- Email: [email protected]
Modelling the time-dependent rheological behavior of semisolid foodstuffs
Journal of Food Engineering 57 (2003) 97–102 www.elsevier.com/locate/jfoodeng
Modelling the time-dependent rheological behavior of semisolid foodstuffs Basim Abu-Jdayil
*
Department of Chemical Engineering, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan Received 15 February 2002; accepted 27 May 2002
Abstract Many of food products exhibited the thixotropic behavior, in which, the apparent viscosity of material decreases with time of shearing at constant shear rate. The structural kinetic model (SKM) was used to characterize the thixotropic behavior of three different kinds of food products. Foods selected for analysis represent the fluid and semisolid food materials. They include milled sesame, concentrated yogurt and mayonnaise. The SKM postulates that the change in the rheological behavior is associated with shear-induced breakdown of the internal structure of the food product. This model for the structure decay with time at constant shear rate assumes nth order kinetics for the decay of the material structure with a rate constant, k. The dependence of the degree and the extent of thixotropy of the materials on the temperature, composition and shear history of the food product was determined. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Structural kinetic model; Milled sesame; Concentrated yogurt; Mayonnaise; Thixotropy
1. Introduction Knowledge of the rheological properties of food products is important for design and process evaluation, process control, and consumer acceptability of a product. In addition, the characterization of time-dependent rheological properties of food systems is important to establish relationships between structure and flow, and to correlate physical parameters with sensory evaluation (Figoni & Shoemaker, 1983). Most food products are of complex rheological nature, and their viscosity depends not only on temperature and composition, but also on shear stress, shear rate, time of shearing, as well as on the previous shear and thermal history (Tiu & Boger, 1974). This is due to the fact that many of food products are dispersions of colloidal sized particles such as solids or immiscible liquids, and their polymer content, whose presence may affect the stability and the rheology of a suspension as a result of interactions between suspended particles and these polymers. Dairy products, for example, are fat droplets, colloidal sized calcium phosphate particles, and various kinds of proteins present which are suspended in a complex aqueous phase
*
Tel.: +962-2-7095-111; fax: +962-2-7095-018. E-mail address: [email protected] (B. Abu-Jdayil).
(Young & Shoemaker, 1990). Tehineh also consists of colloidal dispersions in oil media, which are rich in lipids and proteins (Abu-Jdayil, Al-Malah, & Asoud, 2002). Tehineh is the product of milled sesame seeds, which were de-hulled and roasted without adding or removing any of its constituents. On the other hand, there are other foods such as mayonnaise, which are more concentrated dispersions of oil in aqueous media stabilized by proteins and/or polysaccharide polymers. When a material is sheared at a constant shear rate, the viscosity of a thixotropic material will decrease over a period of time, implying a progressive breakdown of structure. Rheopectic materials manifest the opposite sort of behavior. The food products containing polymers exhibit thixotropic behavior, such as for concentrated yogurt, milled sesame, milled black cumin paste and mayonnaise. Although many researchers have investigated the time-dependent rheological behavior of materials, in general, the thixotropic characteristics of many foodstuffs are not so carefully studied in food processing. Modelling of the thixotropic behavior of food products has been based on empirical equations, such as the Weltman model (Weltman, 1943) or based on rate concepts (e.g., Davis, 1973; Joye & Poehlein, 1971; Tiu & Boger, 1974) to predict some form of exponential behavior when a constant shear rate is applied.
0260-8774/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 0 2 ) 0 0 2 7 7 - 7
98
B. Abu-Jdayil / Journal of Food Engineering 57 (2003) 97–102
Thixotropic behavior of commercial mayonnaise had been fitted with a series of two first-order rate functions (Figoni & Shoemaker, 1983). But this function was tested only at low shear rates, (0.0169–0.530 s1 ), which is not the range most relevant to food texture studies. In addition, the periods of time that the samples were sheared were not sufficiently long for the final viscosity to reach equilibrium. De Kee, Code, and Turcotte (1983) developed a model for viscosity decay at constant shear rate, which consisted of an exponential form in which two terms of an infinite series were required. But they found that the data for suspensions such as tomato juice did not follow the proposed model. The objective of the present study is to modify and demonstrate a simple, systematic and quantitative method, with a minimum number of parameters, for characterizing the thixotropic behavior of food products. The time-dependent flow behavior of three different types of foodstuff was investigated under the effect of different conditions. From the results obtained, a thixotropic model for food products, with two parameters, has been modified based on a consideration of the shear-induced change in the food structure with shearing time.
2. Theoretical background The thixotropic behavior of food products can be modelled using the structural kinetic model (SKM), which has been successfully employed for concentrated suspensions of minerals (Nguyen & Boger, 1985) and for starch pastes (Nguyen, Jensen, & Kristensen, 1998). This kinetic approach has also been successfully applied to concentrated yogurt (labneh) behavior as affected by the storage time (Abu-Jdayil & Mohameed, 2002) and to the milled black cumin (Abu-Jdayil, in press). The kinetic structural approach assumes that the change in the rheological behavior is associated with shear-induced breakdown of the internal structure in the food product. The analogy with chemical reactions can be used to express the structural breakdown process in the following form: Structured state ! Non-structured state
ð1Þ
The rate of breakdown of the food structure during the shearing process depends on the kinetics of the above reaction. The model assumes that the structure of food products breaks down irreversibly under the effect of shear without significant buildup. The results from the time-dependent measurements at constant shear rates and from the measured flow curves after long periods of shearing should prove this assumption. The structured state of the thixotropic structure at any time t and under an applied shear rate, c_ , can be represented by a dimensional structural parameter
W ¼ Wðt; c_ Þ
ð2Þ
which is defined as follows: Wðt; c_ Þ ¼
ðg g1 Þ ðg0 g1 Þ
ð3Þ
where g0 is the initial apparent viscosity at t ¼ 0 (structured state), and g1 is the equilibrium apparent viscosity as t ! 1 (non-structured state). Note that, both g0 and g1 are functions of the applied shear rate only. The dimensionless structural parameter, W, is subjected to the following conditions: initially, at the fully structured state, t ¼ 0; W ¼ W0 , and at non-structured state, t ! 1; W ¼ W1 . The rate of structural breakdown can be expressed as:
dW n ¼ kðW W1 Þ dt
ð4Þ
where k ¼ kðc_ Þ is the rate constant, and n is the order of the structure breakdown reaction. At a constant applied shear rate, integration of Eq. (4) from t ¼ 0 to t yields: ðW W1 Þ1n ¼ ðn 1Þkt þ ðW0 W1 Þ1n
ð5Þ
Substituting Eq. (3) into (5) yields for a constant shear rate: 1n ðg g1 Þ ¼ ðn 1Þkt þ 1 ð6Þ ðg0 g1 Þ The form of Eq. (6), which is valid only under the constant shear rate conditions, allows a simple way for testing the validity of the model and determining of the model parameters n and k.
3. Materials and methods 3.1. Samples Tehineh was obtained from a local company in Jordan. Tehineh is the product of the milled sesame seeds, which were dehulled and roasted without adding or removing any of its constituents. Tehineh is rich in lipids (57–65 wt.%) and proteins (23–27 wt.%). It contains also carbohydrates (6.4–9 wt.%) and some minerals (Abu-Jdayil et al., 2002). Concentrated yogurt, also known as labneh, is an acidified dairy product usually made from cowÕs milk. Commercial labneh samples were taken from two different producers in Jordan. The samples of labneh were chosen so that both samples have nearly the same total solids (22.88% and 22.11%) but different protein contents (9.85% and 7.78%). All samples tested were produced from cowÕs milk and filled in 200 g press-to-close plastic containers. The labneh samples were manufactured by using the mechanical method of whey separation. In both samples, the concentrated product is
B. Abu-Jdayil / Journal of Food Engineering 57 (2003) 97–102
manufactured from set yogurt that is basically prepared from heated milk and thermophilic yogurt starter cultures using the standard procedure for yogurt manufacture (Abu-Jdayil, Shaker, & Jumah, 2000). The product is concentrated by removing the whey using centrifugal separation (separator) and then cream (with different fat content) is added and mixed to produce the finished product. Three samples of model mayonnaise with different oil contents (46, 58 and 64 wt.%) were prepared. The corn oil (Mazola, Best Foods Co., Jordan) was used to prepare the o/w emulsion. Egg yolk, obtained from fresh eggs, was separated from the egg white and then used as an emulsifier. A constant egg yolk content of 10 wt.% was used in all samples. White vinegar with 5.5 wt.% acetic acid was used as a continuous phase. Heating the mixture of the egg yolk and the white vinegar to 60 °C with mild agitation prepared the samples, then the oil was added slowly with heating and agitation. After that, the sample was stored at 8 °C overnight before conducting the rheological tests. 3.2. Rheological measurements Rheological properties of tehineh were measured with a Haake-M5 viscometer equipped with the SV1 Searle-type system (bob length ¼ 60 mm; bob diameter ¼ 10:5 mm; gap width ¼ 1 mm). On the other hand, the flow properties of the labneh and mayonnaise were measured with a Haake VT500 rotational viscometer (Searle type) using MV1 and MV3 systems. Both systems have the same outer cylinder. MV1 (bob length ¼ 60 mm; bob diameter ¼ 20:04 mm; gap width ¼ 0:96 mm) was used for labneh, while MV3 (bob length ¼ 60 mm; bob diameter ¼ 15:20 mm; gap width ¼ 5:8 mm) was used to carry out the measurements on the model mayonnaise. Samples were allowed to relax (more than 10 min) prior to measure their viscosity. Pumping water to the jacketed vessel of the viscometer, in all cases, controlled temperature of the samples during measurement to a precision of 0.1 °C. It should be stated that no surface slip was observed in the viscometer systems. In order to investigate the reproducibility of the results, two replicates were made for most of the experiments and the reproducibility was 5% on average.
shear rate could be fitted well with a second-order SKM, i.e. with Eq. (6) using n ¼ 2. 4.1. Tehineh samples Tehineh samples were sheared for a period of 300 min at different values of constant shear rate and at three different temperatures. The tehineh samples exhibited thixotropic behavior under all investigated conditions. Fig. 1 shows the dependency of the apparent viscosity of tehineh on the time of shearing at c_ ¼ 102 s1 for different values of temperature. The applicability of the second-order SKM to the viscosity data of tehineh is illustrated in Fig. 2, where plots of ½ðg0 g1 Þ=ðg g1 Þ 1 versus t at different shear rates are linear. A good comparison between the model fitted results (solid lines) and the experimental apparent viscosity–time data for tehineh can be seen in Fig. 1. The effects of temperature and shear rate on the thixotropic behavior of tehineh were investigated. The rate constant, k can be considered as a measure of the rate of the structure breakdown, i.e. the degree of
Fig. 1. Effect of temperature on the thixotropic behavior of tehineh at constant shear rate ¼ 102 s1 .
4. Results and discussion The food samples used in this investigation had been subjected to a long shearing period at constant values of shear rate, to ensure that the material reached a completely destructed structure at which the rheological behavior is no longer dependent on shearing time. For all food samples studied, it was found that their timedependent apparent viscosity data at constant values of
99
Fig. 2. Testing of the second-order SKM with tehineh at 5 °C.
100
B. Abu-Jdayil / Journal of Food Engineering 57 (2003) 97–102
thixotropy. On other hand, the ratio of initial to equilibrium viscosity, g0 =g1 , can be considered as a relative measure of the amount of structure breakdown, or in other words as a relative measure of the extent of thixotropy. The values of k and g0 =g1 as a function of the applied shear rate and the temperature are reported in Table 1. As one expects for a thixotropic structured material, k generally increases with increasing shear rate and temperature. This means that the breakdown rate of the crosslinked protein structure in tehineh under the application of the external shear stress increases with increasing temperature and applied shear stress. It should be stated here, that the protein content of tehineh is relatively high and varies between 23 and 27 wt.% (Abu-Jdayil et al., 2002). Table 1 shows also that the amount of structure breakdown (g0 =g1 ) increases with shear rate.
Table 2 The degree and the extent of thixotropy of labneh samples, evaluated at a constant shear rate of 106 s1 and 25 °C
4.2. Labneh samples The thixotropic behavior of labneh was previously investigated (Abu-Jdayil, Jumah, & Shaker, in press; Abu-Jdayil et al., 2000). In these investigations an empirical model (Weltman model) was used to describe the thixotropic behavior of different labneh samples. As mentioned before, the two labneh samples used in this study have approximately the same total solid and different protein contents. These samples were sheared at constant shear rate of 106 s1 for 2 h. Fig. 3 shows the apparent viscosity of labneh samples as a function of shearing time fitted with the SKM. At a constant shear rate, the apparent viscosity of both samples decreases rapidly with time within the first 5 min of shearing and reaches a constant value corresponding to an equilibrium state after approximately 40 min. As can be shown in Fig. 3, the rate and extent of viscosity reduction of labneh samples depend on protein content. This dependence can be quantified by determining the parameters k and g0 =g1 . The values of these parameters are summarized in Table 2. The labneh sample with low protein content (7.78 wt.%) shows greater values of k Table 1 The degree and extent of thixotropy of tehineh samples, evaluated at different shear rates and different temperatures Temperature (°C) c_ (s1 )
Fig. 3. Effect of protein content on the thixotropic behavior of labneh at constant shear rate ¼ 106 s1 .
k 103 (min1 )
g0 =g1
g0 (mPa s)
5
15.2 102.0 202.0
17.3 18.7 28.4
1.696 1.724 1.756
5089 5000 4215
25
15.2 102.0 600.0
19.7 22.4 86.3
1.986 1.809 2.237
2185 1809 1611
45
15.2 102.0 600.0
32.9 48.1 114.2
1.664 2.029 2.008
1281 820 803
Protein content (wt.%)
k 103 (min1 )
g0 =g1
g0 (mPa s)
9.85 7.78
130.0 142.0
2.264 3.952
530 310
and g0 =g1 than the labneh sample with higher protein content (9.85 wt.%). This result suggests that the rate and the extent of breakdown of the network structure in labneh under shearing decreased with increasing the protein content. A stronger and much denser gel structure can be expected as a result of more protein–protein interactions at higher protein levels (Ozer, Bell, Grandison, & Robinson, 1998a). In addition, the scanning electron microscopy results showed that the higher protein content labneh samples had more compact structure and smaller voids than their lower protein content counterparts (Ozer, Stenning, Grandison, & Robinson, 1998b). It was found previously that the rate and extent of thixotropic behavior of labneh depend also on both the applied shear rate and the storage time (Abu-Jdayil & Mohameed, 2002). 4.3. Model mayonnaise samples In this part the rheological time-dependent behavior of a model mayonnaise was investigated. We called our mayonnaise a model mayonnaise because, real mayonnaise is an emulsified semisolid food containing not less than 65% vegetable oil dispersed in a continuous phase of water, egg yolk, acidifying agent, salt, sugar and spices (Gallegos, Berjano, & Choplin, 1992). But in this study we prepared oil-in-water emulsions (mayonnaise) with different oil contents, staring with 46 wt.%. In addition, the additives like salt, sugar were not added to
B. Abu-Jdayil / Journal of Food Engineering 57 (2003) 97–102
our emulsion, since they would have significant effects on the time-dependent behavior, and this study aimed to investigate the effect of oil content only. In this part of the study, the egg yolk was fixed at a constant value of 10 wt.% and the oil content was varied between 46 and 64 wt.%. It is clear that the rest was the vinegar solution. The model mayonnaise samples were sheared at different values of constant shear rates (2.20, 19.93 and 79.02 s1 ) for 120 min. In fact the viscosity at 79.93 s1 is closely correlated to the sensorial perception in the mouth, while the low shear rate values (2.20 and 19.93 s1 ) correspond to the product pouring (Sherman, 1988). At an oil content of 46 wt.%, the prepared emulsion showed a time-independent flow behavior. The same behavior was also observed for the oil content of 58 wt.% at low shear rate. Increasing either the oil content or the shear rate led to a thixotropic behavior. It was noticed that the apparent viscosity of all samples reaches an equilibrium value in <40 min. It was found that the second-order SKM fits adequately the thixotropic behavior of the model mayonnaise. Fig. 4 shows the applicability of the model to the rheological data of mayonnaise, where plots of ½1=W 1 versus t at different shear rates are linear. Fig. 5 illustrates that the model provides very good fit of the mayonnaise experimental viscosity versus time data. As shown in Table 3, the rate of structure breakdown, k, increases with increasing both the shear rate and oil content. The decrease in the apparent viscosity of mayonnaise with shear rate increase probably is due to flocculation–deflocculation of the oil droplets (Figoni & Shoemaker, 1983). The increase in the rate of structure breakdown of mayonnaise with shear rate suggests that the deflocculation of oil droplets dominants in the system at high shear rate, leading to a reduction in the apparent viscosity. Fig. 5 shows that, at a constant shear rate the apparent viscosity of mayonnaise increases with increasing
Fig. 4. Testing of the second-order SKM with model mayonnaise at different values of oil contents and shear rates.
101
Fig. 5. Effect of oil content on the thixotropic behavior of model mayonnaise at constant shear rate ¼ 19:932 s1 .
Table 3 The degree and extent of thixotropy of mayonnaise samples, evaluated at different shear rates and different oil contents Oil content (wt.%)
c_ (s1 )
k 103 (min1 )
g0 =g1
g0 (mPa s)
46
2.20 19.93 79.02
– – –
– – –
– – –
58
2.20 19.93 79.02
– 109.6 273.8
– 1.022 1.130
–
2.20 19.93 79.93
151.6 238.4 293.4
1.126 1.135 1.176
39,400 6240 2200
64
2710 1050
oil contents. It is well known in emulsion rheology literature that the emulsion becomes more viscous as the amount of the dispersed phase is increased (Borwankar, Frye, Blaurock, & Sasevich, 1992). This seems to be the case here. The increase of k with increasing oil content can be explained by considering that the size of oil droplets and the aggregates increase with increasing oil content. The breakdown of large aggregates continually generates smaller aggregates during the shearing process. Since the extent of the attractive forces between aggregates depends on the size of the aggregates (Figoni & Shoemaker, 1983), the breakdown rate of large aggregates should be greater than for the smaller aggregates. In addition, the irreversible structural breakdown is associated with the coalescence of droplets (De Kee & Turcotte, 1980). It is expected that the degree of oil droplet coalescence increased with increasing the oil content leading to an increase in the rate of structure breakdown. Table 3 shows that the extent of thixotropy, g0 =g1 , increases with shear rate and oil content. But this variation is relatively small. Figoni and Shoemaker (1983) found that the extent of structural breakdown of
102
B. Abu-Jdayil / Journal of Food Engineering 57 (2003) 97–102
mayonnaise showed no trend of either increasing or decreasing with shear rate. But this was due to the narrow range of shear rates used (0.0169–0.530 s1 ). A comparison of the data presented in Tables 1–3 suggest that the rate of structure breakdown for mayonnaise is greater than that for labneh and tehineh as judged from the values of k at approximately the same value of temperature and shear rate. This is valid for the mayonnaise with oil content equal to or greater than 58 wt.%. On the other hand, the values of g0 =g1 reported in Tables 1–3 indicate that the amount of structure breakdown of labneh is more significant than that for tehineh and mayonnaise. For example, labneh lost about 75% of its initial viscosity compared with 45% in the case of tehineh at approximately a shear rate of 100 s1 .
5. Conclusions The time-dependent flow behavior of some food products possessing thixotropic characteristics was analyzed and modeled using the SKM. The SKM postulates that the change in the rheological behavior is associated with shear-induced breakdown of the internal structure of the food product. This method provides an improved means for characterizing the flow properties of timedependent fluid foods under shear. The SKM was expressed in a form that allows a simple way for testing the validity of the model and determining the model parameters n and k. The second-order SKM for viscosity decay with time at constant shear rate was applied successfully to the results for tehineh (milled sesame), labneh (concentrated yogurt) and model mayonnaise in the shear rate range of 2.20–600 s1 . The rate of structure breakdown (degree of thixotropy) increases with increasing both temperature and shear rate. On the other hand, the amount of structure breakdown (extent of thixotropy) increases with increasing shear rate.
Acknowledgement Research supported by the Deanship of Scientific Research at Jordan University of Science and Technology.
References Abu-Jdayil, B. (in press). Rheology of milled black cumin (Nagilla sativa L.). Rheologica Acta. Abu-Jdayil, B., Al-Malah, K., & Asoud, H. (2002). Rheological characterization of milled sesame (tehineh). Food Hydrocolloids, 16, 55–61. Abu-Jdayil, B., Jumah, R. Y., & Shaker, R. R. (in press). Rheological Properties of a Concentrated Fermented Product, Labneh, Produced from Bovine Milk: Effect of Production Method. International Journal of Food Properties. Abu-Jdayil, B., & Mohameed, H. (2002). Experimental and modelling studies of the flow properties of concentrated yogurt as affected by the storage time. Journal of Food Engineering, 52, 359–365. Abu-Jdayil, B., Shaker, R. R., & Jumah, R. Y. (2000). Rheological behavior of concentrated yogurt (Labneh). International Journal of Food Properties, 3, 207–216. Borwankar, R. P., Frye, L. A., Blaurock, A. E., & Sasevich, F. J. (1992). Rheological characterization of melting of margarines and tablespreads. Journal of Food Engineering, 16, 55–74. Davis, S. S. (1973). Rheological properties of semi-solid foodstuffs. Journal of Texture Studies, 4, 15–40. De Kee, D., Code, R. K., & Turcotte, G. (1983). Flow properties of time-dependent foodstuffs. Journal of Rheology, 27, 581–604. De Kee, D., & Turcotte, G. (1980). Viscosity of biomaterials. Chemical Engineering Communications, 6, 273–282. Figoni, P. I., & Shoemaker, C. F. (1983). Characterization of time dependent flow properties of mayonnaise under steady shear. Journal of Texture Studies, 14, 431–442. Gallegos, C., Berjano, M., & Choplin, L. (1992). Linear viscoelastic behavior of commercial and model mayonnaise. Journal of Rheology, 36, 465–478. Joye, D. D., & Poehlein, G. W. (1971). Characteristics of thixotropic behavior. Journal of Rheology, 15, 51–61. Nguyen, Q. D., & Boger, D. V. (1985). Thixotropic behavior of concentrated bauxite residue suspensions. Rheologic Acta, 24, 427–437. Nguyen, Q. D., Jensen, C. T. B., & Kristensen, P. G. (1998). Experimental and modelling studies of the flow properties of maize and waxy starch pastes. Chemical Engineering Journal, 70, 165–171. Ozer, B. H., Bell, A. E., Grandison, A. S., & Robinson, R. K. (1998a). Rheological properties of concentrated yoghurt (labneh). Journal of Texture Studies, 29, 67–79. Ozer, B. H., Stenning, R. A., Grandison, A. S., & Robinson, R. K. (1998b). Rheology and Microstructure of labneh (concentrated yoghurt). Journal of Dairy Science, 82, 682–689. Sherman, P. (1988). The sensory-rheological interface. In J. M. V. Blanshard & J. R. Mitchell (Eds.), Food Structure Its Creation and Evaluation. Oxford: Butterworths-Heinemann. Tiu, C., & Boger, D. V. (1974). Complete rheological characterization of time-dependent food products. Journal of Texture Studies, 5, 329–338. Young, L. S., & Shoemaker, C. F. (1990). Time-dependent flow measurements of Na-caseinate coated polystyrene latices. Journal of Rheology, 34, 1149–1159. Weltman, R. N. (1943). Breakdown of thixotropic structure as a function of time. Journal of Applied Physics, 14, 343–350.
Modelling the time-dependent rheological behavior of semisolid foodstuffs Basim Abu-Jdayil
*
Department of Chemical Engineering, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan Received 15 February 2002; accepted 27 May 2002
Abstract Many of food products exhibited the thixotropic behavior, in which, the apparent viscosity of material decreases with time of shearing at constant shear rate. The structural kinetic model (SKM) was used to characterize the thixotropic behavior of three different kinds of food products. Foods selected for analysis represent the fluid and semisolid food materials. They include milled sesame, concentrated yogurt and mayonnaise. The SKM postulates that the change in the rheological behavior is associated with shear-induced breakdown of the internal structure of the food product. This model for the structure decay with time at constant shear rate assumes nth order kinetics for the decay of the material structure with a rate constant, k. The dependence of the degree and the extent of thixotropy of the materials on the temperature, composition and shear history of the food product was determined. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Structural kinetic model; Milled sesame; Concentrated yogurt; Mayonnaise; Thixotropy
1. Introduction Knowledge of the rheological properties of food products is important for design and process evaluation, process control, and consumer acceptability of a product. In addition, the characterization of time-dependent rheological properties of food systems is important to establish relationships between structure and flow, and to correlate physical parameters with sensory evaluation (Figoni & Shoemaker, 1983). Most food products are of complex rheological nature, and their viscosity depends not only on temperature and composition, but also on shear stress, shear rate, time of shearing, as well as on the previous shear and thermal history (Tiu & Boger, 1974). This is due to the fact that many of food products are dispersions of colloidal sized particles such as solids or immiscible liquids, and their polymer content, whose presence may affect the stability and the rheology of a suspension as a result of interactions between suspended particles and these polymers. Dairy products, for example, are fat droplets, colloidal sized calcium phosphate particles, and various kinds of proteins present which are suspended in a complex aqueous phase
*
Tel.: +962-2-7095-111; fax: +962-2-7095-018. E-mail address: [email protected] (B. Abu-Jdayil).
(Young & Shoemaker, 1990). Tehineh also consists of colloidal dispersions in oil media, which are rich in lipids and proteins (Abu-Jdayil, Al-Malah, & Asoud, 2002). Tehineh is the product of milled sesame seeds, which were de-hulled and roasted without adding or removing any of its constituents. On the other hand, there are other foods such as mayonnaise, which are more concentrated dispersions of oil in aqueous media stabilized by proteins and/or polysaccharide polymers. When a material is sheared at a constant shear rate, the viscosity of a thixotropic material will decrease over a period of time, implying a progressive breakdown of structure. Rheopectic materials manifest the opposite sort of behavior. The food products containing polymers exhibit thixotropic behavior, such as for concentrated yogurt, milled sesame, milled black cumin paste and mayonnaise. Although many researchers have investigated the time-dependent rheological behavior of materials, in general, the thixotropic characteristics of many foodstuffs are not so carefully studied in food processing. Modelling of the thixotropic behavior of food products has been based on empirical equations, such as the Weltman model (Weltman, 1943) or based on rate concepts (e.g., Davis, 1973; Joye & Poehlein, 1971; Tiu & Boger, 1974) to predict some form of exponential behavior when a constant shear rate is applied.
0260-8774/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 0 2 ) 0 0 2 7 7 - 7
98
B. Abu-Jdayil / Journal of Food Engineering 57 (2003) 97–102
Thixotropic behavior of commercial mayonnaise had been fitted with a series of two first-order rate functions (Figoni & Shoemaker, 1983). But this function was tested only at low shear rates, (0.0169–0.530 s1 ), which is not the range most relevant to food texture studies. In addition, the periods of time that the samples were sheared were not sufficiently long for the final viscosity to reach equilibrium. De Kee, Code, and Turcotte (1983) developed a model for viscosity decay at constant shear rate, which consisted of an exponential form in which two terms of an infinite series were required. But they found that the data for suspensions such as tomato juice did not follow the proposed model. The objective of the present study is to modify and demonstrate a simple, systematic and quantitative method, with a minimum number of parameters, for characterizing the thixotropic behavior of food products. The time-dependent flow behavior of three different types of foodstuff was investigated under the effect of different conditions. From the results obtained, a thixotropic model for food products, with two parameters, has been modified based on a consideration of the shear-induced change in the food structure with shearing time.
2. Theoretical background The thixotropic behavior of food products can be modelled using the structural kinetic model (SKM), which has been successfully employed for concentrated suspensions of minerals (Nguyen & Boger, 1985) and for starch pastes (Nguyen, Jensen, & Kristensen, 1998). This kinetic approach has also been successfully applied to concentrated yogurt (labneh) behavior as affected by the storage time (Abu-Jdayil & Mohameed, 2002) and to the milled black cumin (Abu-Jdayil, in press). The kinetic structural approach assumes that the change in the rheological behavior is associated with shear-induced breakdown of the internal structure in the food product. The analogy with chemical reactions can be used to express the structural breakdown process in the following form: Structured state ! Non-structured state
ð1Þ
The rate of breakdown of the food structure during the shearing process depends on the kinetics of the above reaction. The model assumes that the structure of food products breaks down irreversibly under the effect of shear without significant buildup. The results from the time-dependent measurements at constant shear rates and from the measured flow curves after long periods of shearing should prove this assumption. The structured state of the thixotropic structure at any time t and under an applied shear rate, c_ , can be represented by a dimensional structural parameter
W ¼ Wðt; c_ Þ
ð2Þ
which is defined as follows: Wðt; c_ Þ ¼
ðg g1 Þ ðg0 g1 Þ
ð3Þ
where g0 is the initial apparent viscosity at t ¼ 0 (structured state), and g1 is the equilibrium apparent viscosity as t ! 1 (non-structured state). Note that, both g0 and g1 are functions of the applied shear rate only. The dimensionless structural parameter, W, is subjected to the following conditions: initially, at the fully structured state, t ¼ 0; W ¼ W0 , and at non-structured state, t ! 1; W ¼ W1 . The rate of structural breakdown can be expressed as:
dW n ¼ kðW W1 Þ dt
ð4Þ
where k ¼ kðc_ Þ is the rate constant, and n is the order of the structure breakdown reaction. At a constant applied shear rate, integration of Eq. (4) from t ¼ 0 to t yields: ðW W1 Þ1n ¼ ðn 1Þkt þ ðW0 W1 Þ1n
ð5Þ
Substituting Eq. (3) into (5) yields for a constant shear rate: 1n ðg g1 Þ ¼ ðn 1Þkt þ 1 ð6Þ ðg0 g1 Þ The form of Eq. (6), which is valid only under the constant shear rate conditions, allows a simple way for testing the validity of the model and determining of the model parameters n and k.
3. Materials and methods 3.1. Samples Tehineh was obtained from a local company in Jordan. Tehineh is the product of the milled sesame seeds, which were dehulled and roasted without adding or removing any of its constituents. Tehineh is rich in lipids (57–65 wt.%) and proteins (23–27 wt.%). It contains also carbohydrates (6.4–9 wt.%) and some minerals (Abu-Jdayil et al., 2002). Concentrated yogurt, also known as labneh, is an acidified dairy product usually made from cowÕs milk. Commercial labneh samples were taken from two different producers in Jordan. The samples of labneh were chosen so that both samples have nearly the same total solids (22.88% and 22.11%) but different protein contents (9.85% and 7.78%). All samples tested were produced from cowÕs milk and filled in 200 g press-to-close plastic containers. The labneh samples were manufactured by using the mechanical method of whey separation. In both samples, the concentrated product is
B. Abu-Jdayil / Journal of Food Engineering 57 (2003) 97–102
manufactured from set yogurt that is basically prepared from heated milk and thermophilic yogurt starter cultures using the standard procedure for yogurt manufacture (Abu-Jdayil, Shaker, & Jumah, 2000). The product is concentrated by removing the whey using centrifugal separation (separator) and then cream (with different fat content) is added and mixed to produce the finished product. Three samples of model mayonnaise with different oil contents (46, 58 and 64 wt.%) were prepared. The corn oil (Mazola, Best Foods Co., Jordan) was used to prepare the o/w emulsion. Egg yolk, obtained from fresh eggs, was separated from the egg white and then used as an emulsifier. A constant egg yolk content of 10 wt.% was used in all samples. White vinegar with 5.5 wt.% acetic acid was used as a continuous phase. Heating the mixture of the egg yolk and the white vinegar to 60 °C with mild agitation prepared the samples, then the oil was added slowly with heating and agitation. After that, the sample was stored at 8 °C overnight before conducting the rheological tests. 3.2. Rheological measurements Rheological properties of tehineh were measured with a Haake-M5 viscometer equipped with the SV1 Searle-type system (bob length ¼ 60 mm; bob diameter ¼ 10:5 mm; gap width ¼ 1 mm). On the other hand, the flow properties of the labneh and mayonnaise were measured with a Haake VT500 rotational viscometer (Searle type) using MV1 and MV3 systems. Both systems have the same outer cylinder. MV1 (bob length ¼ 60 mm; bob diameter ¼ 20:04 mm; gap width ¼ 0:96 mm) was used for labneh, while MV3 (bob length ¼ 60 mm; bob diameter ¼ 15:20 mm; gap width ¼ 5:8 mm) was used to carry out the measurements on the model mayonnaise. Samples were allowed to relax (more than 10 min) prior to measure their viscosity. Pumping water to the jacketed vessel of the viscometer, in all cases, controlled temperature of the samples during measurement to a precision of 0.1 °C. It should be stated that no surface slip was observed in the viscometer systems. In order to investigate the reproducibility of the results, two replicates were made for most of the experiments and the reproducibility was 5% on average.
shear rate could be fitted well with a second-order SKM, i.e. with Eq. (6) using n ¼ 2. 4.1. Tehineh samples Tehineh samples were sheared for a period of 300 min at different values of constant shear rate and at three different temperatures. The tehineh samples exhibited thixotropic behavior under all investigated conditions. Fig. 1 shows the dependency of the apparent viscosity of tehineh on the time of shearing at c_ ¼ 102 s1 for different values of temperature. The applicability of the second-order SKM to the viscosity data of tehineh is illustrated in Fig. 2, where plots of ½ðg0 g1 Þ=ðg g1 Þ 1 versus t at different shear rates are linear. A good comparison between the model fitted results (solid lines) and the experimental apparent viscosity–time data for tehineh can be seen in Fig. 1. The effects of temperature and shear rate on the thixotropic behavior of tehineh were investigated. The rate constant, k can be considered as a measure of the rate of the structure breakdown, i.e. the degree of
Fig. 1. Effect of temperature on the thixotropic behavior of tehineh at constant shear rate ¼ 102 s1 .
4. Results and discussion The food samples used in this investigation had been subjected to a long shearing period at constant values of shear rate, to ensure that the material reached a completely destructed structure at which the rheological behavior is no longer dependent on shearing time. For all food samples studied, it was found that their timedependent apparent viscosity data at constant values of
99
Fig. 2. Testing of the second-order SKM with tehineh at 5 °C.
100
B. Abu-Jdayil / Journal of Food Engineering 57 (2003) 97–102
thixotropy. On other hand, the ratio of initial to equilibrium viscosity, g0 =g1 , can be considered as a relative measure of the amount of structure breakdown, or in other words as a relative measure of the extent of thixotropy. The values of k and g0 =g1 as a function of the applied shear rate and the temperature are reported in Table 1. As one expects for a thixotropic structured material, k generally increases with increasing shear rate and temperature. This means that the breakdown rate of the crosslinked protein structure in tehineh under the application of the external shear stress increases with increasing temperature and applied shear stress. It should be stated here, that the protein content of tehineh is relatively high and varies between 23 and 27 wt.% (Abu-Jdayil et al., 2002). Table 1 shows also that the amount of structure breakdown (g0 =g1 ) increases with shear rate.
Table 2 The degree and the extent of thixotropy of labneh samples, evaluated at a constant shear rate of 106 s1 and 25 °C
4.2. Labneh samples The thixotropic behavior of labneh was previously investigated (Abu-Jdayil, Jumah, & Shaker, in press; Abu-Jdayil et al., 2000). In these investigations an empirical model (Weltman model) was used to describe the thixotropic behavior of different labneh samples. As mentioned before, the two labneh samples used in this study have approximately the same total solid and different protein contents. These samples were sheared at constant shear rate of 106 s1 for 2 h. Fig. 3 shows the apparent viscosity of labneh samples as a function of shearing time fitted with the SKM. At a constant shear rate, the apparent viscosity of both samples decreases rapidly with time within the first 5 min of shearing and reaches a constant value corresponding to an equilibrium state after approximately 40 min. As can be shown in Fig. 3, the rate and extent of viscosity reduction of labneh samples depend on protein content. This dependence can be quantified by determining the parameters k and g0 =g1 . The values of these parameters are summarized in Table 2. The labneh sample with low protein content (7.78 wt.%) shows greater values of k Table 1 The degree and extent of thixotropy of tehineh samples, evaluated at different shear rates and different temperatures Temperature (°C) c_ (s1 )
Fig. 3. Effect of protein content on the thixotropic behavior of labneh at constant shear rate ¼ 106 s1 .
k 103 (min1 )
g0 =g1
g0 (mPa s)
5
15.2 102.0 202.0
17.3 18.7 28.4
1.696 1.724 1.756
5089 5000 4215
25
15.2 102.0 600.0
19.7 22.4 86.3
1.986 1.809 2.237
2185 1809 1611
45
15.2 102.0 600.0
32.9 48.1 114.2
1.664 2.029 2.008
1281 820 803
Protein content (wt.%)
k 103 (min1 )
g0 =g1
g0 (mPa s)
9.85 7.78
130.0 142.0
2.264 3.952
530 310
and g0 =g1 than the labneh sample with higher protein content (9.85 wt.%). This result suggests that the rate and the extent of breakdown of the network structure in labneh under shearing decreased with increasing the protein content. A stronger and much denser gel structure can be expected as a result of more protein–protein interactions at higher protein levels (Ozer, Bell, Grandison, & Robinson, 1998a). In addition, the scanning electron microscopy results showed that the higher protein content labneh samples had more compact structure and smaller voids than their lower protein content counterparts (Ozer, Stenning, Grandison, & Robinson, 1998b). It was found previously that the rate and extent of thixotropic behavior of labneh depend also on both the applied shear rate and the storage time (Abu-Jdayil & Mohameed, 2002). 4.3. Model mayonnaise samples In this part the rheological time-dependent behavior of a model mayonnaise was investigated. We called our mayonnaise a model mayonnaise because, real mayonnaise is an emulsified semisolid food containing not less than 65% vegetable oil dispersed in a continuous phase of water, egg yolk, acidifying agent, salt, sugar and spices (Gallegos, Berjano, & Choplin, 1992). But in this study we prepared oil-in-water emulsions (mayonnaise) with different oil contents, staring with 46 wt.%. In addition, the additives like salt, sugar were not added to
B. Abu-Jdayil / Journal of Food Engineering 57 (2003) 97–102
our emulsion, since they would have significant effects on the time-dependent behavior, and this study aimed to investigate the effect of oil content only. In this part of the study, the egg yolk was fixed at a constant value of 10 wt.% and the oil content was varied between 46 and 64 wt.%. It is clear that the rest was the vinegar solution. The model mayonnaise samples were sheared at different values of constant shear rates (2.20, 19.93 and 79.02 s1 ) for 120 min. In fact the viscosity at 79.93 s1 is closely correlated to the sensorial perception in the mouth, while the low shear rate values (2.20 and 19.93 s1 ) correspond to the product pouring (Sherman, 1988). At an oil content of 46 wt.%, the prepared emulsion showed a time-independent flow behavior. The same behavior was also observed for the oil content of 58 wt.% at low shear rate. Increasing either the oil content or the shear rate led to a thixotropic behavior. It was noticed that the apparent viscosity of all samples reaches an equilibrium value in <40 min. It was found that the second-order SKM fits adequately the thixotropic behavior of the model mayonnaise. Fig. 4 shows the applicability of the model to the rheological data of mayonnaise, where plots of ½1=W 1 versus t at different shear rates are linear. Fig. 5 illustrates that the model provides very good fit of the mayonnaise experimental viscosity versus time data. As shown in Table 3, the rate of structure breakdown, k, increases with increasing both the shear rate and oil content. The decrease in the apparent viscosity of mayonnaise with shear rate increase probably is due to flocculation–deflocculation of the oil droplets (Figoni & Shoemaker, 1983). The increase in the rate of structure breakdown of mayonnaise with shear rate suggests that the deflocculation of oil droplets dominants in the system at high shear rate, leading to a reduction in the apparent viscosity. Fig. 5 shows that, at a constant shear rate the apparent viscosity of mayonnaise increases with increasing
Fig. 4. Testing of the second-order SKM with model mayonnaise at different values of oil contents and shear rates.
101
Fig. 5. Effect of oil content on the thixotropic behavior of model mayonnaise at constant shear rate ¼ 19:932 s1 .
Table 3 The degree and extent of thixotropy of mayonnaise samples, evaluated at different shear rates and different oil contents Oil content (wt.%)
c_ (s1 )
k 103 (min1 )
g0 =g1
g0 (mPa s)
46
2.20 19.93 79.02
– – –
– – –
– – –
58
2.20 19.93 79.02
– 109.6 273.8
– 1.022 1.130
–
2.20 19.93 79.93
151.6 238.4 293.4
1.126 1.135 1.176
39,400 6240 2200
64
2710 1050
oil contents. It is well known in emulsion rheology literature that the emulsion becomes more viscous as the amount of the dispersed phase is increased (Borwankar, Frye, Blaurock, & Sasevich, 1992). This seems to be the case here. The increase of k with increasing oil content can be explained by considering that the size of oil droplets and the aggregates increase with increasing oil content. The breakdown of large aggregates continually generates smaller aggregates during the shearing process. Since the extent of the attractive forces between aggregates depends on the size of the aggregates (Figoni & Shoemaker, 1983), the breakdown rate of large aggregates should be greater than for the smaller aggregates. In addition, the irreversible structural breakdown is associated with the coalescence of droplets (De Kee & Turcotte, 1980). It is expected that the degree of oil droplet coalescence increased with increasing the oil content leading to an increase in the rate of structure breakdown. Table 3 shows that the extent of thixotropy, g0 =g1 , increases with shear rate and oil content. But this variation is relatively small. Figoni and Shoemaker (1983) found that the extent of structural breakdown of
102
B. Abu-Jdayil / Journal of Food Engineering 57 (2003) 97–102
mayonnaise showed no trend of either increasing or decreasing with shear rate. But this was due to the narrow range of shear rates used (0.0169–0.530 s1 ). A comparison of the data presented in Tables 1–3 suggest that the rate of structure breakdown for mayonnaise is greater than that for labneh and tehineh as judged from the values of k at approximately the same value of temperature and shear rate. This is valid for the mayonnaise with oil content equal to or greater than 58 wt.%. On the other hand, the values of g0 =g1 reported in Tables 1–3 indicate that the amount of structure breakdown of labneh is more significant than that for tehineh and mayonnaise. For example, labneh lost about 75% of its initial viscosity compared with 45% in the case of tehineh at approximately a shear rate of 100 s1 .
5. Conclusions The time-dependent flow behavior of some food products possessing thixotropic characteristics was analyzed and modeled using the SKM. The SKM postulates that the change in the rheological behavior is associated with shear-induced breakdown of the internal structure of the food product. This method provides an improved means for characterizing the flow properties of timedependent fluid foods under shear. The SKM was expressed in a form that allows a simple way for testing the validity of the model and determining the model parameters n and k. The second-order SKM for viscosity decay with time at constant shear rate was applied successfully to the results for tehineh (milled sesame), labneh (concentrated yogurt) and model mayonnaise in the shear rate range of 2.20–600 s1 . The rate of structure breakdown (degree of thixotropy) increases with increasing both temperature and shear rate. On the other hand, the amount of structure breakdown (extent of thixotropy) increases with increasing shear rate.
Acknowledgement Research supported by the Deanship of Scientific Research at Jordan University of Science and Technology.
References Abu-Jdayil, B. (in press). Rheology of milled black cumin (Nagilla sativa L.). Rheologica Acta. Abu-Jdayil, B., Al-Malah, K., & Asoud, H. (2002). Rheological characterization of milled sesame (tehineh). Food Hydrocolloids, 16, 55–61. Abu-Jdayil, B., Jumah, R. Y., & Shaker, R. R. (in press). Rheological Properties of a Concentrated Fermented Product, Labneh, Produced from Bovine Milk: Effect of Production Method. International Journal of Food Properties. Abu-Jdayil, B., & Mohameed, H. (2002). Experimental and modelling studies of the flow properties of concentrated yogurt as affected by the storage time. Journal of Food Engineering, 52, 359–365. Abu-Jdayil, B., Shaker, R. R., & Jumah, R. Y. (2000). Rheological behavior of concentrated yogurt (Labneh). International Journal of Food Properties, 3, 207–216. Borwankar, R. P., Frye, L. A., Blaurock, A. E., & Sasevich, F. J. (1992). Rheological characterization of melting of margarines and tablespreads. Journal of Food Engineering, 16, 55–74. Davis, S. S. (1973). Rheological properties of semi-solid foodstuffs. Journal of Texture Studies, 4, 15–40. De Kee, D., Code, R. K., & Turcotte, G. (1983). Flow properties of time-dependent foodstuffs. Journal of Rheology, 27, 581–604. De Kee, D., & Turcotte, G. (1980). Viscosity of biomaterials. Chemical Engineering Communications, 6, 273–282. Figoni, P. I., & Shoemaker, C. F. (1983). Characterization of time dependent flow properties of mayonnaise under steady shear. Journal of Texture Studies, 14, 431–442. Gallegos, C., Berjano, M., & Choplin, L. (1992). Linear viscoelastic behavior of commercial and model mayonnaise. Journal of Rheology, 36, 465–478. Joye, D. D., & Poehlein, G. W. (1971). Characteristics of thixotropic behavior. Journal of Rheology, 15, 51–61. Nguyen, Q. D., & Boger, D. V. (1985). Thixotropic behavior of concentrated bauxite residue suspensions. Rheologic Acta, 24, 427–437. Nguyen, Q. D., Jensen, C. T. B., & Kristensen, P. G. (1998). Experimental and modelling studies of the flow properties of maize and waxy starch pastes. Chemical Engineering Journal, 70, 165–171. Ozer, B. H., Bell, A. E., Grandison, A. S., & Robinson, R. K. (1998a). Rheological properties of concentrated yoghurt (labneh). Journal of Texture Studies, 29, 67–79. Ozer, B. H., Stenning, R. A., Grandison, A. S., & Robinson, R. K. (1998b). Rheology and Microstructure of labneh (concentrated yoghurt). Journal of Dairy Science, 82, 682–689. Sherman, P. (1988). The sensory-rheological interface. In J. M. V. Blanshard & J. R. Mitchell (Eds.), Food Structure Its Creation and Evaluation. Oxford: Butterworths-Heinemann. Tiu, C., & Boger, D. V. (1974). Complete rheological characterization of time-dependent food products. Journal of Texture Studies, 5, 329–338. Young, L. S., & Shoemaker, C. F. (1990). Time-dependent flow measurements of Na-caseinate coated polystyrene latices. Journal of Rheology, 34, 1149–1159. Weltman, R. N. (1943). Breakdown of thixotropic structure as a function of time. Journal of Applied Physics, 14, 343–350.