REGRESSION MODELS FOR DENSITY AND VISCOSITY OF ...

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Bulgarian Journal of Agricultural Science, 14 (No 6) 2008, 542-548 Agricultural Academy

REGRESSION MODELS FOR DENSITY AND VISCOSITY OF ULTRAFILTRATION MILK CONCENTRATES K. DINKOV, M. DUSHKOVA* and N. TOSHKOV University of Food Technologies, Department of Process Engineering, BG - 4002 Plovdiv, Bulgaria

Abstract DINKOV, K., M. DUSHKOVA and N. TOSHKOV, 2008. Regression models for density and viscosity of ultrafiltration milk concentrates. Bulg. J. Agric. Sci., 14: 542-548 Ultrafiltration of skim and standardized milk was carried out with a UF25-PAN polyacrylnitrilic membrane with 25 kDa molecular weight cut-off at volume reduction factors VRF=2, VRF=3, VRF=4 and VRF=5. The density and viscosity values of the initial milks and the ultrafiltration milk concentrates obtained from them were experimentally established. Mathematical models for the dependence of density and viscosity on the combined influence of the dry matter and temperature of ultrafiltration concentrates from skim and standardized milk were obtained. The results demonstrated an increase in the ultrafiltration concentrate density of 1.03 times for skim milk and 1.04 times for standardized milk under volume reduction factor variation from two to five, and an increase in ultrafiltration concentrate viscosity of 2.6 times for skim milk and 2.8 times for standardized milk under volume reduction factor variation from two to five.

Key words: ultrafiltration, milk concentrates, density, viscosity Abbreviations: PAN – polyacrylnitrilic; UF – ultrafiltration; VRF – volume reduction factor; DM – dry matter

Introduction Ultrafiltration is a baromembrane process which has already been put to practical use and applied to experiments in various branches of food industry, its widest application being in dairy industry (Brans, 2004; Daufin et al., 1998; Daufin et al., 2001; Maubois, 1991; Saboya and Maubois, 2000). The rational use and subsequent technological treatment of the ultrafiltration milk concentrates obtained requires extensive knowledge of their physical and rheological characteristics. The wide variety of ultrafiltration membranes used, of methods and ultrafiltration process conditions impedes the use of collected data. The publication of E-mail: [email protected]

similar data for ultrafiltration concentrates still lags behind investigations of the process itself, which in some cases hinders the use of the theoretical and practical results obtained under ultrafiltration separation. The density and viscosity of milk and ultrafiltration concentrates have been investigated by many authors (Herceg and Lelas, 2005; Oguntunde and Akintoye, 1991; Marcelo and Rizvi, 2008; Rattray and Jelen, 1995; Sopade et al., 2008). Nevertheless, experimental data need to be further accumulated with a view to their completeness and to the manufacture of typical Bulgarian products under industrial or laboratory conditions. The investigation of the density and viscosity of

Regression Models or Density and Viscosity of Ultrafiltration Milk Concentrates

ultrafiltration concentrates obtained from various milk types at various degrees of concentration (various volume reduction factors) and various temperatures was one of the principal aims of the present investigation. Furthermore, there was an evident need for generalization and mathematical processing of the data gathered aimed at obtaining regression models for their fast and accurate determination.

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Materials and Methods The raw material used in the investigations was pasteurized skim and standardized (3% fat) cow milk. The ultrafiltration separation of the two milk types was carried out on laboratory equipment demonstrated in (Dushkova and Dinkov, 2005). The working elements of the membrane module were fitted with a UF25-

Table 1 Density dependence on the dry matter (VRF variation) and temperature of ultrafiltration concentrates from skim cow milk

Skim milk t, ºC

20 Conf. Interval 30 Conf. interval 40 Conf. interval 50 Conf. interval 60 Conf. Interval

Dry matter DM=8.5 % 1.033 1.032 1.033 1.033± 0.001 1.030 1.029 1.030 1.030± 0.001 1.027 1.028 1.026 1.027± 0.001 1.024 1.023 1.023 1.023± 0.001 1.016 1.015 1.014 1.015± 0.001

Density, kg.dm-3 UF concentrate UF at VRF=2 concentrate at VRF=3 Dry matter Dry matter DM=11.3 % DM=14.3 % 1.039 1.047 1.038 1.048 1.037 1.047 1.038± 1.047± 0.001 0.001 1.035 1.042 1.034 1.044 1.035 1.046 1.035± 1.044± 0.001 0.002 1.030 1.039 1.031 1.041 1.032 1.040 1.032± 1.040± 0.001 0.001 1.028 1.035 1.026 1.036 1.027 1.037 1.027± 1.036± 0.001 0.001 1.020 1.028 1.022 1.030 1.021 1.031 1.021± 1.030± 0.001 0.002

UF concentrate at VRF=4 Dry matter DM =17.0 % 1.058 1.057 1.056 1.057± 0.001 1.053 1.055 1.054 1.054± 0.001 1.048 1.050 1.052 1.050± 0.002 1.045 1.047 1.046 1.046± 0.001 1.040 1.041 1.039 1.040± 0.001

UF concentrate at VRF=5 Dry matter DM=19.8 % 1.066 1.068 1.067 1.067± 0.002 1.065 1.064 1.064 1.064± 0.001 1.062 1.060 1.061 1.061± 0.001 1.055 1.057 1.056 1.056± 0.001 1.051 1.049 1.050 1.050± 0.001

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K. Dinkov, M. Dushkova and N. Toshkov

Table 2 Density dependence on the dry matter (VRF variation) and temperature of ultrafiltration concentrates from standardized cow milk

t, 0C

20 Conf. interval 30 Conf. interval 40 Conf. interval 50 Conf. interval 60 Conf. interval

Standardized milk Dry matter DM=11.2% 1.029 1.03 1.03 1.030± 0.001 1.026 1.027 1.028 1.027± 0.001 1.022 1.024 1.024 1.023± 0.002 1.018 1.019 1.02 1.019± 0.001 1.014 1.013 1.014 1.014± 0.001

Density, kg.dm-3 UF UF concentrate concentrate at VRF=2 at VRF=3 Dry matter Dry matter DM =16.2 % DM =19.9 % 1.041 1.055 1.039 1.054 1.04 1.054 1.040± 1.054± 0.001 0.001 1.037 1.05 1.036 1.052 1.038 1.051 1.037± 1.051± 0.001 0.001 1.032 1.047 1.033 1.048 1.034 1.047 1.033± 1.047± 0.001 0.001 1.027 1.044 1.03 1.042 1.029 1.043 1.029± 1.043± 0.002 0.001 1.024 1.037 1.025 1.038 1.024 1.039 1.024± 1.038± 0.001 0.001

PAN polyacrylnitrilic membrane with 25 kDa molecular weight cut-off (“Ekofilter JSC”, Bulgaria). In all experiments, samples of the initial skim and standardized milk and of the retentates after concentration to VRF=2, VRF=3, VRF=4 and VRF=5 were taken for analysis.

UF concentrate at VRF=4 Dry matter DM =23.4 % 1.067 1.068 1.068 1.068± 0.001 1.065 1.063 1.064 1.064± 0.001 1.059 1.061 1.063 1.061± 0.002 1.058 1.057 1.056 1.057± 0.001 1.051 1.053 1.052 1.052± 0.001

UF concentrate at VRF=5 Dry matter DM =27.0 % 1.082 1.083 1.084 1.083± 0.001 1.08 1.078 1.078 1.079± 0.002 1.075 1.076 1.075 1.075± 0.001 1.07 1.071 1.072 1.071± 0.001 1.066 1.068 1.067 1.067± 0.001

The density was measured by means of the standard picnometric method. The viscosity was measured using a Hepler viscosimeter and a Rheotest-2 viscosimeter. The dry matter of the initial milks and of the fractions obtained under all investigated ultrafiltration con-

Regression Models or Density and Viscosity of Ultrafiltration Milk Concentrates

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Table 3 Regression models for density (ρ) dependence on the dry matter (DM) and temperature (t) of skim and standardized milk and of ultrafiltration concentrates obtained from them Object of investigation 1.Skim milk UF concentrate 2.Standardized milk UF concentrate

Regression model ρ = 0 ,992351 .t − 0 ,014761 .DM

0 , 038641

ρ = 0 ,992351 .t

0 , 038641

− 0 , 014761

.DM

ditions were analyzed (ISO 6731: 1989). The values presented were obtained on the basis of three repetitions of experiments. The experimental data were processed by means of the method of least squares using nonlinear regression software.

Results and Discussion Tables 1 and 2 show the experimental data for density dependence on the dry matter (volume reduction factor variation VRF) and temperature of ultrafiltration concentrates obtained from skim and standardized cow milk. The experimental data were processed and regression models were obtained. The data are shown in Table 3. The data and models presented confirmed the familiar density dependences, i.e. density rose with the increase in dry matter and decreased with the rise in temperature. The novelty here lies in the obtained regression models for density dependence on the dry matter and temperature of concentrates under complete ultrafiltration concentration of skim and standardized milk with a UF25-PAN polymeric membrane. The comparative results on density at increasing volume reduction factors from 2 to 5 are another point of interest: density increased slightly but statistically significant (level of significance 0.05) 1.03 times for skim and 1.04 times for standardized milk at the same temperature. Within the investigated temperature range from 20°C to 60°C, density decreased slightly but statistically significant (level of significance 0.05): 1.02 times for skim and standardized milk concentrates.

Mean error of approximation

Correlation coefficient

1.11%

0.97

0.48%

0.97

The studies carried out with a Rheotest 2 rotational viscosimeter demonstrated insignificant viscosity anomaly only for the highest concentrations and lowest temperatures. Therefore all concentrates from VRF=2 to VRF=5 can be regarded as Newtonian liquids. The experimental data on viscosity dependence on the dry matter and temperature of the above-mentioned concentrates are shown in Table 4 and 5. The regression models obtained are presented in Table 6. It can be seen that for all skim and standardized milk concentrates the increase in dry matter led to an increase in density which became more pronounced with the rise in dry matter. The viscosity increased with the increase in volume reduction factor from two to five: 2.6 times for the skim milk concentrates and 2.8 times for standardized milk concentrates. On the other hand, a typical monotonous viscosity decrease with the rise in temperature was observed for all skim and standardized milk concentrates. This allowed ultrafiltration concentration to be carried out at a temperature close to the maximum permissible limit for the membrane used. Within the observed temperature range from 20°C to 60°C the viscosity decreased around 3.78 times for skim milk concentrate and 3.66 times for standardized milk concentrate.

Conclusions On the basis of ultrafiltration concentration of skim and standardized cow milk under volume reduction factor variation from 2 to 5 and subsequent measurement of density and viscosity under various tempera-

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K. Dinkov, M. Dushkova and N. Toshkov

Table 4 Viscosity dependence on the dry matter (VRF variation) and temperature of ultrafiltration concentrates from skim cow milk

Skim milk 0

t, C

20 Conf. interval 30 Conf. interval 40 Conf. interval 50 Conf. interval 60 Conf. interval

Dry matter DM=8.5 % 1.75 1.7 1.8 1.75± 0.05 1.15 1.2 1.24 1.20± 0.05 0.92 0.97 1.02 0.97± 0.05 0.7 0.74 0.78 0.74± 0.04 0.66 0.58 0.62 0.62± 0.04

Viscosity, mPa.s UF UF concentrate concentrate at VRF=2 at VRF=3 Dry matter Dry matter DM=11.3 % DM=14.3 % 2.38 3.53 2.43 3.41 2.48 3.47 2.43± 3.47± 0.05 0.06 1.69 2.58 1.77 2.63 1.73 2.53 1.73± 2.58± 0.04 0.05 1.25 1.8 1.2 1.85 1.3 1.75 1.25± 1.80± 0.05 0.05 0.94 1.25 1.02 1.2 0.98 1.3 0.98± 1.25± 0.04 0.05 0.78 0.99 0.74 0.95 0.82 0.91 0.78± 0.95± 0.04 0.04

tures, the following were established: mathematical models of density dependence on the combined influence of dry matter and temperature of skim and standardized concentrates; results demonstrating the increase in the density of ultrafiltration concentrates by 1.03 times for skim milk and 1.04 times for standardized milk under volume reduction factor variation from

UF concentrate at VRF=4 Dry matter DM =17.0 % 4.9 4.95 5 5.00± 0.05 3.5 3.6 3.55 3.55± 0.05 2.44 2.5 2.55 2.50± 0.05 1.8 1.7 1.75 1.75± 0.05 1.2 1.3 1.25 1.25± 0.05

UF concentrate at VRF=5 Dry matter DM=19.8 % 7.1 7.2 7.29 7.20± 0.1 5 5.07 4.94 5.00± 0.07 3.2 3.3 3.25 3.25± 0.05 2.3 2.2 2.25 2.25± 0.05 1.59 1.69 1.64 1.64± 0.05

two to five; mathematical models of viscosity dependence on the combined influence of dry matter and temperature of skim and standardized concentrates ; results demonstrating the increase in density of ultrafiltration concentrates by 2.6 times for skim milk and 2.8 times for standardized milk under volume reduction factor variation from two to five.

547

Regression Models or Density and Viscosity of Ultrafiltration Milk Concentrates

Table 5 Viscosity dependence on the dry matter (VRF variation) and temperature of ultrafiltration concentrates from standardized cow milk

t, 0C

20 Conf. interval 30 Conf. interval 40 Conf. interval 50 Conf. interval 60 Conf. interval

Standardized milk Dry matter DM=11.2% 2.06 2.01 1.96 2.01± 0.05 1.46 1.51 1.56 1.51± 0.05 0.92 0.97 1.02 0.97± 0.05 0.74 0.79 0.69 0.74± 0.04 0.66 0.58 0.62 0.62± 0.04

Viscosity, mPa.s UF UF concentrate concentrate at VRF=2 at VRF=3 Dry matter Dry matter DM =16.2 % DM =19.9 % 4.1 5.65 4.16 5.72 4.21 5.79 4.16± 5.72± 0.06 0.07 3 3.95 3.1 3.89 3.05 4 3.05± 3.95± 0.05 0.06 2.17 2.67 2.22 2.77 2.29 2.72 2.22± 2.72± 0.05 0.05 1.5 1.8 1.54 1.9 1.45 1.85 1.50± 1.85± 0.05 0.05 1.05 1.43 1.15 1.48 1.1 1.52 1.10± 1.48± 0.05 0.05

References Brans, G., C. G. P. H. Schroen, R. G. M. van der Sman and R. M. Boom, 2004. Membrane fractionation of milk: state of the art and challenges. J. Membrane Sci., 243(1-2): 263-272.

UF concentrate at VRF=4 Dry matter DM =23.4 % 8.46 8.55 8.65 8.55± 0.1 5.75 5.82 5.68 5.75± 0.07 4.14 4.25 4.2 4.20± 0.06 3 3.1 3.05 3.05± 0.05 2.51 2.46 2.55 2.51± 0.05

UF concentrate at VRF=5 Dry matter DM =27.0 % 11.75 11.85 11.95 11.85± 0.1 8.17 8.08 7.98 8.08± 0.1 5.66 5.73 5.59 5.66± 0.07 4.09 4.14 4.19 4.14± 0.05 3.25 3.3 3.35 3.30± 0.05

Daufin G., F. Reno and P. Aimar, 1998. Les Separations par Membrane dans les Procédés de l’Industrie Alimentaire, Technical document; Chapter 7, pp. 282–371. Daufin G., J. P. Escudier, H. Carrere, S. Berot, L. Fillaudeau and M. Decloux, 2001. Recent and

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Table 6 Regression models for density (µ) dependence on the dry matter (DM) and temperature (t) of skim and standardized milk and of ultrafiltration concentrates obtained from them Object of investigation 1.Skim milk UF concentrate 2.Standardized milk UF concentrate

Regression model µ = 1 ,029101 .t − 1 ,14330 .DM

1 ,789356

µ = 1,029101.t

1,789356

−1,14330

.DM

emerging applications of membrane processes in the food and dairy industry, Trans. IChemE, 79: 89. Dushkova, M. and K. Dinkov, 2005. Investigation of process characteristics and of principal components of ultrafiltration retentates. Biotechnology and Biotechnological Equipment, 2(19): 179-182. Herceg, Z. and V. Lelas, 2005. The influence of temperature and solid matter content on the viscosity of whey protein concentrates and skim milk powder before and after tribomechanical treatment. J. Food Eng., 66: 433-438. Marcelo, P. and S. Rizvi, 2008. Physicochemical properties of liquid virgin whey protein isolate. Int. Dairy J., 18: 236-246. Maubois, J. L., 1991. New applications of membrane technology in the dairy industry. Australian J. Dairy

Mean error of approximation

Correlation coefficient

11.45%

0.99

8.07%

0.997

Technol., 46(11): 91-95. Oguntunde, A. O. and O. A. Akintoye, 1991. Measurement and Comparison of Density, Specific Heat and Viscosity of Cow’s Milk and Soymilk. J. Food Eng, 13: 221-230. Rattray, W., P. Jelen, 1995. Viscous behavior of whey protein concentrate dispersions. Int. Dairy J., 5: 673-684. Saboya, L. V., J. L. Maubois, 2000. Current developments of microfiltration technology in the dairy industry. Lait, 80: 541-546 Sopade, P. A., P. J. Halley, J. A. Y. Cichero, L. C. Ward, L. S.Hui, K. H. Teo, 2008. Rheological characterization of food thickeners marketed in Australia in various media for the management of dysphagia. J. Food Eng., 84: 553-562.

Received August, 10, 2008; accepted for printing October, 5, 2008.