maingonnat (1992) presented an approach to the description of the time dependent properties of yoghurt at constant shear rate on the basis of a state equation, a kinetic equation and the parameter, introduced to describe the structural state of the material as a function of the shear rate and time, as previously suggested by Cheng & Evans (1965). The aim of this work is to make a contribution to the knowledge of the rheological properties of both low-fat and full-fat stirred commercial yoghurts, with particular focus on the effects of temperature variation, for which little information is available in the current literature.
MATERIALS
AND
METHODS
The full-fat (4% fat content) and the low-fat (0.4% fat content) yoghurts studied in this work were two commercial samples, obtained from Torvis Latterie Friulane, Cervignano (UD), Italy. The corresponding total solids contents were 14.6 and 13.5% respectively, as ascertained by drying the samples at 72 “C, under vacuum, to constant weight. All rheological measurements were carried out with a rotational rheometer Haake Rotovisko RV 100 (Haake Mess-Technik, GmbH, Dieselstrasse 4, D-7500 Karlsruhe 41, Germany), measuring head CVlOO, mounted with a coaxial cylinder sensor system ZB 15 (Couette type), with RI/R2 = 1.078, RI-R2 = 0.545mm (Ri = radius of the rotating cup, R2 = radius of the stationary bob). Continuous shear flow tests were performed in the 0.3-300 ss’ range. The application of a stepwise procedure of constant shear rates does not lead to stress constant values in a reasonable time (De Lorenzi & Torriano, 1991; Doveri et al., 1992). Therefore, recourse was made to the technique of the hysteresis cycles, since it was experimentally observed that consecutive repeating of up and down cycles leads to r (shear stress) values which, at corresponding shear rates, become closer and closer to one another. Practically, we have observed that the values given in the down-curves of the fifth and sixth cycles of 6 + 6 minutes are so close for both yoghurts studied that it may be assumed that conditions very near the true equilibrium are reached in the down part of the sixth cycle. Accepting this approximation allows flow curves to be determined on the basis of the values of the down part of the sixth cycle. Data repeatability was assessed by running each test in triplicate; the differences between the higher and lower shear stress values at the corresponding shear rates never exceeded 5%. Oscillatory shear flow tests were carried out both at constant frequency w and strain y. In strain sweep tests, y was varied between 7% and 240% at the frequencies w of 1.88
Rheological
behaviour of low-fat and full-fat
663
stirred yoghurt
rad s-’ and 6.28 rad s-‘, respectively. For the frequency sweep tests, frequency was varied between 0.314 rad s-l and 12.56 rad s-’ at the strains of 12,24 and 240%. The results of the oscillatory flow tests were analysed, at the first approximation, on the basis of the viscoelastic quantities G* and 6, where G*, the complex modulus, measures the proportionality between the applied sinusoidal strain and the resulting stress; 6 is the phase lag, defined as arctg(G”/G’); G’ is the real in-phase component of G* and G” is the imaginary, 7c/2 out-of-phase component, of G*. For the correlation of the continuous flow curves three models were tested: the Herschel & Bulkley (1926), the generalized Casson (Tscheuschner & Wiinsche, 1979) and the De K&e-Turcotte model (De K&e & Turcotte, 1980; De Kee & Turcotte, 1983). Model parameters were calculated with the non-linear least square method by using the Marquardt algorithm and minimizing the following objective function: C (yexp - y,,~)~. The quality of fitting was expressed in terms of average standard deviation, ASD, i.e.: [X(yexp - y,,,)* /(N - P)]“~, where N is the number of the experimental data and p the number of the model parameters.
RESULTS Continuous
AND
DISCUSSION
shear flow tests
Flow curves between 0.3 and 300 s-l, obtained at different temperatures, are reported in Figs 1 and 2 for the low-fat and the full-fat yoghurt, respectively. In both cases, the curvature of the stress profiles displays a discontinuity in a narrow shear rate range around 10 s-‘. Similar phenomena of discontinuity in the flow curve are reported in the literature and attributed to different causes, like dry friction of the material on the viscometer surfaces, slip at the wall, fracture, non homogeneity with secondary flow or plug flow (Windhab, 1988; Magnin & Piau, 1990). In the case of the yoghurts examined, the phenomenon may be mainly due
I I
b.,
I IO
I 100
I IO00
Shear rate (s-l)
Fig. 1. Flow curves for the low-fat yoghurt at different temperatures: (0)
12”C, (A)
16”C, (A)
2O”C, (0)
(1) 4 “C, (U) 8 “C,
24”C, (+) 28°C.
L. De Lorenzi et al.
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I1 0.1
0
I I
I IO
I 100
I
IO00
Shear rate (s-l)
Fig. 2. Flow
curves for the low-fat yoghurt at different temperatures: (m) 4°C (0) 8 “C, (0) 12°C (A) 16°C (A) 20°C (0) 24°C (+) 28°C.
to the progressive evolution of the shear flow into a plug flow, when shear rate is progressively decreased toward the critical shear rate value. By correlating the flow curves with the above mentioned models, at shear rates above the critical shear rate range, in which fluid discontinuity phenomena develop, the best fitting was obtained with the De K&e-Turcotte model, es.(l): z = 7, + ni+i
(1)
where z, (Pa) is the yield stress, nl (Pas) is a viscosity parameter, correlated with the structural state of the material, tl (s) is a time parameter, that may be useful in the study of time-dependent properties of materials. The ASD, for the De Kte-Turcotte model was found to be from two to three orders of magnitude better in comparison with the Herschel-Bulkley and extended Casson models. Thus, all further considerations in this work concern this model only. De K&e-Turcotte model parameters and the relevant ASD values are reported in Table 1 for the full-fat and low-fat yoghurts, at seven temperatures between 4 and 28 “C. An examination of data in Table 1 reveals a singular behaviour of z, with temperature. Indeed, the model gives z, values decreasing with temperature for low-fat yoghurt, whereas for full-fat yoghurt a maximum around 16 or 20°C is indicated. It may be suggested that, in absence of shear, increasing temperatures weakens the structure of the low-fat yoghurt; consequently, z, diminishes. The presence of milk fat inverts this trend up to a certain critical temperature, beyond which the temperature weakening effect on structure prevails. The values of r0 are comparable with those reported by other authors (Ramaswamy & Basak, 1991a, Ramaswamy & Basak, 1991b). Parameters nl and ti display a regular behaviour with the temperature, the former decreasing, as it could be expected, the latter increasing with increasing temperature. Figure 3 shows an extension of the De KCe-Turcotte model in comparison with the relevant experimental data for full fat yoghurt at 4°C and low fat yoghurt at
Rheological
Low-fat
behaviour of low-fat and full-fat
TABLE 1 Parameters and ASD according
and Full-fat Yoghurts: Low-fat yoghurt
8°C 24 “C T” (Pa) 10.035 t, (Pa) nl (Pa. s) 0.155 nl (Pa. s) 11 6) 0.002 003 t1 (s) ASD 0.000 389 ASD 12°C r0 (Pa) nl (Pa. s)
28 “C 9.128 r, (Pa) 0.145 nl (Pa. s) 0.002 191 tl (s) 0.000 406 ASD
tl (s)
ASD 16°C r. (Pa) nr (Pa. s) ?I 6)
For Definition
Model
9.663 0.149 0.002 426 0.000 470
6.772 0.126 0.002 79 1 0.000 325
8°C 24 “C z, (Pa) 8.250 z, (Pa) ql (Pa. s) 0.140 7]1(Pa. s) tl (s) 0.001435 tl (s) ASD 0.000 455 ASD
8.641 0.143 0.002 608 0.000 444
6.633 0.107 0.002 648 0.000 179
12 “C 28 “C z, (Pa) 9.031 z, (Pa) vl (Pa. s) 0.156 7j1(Pa. s) II 6) 0.002 079 fl (s) ASD 0.000 487 ASD
7.0100 0.145 0.003 124 0.000 684
16°C 5, (Pa) 9.632 q (Pa. s) 0.153 II (s) 0.002 241 ASD 0.000 512
8-958 0.144 0.002 468 0~000417
ASD
to De K&e-Turcotte
4°C 20 “C ‘5, (Pa) 7.421 r0 (Pa) nl (Pa. s) 0.155 nl (Pa. s) II 6) 0.001 394 tl (s) ASD 0~000441 ASD
20°C r, (Pa) 7.618 nl (Pa. s) 0.124 0.001 898 t, (s) 0.002 427 0.000 487 ASD 0.000 27 1
tl (s)
665
Full-fat yoghurt
4°C t, (Pa) 10.237 nr (Pa. s) 0.162 ASD
stirred yoghurt
of Parameters
see eq. 1 in text.
IOO-
3
k
le-p .40 .
z g
z
IO
________________------.
2
5
.
. l
.
.+
4
,.-5p
-0-e
T__--
0
0
o
0 0
. 0 0 0
I 0. I
I I
I IO
Shear rate
Fig. 3. Experimental fat yoghurts: LFY,
I 100
I
IO00
(s-l)
flow curves and De Kee-Turcotte model curves for low-fat and full8 “C, experimental (e), model (-). FFY, 4°C experimental (O), model (- - -),
L. De Lorenzi et al
666
8”C, as examples of the model application. The d&continuities in the experimental flow curves around the shear rate of 10 SC’ and the anomalous behaviour at lower shear rates, with regard to that predicted by the De K&e-Turcotte model, are clearly evident. The validity of the De Kee-Turcotte model was ascertained up to 300 s-‘. Oscillatory
flow tests
Tests performed under oscillatory flow conditions are useful tools for the characterization of the viscoelastic properties of materials. Generally, the first step in a routine oscillatory analysis consists in assessing the extension of the linear viscoelastic regime by means of a strain sweep test at constant frequency of oscillation cc). For both low-fat and full-fat yoghurts, no linear viscoelastic region was observed, even at the lowest strain imposed, independently of the applied frequency, as evidenced in Fig. 4. The complex modulus G* clearly decreases with increasing strain. The rate of decrease of G* with y is more pronounced at lower w, and in the low strain range. This seems to suggest that the linear viscoelastic region for both yogurt samples is confined to very low strain values, well beyond the experimental window explored. Moreover, this marked strain sensitivity allows to classify yoghurts as very weakly structured fluids. Nevertheless, in the non-linear region the canonical viscoelastic quantities, such as the complex modulus G* and the phase lag 6, can be still employed as first approximation terms for a comparison among similar systems. In this sense, Fig. 4 shows that the presence of milk fat results only in an increase of the G* values, whatever the strain applied. Temperature variations do not modify the non-linear characteristics of both types of yoghurts. Figure 5 shows that, for the low-fat yoghurt, a temperature
II 0.0 I
I 0.10
I I
I IO
Strain
Fig. 4. Complex modulus G* vs. strain curves for low-fat (LFY) and full-fat (FFY) yoghurts at two different frequencies of oscillation: (m) I %3 rad/s LFY, (0) 6.28 rad/s LFY, (A) 1438 rad/s FFY, (A) 6.28 rad/s FFY.
Rheological
behaviour of low-fat and full-fat
667
stirred yoghurt
IOO-
II
I
0.01
0.10
I
I
I
IO
Strain
Fig. 5. Complex modulus G* vs. strain curves for the low-fat yoghurt at w = 138 rad/s and different temperatures: (W) 4”C, (0) 8”C, (a) 12”C, (0) 16”C, (A) 2O”C, (A) 24°C
and(x)
28°C.
increase leads only to a quantitative downward shifting of the G* curves. Analogous considerations can be extended to the full-fat sample. In order to separate the viscous and elastic contributions to the total stress response of these materials, 6 was plotted vs Jofor both the low-fat and the full-fat yoghurts at different temperatures and at constant frequency o = 6,28 rad s-l. As can be seen from Fig. 6, increasing strain results in a progressive structural
9080 70 60 _ e
50-
cc
4030 20 IO t 01 0.01
I 0.10
I I
I IO
Strain
Fig. 6. Phase lag 6 vs. strain curves for low-fat (LFY) yoghurt and full-fat (FFY) yoghurts
at o = 6.28 rad/s and different tempepratures: (0) 4°C LFY, (0) 12°C LFY, (0) 20°C LY, (a) 28°C LFY, (0) 4°C FFY, (a) 20°C FFY.
L. De Lorenzi et al
668
break-down and, correspondingly, 6 increases, converging to the limiting value of 90”, as expected. By combining the experimental evidence for G* and 6, we may conclude that the imposed strain exerts its major effect on the elastic component G’, which decreases more rapidly than the viscous one G” with the increasing strain. An alternative for the evaluation of the strain amplitude influence on the mechanical response of the systems under investigation may be the analysis of the frequency dependence of the complex modulus. Figure 7 reports the behavior of G* vs. o for both the low-fat and the full-fat samples at 20°C and three different strains. For both yoghurts, doubling y from 12 to 24% results only in a quantitative reduction of the G* values, more marked in the case of the fullfat sample, whereas a ten-fold strain variation (24% + 240%) produces also a net change in the relevant G* profiles. Although all data refer to the nonlinear region, the shapes of the and G* vs. o curves obtained at y = 12 and 24% still resemble those typical of weakly structured materials. On the contrary, S-shaped curves are obtained at very high strains, as a consequence of the strong influence of the amplitude of deformation in the low frequency region. The slight dependence of the phase lag 6 on the frequency w, as depicted in Fig. 8, implies that all the G* - w profiles can be decomposed into two parallel curves of G’ and G” vs. o; once again, this is an evidence that the systems under investigation exhibit features typical of weakly structured materials (Lapasin et al., 1992). Finally, as can be seen in Fig. 9, temperature variations do not modify appreciably the shape of the G* vs. w curves, and only at 28 “C a substantial decrease of the G* values can be observed.
II 0.1
I I
I IO
I 100
Frequency (rad/s) Fig. 7. Complex modulus G* vs. frequency curves for low-fat (LFY) and full-fat (FFY) yoghurts at 20 “C and three different strains: (0) 12% strain LFY, (A) 24% strain LFY, (0) 240% strain LFY, (m) 12% strain WTr (A) 24% strain FFY, (+) 240% strain
Rheological
behaviour of low-fat andfull-fat
669
stirred yoghurt
90 * ++*+s 80 I 70 * 60 ~ h e
50-
Lc 403020 IO01 0.1
I I0
I I
Frequency
I 100
(rad/s)
Fig. 8. Phase lag 6 vs. frequency curves for low-fat (LFY) and full-fat (FFY) yoghurts at 20°C and three different strains: (m) 12% strain LFY, (+) 24% strain LFY, (A) 240% strain LFY, (x) 12% strain FFY, (*) 24% FFY, (+) 240% strain FFY.
2
0
0
oooooooo
&
0 ooooo
loI 0. I
Fig. 9. Complex
modulus
0000
0000
000
00
I
IO
Frequency
100
(radls)
curves for the full-fat yoghurt at y = 12% and (0) 4”C, (0) 12”C, (A) 2O”C, (0) 28°C.
G* vs. frequency
different temperatures
CONCLUSIONS Both full-fat and low-fat yoghurt were found to be pseudoplastic materials with yield value and appreciable elastic components, which were more marked in the full-fat than in the low-fat type.
670
L. De Lorenzi et al.
Discontinuity phenomena were observed in continuous flow experiments, when shear rate was decreased under a certain critical i range. It may be suggested that these phenomena be mainly due to the onset of a plug flow at low shear rates. Fitting continuous flow data to adequate models allowed evaluation of rheological parameters to obtain useful information on the rheological behaviour of the materials. In this context the yield stress z, is of special interest. Indeed, z, brings out the presence of different structural states in full-fat and low-fat yoghurts and the relevant temperature effects. In the oscillatory flow tests no linear viscoelastic region was observed, even at the lowest strains applied. This means that the linear viscoelastic behaviour is confined to very low strains and suggests to classify yoghurt as a weakly structured material. On the basis of the variation of the phase lag 6 with strain, strain sweep tests at first approximation describe the evolution of the material properties, which change from those of a predominantly viscoelastic solid to those of predominantly liquid with elastic components during the test performance. Moreover, strain sweep tests brought out gradual structural weakening with increasing temperature for both yoghurts. Higher values of G* at low strains were obtained for the full-fat yoghurt in comparison with the low-fat yoghurt. The opposite is seen at high strains. For both yoghurts stronger breakdown effects are shown at the lower frequency tested. Frequency sweep tests displayed different behaviours, in dependence on the different strains applied. Although all data refer to the non-linear region, the shape of the G* vs. o at the lower strain and the phase lag 6 dependence on w confirm that yoghurt behaves as a weakly structured material. The structure of the full-fat yoghurt exhibits a larger resistance in comparison to that of the low-fat yoghurt. For both yoghurts progressively increasing temperatures weakened the structure, according to a very regular pattern. ACKNOWLEDGEMENT The authors 60% fund.
wish to acknowledge
the financial
support
from the Italian
MURST
REFERENCES Benezech, T. & Maingonnat, J. (1992). Flow properties of stirred yoghurt: modelling and influence of cooling conditions. Proc. XIth Int. Congr. on Rheology, Brussels, pp. 693-5. Biliaderis, C., Khan, M. & Blank, G. (1992). Rheological and sensory properties of yogurt from skim milk and ultratiltered retentates. ht. Dairy J., 2, 31 l-23. Bohlin, L., Hegg, P.O. & Ljusberg-Wahren, H. (1984). Viscoelastic properties of coagulating milk. 1. Dairy Sci., 67(4), 729-34. Cheng, D.C.H. & Evans, F. (1965). Phenomenological characterization of the rheological behaviour of inelastic reversible thixotropic and antithixotropic fluids. Brit. J Appl. Phys., 16, 1599-617. Dannenberg, F. & Kessler, H. (1988). Application of reaction kinetics to the denaturation of whey proteins in heated milk. Milchwissenschuft, 43(l), 3-7. De Lorenzi, L. & Torriano, G. (1991). Una semplice procedura per la caratterizzazione reologica dello yoghurt. I quaderni dell’Istituto Lattiero Caseario di Thiene, 30, Thiene Italy, 147-64.
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andfull-fat
stirred yoghurt
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De K&e, D. & Turcotte, G. (1980). Viscosity of biomaterials. Chem. Eng. Commun., 6,2733 82. De Kee, D. & Turcotte, G. (1983). Flow properties of time-dependent foodstuffs. J. Rheol., 27(6), 581-604. Doveri, P.P., De Lorenzi, L., Tapparo, M. & Torriano, G. (1992). Caratterizzazione reologica di yogurt interi. Ind. Conserve, 67(2), 227733. Herschel, W.H. & Bulkley, R. (1926). Konsistenzmessungen von Gummi-Benzollijsungen. Kolloid Z., 39, 291-300. Kalab, M. & Emmons, D. (1974). Milk gel structure III. Microstructure of skim milk powder and gels as related to the drying procedure. Milchwissenschaft, 29( lo), 585-9. Labropoulos, A., Collins, W. & Stone, W. (1984). Effects of ultra-high temperature and vat processes on heat-induced rheological properties of yoghurt. J. Dairy Sci., 67, 405-9. Labropoulos, A., Palmer, J.K. & Lopez, A. (1981). Whey protein denaturation of UHT processed milk and its effect on rheology of yoghurt. J. Texture Studies, 12, 365574. Lapasin, R., Pricl, S. & Tracanelli, P. (1992). Different behaviors of concentrated. polysaccharide systems in large-amplitude oscillating shear flows. Rheol. Acta, 31, 37480. Magnin, A. & Piau, I.M. (1990). Shear rheometry of fluid with yield stress. J. NonNewtonian Fluid Mech., 36, 85-98. Olson, N. & Bottazzi, V. (1977). Rheology of milk gels formed by milk-clotting enzymes J. Food Sci., 42(3), 669-73. O’Neil, J., Kleyn, D. & Hare, L. (1990). Consistency and compositional characteristics of commercial yoghurts. J. Dairy Sci., 62(6), 1032-6. Ramaswamy, H.S. & Basak, S. (199la). Time dependent stress decay rheology of stirred yoghurt. Znt. Dairy J., 1, 17-31. Ramaswamy, H.S. & Basak, S. (1991b). Rheology of stirred yoghurts. J. Texture Studies, 22, 23141. Ramaswamy, H.S. & Basak, S. (1992). Pectin and raspberry concentrate effects on the rheology of stirred commercial yoghurt. J. Food Sci., 57(2), 357-60. Rohm, H. (1989). Viskositat und Thixotropie von Ioghurt. Miichwissenschaft, 44(6), 340-2. Schmidt, R., Sistrunk, C., Richter, R. & Cornell, J. (1980). Heat treatment and storage effects on texture characteristics of milk and yoghurt systems fortified with oilseed proteins. J. Food Sci., 45, 471-5. Sharma, S.K., Hill, A.R., Goff, H.D. & Yada, R. (1989). Measurement of coagulation time and curd firmness of renneted milk using a Nametre viscometer. Miichwissenschaft, 44( 11) 682-5. Steventon, A.J., Parkinson, C.J., Fryer, P.J. & Bottomley, R.C. (1991). The rheology of yoghurt. In Rheology of Food, Pharmaceutical and Biological Materials with General Rheology, ed. E. Carter, Elsevier Applied Science, Barking, 196-210. Teggdtz, J. & Morris, H. (1990). Changes in rheology and microstructure of ropy yoghurt during shearing. Food Structure, 9, 133-.8. Tscheuschner, H.D. & Wtinsche, D. (1979). Rheological properties of chocolate masses and the influence of some factors. In Food Texture and Rheology, ed. P. Sherman, Academic Press, London, pp. 355-68. Weltman, R.N. (1943). Breakdown of thixotropic structure as function of time. J. Appl. Phys., 14, 343350. Windhab, E. (1988). A new method for the highly sensitive determination of the yield stress and flow behaviour of concentrated suspensions. Xth Int. Congr. on Rheology, Sydney, 2, 37226. Windhab, E. (199 1). Caratterizzazione reologica e strutturale di prodotti alimentari dispersi. I quaderni dell’lstituto Lattiero Caseario di Thiene, 30, Thiene Italy, 95-l 19. Zoon, P., van Vliet, T. & Walstra, P. (1988). Rheological properties of rennet-induced skim milk gels. 1. Introduction. Neth. Milk Dairy, 42, 249969. Zoon, P., van Vliet, T. & Walstra, P. (1989). Rheological properties of rennet-induced skim milk gels. 5. Behavior at large deformation. Neth. Milk Dairy, 43, 35-52.
0958-6946(95)00047-6
Rheological Behaviour of Low-fat and Full-fat Stirred Yoghurt
L. De Lorenzi, Department
S. Pricl & G. Torriano
of Chemical, Environmental and Raw Materials Engineering, Trieste, Piazzale Europa 1, 1-34127 Trieste, ltaly
University of
(Received January 3 1 1994: revised version accepted November 5 1994)
ABSTRACT The rheological properties of a low-j& and a full-fat yoghurt were investigated under continuous and oscillatory flow conditions with a rotational coaxial-cylinder viscometer at dtfferent temperatures. In continuous shearjlohj tests, flow instability phenomena were detected below a critical shear rate value. Flow curves were correlated with the three parameter De Kee-Turcotte model, and the temperature dependence of the relevant parameters was demonstrated. The non-linear viscoelastic properties of both types of yoghurt were described, at first approximation, in terms of the complex modulus G* and phase lag 6. The efiects of temperature on weakening of the yoghurt structure was illustrated.
INTRODUCTION Yoghurt is a material with non-Newtonian flow properties and with strong timedependence of both the thixotropic and viscoelastic types. The flow curve shows yield value at zero shear. This plastic material is characterized by the presence of a labile structure, which is broken down under shear and slowly and only partially builds up in rest conditions or in conditions of lower shear. Flow properties are temperature dependent. The flow properties of yoghurt have been the subject of investigations by several authors. Approaches to the rheological characterization of yoghurt may be quite different, depending on the aim of the research, the experimental techniques adopted or the experimental data treatment. The microstructure of yoghurt is the main subject of papers, where the flow, properties play only a secondary role (Kalab & Emmons, 1974; Teggatz & Morris, 1990). In other works, the flow properties were correlated with the parameters of the manufacturing process (Labropoulos et al., 1981; Labropoulos et al., 1984; Olson & Bottazzi, 1977; Schmidt et al., 1980); addi661
662
L. De Lorenzi et al.
tion of texture modifiers, like pectin or fruits (Ramaswamy & Basak, 1992); sensory properties (Biliaderis et al., 1992; Rohm, 1989) or composition (O’Neil et al., 1990; Windhab, 1991). Some kinetic aspects of the coagulation time were investigated in connection with the flow properties (Sharma et al., 1989; Dannenberg & Kessler, 1988). The logarithmic time model of Weltman (1943) and the Herschel-Bulkley model (1926) were applied in recent investigations, aimed at a general characterization of yoghurt rheology from steady flow tests (Ramaswamy & Basak, 199la, Ramaswamy & Basak, 1991b). A flow characterization was also attempted by means of oscillatory flow tests (Zoon et al., 1988; Zoon et al. 1989; Steventon et al., 1991; Bohlin et af., 1984) whereas the works of De KCe & Turcotte (1983) and De KCe & Turcotte (1990) and of Benezech & Maingonnat (1992) presented an approach to the description of the time dependent properties of yoghurt at constant shear rate on the basis of a state equation, a kinetic equation and the parameter, introduced to describe the structural state of the material as a function of the shear rate and time, as previously suggested by Cheng & Evans (1965). The aim of this work is to make a contribution to the knowledge of the rheological properties of both low-fat and full-fat stirred commercial yoghurts, with particular focus on the effects of temperature variation, for which little information is available in the current literature.
MATERIALS
AND
METHODS
The full-fat (4% fat content) and the low-fat (0.4% fat content) yoghurts studied in this work were two commercial samples, obtained from Torvis Latterie Friulane, Cervignano (UD), Italy. The corresponding total solids contents were 14.6 and 13.5% respectively, as ascertained by drying the samples at 72 “C, under vacuum, to constant weight. All rheological measurements were carried out with a rotational rheometer Haake Rotovisko RV 100 (Haake Mess-Technik, GmbH, Dieselstrasse 4, D-7500 Karlsruhe 41, Germany), measuring head CVlOO, mounted with a coaxial cylinder sensor system ZB 15 (Couette type), with RI/R2 = 1.078, RI-R2 = 0.545mm (Ri = radius of the rotating cup, R2 = radius of the stationary bob). Continuous shear flow tests were performed in the 0.3-300 ss’ range. The application of a stepwise procedure of constant shear rates does not lead to stress constant values in a reasonable time (De Lorenzi & Torriano, 1991; Doveri et al., 1992). Therefore, recourse was made to the technique of the hysteresis cycles, since it was experimentally observed that consecutive repeating of up and down cycles leads to r (shear stress) values which, at corresponding shear rates, become closer and closer to one another. Practically, we have observed that the values given in the down-curves of the fifth and sixth cycles of 6 + 6 minutes are so close for both yoghurts studied that it may be assumed that conditions very near the true equilibrium are reached in the down part of the sixth cycle. Accepting this approximation allows flow curves to be determined on the basis of the values of the down part of the sixth cycle. Data repeatability was assessed by running each test in triplicate; the differences between the higher and lower shear stress values at the corresponding shear rates never exceeded 5%. Oscillatory shear flow tests were carried out both at constant frequency w and strain y. In strain sweep tests, y was varied between 7% and 240% at the frequencies w of 1.88
Rheological
behaviour of low-fat and full-fat
663
stirred yoghurt
rad s-’ and 6.28 rad s-‘, respectively. For the frequency sweep tests, frequency was varied between 0.314 rad s-l and 12.56 rad s-’ at the strains of 12,24 and 240%. The results of the oscillatory flow tests were analysed, at the first approximation, on the basis of the viscoelastic quantities G* and 6, where G*, the complex modulus, measures the proportionality between the applied sinusoidal strain and the resulting stress; 6 is the phase lag, defined as arctg(G”/G’); G’ is the real in-phase component of G* and G” is the imaginary, 7c/2 out-of-phase component, of G*. For the correlation of the continuous flow curves three models were tested: the Herschel & Bulkley (1926), the generalized Casson (Tscheuschner & Wiinsche, 1979) and the De K&e-Turcotte model (De K&e & Turcotte, 1980; De Kee & Turcotte, 1983). Model parameters were calculated with the non-linear least square method by using the Marquardt algorithm and minimizing the following objective function: C (yexp - y,,~)~. The quality of fitting was expressed in terms of average standard deviation, ASD, i.e.: [X(yexp - y,,,)* /(N - P)]“~, where N is the number of the experimental data and p the number of the model parameters.
RESULTS Continuous
AND
DISCUSSION
shear flow tests
Flow curves between 0.3 and 300 s-l, obtained at different temperatures, are reported in Figs 1 and 2 for the low-fat and the full-fat yoghurt, respectively. In both cases, the curvature of the stress profiles displays a discontinuity in a narrow shear rate range around 10 s-‘. Similar phenomena of discontinuity in the flow curve are reported in the literature and attributed to different causes, like dry friction of the material on the viscometer surfaces, slip at the wall, fracture, non homogeneity with secondary flow or plug flow (Windhab, 1988; Magnin & Piau, 1990). In the case of the yoghurts examined, the phenomenon may be mainly due
I I
b.,
I IO
I 100
I IO00
Shear rate (s-l)
Fig. 1. Flow curves for the low-fat yoghurt at different temperatures: (0)
12”C, (A)
16”C, (A)
2O”C, (0)
(1) 4 “C, (U) 8 “C,
24”C, (+) 28°C.
L. De Lorenzi et al.
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I1 0.1
0
I I
I IO
I 100
I
IO00
Shear rate (s-l)
Fig. 2. Flow
curves for the low-fat yoghurt at different temperatures: (m) 4°C (0) 8 “C, (0) 12°C (A) 16°C (A) 20°C (0) 24°C (+) 28°C.
to the progressive evolution of the shear flow into a plug flow, when shear rate is progressively decreased toward the critical shear rate value. By correlating the flow curves with the above mentioned models, at shear rates above the critical shear rate range, in which fluid discontinuity phenomena develop, the best fitting was obtained with the De K&e-Turcotte model, es.(l): z = 7, + ni+i
(1)
where z, (Pa) is the yield stress, nl (Pas) is a viscosity parameter, correlated with the structural state of the material, tl (s) is a time parameter, that may be useful in the study of time-dependent properties of materials. The ASD, for the De Kte-Turcotte model was found to be from two to three orders of magnitude better in comparison with the Herschel-Bulkley and extended Casson models. Thus, all further considerations in this work concern this model only. De K&e-Turcotte model parameters and the relevant ASD values are reported in Table 1 for the full-fat and low-fat yoghurts, at seven temperatures between 4 and 28 “C. An examination of data in Table 1 reveals a singular behaviour of z, with temperature. Indeed, the model gives z, values decreasing with temperature for low-fat yoghurt, whereas for full-fat yoghurt a maximum around 16 or 20°C is indicated. It may be suggested that, in absence of shear, increasing temperatures weakens the structure of the low-fat yoghurt; consequently, z, diminishes. The presence of milk fat inverts this trend up to a certain critical temperature, beyond which the temperature weakening effect on structure prevails. The values of r0 are comparable with those reported by other authors (Ramaswamy & Basak, 1991a, Ramaswamy & Basak, 1991b). Parameters nl and ti display a regular behaviour with the temperature, the former decreasing, as it could be expected, the latter increasing with increasing temperature. Figure 3 shows an extension of the De KCe-Turcotte model in comparison with the relevant experimental data for full fat yoghurt at 4°C and low fat yoghurt at
Rheological
Low-fat
behaviour of low-fat and full-fat
TABLE 1 Parameters and ASD according
and Full-fat Yoghurts: Low-fat yoghurt
8°C 24 “C T” (Pa) 10.035 t, (Pa) nl (Pa. s) 0.155 nl (Pa. s) 11 6) 0.002 003 t1 (s) ASD 0.000 389 ASD 12°C r0 (Pa) nl (Pa. s)
28 “C 9.128 r, (Pa) 0.145 nl (Pa. s) 0.002 191 tl (s) 0.000 406 ASD
tl (s)
ASD 16°C r. (Pa) nr (Pa. s) ?I 6)
For Definition
Model
9.663 0.149 0.002 426 0.000 470
6.772 0.126 0.002 79 1 0.000 325
8°C 24 “C z, (Pa) 8.250 z, (Pa) ql (Pa. s) 0.140 7]1(Pa. s) tl (s) 0.001435 tl (s) ASD 0.000 455 ASD
8.641 0.143 0.002 608 0.000 444
6.633 0.107 0.002 648 0.000 179
12 “C 28 “C z, (Pa) 9.031 z, (Pa) vl (Pa. s) 0.156 7j1(Pa. s) II 6) 0.002 079 fl (s) ASD 0.000 487 ASD
7.0100 0.145 0.003 124 0.000 684
16°C 5, (Pa) 9.632 q (Pa. s) 0.153 II (s) 0.002 241 ASD 0.000 512
8-958 0.144 0.002 468 0~000417
ASD
to De K&e-Turcotte
4°C 20 “C ‘5, (Pa) 7.421 r0 (Pa) nl (Pa. s) 0.155 nl (Pa. s) II 6) 0.001 394 tl (s) ASD 0~000441 ASD
20°C r, (Pa) 7.618 nl (Pa. s) 0.124 0.001 898 t, (s) 0.002 427 0.000 487 ASD 0.000 27 1
tl (s)
665
Full-fat yoghurt
4°C t, (Pa) 10.237 nr (Pa. s) 0.162 ASD
stirred yoghurt
of Parameters
see eq. 1 in text.
IOO-
3
k
le-p .40 .
z g
z
IO
________________------.
2
5
.
. l
.
.+
4
,.-5p
-0-e
T__--
0
0
o
0 0
. 0 0 0
I 0. I
I I
I IO
Shear rate
Fig. 3. Experimental fat yoghurts: LFY,
I 100
I
IO00
(s-l)
flow curves and De Kee-Turcotte model curves for low-fat and full8 “C, experimental (e), model (-). FFY, 4°C experimental (O), model (- - -),
L. De Lorenzi et al
666
8”C, as examples of the model application. The d&continuities in the experimental flow curves around the shear rate of 10 SC’ and the anomalous behaviour at lower shear rates, with regard to that predicted by the De K&e-Turcotte model, are clearly evident. The validity of the De Kee-Turcotte model was ascertained up to 300 s-‘. Oscillatory
flow tests
Tests performed under oscillatory flow conditions are useful tools for the characterization of the viscoelastic properties of materials. Generally, the first step in a routine oscillatory analysis consists in assessing the extension of the linear viscoelastic regime by means of a strain sweep test at constant frequency of oscillation cc). For both low-fat and full-fat yoghurts, no linear viscoelastic region was observed, even at the lowest strain imposed, independently of the applied frequency, as evidenced in Fig. 4. The complex modulus G* clearly decreases with increasing strain. The rate of decrease of G* with y is more pronounced at lower w, and in the low strain range. This seems to suggest that the linear viscoelastic region for both yogurt samples is confined to very low strain values, well beyond the experimental window explored. Moreover, this marked strain sensitivity allows to classify yoghurts as very weakly structured fluids. Nevertheless, in the non-linear region the canonical viscoelastic quantities, such as the complex modulus G* and the phase lag 6, can be still employed as first approximation terms for a comparison among similar systems. In this sense, Fig. 4 shows that the presence of milk fat results only in an increase of the G* values, whatever the strain applied. Temperature variations do not modify the non-linear characteristics of both types of yoghurts. Figure 5 shows that, for the low-fat yoghurt, a temperature
II 0.0 I
I 0.10
I I
I IO
Strain
Fig. 4. Complex modulus G* vs. strain curves for low-fat (LFY) and full-fat (FFY) yoghurts at two different frequencies of oscillation: (m) I %3 rad/s LFY, (0) 6.28 rad/s LFY, (A) 1438 rad/s FFY, (A) 6.28 rad/s FFY.
Rheological
behaviour of low-fat and full-fat
667
stirred yoghurt
IOO-
II
I
0.01
0.10
I
I
I
IO
Strain
Fig. 5. Complex modulus G* vs. strain curves for the low-fat yoghurt at w = 138 rad/s and different temperatures: (W) 4”C, (0) 8”C, (a) 12”C, (0) 16”C, (A) 2O”C, (A) 24°C
and(x)
28°C.
increase leads only to a quantitative downward shifting of the G* curves. Analogous considerations can be extended to the full-fat sample. In order to separate the viscous and elastic contributions to the total stress response of these materials, 6 was plotted vs Jofor both the low-fat and the full-fat yoghurts at different temperatures and at constant frequency o = 6,28 rad s-l. As can be seen from Fig. 6, increasing strain results in a progressive structural
9080 70 60 _ e
50-
cc
4030 20 IO t 01 0.01
I 0.10
I I
I IO
Strain
Fig. 6. Phase lag 6 vs. strain curves for low-fat (LFY) yoghurt and full-fat (FFY) yoghurts
at o = 6.28 rad/s and different tempepratures: (0) 4°C LFY, (0) 12°C LFY, (0) 20°C LY, (a) 28°C LFY, (0) 4°C FFY, (a) 20°C FFY.
L. De Lorenzi et al
668
break-down and, correspondingly, 6 increases, converging to the limiting value of 90”, as expected. By combining the experimental evidence for G* and 6, we may conclude that the imposed strain exerts its major effect on the elastic component G’, which decreases more rapidly than the viscous one G” with the increasing strain. An alternative for the evaluation of the strain amplitude influence on the mechanical response of the systems under investigation may be the analysis of the frequency dependence of the complex modulus. Figure 7 reports the behavior of G* vs. o for both the low-fat and the full-fat samples at 20°C and three different strains. For both yoghurts, doubling y from 12 to 24% results only in a quantitative reduction of the G* values, more marked in the case of the fullfat sample, whereas a ten-fold strain variation (24% + 240%) produces also a net change in the relevant G* profiles. Although all data refer to the nonlinear region, the shapes of the and G* vs. o curves obtained at y = 12 and 24% still resemble those typical of weakly structured materials. On the contrary, S-shaped curves are obtained at very high strains, as a consequence of the strong influence of the amplitude of deformation in the low frequency region. The slight dependence of the phase lag 6 on the frequency w, as depicted in Fig. 8, implies that all the G* - w profiles can be decomposed into two parallel curves of G’ and G” vs. o; once again, this is an evidence that the systems under investigation exhibit features typical of weakly structured materials (Lapasin et al., 1992). Finally, as can be seen in Fig. 9, temperature variations do not modify appreciably the shape of the G* vs. w curves, and only at 28 “C a substantial decrease of the G* values can be observed.
II 0.1
I I
I IO
I 100
Frequency (rad/s) Fig. 7. Complex modulus G* vs. frequency curves for low-fat (LFY) and full-fat (FFY) yoghurts at 20 “C and three different strains: (0) 12% strain LFY, (A) 24% strain LFY, (0) 240% strain LFY, (m) 12% strain WTr (A) 24% strain FFY, (+) 240% strain
Rheological
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669
stirred yoghurt
90 * ++*+s 80 I 70 * 60 ~ h e
50-
Lc 403020 IO01 0.1
I I0
I I
Frequency
I 100
(rad/s)
Fig. 8. Phase lag 6 vs. frequency curves for low-fat (LFY) and full-fat (FFY) yoghurts at 20°C and three different strains: (m) 12% strain LFY, (+) 24% strain LFY, (A) 240% strain LFY, (x) 12% strain FFY, (*) 24% FFY, (+) 240% strain FFY.
2
0
0
oooooooo
&
0 ooooo
loI 0. I
Fig. 9. Complex
modulus
0000
0000
000
00
I
IO
Frequency
100
(radls)
curves for the full-fat yoghurt at y = 12% and (0) 4”C, (0) 12”C, (A) 2O”C, (0) 28°C.
G* vs. frequency
different temperatures
CONCLUSIONS Both full-fat and low-fat yoghurt were found to be pseudoplastic materials with yield value and appreciable elastic components, which were more marked in the full-fat than in the low-fat type.
670
L. De Lorenzi et al.
Discontinuity phenomena were observed in continuous flow experiments, when shear rate was decreased under a certain critical i range. It may be suggested that these phenomena be mainly due to the onset of a plug flow at low shear rates. Fitting continuous flow data to adequate models allowed evaluation of rheological parameters to obtain useful information on the rheological behaviour of the materials. In this context the yield stress z, is of special interest. Indeed, z, brings out the presence of different structural states in full-fat and low-fat yoghurts and the relevant temperature effects. In the oscillatory flow tests no linear viscoelastic region was observed, even at the lowest strains applied. This means that the linear viscoelastic behaviour is confined to very low strains and suggests to classify yoghurt as a weakly structured material. On the basis of the variation of the phase lag 6 with strain, strain sweep tests at first approximation describe the evolution of the material properties, which change from those of a predominantly viscoelastic solid to those of predominantly liquid with elastic components during the test performance. Moreover, strain sweep tests brought out gradual structural weakening with increasing temperature for both yoghurts. Higher values of G* at low strains were obtained for the full-fat yoghurt in comparison with the low-fat yoghurt. The opposite is seen at high strains. For both yoghurts stronger breakdown effects are shown at the lower frequency tested. Frequency sweep tests displayed different behaviours, in dependence on the different strains applied. Although all data refer to the non-linear region, the shape of the G* vs. o at the lower strain and the phase lag 6 dependence on w confirm that yoghurt behaves as a weakly structured material. The structure of the full-fat yoghurt exhibits a larger resistance in comparison to that of the low-fat yoghurt. For both yoghurts progressively increasing temperatures weakened the structure, according to a very regular pattern. ACKNOWLEDGEMENT The authors 60% fund.
wish to acknowledge
the financial
support
from the Italian
MURST
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stirred yoghurt
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