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Simulation of Yoghurt Flow and Prediction of Its End-of-Process Properties Using Rheological Measurements
0960±3085/99/$10.00+0.00 Institution of Chemical Engineers Trans IChemE, Vol 77, Part C, March 1999
SIMULATION OF YOGHURT FLOW AND PREDICTION OF ITS END-OF-PROCESS PROPERTIES USING RHEOLOGICAL MEASUREMENTS Y. S. FANGARY, M. BARIGOU and J. P. K. SEVILLE (FELLOW) School of Chemical Engineering, The University of Birmingham, Edgbaston, UK
Y
oghurt is a rheologically complex material with shear thinning, thixotropic, viscoelastic, and yield stress characteristics. The rheological properties of yoghurt depend on its shear history and, therefore, measurement of equilibrium properties is not suf® cient for process design purposes. Physical processing, which occurs mainly in the form of ¯ ow through the ® nal dispensing line and ® lling head, brings about irreversible changes in the product textural properties. This poses the challenging manufacturing problem of predicting the end-of-process textural properties that are most acceptable to the consumer. This paper proposes a procedure based on simple rheological measurements to predict the effects of yoghurt ¯ ow through pipes and ® lling heads on its end-of-process viscosity and viscoelasticity. The procedure is illustrated using three commercial types of yoghurt. For pipeline design purposes, it is shown that pressure drop can be predicted by using rheological data for an equivalent system that is purely viscous. Keywords: yoghurt; rheology; ¯ ow; viscoelastic properties; gel structure; pressure drop
INTRODUCTION
Yoghurt is a material with shear thinning, thixotropic, viscoelastic, and yield stress characteristics. It has an internal heterogeneous microstructure which results from the interaction of milk proteins and fat molecules (see, for example, Benezech and Maingonnat3 and Steventon et al.4 ). The rheological properties of yoghurt depend on its shear history and, therefore, the measurement of equilibrium properties is not suf® cient for process design purposes. Relatively few studies have addressed the problem of modelling yoghurt ¯ ow and predicting its shearing effects on the ® nal product viscosity and viscoelasticity3 ,5 ,6 . The most successful model to describe the steady-shear rheological behaviour of yoghurt has been the Herschel-Bulkley model:
Yoghurt is a dairy food with complex rheology that depends on temperature, solids concentration and the physical state of fats and proteins present in the milk. An understanding of the rheological properties of yoghurt is important to texture, stability, and process design. Texture is considered one of the four quality attributes of any food material, the other three being ¯ avour, appearance, and nutrition. It is also crucial to consumer acceptability of the product, and is strongly related to the product rheology. The gel structure and ¯ ow properties of yoghurt are the main factors affecting its texture. Sensory evaluation studies of dairy products have shown that correlations do exist between fundamental rheological parameters such as viscosity and gel strength, and sensory textural evaluations such as creaminess and mouthfeel of ¯ uids such as yoghurt1 . Therefore, characterization of the ¯ ow behaviour and gel strength of yoghurt is important for the de® nition and quali® cation of the quality of the product as well as for the design and sizing of process distribution lines. Although the chemistry of yoghurt has been extensively studied, the processing has not. One of the special dif® culties in yoghurt manufacturing is that yoghurt textural properties may from time to time need to be altered in response to a change in consumer perception, which would, consequently, require changes in rheological properties such as viscosity and viscoelasticity. Hence, it is important that manufacturers can predict and control these properties. Tamine and Robinson2 reported that low viscosity is a common manufacturing defect of yoghurt. One of the remedies they proposed is an improvement in the dispensing assembly.
t
to
K Çc n
1
where t is the shear stress in the material, to is the apparent yield stress, K is the consistency factor, n is the ¯ ow behaviour index, and Çc is the shear rate. The apparent yield stress is a useful model property which represents the critical value of shear stress below which the ¯ ow of the material becomes negligible. The existence of an apparent yield stress is generally linked to the existence of an interactive or cross-linked structure that needs to be disintegrated before appreciable ¯ ow can be observed such as in the case of materials with a gel structure. In general, however, its existence is arguable as often rheological measurements cannot be performed at suf® ciently low shear rates to ascertain whether a yield stress exists, or whether the material exhibits extreme shear thinning and a large zero shear viscosity. Physical processing brings about irreversible changes in the product textural and sensoric properties. This poses the 33
34
FANGARY et al.
challenging manufacturing problem of predicting the endof-process textural properties that are most acceptable to the consumer. One of the main areas where yoghurt can incur considerable structural and viscosity decay is the last stage of the manufacturing process when the product is fed through the dispensing assembly line. Figure 1 shows a schematic diagram of a typical industrial yoghurt dispensing assembly line. It consists of a yoghurt buffer tank, pump, transport pipeline and a manifold consisting of a set of ® lling nozzles. During ¯ ow through the pipeline and the ® lling nozzles, the product is subjected to considerable shearing which results in viscosity decay and partial structural breakdown. The question that usually faces the manufacturer is whether at the delivery end of the process the yoghurt will have acceptable textural properties, i.e. the right viscosity and gel strength, and how much of the incurred product structural breakdown is recovered in the pots. Previous attempts to model the transient rheological properties of yoghurt have not produced generalized models as the experimental data and hence the relationships derived tend to be mainly product speci® c. This paper proposes an experimental procedure to simulate the shear history of yoghurt through processing equipment, and provide the process designer with speci® c accurate rheological data to size process lines and predict the end-of-process textural properties of the product.
elasticity parameters and temperature. The effect of temperature on rheological model parameters such as K and n is particularly important. Another characteristic that might be in¯ uenced by temperature is thixotropy. Information on these aspects is important for adequate designs of pumped ¯ ow systems. The experimental procedure proposed here is illustrated for a yoghurt temperature of 20°C. However, when considering the design of a real yoghurt distribution system the procedure must be applied at the actual temperature of the process. Therefore, rheological data must be collected at that particular temperature to enable accurate prediction of the yoghurt end-of-process textural properties and, hence, allow correct design and sizing of process distribution lines. The experimental programme consisted of the following series of tests.
EXPERIMENTAL
The yoghurt dispensing assembly of a manufacturing process is schematically represented in Figure 1. In order to simulate yoghurt ¯ ow through the main pipe of the assembly a constant shear rate was imposed on a yoghurt sample for a period of 10 minutes. This period of time was estimated to be representative of the average residence time of yoghurt ¯ owing in the pipe as informed by the Eden Vale process. The experiment was carried out for a set of shear rate values: 100, 150, 200 and 500 s ± 1 . Following each 10minute shearing period the same sample was immediately subjected to a step change in shear rate, and shearing continued for 1 minute at a higher constant shear rate within the series: 800, 1000, 1100 and 1250 s ± 1 ; hence, a total of 16 shear history curves were determined using a fresh yoghurt sample for each. The second 1-minute shearing test at a higher shear rate was intended to simulate yoghurt ¯ ow through the ® lling nozzles. The values of the shear rates used, i.e. 100±500 s ± 1 and 800±1250 s ± 1 were estimated from the maximum shear rates occurring in real processing conditions. The residence time of yoghurt in the manifold and ® lling nozzle is much shorter than 1 minute, but this was the minimum length of time needed to carry out the experiments. Results showed that the yoghurt viscosity after 1 minute of shearing was only slightly lower than that after approximately 5 seconds which is the estimated time of ¯ ow through the ® lling head. Such small underestimation of the ® nal viscosity will not signi® cantly affect the predictions of the end-of-process properties of the product, and at worst can act as a small safety factor.
Steady-Shear Behaviour The ® rst experiments consisted of characterising the steady-state rheological behaviour of the three yoghurt types considered. Flow curves for the three yoghurt products used were, thus, generated using controlled shear-stress sweeps over the range 0±170 Pa.
Simulation of Shear History The experimental strategy was based on real products and process data acquired from the yoghurt manufacturing process of Eden Vale, Cuddington, UK. Three different yoghurt bases (A, B, and C), differing mainly in the type of culture used to produce them, were supplied by Eden Vale and were used in the experimental programme to simulate yoghurt ¯ ow through the process. Rheological tests were performed using a stress-controlled Carri-Med rheometer CSL-100 with cone and plate geometry (cone angle 2°; cone diameter 4 cm); the gap between the cone and the plate was set at 50 mm. The cone-and-plate geometry has the added advantage of causing less damage to delicate products like yoghurt during loading of the sample than other con® gurations such as coaxial cylinders. The temperature of the rheometer cell was controlled at 20 6 0.1°C. One of the most important aspects of rheological measurement and modelling is the relationship between the viscosity and
Simulation of Structural Breakdown Figure 1. Schematic diagram of ® nal yoghurt dispensing assembly.
During the ® nal stage of the process, i.e. ¯ ow through distribution pipe and ® ttings, the yoghurt viscoelasticity Trans IChemE, Vol 77, Part C, March 1999
SIMULATION OF YOGHURT FLOW USING RHEOLOGICAL MEASUREMENTS
35
deteriorates by a considerable amount, approximately by 35% as measured in this study. Some of this viscoelasticity loss will be recovered in the pots, however. In order to determine the extent of recovery of yoghurt viscoelastic properties after packing, the following procedure was proposed: (i) First, the viscoelastic region was determined by an oscillatory shear sweep using oscillatory shear stress values in the range 0.25 to 10 Pa. All three yoghurt bases started to show a change in viscoelastic properties under a shear stress of approximately 3 Pa. Yoghurt samples were, therefore, subjected to a shear sweep at a frequency of 1 Hz and an applied stress of 0.5 Pa in order to determine the storage modulus, G , in the linear viscoelastic region. The storage modulus represents the elastic (in-phase) component of the yoghurt rheology and can be thought of as the effective gel strength of the yoghurt. Therefore, it can be used to quantify the breakdown of yoghurt structure during the process and its recovery in the pots. This initial dynamic test was performed on all the samples in order to ensure that for a given type of yoghurt (A, B, C) all samples used in the tests had the same G value at the start of the experiment within a ® xed margin of 6 15%; the reference value for this margin of error was taken to be the highest value possible, determined experimentally, for the type of yoghurt under consideration. The lack of reproducibility in the initial G value is mainly attributed to possible structural damage incurred during loading of the test sample on the instrument, which can be minimized by careful handling of the yoghurt but would be very dif® cult to avoid completely. Samples with G values outside this margin of error were discarded. (ii) At the end of the initial oscillatory test the sample was immediately subjected to steady shearing for 3 minutes. The shear rates used were those employed to simulate the shearhistory of the product through the ® lling nozzles, i.e. 800, 1000, 1100 and 1250 s ± 1 . (iii) The steady shearing tests were immediately followed by an oscillatory time sweep for 1 minute, again at a frequency of 1 Hz and an applied stress of 0.5 Pa, to determine the value of the storage modulus and its recovery with time. A 1-minute period was judged to be suf® cient for structural equilibration to have take place since longer test periods did not reveal any further signi® cant recovery in the G value. It is worth noting that in the oscillatory mode the instrument could not be programmed to perform two shearing tests at different shear rates followed by an
Figure 3. Effect of applied shear stress on yoghurt viscosity.
oscillatory test. The instrument can only perform one preshear followed by a dynamic test. Hence, the experimental strategy of a 10-minute shear followed by a 1-minute shear, adopted in the ¯ ow mode for shear-history determination as described in the previous section, could not be repeated to measure structural breakdown under the dynamic mode because of instrument limitation. Experimental measurements, however, con® rmed that a 3-minute shearing period at the high shear rates used was entirely adequate for simulating the cumulative structural breakdown incurred due to yoghurt ¯ ow through both delivery pipe and nozzle. RESULTS AND DISCUSSION Flow Curves of Yoghurt Figure 2 shows the ¯ ow curves generated by the controlled shear-ramp experiments for the three yoghurt bases used. The data are also presented as viscosity-stress curves in Figure 3. Here, it can be clearly seen that yoghurt exhibits a shear-thinning behaviour with an initial region of Newtonian behaviour in which the viscosity is almost constant, followed by a region of decreasing, shear-thinning viscosity spanning several decades of shear stress. The initial zero shear rate viscosity represents the viscosity of the fully structured ¯ uid. The ¯ ow curves were well described by the Herschel-Bulkley model, equation (1), with parameter values as given in Table 1. The apparent yield stress was estimated by extrapolating the ¯ ow curve to zero shear rate. It is worth noting that different methods of yield stress determination may give signi® cantly different values. The yield stress values obtained for the yoghurt bases used were consistent with values reported in the literature7 . Flow effects on Yoghurt Viscosity Typical results of the shear-history simulations, described above, used to determine the viscosity changes in the main transport pipe and the ® lling nozzles are shown in Figure 4.
Table 1. Herschel-Bulkley model parameters for yoghurt bases used.
Figure 2. Flow curves of yoghurt bases A, B, C.
Trans IChemE, Vol 77, Part C, March 1999
Yoghurt type
to (Pa)
K (Pa sn)
n (-)
A B C
14.85 8.15 6.06
3.39 8.57 9.47
0.46 0.34 0.33
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FANGARY et al.
Figure 6. Schematic diagram of oscillatory experiments: (a) oscillatory shear sweep; (b) constant shear-rate ramp; (c) oscillatory time sweep.
Figure 4. Schematic diagram of the consecutive 10-minute and 1-minute constant shear-rate periods.
The curves shown represent the viscosity history of yoghurt when subjected to a 10-minute shear at a given shear rate Çc i , simulating ¯ ow through the delivery pipe, followed by a 1minute shear at a higher shear rate Çc f , simulating ¯ ow through a ® lling nozzle. The results are plotted in Figure 5 in the form of relative viscosity change gf /gi against the ratio of initial to ® nal shear rate, Çc i / Çc f ; where gi is the initial viscosity of the original yoghurt sample at the start of the experiment, i.e. at time zero, which would correspond to the viscosity of yoghurt entering the delivery pipe in Figure 1. This initial viscosity can be obtained from the ¯ ow curve as represented by the rheological model of the yoghurt, i.e. equation (1), at shear rate Çc i . The parameter gf represents the ® nal viscosity value measured at the end of the experiment, and would correspond to the end-of-process viscosity of yoghurt as it exists from the ® lling nozzle. It must be pointed out that gf cannot be estimated from the ¯ ow curve as represented by equation (1) because of thixotropic effects induced by an appreciable residence time in the dispensing line. The results in Figure 5 were ® tted by the following correlation gf
0.70 gi
Çc i Çc f
0.6
conditions and the types of yoghurt used here and is, therefore, not general. However, similar correlations could be developed for other situations. Flow Effects on Yoghurt Structure The experimental strategy, described in the previous section on simulation of structural breakdown, to determine the effects of ¯ ow on the viscoelastic properties of yoghurt is schematically represented in Figure 6. The experimental measurements are used to determine the extent of structural damage measured by the decay in the storage modulus G after the yoghurt has been subjected to shearing equivalent to that occurring in the dispensing line, and the extent of structural recovery once shearing has ceased. Figure 7 shows the relationship between the intensity of shearing and the percentage loss in G after a 1-minute time sweep; the percentage loss is de® ned as: % loss
G ver G f G ver
3
where, G ver is the maximum G value of unsheared yoghurt in the viscoelastic region, and G f is the value of G after a 1minute time sweep immediately following shearing. The value G f would in practice give a measure of the gel strength of yoghurt in the pots. Figure 7 shows, as expected, that the % loss in the G value increases as a function of shear rate.
2 Pressure Drop Prediction
As the ® nal shear rate cÇ f is known, equation (2) can be used to predict the ® nal product viscosity gf . It is important to note that equation (2) applies to the speci® c experimental
In order to determine the pumping requirements for any ¯ uid, it is necessary to know the pressure drop through the ¯ ow system for a given ¯ ow rate. Rheological properties
Figure 5. Effect of shear history on ® nal yoghurt viscosity.
Figure 7. Percentage loss in storage modulus as a function of applied shear rate.
Trans IChemE, Vol 77, Part C, March 1999
SIMULATION OF YOGHURT FLOW USING RHEOLOGICAL MEASUREMENTS
have a strong in¯ uence on the calculations and this information is needed to select optimum pipe diameters and to size pumps. The standard treatment of this subject can be found in various textbooks. The main non-Newtonian pressure-drop prediction models have been reviewed by Holdsworth7 . The following assumptions are usually implicit in the development of such mathematical models: ¯ ow is viscous and steady, ¯ uid is incompressible, end effects are negligible, ¯ uid properties are not a function of pressure or time, ¯ ow is isothermal, and no slip occurs at the walls. For a non-time dependent ¯ uid whose rheological behaviour can be described by the Herschel-Bulkley model, equation (1), the volumetric ¯ ow rate and pressure drop in a pipe of circular cross section are related by the exact expression7 :
37
solution. For yoghurt type A, for example, as shown in Figure 8, most points fall on the ¯ ow curve corresponding to the 1 wt% CMC solution. It is, thus, possible to calculate the pressure drop in yoghurt pipe ¯ ow using rheological data, i.e. K, n values, for a CMC solution of an appropriate concentration. For a power law ¯ uid such as CMC, the exact equation relating pressure drop to volumetric ¯ ow rate is7 : Q
p R3
n 3n
1
RDP 2LK
1/n
6
Referring to Figure 4, the viscosity values on the yoghurt shear-history curve corresponding to point N, marking the end of the 10-minute shearing period, are plotted against their corresponding shear rate values in Figure 8. Here, it can be seen that the viscosity of yoghurt at a given shear rate can be matched by the viscosity of some appropriate CMC
Although equation (6) is an exact solution for a power law ¯ uid, it was decided to test it experimentally in order to check its ability to predict pressure drop in a real industrial environment. Flow experiments were performed with CMC solutions of different concentrations (0.7, 0.85, 1 wt%) in a straight horizontal pipe of internal diameter 21.2 mm and 6 m length . A galvanized steel pipe was chosen because of its relatively rough surface to minimize slip at the wall. A positive displacement pump was used to drive the ¯ uid through the pipe, and the ¯ ow rate was measured by stopwatch and bucket. Equation (6) assumes conditions of fully developed ¯ ow and, hence, the pipe was designed so that the distance from the entrance of the pipe to the ® rst pressure tapping was 2.54 m, which is signi® cantly longer than the 100 pipe-diameter length usually recommended for the establishment of fully developed laminar ¯ ow. Pressure drop was measured using a U-tube differential mercury manometer over a pipe length of 2.69 m, leaving a distance of 0.77 m between the downstream pressure tapping and the pipe outlet. The other conditions of laminar, steady, and isothermal ¯ ow were also satis® ed. Equation (6) was used in conjunction with the rheological data, i.e. K, n values, determined for the CMC solutions from cone-and-plate viscometry as shown in Figure 8, to predict the pressure drop in this experimental set-up. The theoretical predictions are compared to the experimental pressure drop measurements in Figure 9. The predictions are within an error margin of 10% for all the CMC solutions employed. Consequently, equation (6) can be safely used to predict pressure drop in pipeline design provided reasonable precautions are taken to ensure that the assumptions upon which its derivation is based are ful® lled.
Figure 8. Matching of yoghurt viscosity with viscosity of CMC solutions.
Figure 9. Experimental validation of equation (6).
Q
pR3 t K 1/n t3w w 2n
to
2n2 1 3n
1 n
n
1
3n 1
tw t o
1
t2w
2n
2n3 1 3n 1 n
1
t2o 4
where L is the length of the pipe, R is the pipe radius, to is the apparent yield stress of the material, tw is the shear stress at the pipe wall, and K and n are the Herschel-Bulkley model parameters as given in equation (1). This equation, however, cannot be applied to the ¯ ow of yoghurt because thixotropic effects are important. An alternative approach would be to simulate the ¯ ow of yoghurt by that of a purely viscous system. Carboxymethylcellulose was chosen for such a purpose and ¯ ow curves were determined, as shown in Figure 8, for solutions of different concentrations (0.7, 0.85, 1 wt%) using the cone-and-plate viscometer. The curves obtained were well represented by the simple power law model: t
K cÇ n
Trans IChemE, Vol 77, Part C, March 1999
5
38
FANGARY et al.
the viscosity and viscoelasticity. Both of these properties are strongly dependent on the shear history of the material and are adversely affected by ¯ ow through the dispensing and packing assembly at the end of the manufacturing process. The ability to predict the end-of-process values of such textural properties is very important for an optimum design of the process and for achieving product textural properties that are most acceptable to the consumer. A procedure based on simple rheological measurements to predict the effects of yoghurt ¯ ow through pipes and ® lling heads on its end-of-process viscosity and viscoelasticity has been proposed and illustrated using three commercial types of yoghurt. By measuring the shear history of yoghurt samples in a viscometer over a range of shear rates and periods of time that are consistent with conditions prevailing in a real process, the end-of-process viscosity of the product could be predicted. The viscoelasticity of the product at the end of the process and the extent of its structural recovery in the pots could also be predicted by simple oscillatory tests. For pipeline design calculations, the time-dependency effects of yoghurt were successfully circumvented by using rheological data for a purely viscous carboxymethylcellulose solution of appropriate concentration.
NOMENCLATURE
Figure 10. Design procedure of yoghurt dispensing assembly line.
In addition to equation (6), a formula is also required for estimating the shear rate range needed to determine the rheological data required for pipeline design calculations. These estimations should be based on the maximum shear rate in the ¯ uid, i.e. the shear rate at the wall. The shear rate at the wall of a pipe can be readily derived for a power law ¯ uid by noting that the wall shear stress is given by tw K Çc nw DPR/2L, and writing equation (6) in terms of the de® nition of a power law ¯ uid, thus: cÇ w
3n 1 4n
4Q pR3
G K L n P DP Q R
storage modulus, Pa ¯ ow consistency index, Pa sn pipe length, m ¯ ow behaviour index, pressure, Pa pressure drop, Pa volumetric ¯ ow rate, m3s ±1 pipe radius, m
Greek g Çc Çc w t t0 tw
letters viscosity, Pa s shear rate, s ±1 wall shear rate, s ±1 shear stress, Pa yield stress, Pa wall shear stress, Pa
Subscripts f ® nal i initial ver viscoelastic region
REFERENCES
7
The entire procedure described in this paper, for designing a pipeline system dispensing yoghurt to a ® lling head assembly and predicting the product end-of-process properties by using small scale rheological measurements, is summarized in the ¯ ow chart of Figure 10. CONCLUSIONS The rheological properties of yoghurt which are important from the viewpoint of consumer acceptability are
1. Shoemaker, C. F., Nantz, J, Bonnans, S., and Noble, A. C., 1992, Rheological characterisation of dairy products, Food Technology, January: 98±104. 2. Tamine, A. Y. and Robinson, R. K., 1985, Yoghurt: Science and Technology (Pergamon Press, Oxford). 3. Benzech, T. and Maingonnat, J. F., 1994, Characterization of the rheological properties of yoghurt- a review, Journal of Food Engineering, 21: 447±472. 4. Steventon, A. J., Parkinson, C. J., Fryer, P. J. and Bottomley, R. C., 1990, The rheology of yoghurt, in Rheology of Food, Pharmaceutical and Biological Materials With General Rheology, Carter, R. E. (ed) (Elsevier Applied Science), pp. 196±210. 5. Basak, S. and Ramaswamy, H. S., 1994, Simultaneous evaluation of shear rate and time dependency of stirred yoghurt as in¯ uenced by added pectin and strawberry concentrate, Journal of Food Engineering, 21: 385±393.
Trans IChemE, Vol 77, Part C, March 1999
SIMULATION OF YOGHURT FLOW USING RHEOLOGICAL MEASUREMENTS 6. Chan Man Fong, C. F., Turcotte, G. and De Kee, D., 1996, Modelling steady and transient rheological properties, Journal of Food Engineering, 27: 63±70. 7. Holdsworth, S. D., 1993, Rheological models used for the prediction of the ¯ ow properties of food products: a literature review, Trans IChemE, Part C, Food Bioprod Proc 71:(C3): 139±179.
ACKNOWLEDGEMENT YSF’ s PhD work is funded as part of a DTI MAFF LINK scheme on food mixing in collaboration with Campden Food and Drink Research
Trans IChemE, Vol 77, Part C, March 1999
39
Association. The collaboration of Eden Vale, one of the LINK project partners, is particularly acknowledged.
ADDRESS Correspondence about this paper should be addressed to Dr M. Barigou, School of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK. The manuscript was received 1 July 1998 and accepted for publication after revision 3 November 1998.
SIMULATION OF YOGHURT FLOW AND PREDICTION OF ITS END-OF-PROCESS PROPERTIES USING RHEOLOGICAL MEASUREMENTS Y. S. FANGARY, M. BARIGOU and J. P. K. SEVILLE (FELLOW) School of Chemical Engineering, The University of Birmingham, Edgbaston, UK
Y
oghurt is a rheologically complex material with shear thinning, thixotropic, viscoelastic, and yield stress characteristics. The rheological properties of yoghurt depend on its shear history and, therefore, measurement of equilibrium properties is not suf® cient for process design purposes. Physical processing, which occurs mainly in the form of ¯ ow through the ® nal dispensing line and ® lling head, brings about irreversible changes in the product textural properties. This poses the challenging manufacturing problem of predicting the end-of-process textural properties that are most acceptable to the consumer. This paper proposes a procedure based on simple rheological measurements to predict the effects of yoghurt ¯ ow through pipes and ® lling heads on its end-of-process viscosity and viscoelasticity. The procedure is illustrated using three commercial types of yoghurt. For pipeline design purposes, it is shown that pressure drop can be predicted by using rheological data for an equivalent system that is purely viscous. Keywords: yoghurt; rheology; ¯ ow; viscoelastic properties; gel structure; pressure drop
INTRODUCTION
Yoghurt is a material with shear thinning, thixotropic, viscoelastic, and yield stress characteristics. It has an internal heterogeneous microstructure which results from the interaction of milk proteins and fat molecules (see, for example, Benezech and Maingonnat3 and Steventon et al.4 ). The rheological properties of yoghurt depend on its shear history and, therefore, the measurement of equilibrium properties is not suf® cient for process design purposes. Relatively few studies have addressed the problem of modelling yoghurt ¯ ow and predicting its shearing effects on the ® nal product viscosity and viscoelasticity3 ,5 ,6 . The most successful model to describe the steady-shear rheological behaviour of yoghurt has been the Herschel-Bulkley model:
Yoghurt is a dairy food with complex rheology that depends on temperature, solids concentration and the physical state of fats and proteins present in the milk. An understanding of the rheological properties of yoghurt is important to texture, stability, and process design. Texture is considered one of the four quality attributes of any food material, the other three being ¯ avour, appearance, and nutrition. It is also crucial to consumer acceptability of the product, and is strongly related to the product rheology. The gel structure and ¯ ow properties of yoghurt are the main factors affecting its texture. Sensory evaluation studies of dairy products have shown that correlations do exist between fundamental rheological parameters such as viscosity and gel strength, and sensory textural evaluations such as creaminess and mouthfeel of ¯ uids such as yoghurt1 . Therefore, characterization of the ¯ ow behaviour and gel strength of yoghurt is important for the de® nition and quali® cation of the quality of the product as well as for the design and sizing of process distribution lines. Although the chemistry of yoghurt has been extensively studied, the processing has not. One of the special dif® culties in yoghurt manufacturing is that yoghurt textural properties may from time to time need to be altered in response to a change in consumer perception, which would, consequently, require changes in rheological properties such as viscosity and viscoelasticity. Hence, it is important that manufacturers can predict and control these properties. Tamine and Robinson2 reported that low viscosity is a common manufacturing defect of yoghurt. One of the remedies they proposed is an improvement in the dispensing assembly.
t
to
K Çc n
1
where t is the shear stress in the material, to is the apparent yield stress, K is the consistency factor, n is the ¯ ow behaviour index, and Çc is the shear rate. The apparent yield stress is a useful model property which represents the critical value of shear stress below which the ¯ ow of the material becomes negligible. The existence of an apparent yield stress is generally linked to the existence of an interactive or cross-linked structure that needs to be disintegrated before appreciable ¯ ow can be observed such as in the case of materials with a gel structure. In general, however, its existence is arguable as often rheological measurements cannot be performed at suf® ciently low shear rates to ascertain whether a yield stress exists, or whether the material exhibits extreme shear thinning and a large zero shear viscosity. Physical processing brings about irreversible changes in the product textural and sensoric properties. This poses the 33
34
FANGARY et al.
challenging manufacturing problem of predicting the endof-process textural properties that are most acceptable to the consumer. One of the main areas where yoghurt can incur considerable structural and viscosity decay is the last stage of the manufacturing process when the product is fed through the dispensing assembly line. Figure 1 shows a schematic diagram of a typical industrial yoghurt dispensing assembly line. It consists of a yoghurt buffer tank, pump, transport pipeline and a manifold consisting of a set of ® lling nozzles. During ¯ ow through the pipeline and the ® lling nozzles, the product is subjected to considerable shearing which results in viscosity decay and partial structural breakdown. The question that usually faces the manufacturer is whether at the delivery end of the process the yoghurt will have acceptable textural properties, i.e. the right viscosity and gel strength, and how much of the incurred product structural breakdown is recovered in the pots. Previous attempts to model the transient rheological properties of yoghurt have not produced generalized models as the experimental data and hence the relationships derived tend to be mainly product speci® c. This paper proposes an experimental procedure to simulate the shear history of yoghurt through processing equipment, and provide the process designer with speci® c accurate rheological data to size process lines and predict the end-of-process textural properties of the product.
elasticity parameters and temperature. The effect of temperature on rheological model parameters such as K and n is particularly important. Another characteristic that might be in¯ uenced by temperature is thixotropy. Information on these aspects is important for adequate designs of pumped ¯ ow systems. The experimental procedure proposed here is illustrated for a yoghurt temperature of 20°C. However, when considering the design of a real yoghurt distribution system the procedure must be applied at the actual temperature of the process. Therefore, rheological data must be collected at that particular temperature to enable accurate prediction of the yoghurt end-of-process textural properties and, hence, allow correct design and sizing of process distribution lines. The experimental programme consisted of the following series of tests.
EXPERIMENTAL
The yoghurt dispensing assembly of a manufacturing process is schematically represented in Figure 1. In order to simulate yoghurt ¯ ow through the main pipe of the assembly a constant shear rate was imposed on a yoghurt sample for a period of 10 minutes. This period of time was estimated to be representative of the average residence time of yoghurt ¯ owing in the pipe as informed by the Eden Vale process. The experiment was carried out for a set of shear rate values: 100, 150, 200 and 500 s ± 1 . Following each 10minute shearing period the same sample was immediately subjected to a step change in shear rate, and shearing continued for 1 minute at a higher constant shear rate within the series: 800, 1000, 1100 and 1250 s ± 1 ; hence, a total of 16 shear history curves were determined using a fresh yoghurt sample for each. The second 1-minute shearing test at a higher shear rate was intended to simulate yoghurt ¯ ow through the ® lling nozzles. The values of the shear rates used, i.e. 100±500 s ± 1 and 800±1250 s ± 1 were estimated from the maximum shear rates occurring in real processing conditions. The residence time of yoghurt in the manifold and ® lling nozzle is much shorter than 1 minute, but this was the minimum length of time needed to carry out the experiments. Results showed that the yoghurt viscosity after 1 minute of shearing was only slightly lower than that after approximately 5 seconds which is the estimated time of ¯ ow through the ® lling head. Such small underestimation of the ® nal viscosity will not signi® cantly affect the predictions of the end-of-process properties of the product, and at worst can act as a small safety factor.
Steady-Shear Behaviour The ® rst experiments consisted of characterising the steady-state rheological behaviour of the three yoghurt types considered. Flow curves for the three yoghurt products used were, thus, generated using controlled shear-stress sweeps over the range 0±170 Pa.
Simulation of Shear History The experimental strategy was based on real products and process data acquired from the yoghurt manufacturing process of Eden Vale, Cuddington, UK. Three different yoghurt bases (A, B, and C), differing mainly in the type of culture used to produce them, were supplied by Eden Vale and were used in the experimental programme to simulate yoghurt ¯ ow through the process. Rheological tests were performed using a stress-controlled Carri-Med rheometer CSL-100 with cone and plate geometry (cone angle 2°; cone diameter 4 cm); the gap between the cone and the plate was set at 50 mm. The cone-and-plate geometry has the added advantage of causing less damage to delicate products like yoghurt during loading of the sample than other con® gurations such as coaxial cylinders. The temperature of the rheometer cell was controlled at 20 6 0.1°C. One of the most important aspects of rheological measurement and modelling is the relationship between the viscosity and
Simulation of Structural Breakdown Figure 1. Schematic diagram of ® nal yoghurt dispensing assembly.
During the ® nal stage of the process, i.e. ¯ ow through distribution pipe and ® ttings, the yoghurt viscoelasticity Trans IChemE, Vol 77, Part C, March 1999
SIMULATION OF YOGHURT FLOW USING RHEOLOGICAL MEASUREMENTS
35
deteriorates by a considerable amount, approximately by 35% as measured in this study. Some of this viscoelasticity loss will be recovered in the pots, however. In order to determine the extent of recovery of yoghurt viscoelastic properties after packing, the following procedure was proposed: (i) First, the viscoelastic region was determined by an oscillatory shear sweep using oscillatory shear stress values in the range 0.25 to 10 Pa. All three yoghurt bases started to show a change in viscoelastic properties under a shear stress of approximately 3 Pa. Yoghurt samples were, therefore, subjected to a shear sweep at a frequency of 1 Hz and an applied stress of 0.5 Pa in order to determine the storage modulus, G , in the linear viscoelastic region. The storage modulus represents the elastic (in-phase) component of the yoghurt rheology and can be thought of as the effective gel strength of the yoghurt. Therefore, it can be used to quantify the breakdown of yoghurt structure during the process and its recovery in the pots. This initial dynamic test was performed on all the samples in order to ensure that for a given type of yoghurt (A, B, C) all samples used in the tests had the same G value at the start of the experiment within a ® xed margin of 6 15%; the reference value for this margin of error was taken to be the highest value possible, determined experimentally, for the type of yoghurt under consideration. The lack of reproducibility in the initial G value is mainly attributed to possible structural damage incurred during loading of the test sample on the instrument, which can be minimized by careful handling of the yoghurt but would be very dif® cult to avoid completely. Samples with G values outside this margin of error were discarded. (ii) At the end of the initial oscillatory test the sample was immediately subjected to steady shearing for 3 minutes. The shear rates used were those employed to simulate the shearhistory of the product through the ® lling nozzles, i.e. 800, 1000, 1100 and 1250 s ± 1 . (iii) The steady shearing tests were immediately followed by an oscillatory time sweep for 1 minute, again at a frequency of 1 Hz and an applied stress of 0.5 Pa, to determine the value of the storage modulus and its recovery with time. A 1-minute period was judged to be suf® cient for structural equilibration to have take place since longer test periods did not reveal any further signi® cant recovery in the G value. It is worth noting that in the oscillatory mode the instrument could not be programmed to perform two shearing tests at different shear rates followed by an
Figure 3. Effect of applied shear stress on yoghurt viscosity.
oscillatory test. The instrument can only perform one preshear followed by a dynamic test. Hence, the experimental strategy of a 10-minute shear followed by a 1-minute shear, adopted in the ¯ ow mode for shear-history determination as described in the previous section, could not be repeated to measure structural breakdown under the dynamic mode because of instrument limitation. Experimental measurements, however, con® rmed that a 3-minute shearing period at the high shear rates used was entirely adequate for simulating the cumulative structural breakdown incurred due to yoghurt ¯ ow through both delivery pipe and nozzle. RESULTS AND DISCUSSION Flow Curves of Yoghurt Figure 2 shows the ¯ ow curves generated by the controlled shear-ramp experiments for the three yoghurt bases used. The data are also presented as viscosity-stress curves in Figure 3. Here, it can be clearly seen that yoghurt exhibits a shear-thinning behaviour with an initial region of Newtonian behaviour in which the viscosity is almost constant, followed by a region of decreasing, shear-thinning viscosity spanning several decades of shear stress. The initial zero shear rate viscosity represents the viscosity of the fully structured ¯ uid. The ¯ ow curves were well described by the Herschel-Bulkley model, equation (1), with parameter values as given in Table 1. The apparent yield stress was estimated by extrapolating the ¯ ow curve to zero shear rate. It is worth noting that different methods of yield stress determination may give signi® cantly different values. The yield stress values obtained for the yoghurt bases used were consistent with values reported in the literature7 . Flow effects on Yoghurt Viscosity Typical results of the shear-history simulations, described above, used to determine the viscosity changes in the main transport pipe and the ® lling nozzles are shown in Figure 4.
Table 1. Herschel-Bulkley model parameters for yoghurt bases used.
Figure 2. Flow curves of yoghurt bases A, B, C.
Trans IChemE, Vol 77, Part C, March 1999
Yoghurt type
to (Pa)
K (Pa sn)
n (-)
A B C
14.85 8.15 6.06
3.39 8.57 9.47
0.46 0.34 0.33
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FANGARY et al.
Figure 6. Schematic diagram of oscillatory experiments: (a) oscillatory shear sweep; (b) constant shear-rate ramp; (c) oscillatory time sweep.
Figure 4. Schematic diagram of the consecutive 10-minute and 1-minute constant shear-rate periods.
The curves shown represent the viscosity history of yoghurt when subjected to a 10-minute shear at a given shear rate Çc i , simulating ¯ ow through the delivery pipe, followed by a 1minute shear at a higher shear rate Çc f , simulating ¯ ow through a ® lling nozzle. The results are plotted in Figure 5 in the form of relative viscosity change gf /gi against the ratio of initial to ® nal shear rate, Çc i / Çc f ; where gi is the initial viscosity of the original yoghurt sample at the start of the experiment, i.e. at time zero, which would correspond to the viscosity of yoghurt entering the delivery pipe in Figure 1. This initial viscosity can be obtained from the ¯ ow curve as represented by the rheological model of the yoghurt, i.e. equation (1), at shear rate Çc i . The parameter gf represents the ® nal viscosity value measured at the end of the experiment, and would correspond to the end-of-process viscosity of yoghurt as it exists from the ® lling nozzle. It must be pointed out that gf cannot be estimated from the ¯ ow curve as represented by equation (1) because of thixotropic effects induced by an appreciable residence time in the dispensing line. The results in Figure 5 were ® tted by the following correlation gf
0.70 gi
Çc i Çc f
0.6
conditions and the types of yoghurt used here and is, therefore, not general. However, similar correlations could be developed for other situations. Flow Effects on Yoghurt Structure The experimental strategy, described in the previous section on simulation of structural breakdown, to determine the effects of ¯ ow on the viscoelastic properties of yoghurt is schematically represented in Figure 6. The experimental measurements are used to determine the extent of structural damage measured by the decay in the storage modulus G after the yoghurt has been subjected to shearing equivalent to that occurring in the dispensing line, and the extent of structural recovery once shearing has ceased. Figure 7 shows the relationship between the intensity of shearing and the percentage loss in G after a 1-minute time sweep; the percentage loss is de® ned as: % loss
G ver G f G ver
3
where, G ver is the maximum G value of unsheared yoghurt in the viscoelastic region, and G f is the value of G after a 1minute time sweep immediately following shearing. The value G f would in practice give a measure of the gel strength of yoghurt in the pots. Figure 7 shows, as expected, that the % loss in the G value increases as a function of shear rate.
2 Pressure Drop Prediction
As the ® nal shear rate cÇ f is known, equation (2) can be used to predict the ® nal product viscosity gf . It is important to note that equation (2) applies to the speci® c experimental
In order to determine the pumping requirements for any ¯ uid, it is necessary to know the pressure drop through the ¯ ow system for a given ¯ ow rate. Rheological properties
Figure 5. Effect of shear history on ® nal yoghurt viscosity.
Figure 7. Percentage loss in storage modulus as a function of applied shear rate.
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SIMULATION OF YOGHURT FLOW USING RHEOLOGICAL MEASUREMENTS
have a strong in¯ uence on the calculations and this information is needed to select optimum pipe diameters and to size pumps. The standard treatment of this subject can be found in various textbooks. The main non-Newtonian pressure-drop prediction models have been reviewed by Holdsworth7 . The following assumptions are usually implicit in the development of such mathematical models: ¯ ow is viscous and steady, ¯ uid is incompressible, end effects are negligible, ¯ uid properties are not a function of pressure or time, ¯ ow is isothermal, and no slip occurs at the walls. For a non-time dependent ¯ uid whose rheological behaviour can be described by the Herschel-Bulkley model, equation (1), the volumetric ¯ ow rate and pressure drop in a pipe of circular cross section are related by the exact expression7 :
37
solution. For yoghurt type A, for example, as shown in Figure 8, most points fall on the ¯ ow curve corresponding to the 1 wt% CMC solution. It is, thus, possible to calculate the pressure drop in yoghurt pipe ¯ ow using rheological data, i.e. K, n values, for a CMC solution of an appropriate concentration. For a power law ¯ uid such as CMC, the exact equation relating pressure drop to volumetric ¯ ow rate is7 : Q
p R3
n 3n
1
RDP 2LK
1/n
6
Referring to Figure 4, the viscosity values on the yoghurt shear-history curve corresponding to point N, marking the end of the 10-minute shearing period, are plotted against their corresponding shear rate values in Figure 8. Here, it can be seen that the viscosity of yoghurt at a given shear rate can be matched by the viscosity of some appropriate CMC
Although equation (6) is an exact solution for a power law ¯ uid, it was decided to test it experimentally in order to check its ability to predict pressure drop in a real industrial environment. Flow experiments were performed with CMC solutions of different concentrations (0.7, 0.85, 1 wt%) in a straight horizontal pipe of internal diameter 21.2 mm and 6 m length . A galvanized steel pipe was chosen because of its relatively rough surface to minimize slip at the wall. A positive displacement pump was used to drive the ¯ uid through the pipe, and the ¯ ow rate was measured by stopwatch and bucket. Equation (6) assumes conditions of fully developed ¯ ow and, hence, the pipe was designed so that the distance from the entrance of the pipe to the ® rst pressure tapping was 2.54 m, which is signi® cantly longer than the 100 pipe-diameter length usually recommended for the establishment of fully developed laminar ¯ ow. Pressure drop was measured using a U-tube differential mercury manometer over a pipe length of 2.69 m, leaving a distance of 0.77 m between the downstream pressure tapping and the pipe outlet. The other conditions of laminar, steady, and isothermal ¯ ow were also satis® ed. Equation (6) was used in conjunction with the rheological data, i.e. K, n values, determined for the CMC solutions from cone-and-plate viscometry as shown in Figure 8, to predict the pressure drop in this experimental set-up. The theoretical predictions are compared to the experimental pressure drop measurements in Figure 9. The predictions are within an error margin of 10% for all the CMC solutions employed. Consequently, equation (6) can be safely used to predict pressure drop in pipeline design provided reasonable precautions are taken to ensure that the assumptions upon which its derivation is based are ful® lled.
Figure 8. Matching of yoghurt viscosity with viscosity of CMC solutions.
Figure 9. Experimental validation of equation (6).
Q
pR3 t K 1/n t3w w 2n
to
2n2 1 3n
1 n
n
1
3n 1
tw t o
1
t2w
2n
2n3 1 3n 1 n
1
t2o 4
where L is the length of the pipe, R is the pipe radius, to is the apparent yield stress of the material, tw is the shear stress at the pipe wall, and K and n are the Herschel-Bulkley model parameters as given in equation (1). This equation, however, cannot be applied to the ¯ ow of yoghurt because thixotropic effects are important. An alternative approach would be to simulate the ¯ ow of yoghurt by that of a purely viscous system. Carboxymethylcellulose was chosen for such a purpose and ¯ ow curves were determined, as shown in Figure 8, for solutions of different concentrations (0.7, 0.85, 1 wt%) using the cone-and-plate viscometer. The curves obtained were well represented by the simple power law model: t
K cÇ n
Trans IChemE, Vol 77, Part C, March 1999
5
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FANGARY et al.
the viscosity and viscoelasticity. Both of these properties are strongly dependent on the shear history of the material and are adversely affected by ¯ ow through the dispensing and packing assembly at the end of the manufacturing process. The ability to predict the end-of-process values of such textural properties is very important for an optimum design of the process and for achieving product textural properties that are most acceptable to the consumer. A procedure based on simple rheological measurements to predict the effects of yoghurt ¯ ow through pipes and ® lling heads on its end-of-process viscosity and viscoelasticity has been proposed and illustrated using three commercial types of yoghurt. By measuring the shear history of yoghurt samples in a viscometer over a range of shear rates and periods of time that are consistent with conditions prevailing in a real process, the end-of-process viscosity of the product could be predicted. The viscoelasticity of the product at the end of the process and the extent of its structural recovery in the pots could also be predicted by simple oscillatory tests. For pipeline design calculations, the time-dependency effects of yoghurt were successfully circumvented by using rheological data for a purely viscous carboxymethylcellulose solution of appropriate concentration.
NOMENCLATURE
Figure 10. Design procedure of yoghurt dispensing assembly line.
In addition to equation (6), a formula is also required for estimating the shear rate range needed to determine the rheological data required for pipeline design calculations. These estimations should be based on the maximum shear rate in the ¯ uid, i.e. the shear rate at the wall. The shear rate at the wall of a pipe can be readily derived for a power law ¯ uid by noting that the wall shear stress is given by tw K Çc nw DPR/2L, and writing equation (6) in terms of the de® nition of a power law ¯ uid, thus: cÇ w
3n 1 4n
4Q pR3
G K L n P DP Q R
storage modulus, Pa ¯ ow consistency index, Pa sn pipe length, m ¯ ow behaviour index, pressure, Pa pressure drop, Pa volumetric ¯ ow rate, m3s ±1 pipe radius, m
Greek g Çc Çc w t t0 tw
letters viscosity, Pa s shear rate, s ±1 wall shear rate, s ±1 shear stress, Pa yield stress, Pa wall shear stress, Pa
Subscripts f ® nal i initial ver viscoelastic region
REFERENCES
7
The entire procedure described in this paper, for designing a pipeline system dispensing yoghurt to a ® lling head assembly and predicting the product end-of-process properties by using small scale rheological measurements, is summarized in the ¯ ow chart of Figure 10. CONCLUSIONS The rheological properties of yoghurt which are important from the viewpoint of consumer acceptability are
1. Shoemaker, C. F., Nantz, J, Bonnans, S., and Noble, A. C., 1992, Rheological characterisation of dairy products, Food Technology, January: 98±104. 2. Tamine, A. Y. and Robinson, R. K., 1985, Yoghurt: Science and Technology (Pergamon Press, Oxford). 3. Benzech, T. and Maingonnat, J. F., 1994, Characterization of the rheological properties of yoghurt- a review, Journal of Food Engineering, 21: 447±472. 4. Steventon, A. J., Parkinson, C. J., Fryer, P. J. and Bottomley, R. C., 1990, The rheology of yoghurt, in Rheology of Food, Pharmaceutical and Biological Materials With General Rheology, Carter, R. E. (ed) (Elsevier Applied Science), pp. 196±210. 5. Basak, S. and Ramaswamy, H. S., 1994, Simultaneous evaluation of shear rate and time dependency of stirred yoghurt as in¯ uenced by added pectin and strawberry concentrate, Journal of Food Engineering, 21: 385±393.
Trans IChemE, Vol 77, Part C, March 1999
SIMULATION OF YOGHURT FLOW USING RHEOLOGICAL MEASUREMENTS 6. Chan Man Fong, C. F., Turcotte, G. and De Kee, D., 1996, Modelling steady and transient rheological properties, Journal of Food Engineering, 27: 63±70. 7. Holdsworth, S. D., 1993, Rheological models used for the prediction of the ¯ ow properties of food products: a literature review, Trans IChemE, Part C, Food Bioprod Proc 71:(C3): 139±179.
ACKNOWLEDGEMENT YSF’ s PhD work is funded as part of a DTI MAFF LINK scheme on food mixing in collaboration with Campden Food and Drink Research
Trans IChemE, Vol 77, Part C, March 1999
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Association. The collaboration of Eden Vale, one of the LINK project partners, is particularly acknowledged.
ADDRESS Correspondence about this paper should be addressed to Dr M. Barigou, School of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK. The manuscript was received 1 July 1998 and accepted for publication after revision 3 November 1998.