Page 1

International Journal of Agricultural Science and Research (IJASR) ISSN 2250-0057 Vol. 3, Issue 4, Oct 2013, 1-10 © TJPRC Pvt. Ltd.

MATHEMATICAL MODELLING OF MASS TRANSFER FOR OSMOTIC DEHYDRATION OF BEETROOT (BETA VULGARIS L.) KULWINDER KAUR & A K SINGH PFE, Punjab Agricultural University, Punjab, India

ABSTRACT The present study was carried out with a view to investigate the osmotic dehydration kinetics in terms of water loss and solute gain. Beetroot slices of 10x10x 3mm size were osmotically dehydrated in combined aqueous solution of salt (525%) and sugar (55- 75 °Brix) with solution to beetroot sample ratio of 4:1 at different solution temperatures ranging from 3060 °C for 30,60,90,120,180 and 240 minutes. The experimental data was fitted to different empirical kinetic models including Azuara, Fick’s, Page, Power and Generalized Exponential. The study revealed that water loss as well as solute gain increased with increase in solution concentration and temperature. Further, Azuara’s model fitted to water loss as well as solutes gain (SG) data represented more accurately the evolution of the complete process close to equilibrium. Generalized exponential model presented best fit for water loss whereas power model showed best predictive capacity for solute gain data. The effective diffusivity was calculated using Fick’s equation which were found in range of 7.15 x 10

-10

to 1x 10-9 and 3.21 x10-9 to 5.08 x

10-9 for water loss and solute gain respectively.

KEYWORDS: Beetroot, Osmotic Dehydration, Mass Transfer, Kinetic Models, Effective Diffusivity INTRODUCTION Beetroot (Beta vulgaris L.) is an excellent source of calcium, magnesium, copper, phosphorus, sodium and iron. The interest of the food industry in betalains has grown since these were identified as natural antioxidants (Escribano et al 1998) which may have positive health effects on humans. In most temperate climates, beets are planted in the spring and harvested in the autumn. Fresh beetroot is highly perishable which needs preservation methods to increase its shelf-life. One of the preservation methods ensuring microbial safety of biological products is drying (Mathlouthi 2001). Drying process applied to fruits and vegetables can be classified in four generation: solar drying, atmospheric drying, sub atmosphere drying and novel drying technologies (Jayaraman and Gupta, 1995). Novel drying technologies include microwave drying, infrared radiation drying, electric or magnetic drying, foam mat drying and osmotic dehydration etc. Osmotic dehydration is one of the most common natural and reliable methods for food preservation which is effective at room temperature. It is the process of water removal by immersion of water containing cellular solute in a concentrated aqueous solution (Ponting, 1973). This results in three types of counter mass transfer phenomena. First, water diffusion from food tissue to osmotic solution, second solute diffusion from osmotic solution to food tissue and third a leaching out of the food tissue’s own solutes into osmotic solution, which is assumed to be quantitatively negligible compared with the first two types mass transfer, but essential with respect to composition of the product. Several factors affect the mass transfer during osmotic dehydration which is solution temperature, concentration of solution, type of osmotic agent, agitation of osmotic solution, time duration, geometry of the food material, variety of food


2

Kulwinder Kaur & A K Singh

material, osmotic solution to fruit ratio, physico-chemical properties of food materials and operating pressure. However, the specific effect of the osmotic solution is of great importance when choosing the solution. Several solutes, alone or in combination have been employed in hypertonic solutions for osmotic dehydration (Tortoe, 2010). Sugar and salt solutions proved to be best choices based on effectiveness, convenience and flavor. Further, the potential for improving food quality through modeling is tremendous but limited by the lack of quantitative data and predictive models. Engineers require quantitative models to design and optimize processes. Therefore, modeling using empirical models namely Azuara, Fick’s second law, page, power law and generalized exponential, provide a useful tools for understanding the osmotic dehydration process of beetroot. The purpose of the present work was to study mass transfer parameters during the osmotic dehydration of beetroot and examine the predictive capacity of Azuara, Fick’s second law, Page, Power law and Generalized exponential equations to the experimental data. Theory Azuara et al. (1992) modeled the rate of water loss (WL) and solute gain (SG) as function of time by using a mass balance on water movement inside the food, obtaining equations with two fitting parameters. In the model formulation, the following relation for WL is established:

(1) where WL∞ is the corresponding value at infinite time (i.e., at equilibrium) and S1 is the constant related to the outward water diffusion rate in the food. Equation (1) can be expressed in linear form as:

(2) The water loss at equilibrium (WL∞) and the constant S1 were estimated from the slope and intercept of the plot (t ⁄ ) vs. t using the eqn (2). Thus, the equations for SG can be written as:

(3)

(4) Where, SG∞ is the corresponding value at infinite time (i.e. at equilibrium) and S 0 is the constant related to the incoming solute diffusion rate in the food. Similarly to WL ∞ and S1, SG∞ and S0 parameters are obtained from the straight line (t ⁄

) vs. t using equation 4. Considering the beetroot slices as slab geometry with initially uniform water or solutes content, the solution for Fick’s

equation for constant process conditions is (Crank, 1975): (5)


Mathematical Modelling of Mass Transfer for Osmotic Dehydration of Beetroot (Beta vulgaris L.)

3

For long drying times (MR<0.6), logarithimic form of equation is used.

(6) (7) Where, A = ln

Similarly, effective diffusivity for solute was calculated by using expression

(8) Where, Dw and Ds= effective diffusivity of water or solute (m2/s) L = slab thickness, half thickness is used as water loss and solute gain occurs on both sides of slab. t = Osmotic dehydration time (seconds) Page (1949), Power law (Rahman, 1992) and Generalized exponential (Henderson, 1974) empirical models are given by the following equations: Page, MR or SGR = exp (-ktn)

(9)

Power law, MR or SGR = -ktn

(10)

Generalized exponential, MR or SGR = A.exp (-kt)

(11)

MATERIALS AND METHODS Sample Preparation Beetroots were procured from local market and then stored at 5 0C prior to experiments. Samples were thoroughly washed with water to remove adhered soil and other debris. The beetroots of 19.5째Brix were hand peeled and cut into 10x 10x 3 mm slices. The average moisture content of the beetroot was found to be 79.17 % on a wet basis. Considering the greater effectiveness of a mixture of solutes over a single solute, a binary solution of salt and sugar was prepared with the proper amount of pure water. Osmotic Dehydration The samples were subjected to osmotic dehydration for 30, 60, 90,120, 180 and 240 minutes in a mixture of salt and sugar with concentration of 5, 15, 25 % (w/v) and (55, 65 and 75째Brix), respectively at solution temperature of 30, 45 and 60째C. For each experiment, the osmotic solution to sample ratio was kept as 4:1 (w/v) in order not to dilute the osmotic solution by water removal during the experiment, which can lead to local reduction of the osmotic driving force during the process. During experimentation, it was assumed that the amount of solute leaching out of beetroots during osmosis was negligible (Biswal & Bozorgmehr, 1992, Lazarides et al 1995). No blanching was done prior to osmosis as it is detrimental to


4

Kulwinder Kaur & A K Singh

the osmotic dehydration process due to loss of semi-permeability of cell membranes (Ponting, 1973) and reduction of βcarotene (Bao & Chang, 1994, Kalra, 1990, Negi & Roy, 2000).All the experiments were done in duplicate and the average value was taken for calculations. Water loss (g/100g of initial mass) and solute gain (g/100g of initial mass) were calculated by equations as given below:

where WL is water loss (g /100 g of initial mass), SG is solutes gain (g /100 g of initial mass), Mο is initial water mass (g), Mt is the water mass at time t in the sample (g), mο is initial total solutes (g), mt is total solutes at time t in the sample (g), respectively. Statistical Analysis The model’s parameters as well as the effective diffusivity values were determined for water loss and solute gain using the non-linear regression from the SPSS version 16.0 software. The best predictive capacity of models for mass transfer was evaluated by obtaining the coefficient of determination R2 and percent mean relative deviation of modulus (P %) as given equation:

According to Deng and Zhao (2008) a model with P value below than 10% is considered acceptable. Therefore, the best model should follow the highest coefficient of determination (R 2) and least P value as criteria.

RESULTS AND DISCUSSIONS The immersion time is an important parameter influencing mass transfer rate of sample during osmotic dehydration. In general, with passage of immersion time during osmotic process, there is reduction in mass transfer rate whereas weight loss continues to increase. A similar result has been reported in present study as shown in Figure 1 to 3. The figures showed that the rate of water loss and solute gain were higher at the initial stage followed by lower diffusion rate for remaining period of dehydration. This might be due to facts that with passage of immersion time the osmotic driving force for water diffusion from sample to solution and solute transfer from solution to sample decreased. Further in salt-sugar mixed osmotic solution, sugar molecules due to high molecular weight accumulated in thin sub surface layer resulting in extra barrier to mass transfer, whereas salt molecules due to smaller size easily diffused inside the cell membrane and generated concentration gradient as a driving force for mass transport during osmotic dehydration. Besides, salt concentration also inhibited the formation of compacted surface layer of sugar and allowed transfer of water as well as solute, but at slower rate. Conway et al (1983) has reported that mass transport data were not significantly changed in the period between 4 h to 20 h. On average about 31.73 (g/100 g of initial mass) of water loss and 6.22 (g/100g of initial mass) of solute gain was observed during 4 hr of osmotic treatment.


Mathematical Modelling of Mass Transfer for Osmotic Dehydration of Beetroot (Beta vulgaris L.)

5

The effect of solution temperature on mass transfer parameters including water loss and solute gain has been presented in Figure 1 (a) and 1 (b). The figures showed that water loss and solute gain increased with increase solution temperature from 30 to 60°C. This might be due to swelling and plasticizing of cell membrane causing cell membrane damage at higher process temperature (Karel, 1976). Another reason for such increase is reduction of solution viscosity at higher temperature, which lowers the resistance to diffusion of solutes into sample tissue and imparted higher solute gain and water loss. On average about 27.24 (g/100 g of initial mass) of water loss and 4.29 (g/100g of initial mass) of solute gain was observed at 60°C solution temperature during 4 hr of osmotic treatment. Further, it was suggested that sample should not be exposed to osmotic solution at higher temperature (above 60°C) for prolong time in order to avoid enzymatic browning and flavor deterioration (Lenart and Flink, 1984). From figures 2 (a) and 2(b) representing effect of different levels of salt concentration on mass transfer parameters, it was observed that water loss and solute gain increased with increase in salt concentration from 5-25% (w/v). This might be due to the reason that with progression of time, sugar and salt can pass through cytoplasmic membrane (Isse and Schubert, 1992). Sugar molecules due to high molecular size accumulated at the surface of the cytoplasm and in that way created thick subsurface layer which make a barrier to water as well as solute transfer. However, presence of salt prevented the formation of crust barrier and led to higher rate of water removal and solute uptake. Further, small size of salt molecules which can easily diffuse through cytoplasm membrane and generated concentration gradient at the vacuole level that allowed higher rate of water removal and weight reduction than solute gain. On average about 27.36 (g/100 g of initial mass) of water loss and 4.28 (g/100g of initial mass) of solute gain was observed at 25 % salt during 4 hr of osmotic treatment. The effect of different sugar concentration on mass transfer parameters has been presented in Figure 3(a) and 3(b). From figure it was observed that water loss (WL) increased with increase in sugar concentration and promoted further moisture reduction in beetroot However, for solute gain (SG) little variation was observed with increase in sugar concentration from 65 to 75°Brix. This might be due to formation of solute barrier with high molecular weight posing an additional resistance to mass exchange and lowering rates of water loss and solute gain. On average about 28.06 (g/100 g of initial mass) of water loss and 4.18 (g/100g of initial mass) of solute gain was observed at 75 °Brix during 4 hr of osmotic treatment. Modeling of Mass Transfer Kinetics The values of model parameters fitted to experimental data, along with the determination coefficient and mean relative deviation of modulus (P %) for Azuara model obtained from the non-linear regression analysis are shown in Table 1 and 2. The parameters S1 and So of Azuara model representing the water loss (WL) and solute gain (SG) rate, respectively because of osmo-convective diffusion mechanism. It was found that S0 decreased with increase in sugar, salt concentration and solution temperature. On the other hand, parameter S1 for WL showed increasing trend with sugar concentration at solution temperature above 45°C whereas no clear trend was observed with increasing salt concentration and solution temperature. Further, WL∞ was observed to increase with solution temperature, sugar and salt concentrations. On the contrary, SG∞ increased with sugar concentration but no change was noticed with increasing level of salt concentration and solution temperature. Nevertheless, Azuara model was effective to identify the equilibrium conditions as much for WL as for SG by obtaining the parameters WL∞ and SG∞ respectively, presenting equilibrium values for the obtained WL and SG in salt sugar solutions (Table 1 and 2) for beetroot. Similar results were reported by Ganjloo et al (2011) for osmotic dehydration of seedless guava cubes.


6

Kulwinder Kaur & A K Singh

The effective diffusivities of water loss and salt gain calculated using Fick’s model are presented in Table 1 and 2. Effective diffusivity for water loss (Dw) was found to increase with increase in solution temperature whereas no trend was observed with increase in sugar and salt concentration. It implied that water loss was mainly affected by solution temperature irrespective of solution concentration. Also, little variation in effective diffusivity for water loss was observed as the temperature varied from 45 to 60 °C, which was in agreement with results reported by Park et al (2002) for osmotic dehydration of pear cubes. This abrupt phenomenon was occurred due to structural changes in cell tissues at higher temperature. For solute gain (SG), effective diffusivity of the solute (Ds) decrease with increase in all process variables including solution temperature, salt and sugar concentration. The effective diffusivity calculated from Fick’s equation was found in range of 7.15 x 10 -10 to 1x 10-9 for water loss and in range of 3.21 x10 -9 to 5.08 x 10-9 for solute gain. The Kinetics parameters along with R2 for page, power law and generalized exponential model (GEM) calculated for water loss (WL) and solute gain (SG) under different experimental conditions has been presented in Table 1 and 2. The statistically analyzed data revealed that for page equation parameter k, no trend was observed with solution concentration and temperature for WL whereas it showed decreasing trend with salt and sugar concentration up to solution temperature of 45 °C for SG. On the other hand parameter n showed no trend with solution concentration and temperature for both WL and SG. In case of power law model, parameter n and k decreased with increase in solution concentration and temperature for SG, while for WL, parameters k and n first increased and then decreased as the temperature varied from 30- 45°C and 45 to 60°C respectively. For generalized exponential model (GEM), parameter a increased with solution concentration and temperature whereas parameter k reflected almost constant value with solution concentration and temperature for both WL and SG. The criteria which were used for qualification of the goodness of fit (R2 and P) revealed that the best fit for water loss experimental data was obtained using generalized exponential model and power law model presented best fit of model against solute gain data as the higher value of R2 and least value of percent mean relative deviation modulus (P%).

CONCLUSIONS The effects of solution concentration and temperature on dehydration kinetics of beetroot during osmotic dehydration were investigated in terms of water loss and solute gain. The results revealed that the rate of water loss and solute gain increased with increasing levels of independent process variables (salt-sugar concentration and temperature). The maximum water loss of 33.39 (g/100g of initial mass) and solute gain of 6.66 (g/100g of initial mass) was observed with salt –sugar concentration of 25- 75 °Brix and solution temperature of 60°C during 4 hr osmotic treatment of beetroot slices having thickness of 3mm and sample to solution ratio of 4:1. However, Azuara model showed adequate prediction of the evolution of the complete process to equilibrium. The best model was observed as Generalized exponential model for water loss and Power law model for solute gain data as the highest R2 and least P% value in comparison to other fitted models. The effective diffusion coefficients obtained from Fick’s second law equation ranged from 7.15 x 10

-10

to 1x 10-9 for water loss and 3.21

x10-9 to 5.08 x 10-9 for solute gain data.

ACKNOWLEDGEMENTS The authors would like to thank the faculty of department of Processing and Food Engineering, Punjab Agricultural University, India for their assistance in the research.


Mathematical Modelling of Mass Transfer for Osmotic Dehydration of Beetroot (Beta vulgaris L.)

7

REFERENCES 1.

Azuara, E., Cortes, R., Garcia, H. S. & Berstian, C. I. (1992). Kinetic model for osmotic dehydration and its relationship with Fick’s second law. International Journal of Food Science and Technology, 27, 239–242.

2.

Bao, B., & Chang, K. C. (1994). Carrot juice color, carotenoids, and non-starchy polysaccharides as affected by processing conditions. Journal of Food Science, 59, 1155–1158.

3.

Biswal, R. N., & Bozorgmehr, K. (1992). Mass transfer in mixed solute osmotic dehydration of apple rings. Transactions of ASAE, 35, 257–262.

4.

Conway, J., Castaigne, F., Picard, G. & Vevan, X. (1983). Mass transfer consideration in the osmotic dehydration of apples. Canadian Institute of Food Science and Technology Journal, 16, 25-29.

5.

Crank, J. (1975). The mathematics of diffusion (2nd ed.). Oxford: Clarendon Press.

6.

Escribano, J., Pedreno, M. A., Garcia-Carmona, F. & Munoz, R. (1998). Characterization of the antiradical activity of betalains from Beta vulgaris L. roots. Phytochem Anal, 9, 24–27.

7.

Ganjloo, A., Rahman, R.A., Bakar, J., Osman, A. & Bimakr, M (2011). Mathematical modelling of mass transfer during osmotic dehydration of seedless guava (Pisidium guajava L.) cubes. International Food Research Journal, 18(3), 1105-10.

8.

Henderson, S. M. (1974). Progress in developing the thin-layer drying equation. Transactions of ASAE, 17, 1167– 1168 ⁄ 1172.

9.

Isse, M.G & Schubert, H. (1992). Osmotic dehydration of mango: mass transfer between mango and syrup. In D. Behrens (Ed.), Proceedings of the fourth world congress of chemical engineering, 728–45.

10. Jayaraman, K. S. & Gupta, D.K. (1995). Drying of fruits and vegetables. In: Handbook of industrial drying. Mujumdar AS

(Ed.). Marcel Dekker Inc., New York, USA. pp. 643-690.

11. Kalra, C. L. (1990). Role of blanching in vegetable processing. Indian Food Packer, September–October, 3–15. 12. Karel M (1976) Technology and applications of new intermediate moisture foods pp 4-28. In Intermediate Moisture Foods Ed. R Davies, G G Birch and K J Parkar. Applied Science Publishers. 13. Lazarides, H. N., Katsanidis, E., & Nickolaidis, A. (1995). Mass transfer kinetics during osmotic preconcentration aiming at minimal solute uptake. Journal of Food Engineering, 25, 151–166. 14. Lenart, A., & Flink, J. M. (1984). Osmotic concentration of potato. I. Criteria for the end-point of the osmosis process. Journal of Food Technology, 19, 45–63. 15. Mathlouthi M (2001) Water content, water activity, water structure and the stability of foodstuffs. Food Cont 12, 409– 417. 16. Negi, P. S., & Roy, S. K. (2000). Effect of low-cost storage and packaging on quality and nutritive value of fresh and dehydrated carrots. Journal of the Science of Food and Agriculture, 80, 2169–2175.


8

Kulwinder Kaur & A K Singh

17. Page, G. E. (1949). Factors influencing the maximum of air drying shelled corn in thin layer. M.Sc. Thesis, USA. Purdue University, Indiana. 18. Park, K. J., Bin, A., Brod, F. P. R., & Park, T. H. K. B. (2002). Osmotic dehydration kinetics of pear D_anjou (Pyrus communis L.). Journal of Food Engineering, 52, 293–298 19. Ponting, J.D. (1973). Osmotic dehydration of fruits - recent modifications and application. Process Biochemistry, 8, 18-20. 20. Rahman, M. S. (1992) Osmotic dehydration kinetics of foods. Indian Food Industry, 11, 20-24. 21. Tortoe Charles (2010). A review of osmodehydration for food industry. African Journal of Food

Science,4(6),303 -

24.

APPENDICES Table 1: Model’s Parameters and Goodness of Fit for Water Loss during Osmotic Dehydration of Beetroot Temp 30

Experiments Sugar 55

65

75

45

55

65

75

60

55

65

75

Salt 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25

S1 0.064 0.042 0.042 0.042 0.043 0.043 0.042 0.042 0.042 0.030 0.034 0.034 0.035 0.040 0.040 0.041 0.041 0.036 0.035 0.036 0.034 0.036 0.043 0.043 0.043 0.043 0.038

Fick’s Second Law Model k R2 Dw 0.047 0.999* 7.15E-10 0.065 0.986* 9.89E-10 0.066 0.990* 1.00E-09 0.066 0.988* 1.00E-09 0.065 0.986* 9.89E-10 0.064 0.982* 9.74E-10 0.065 0.979* 9.89E-10 0.064 0.976* 9.74E-10 0.064 0.979* 9.74E-10 0.081 0.969* 1.23E-09 0.073 0.965* 1.11E-09 0.075 0.980* 1.14E-09 0.069 0.948* 1.05E-09 0.068 0.993* 1.03E-09 0.067 0.993* 1.02E-09 0.068 0.993* 1.03E-09 0.067 0.990* 1.02E-09 0.068 0.946* 1.03E-09 0.078 0.991* 1.19E-09 0.074 0.989* 1.13E-09 0.074 0.989* 1.13E-09 0.069 0.965* 1.05E-09 0.067 0.997* 1.02E-09 0.066 0.997* 1.00E-09 0.067 0.996* 1.02E-09 0.068 0.996* 1.03E-09 0.069 0.974* 1.05E-09

Azuara Model WL∞ R2 27.193 0.997 * 31.980 0.993* 32.298 0.993* 32.555 0.993* 32.634 0.994* 32.772 0.993* 33.133 0.993* 33.288 0.992* 33.432 0.993* 34.396 0.981* 34.194 0.983* 34.730 0.986* 34.794 0.985* 35.080 0.992* 35.183 0.993* 35.393 0.993* 35.626 0.993* 35.778 0.986* 34.372 0.989* 34.397 0.988* 34.397 0.986* 34.730 0.987* 34.925 0.994* 35.063 0.994* 35.120 0.995* 35.405 0.995* 35.738 0.990*

k 3.828 4.866 5.109 5.153 5.224 4.972 4.943 4.681 4.624 5.211 4.408 5.005 3.775 5.130 5.044 5.161 5.189 3.898 6.357 5.182 5.410 4.065 5.384 5.424 5.747 6.087 4.484

Page Model n -0.783 -0.760 -0.771 -0.771 -0.781 -0.770 -0.763 -0.752 -0.751 -0.700 -0.678 -0.711 -0.655 -0.758 -0.755 -0.763 -0.767 -0.670 -0.772 -0.729 -0.737 -0.678 -0.780 -0.786 -0.801 -0.816 -0.713

R2 0.840* 0.793* 0.801* 0.797* 0.803* 0.795* 0.790* 0.776* 0.779* 0.744* 0.752* 0.778* 0.705* 0.802* 0.802* 0.805* 0.805* 0.717* 0.837* 0.795* 0.799* 0.733* 0.820* 0.820* 0.822* 0.824* 0.751*

Power Law Model k n R2 -0.513 0.119 0.977* -0.395 0.166 0.954* -0.391 0.168 0.960* -0.387 0.170 0.957* -0.394 0.167 0.960* -0.399 0.165 0.954* -0.393 0.167 0.950* -0.397 0.165 0.942* -0.401 0.163 0.944* -0.298 0.213 0.915* -0.337 0.190 0.913* -0.331 0.194 0.936* -0.358 0.179 0.883* -0.375 0.174 0.959* -0.379 0.173 0.959* -0.380 0.173 0.961* -0.382 0.172 0.961* -0.366 0.176 0.892* -0.341 0.190 0.946* -0.335 0.193 0.950* -0.361 0.178 0.903* -0.387 0.169 0.966* -0.391 0.168 0.966* -0.388 0.317 0.966* -0.384 0.173 0.969* -0.366 0.178 0.922* -0.358 0.181 0.945*

k -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002

GEM Model a 0.176 0.703 0.701 0.699 0.704 0.706 0.701 0.703 0.705 0.623 0.648 0.649 0.662 0.689 0.69 0.692 0.694 0.669 0.651 0.659 0.656 0.668 0.699 0.703 0.703 0.702 0.677

R2 0.974* 0.986* 0.985* 0.984* 0.98* 0.982* 0.984* 0.986* 0.987* 0.993* 0.997* 0.995* 0.992* 0.989* 0.989* 0.988* 0.986* 0.99* 0.975* 0.986* 0.985* 0.985* 0.971* 0.967* 0.959* 0.956* 0.981*

Note: * P (%) implies significant at 10 % level

Table 2: Model’s Parameters and Goodness of Fit for Solute Gain during Osmotic Dehydration of Beetroot Experiments Sug Sal ar t 55 5 15 25 65 5 15 25 75 5 15 25 45 55 5 15 25 65 5 15 25 75 5 15 25 60 55 5 15 Te mp 30

Fick’s Second Law Model

Azuara Model SO 17.317 17.288 16.757 17.172 15.839 14.129 13.799 13.070 12.589 17.088 16.365 15.947 10.433 10.706 10.348 10.346 10.203 10.117 15.194 17.054

SG∞ 0.002 0.002 0.002 0.002 0.003 0.003 0.004 0.004 0.004 0.002 0.002 0.003 0.006 0.006 0.006 0.007 0.007 0.007 0.003 0.002

R2 0.907* 0.913* 0.913* 0.916* 0.915* 0.969* 0.976* 0.986* 0.990* 0.896* 0.910* 0.951* 0.822 0.836 0.863 0.867 0.867 0.879 0.970* 0.912*

Slope 0.334 0.333 0.329 0.329 0.32 0.304 0.301 0.291 0.284 0.332 0.328 0.321 0.233 0.234 0.223 0.222 0.217 0.212 0.317 0.329

R2 0.936* 0.934* 0.929* 0.930* 0.921* 0.930* 0.930* 0.937* 0.935* 0.929* 0.928* 0.934* 0.973* 0.969* 0.974* 0.975* 0.971* 0.973* 0.944 0.932

Page Model

Ds

k

5.08E-09 5.07E-09 5.01E-09 5.01E-09 4.87E-09 4.62E-09 4.58E-09 4.43E-09 4.32E-09 5.05E-09 4.99E-09 4.88E-09 3.54E-09 3.56E-09 3.39E-09 3.38E-09 3.30E-09 3.23E-09 4.82E-09 5.01E-09

358.289 348.593 307.687 295.720 287.671 224.038 210.421 181.852 166.086 315.171 301.363 253.516 51.063 53.954 46.210 45.594 41.745 38.580 265.783 351.346

n -1.443 -1.439 -1.415 -1.405 -1.414 -1.365 -1.354 -1.325 -1.311 -1.418 -1.413 -1.371 -1.033 -1.049 -1.021 -1.019 -1.003 -0.989 -1.386 -1.449

Power Law Model R2 0.927 0.928 0.931 0.930 0.933 0.924 0.925 0.922 0.925 0.929 0.939 0.930 0.800 0.810 0.805 0.807 0.799 0.796 0.920 0.923

k -0.017 -0.018 -0.019 -0.019 -0.022 -0.024 -0.026 -0.027 -0.030 -0.018 -0.020 -0.020 -0.033 -0.034 -0.038 -0.039 -0.042 -0.044 -0.020 -0.019

n 0.745 0.740 0.729 0.730 0.703 0.685 0.677 0.664 0.647 0.736 0.724 0.722 0.623 0.618 0.595 0.591 0.580 0.567 0.721 0.731

GEM Model R2

0.985* 0.985* 0.985* 0.986* 0.980* 0.983* 0.984* 0.985* 0.985* 0.985* 0.983* 0.987* 0.971* 0.973* 0.973* 0.974* 0.970* 0.970* 0.987* 0.981*

k

a

-0.006 -0.006 -0.005 -0.005 -0.005 -0.005 -0.005 -0.005 -0.005 -0.005 -0.005 -0.005 -0.005 -0.005 -0.005 -0.005 -0.005 -0.004 -0.005 -0.005

0.285 0.287 0.291 0.29 0.306 0.315 0.318 0.324 0.332 0.288 0.293 0.291 0.328 0.333 0.344 0.345 0.351 0.357 0.296 0.295

R2 0.881 0.88 0.879 0.882 0.867 0.873 0.873 0.877 0.874 0.881 0.876 0.887 0.942* 0.937 0.943* 0.943* 0.944* 0.947* 0.885 0.872


9

Mathematical Modelling of Mass Transfer for Osmotic Dehydration of Beetroot (Beta vulgaris L.)

Table 2:Contd., 65

75

25 5 15 25 5 15 25

15.608 10.346 10.428 10.299 10.262 10.135 10.099

0.003 0.006 0.006 0.007 0.007 0.007 0.007

0.943* 0.857 0.872 0.878 0.886 0.878 0.885

0.329 0.23 0.228 0.222 0.221 0.214 0.211

0.932 0.982* 0.977* 0.977* 0.980 0.973 0.971

5.01E-09 3.50E-09 3.47E-09 3.38E-09 3.36E-09 3.26E-09 3.21E-09

249.528 49.359 52.253 47.663 46.954 40.973 39.221

-1.375 -1.028 -1.051 -1.034 -1.032 -1.004 -0.999

0.933 0.812 0.818 0.811 0.813 0.798 0.797

-0.021 -0.035 -0.038 -0.040 -0.041 -0.044 -0.047

0.708 0.612 0.599 0.588 0.584 0.570 0.559

0.985* 0.976* 0.976* 0.975* 0.976* 0.969* 0.968*

-0.005 -0.005 -0.005 -0.005 -0.005 -0.004 -0.004

0.299 0.333 0.345 0.35 0.352 0.358 0.364

Note: * P (%) implies significant at 10 % level

Figure 1: Combine Effect of Immersion Time and Solution Temperature on (a) Water Loss and (b) Solute Gain during Osmotic Dehydration of Beetroot

Figure 2: Combine Effect of Immersion Time and Salt Concentration on (a) Water Loss and (b) Solute Gain during Osmotic Dehydration of Beetroot

Figure 3: Combine Effect of Immersion Time and Sugar Concentration on (a) Water Loss and (b) Solute Gain during Osmotic Dehydration of Beetroot

0.879 0.946* 0.934 0.937 0.938* 0.94* 0.938*


1 mathematical modelling full  

The present study was carried out with a view to investigate the osmotic dehydration kinetics in terms of water loss and solute gain. Beetro...

Read more
Read more
Similar to
Popular now
Just for you