TIME-INDEPENDENT FLOW MODELING OF THE RHEOLOGICAL BEHAVIOUR OF LASSI

TIME-INDEPENDENT FLOW MODELING OF LASSI, THE INDIAN DRINKING YOGHURTH.A. PUSHPADASS*, R.N. SARASWAT, F.M.E. EMERALD and B.V. BALASUBRAMANYAM

This study was conducted at National Dairy Research Institute, Southern Regional Station, Bangalore 560 030, India.

*Corresponding author: E-mail: heartwin1@gmail.com; Ph: 0091-80-25710661; Fax: 0091-80-25710161

ABSTRACT

The rheological behaviour of lassi was studied by using a computer-controlled rotational viscometer over a range of total solids (TS), sugar contents and stabilizers. The stabilizers tested were carrageenan, pectin and locust bean gum (LBG) at 0, 0.05, 0.10 and 0.15% concentrations (w/w). The RVDV-II+Pro viscometric data were converted into the basic shear stress vs. shear rate form using Mitschka method. From the shear rate-shear stress data, the flow nature of lassi was evaluated. The apparent viscosities of the systems were found to decrease with increasing shear rate, indicating pseudoplastic behaviour with yield stress. The flow behaviour of lassi was adequately described by the Herschel-Bulkley and Casson models with a high coefficient of determination (R2) and low root mean square error (RMSE) value. The Herschel-Bulkley yield stress (0), consistency coefficient (K) and the flow behaviour index (n) ranged from 0.638-7.725 Pa, 0.330-0.834 Pa.sn and 0.514-0.701, respectively. The main and most interaction effects of the selected factors on the apparent viscosity, yield stress, Any increase in the concentration of milk solids in lassi was accompanied by an increase in the pseudoplasticity, consistency coefficient and yield stress while the effect of sugar on flow behaviour was quite opposite. The flow parameters of lassi were positively influenced by carrageenan and pectin in some cases. Carrageenan at 0.15% concentration was found to be the most suitable stabilizer for lassi when added before fermentation of milk. On the other hand, lassi stabilized with LBG showed visible whey separation owing to precipitation of milk proteins.KEYWORDS

Lassi, fermented milk, flow models, rheology, stabilizer, viscometer.INTRODUCTIONFermented milk products are popular because of their therapeutic and nutritional qualities. Lassi is one such popular fermented ready-to-serve milk beverage in India, resembling the stirred yoghurt drink. It is the viscous liquid obtained after churning of dahi (Indian yoghurt) and adding sugar into it. The major quality characteristics of lassi include thick uniform body, smooth texture and a good blend of acid and diacetyl flavours (Vedamuthu 1985). It is estimated that about 7.0% of milk produced in India is converted into dahi and lassi (Aneja et al. 2002). Dahi and fermented milks have been one of the strongest growth areas of the Indian dairy industry in recent years. Several brands of dahi and lassi have flooded the market to meet the consumer demand. In order to make lassi, dahi is prepared by inoculating mixed cultures of lactic acid bacteria into milk that ferment lactose to lactic acid. The fermentation time is about 12 h. The final quality of lassi depends on the composition of milk, type of inoculating microorganisms and processing conditions. The key quality attributes of lassi, considered essential by consumers, are its rheological properties such as body and consistency. Lassi, which is normally diluted with water, may have low fat and milk solids content as compared to dahi. Hence, it may show sedimentation on storage as the aggregated milk proteins are heavy and possess the tendency to sediment, causing syneresis or wheying off. As a consequence, the mouth-feel and consumer appeal may be poor, particularly when stored. This problem could be circumvented by different methods that are permitted under the legal standards. Labropoulos et al. (1984) postulated three approaches for improving the body and texture of yoghurt, which will also be applicable to lassi, as (i) increasing the total solids, (ii) addition of hydrocolloids and (iii) control of heating temperature and time of milk. On the other hand, Tamine and Robinson (1999) reported that it was essential to add stabilizer(s) at suitable concentrations to improve the quality of fermented milk products and, simultaneously, to standardize the total solids content. The most common stabilizers in fermented milks are starch, carrageenan, pectin, sodium carboxy methyl cellulose, agar, guar gum, xanthan gum, locust bean gum (LBG) and gelatin. These stabilizers could be added as a single compound or as a blend (Chandan et al. 2006). The addition of stabilizers is expected to give the fermented milks a more full-bodied taste or mouth-feel. This is because the swelling action of the stabilizer binds free water into bound water, thereby concentrating the solids in the mixture and imparting higher viscosity.

The knowledge of rheological properties is of importance in processing, handling, process design, product development and quality control. Also, it is essential to understand the relationships between the rheological behaviour of lassi and the compositional factors and processing conditions that influence such behaviour. For example, the rheological behaviour of lassi could be affected by milk solids and sugar content and the type of stabilizer used and its concentration. The flow behaviour of fermented milks could be described by different time-independent and time-dependent rheological models depending on the nature of the product. Ostwald de Waele (power law), Herschel-Bulkley, Cassons and Cross equations are commonly reported in literature (Holdsworth 1993) to describe the non-Newtonian behaviour of many dairy products, particularly that of yoghurt (Benezech and Maingonnat, 1994; Rao 1999; Lee and Lucey 2006). In these models, the stress-strain relationship of the product is determined without studying the time-dependent effects. Sometimes, more than one rheological model may be required to characterize the rheological properties of a non-Newtonian food when a broad range of shear rates was encountered.Although there is extensive literature on the rheological characterization of fermented milk products like yoghurt and yoghurt drinks, literally no work has been done on dahi and lassi with viscometers capable of yielding rheological data. The rheological behaviour of lassi is expected to be different from that of yoghurt because the water and sugar contents of lassi are considerably more than that of yoghurt and the fermentation conditions are quite different. Therefore, this study was undertaken with the objectives of analyzing the effects of milk solids, sugar and type of stabilizer and its concentration on the apparent viscosity of lassi, and to model the rheological behaviour of lassi using time-independent flow models. MATERIALS AND METHODSPreparation of LassiFresh raw milk and LF-40 dahi culture were obtained respectively from the experimental dairy plant and dairy bacteriology section of the Southern Regional Station of National Dairy Research Institute. The raw milk was standardized to 3.0% fat and 8.5% SNF, and it was homogenized in a triple-action homogenizer (Model APV, Crepaco, Chicago, IL) operating at 13.79 MPa pressure in the first stage. The homogenized milk was subjected to heat treatment at 85C for 10 min by indirect heating, and subsequently cooled to 30C. This time-temperature combination of heat treatment was selected based on earlier findings of Das (1991) and Bienvenue et al. (2003), who reported that a desirable body and texture of cultured milk products was obtained when milk was heated to 85-90C for 10-30 min. The heat treatment, closer to the boiling point of milk, was expected to cause more denaturation of whey proteins, thereby improving the textural and rheological properties of products like yoghurts and cultured milks (Lee and Lucey 2003; Kessler 1998; Walstra et al. 1999; Chandan et al. 2006; Nilsson et al. 2006). After heat treatment and cooling, LF-40 dahi culture at 1.5% (w/w) was added to 500 mL samples of milk taken in 600 mL glass beakers. Carrageenan, pectin and LBG (Hi-Media Laboratories Pvt. Ltd, Mumbai, India) were tested independently as stabilizers to improve the consistency of lassi. These stabilizers, at concentrations of 0, 0.05, 0.10 and 0.15% (w/v of milk), were dissolved in small quantity of warm milk before addition to inoculated milk at 30C.

The cultured milk was then incubated at 30C for 20 h to make dahi/curd. The incubation temperature was closely related to the LF-40 strains used. After fermentation, sugar at concentrations of 10, 15 and 20% (w/v) was added to the curd. Also, calculated quantities of water were added to the curd to achieve 11.50, 10.35 and 9.20% milk solids in lassi. The addition of water was about 0, 10 and 20% on weight basis of curd. The curd-sugar mixture was then gently stirred 30 times using a hand-held stainless steel vertical agitator to blend the water and to dissolve the added sugar.

Determination of Apparent Viscosity of Lassi

The apparent viscosities of lassi samples were determined using a rotational viscometer (Model RVDV-II+Pro, Brookfield Engineering laboratory, Stoughton, MA) at spindle speeds of 10-100 rpm (in steps of 10 rpm) in a continuous run mode. The viscosity measurements were carried out at 30C. The RV3 spindle was used for viscosity measurements, except for samples stabilized with LBG at 0.15% where RV2 was used. The spindles were selected such that the measurement range of torque in the viscometer was maintained within the range of 10 to 95%. The disc spindle was inserted into the sample at a depth indicated by the notch on the spindle, and the depth was kept constant throughout the study. As mentioned in the previous paragraph, the samples for viscosity measurement were taken in 600 mL beakers having a diameter of 90 mm.

The viscometer was operated in an external mode using a computer loaded with Rheocalc v. 3.1.1 software supplied by Brookfield Engineering Laboratory. At each rpm, shearing of the sample was done for 30 s before the speed was ramped up to the next level. The torque and apparent viscosity data were collected at 10 s interval for each rpm. The data were acquired using the same software.

Conversion of Viscometric Data and Time-independent Flow Modeling of Lassi

The RVDV viscometric data were converted into shear stress and shear rate form by Mitschka method (Briggs and Steffe 1997). The flow behaviour index n was determined as the slope of the log10 of shear stress vs. log10 of rpm plot as shown in the equation below:

The shear stress, , was given by the equation:

=.(C*dial reading)

where n was the flow behaviour index (dimensionless), was shear stress conversion factor (Pa), N was the rotational speed in rpm and C was the spring constant (C=1 for the RV model). The parameter was a function of spindle number. The dial reading represented the percent torque displayed on the Brookfield viscometer.

The average shear rate, , was computed using the equation:

where KNY was the shear rate conversion factor. Values of KNY as a function of the spindle number and flow behaviour index were obtained from Briggs and Steffe (1997). The Ostwald De Waele (Power law), Casson and Herschel-Bulkley constitutive models shown below were fitted to the shear stress-shear rate data.

(Ostwald De Waele model)

(Herschel-Bulkley model)

(Cassons model)

where was the shear stress (Pa), 0 was the yield stress (Pa), was the shear rate (s-1), a was the apparent viscosity (Pa.s) (Casson viscosity) and K was the consistency coefficient (Pa.sn). The constant n is a measure of the extent of departure from Newtonian behaviour while K is a measure of viscosity or consistency. These models relate the shear stress of lassi to the shear rate, thus enabling the apparent viscosity to be calculated.The Ostwald De Waele model was fitted by plotting ln against ln. The slope of this straight line relationship yielded the flow behaviour index n while the intercept directly gave the consistency coefficient K. For Cassons relationship, the linear regression of over resulted in a straight line with intercept. The yield stress thus obtained was substituted into the Herschel-Bulkley model, and the parameter ln was plotted against ln to determine the model parameters.

Analytical Methods

The solids content in milk was determined by adding the SNF and fat percentages. However, for lassi, about 5 g of sample was weighed accurately on to a dried and cooled petri dish. The dish was transferred to an oven being maintained at 1051C. After 4 h, the samples were taken out, cooled in a desiccator and the weights were recorded. The pH of milk and lassi samples was measured directly using a glass electrode pH meter (Model pH Tutor, Eutech Instruments, Singapore). The titratable acidity (TA) of lassi was determined according to Bureau of Indian Standards (BIS 1980). In each analysis, 10 mL of the sample was diluted with 2 parts of water and the solution was titrated against 0.1N NaOH using two drops of phenolphthalein as indicator. The acidity was expressed as percent lactic acid.

Syneresis Test

Whey separation (expressed in terms of whey volume) was determined by taking 10 mL of sample in graduated tubes, and centrifuging (Model SBV, International Centrifuge, Boston, MA) them at 3500 rpm for 10 min. After centrifugation, the volume of the supernatant liquid was read from the tube, and the values were expressed in percentage.

Experimental Design and Statistical Analyses

The effects of all four factors namely sugar content (0, 10 and 20%), milk solids content (9.20, 10.35 and 11.50%), stabilizer type (carrageenan, LBG and pectin) and stabilizer concentration (0, 0.05, 0.1 and 0.15%) were studied using a factorial experimental design, which resulted in 81 formulations (3 x 3 x 3 x 4 levels). Each formulation was made 3 times and tested in the viscometer, and the results were averaged. The root mean square error (RMSE), defined below, was used to decide the model that provided the best fit of the experimental data.

where n was the number of measurements, was the experimental shear stress (Pa) and was the predicted shear stress (Pa) corresponding to each fitted model. The data on apparent viscosity and Herschel-Bulkley model parameters were analyzed using Proc Mixed procedure of SAS (V. 9.1, SAS Institute Inc., Cary, NC), with the significance level of 0.05. The differences between the treatment means were compared using lsmeans statement.

RESULTS AND DISCUSSION

pH and Titratable Acidity

The pH of lassi varied from 4.14 to 4.32 while the titratable acidity ranged from 0.99 to 1.32% (lactic acid). With increase in milk solids content, the pH decreased while the titratable acidity increased marginally. This could be reasoned to the simple dilution effect of water that was added to reduce the milk solids content from 11.50 to 9.20%. Sugar did not significantly affect the pH and titratable acidity of lassi because it was added after fermentation, and thus, it did not interfere with the fermentation process to change the pH. Conversion of Viscometric Data by Mitschka MethodThe data obtained from the RVDV-II+Pro rotational viscometer were converted into basic shear stress vs. shear rate form by the method outlined by Briggs and Steffe (1997). A typical plot of log10 of shear stress vs. log10 of rpm that was used to compute the flow behaviour index and shear rate is presented in Fig. 1. The typical rheograms for lassi at different milk solids content are presented in Fig. 2. The flow curves were plotted in linear scales so as to estimate the possible shear sensitivity of the system. From Fig. 2, it is evident that the shear stress increased linearly with shear rate. This trend was observed at all sugar concentrations and in the presence of all stabilizers. The shape of the upward flow curve in Fig. 2 indicated the presence of yield stress in lassi. The effects of yield stresses on flow behaviour curves were evident at low shear rates because the flow behaviour at low shear rates was strongly influenced by yield phenomena and wall effects.

TABLE 1

RANGES OF FLOW BEHAVIOUR INDEX, SHEAR STRESS AND SHEAR RATE FOR LASSI SampleFlow behaviour index, nShear stress, PaShear rate, s-1

Carrageenan

10% Sugar0.234-0.2728.35-17.027.23-85.48

15% Sugar0.276-0.3263.54-12.036.23-72.10

20% Sugar0.267-0.3333.17-11.826.15-61.46

Pectin

10% Sugar0.245-0.3193.61-14.896.37-77.88

15% Sugar0.321-0.3733.17-13.725.70-63.37

20% Sugar0.315-0.3862.45-10.635.40-63.95

LBG

10% Sugar0.310-0.5081.61-14.974.46-64.37

15% Sugar0.337-0.5431.88-11.644.27-63.37

20% Sugar0.346-0.5751.86-10.414.73-59.76

The calculated flow behaviour index and shear stress and shear rate values of lassi depended on the sugar content and type of stabilizer (Table 1). The flow behaviour index at 30C ranged from 0.234 and 0.333 for carrageenan, 0.245 to 0.386 for pectin and from 0.310 and 0.575 for LBG. From the flow behaviour indices, it could be stated that the lassi exhibited strong pseudoplastic (shear thinning) behaviour. This type of non-Newtonian flow behaviour in lassi was expected as it was commonly reported in yoghurts and in some fermented milks (Parnell-Clunies et al. 1986b; Keogh and OKennedy 1998; Schmidt et al. 1980 and Lee and Lucey 2006). The pseudoplastic behaviour was reasoned to the fact that the increased shear rate deformed and/or rearranged particles, resulting in lower flow resistance and viscosity. Morris et al. (1981) explained that shear thinning was observed when the rate of shear exceeded the rate at which new entanglements could be formed in the product. The authors also added that the depletion in the concentration of non-specific crosslinks led to the observed reduction in viscosity at high shear rates.

FIG. 1. Plot of log10 shear stress (Pa) vs. log10 spindle speed (rpm) for computation of flow behaviour index and shear rate under Mitschka method.

Fig. 2. Rheograms of lassi containing 10% sugar and 11.50% milk solids and different stabilizers

Mathematical Modeling of Time-independent Flow Behaviour of LassiIn this study, the Ostwald De Waele, Casson and Herschel-Bulkley models were used as tools for calculation of the relationship between the shear stress and shear rate of lassi. The fitted rheological parameters of the various flow models are presented in Tables 2-4.

Applicability of Ostwald De Waele Model

The ln-ln plot of shear stress vs. shear rate was done to obtain the model coefficients. The applicability of Ostwald De Waele model to one set of data is illustrated in Fig. 3. The slope of the fit was the flow behaviour index while the exponential value of the model intercept yielded the consistency coefficient. The magnitudes of the coefficient of determination (R2) were between 0.930 and 0.996 for all samples while the root mean squared error (RMSE) ranged from 0.108 to 0.496 (Tables 2 to 4). In general, higher values of RMSE were observed at 11.50% milk solids content, at which the lassi samples exhibited relatively intense shear-thinning. Though the Ostwald De Waele model was reported to be good for pseudoplastic fluids, from the R2 and RMSE data, it could be concluded that this model did not fit the rheological data of lassi adequately.

Fig. 3. Ostwald De Waele plot of lassi containing 10% sugar, 9.20% milk solids and LBG as stabilizerApplicability of Cassons Model

The Casson model is a direct linear relationship between the square root of shear stress and shear rates. The applicability of Cassons model to one set of data is illustrated in Fig. 4. In general, the experimental data of lassi were in better agreement with the Cassons model than with Ostwald De Waele and Herschel-Bulkely models (Tables 2-4). The R2 values ranged from 0.951 to 0.999 while the RMSE varied from as low as 0.037 to a high of 0.246. The yield stress was calculated from the intercept of the model by linear regression. The magnitude of the Cassons viscosity ranged from 0.016 to 0.102 Pa.s for all samples while the yield stress varied from 0.638 to 7.725 Pa.

The Cassons viscosity increased with increasing milk solids content and with increasing concentrations of LBG stabilizer. The highest Casson viscosities were observed in lassi containing LBG as stabilizer. This could be due to the precipitation of the hard milk proteins in solution, which encountered the moving spindle to result in higher values. Similarly, the Cassons yield stress increased with increasing concentrations of milk solids and carrageenan and pectin stabilizers. On the other hand, the Cassons yield stress decreased with increasing concentrations of sugar and LBG stabilizer. Applicability of Herschel-Bulkley Model

In this model, the values of yield stress determined from the Cassons model were subtracted from the shear stress values. The magnitudes of the parameters K and n were determined from the linear regression analysis of ln () vs. ln . The applicability of Herschel-Bulkley model to one set of data is shown in Fig. 5. The Herschel-Bulkley flow behaviour index varied widely from 0.514 to 0.701 while the consistency coefficient ranged from 0.330 to 0.834 Pa.sn for all samples. The R2 values ranged from 0.954 to 0.999 while the RMSE ranged from 0.061 to 0.313. Such wide variation in the magnitude of flow behaviour index and consistency coefficient suggested that the lassi samples widely varied in their viscosity and mouthfeel when added with water, sugar and different hydrocolloids.It could be concluded from R2 and RMSE data that the Cassons model was the best one for lassi. The Ostwald De Waele model did not fit very well because of the yield stress. In foods exhibiting yield stress, Pelegrine et al. (2002) reported that the experimental data might not fit well to the Ostwald De Waele model with greater precision. Both Casson and Herschel-Bulkley models accounted for the yield stress value, and hence, they gave superior fit. Charm (1963) postulated that the Casson model adequately described the flow behaviour of tomato purees possessing yield stress. The author also found that the yield stress estimated from Casson model and that measured with a narrow gap concentric cylinder were closely related.

Though Cassons was the best model for lassi, further discussions in this paper would be focused on Herschel-Bulkley model because it was not only closely matched with Casson model in terms of R2 and RMSE but also gave a marginally superior fit of the lassi data in some cases. Also, the Herschel-Bulkley model yields three useful parameters namely, yield stress, consistency coefficient and flow behaviour index as compared to the two-parameter Casson model.

Fig. 4. Cassons plot of lassi containing 10% sugar, 9.20% milk solids and LBG as stabilizer

Fig. 5. Herschel-Bulkley plot of lassi containing 10% sugar, 9.20% milk solids and LBG as stabilizer

Effects of Various Factors on Rheological Behaviour of LassiStatistical analysis showed that the main effects of sugar and milk solids, as well as,stabilizer type and its concentration, on the initial apparent viscosity of lassi and the Herschel-Bulkley model parameters (Table 5) were highly significant ( F ValueF ValuePr> F ValueF ValuePr> F ValueF ValuePr> F Value

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