Numerical Solution of the Equations of Salt Diffusion into the Potato Tissues

Authors: Behrouz Mosayebi Dehkordi, Frazaneh Hashemi, Ramin Mostafazadeh

Abstract:

Fick's second law equations for unsteady state diffusion of salt into the potato tissues were solved numerically. The set of equations resulted from implicit modeling were solved using Thomas method to find the salt concentration profiles in solid phase. The needed effective diffusivity and equilibrium distribution coefficient were determined experimentally. Cylindrical samples of potato were infused with aqueous NaCl solutions of 1-3% concentrations, and variations in salt concentrations of brine were determined over time. Solute concentrations profiles of samples were determined by measuring salt uptake of potato slices. For the studied conditions, equilibrium distribution coefficients were found to be dependent on salt concentrations, whereas the effective diffusivity was slightly affected by brine concentration.

Keywords: Brine, Diffusion, Diffusivity, Modeling, Potato

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062350

References:

[1] 4. R. L. Garrote, R. A. Bertone, and E. R. Silva, "Effect of soakingblanching conditions on glucose losses in potato slices," Can. Inst. Food Sci. Technology J.,1984, vol. 17, pp. 111-113.
[2] A. N. Califano and A. Calvelo. "Heat and mass transfer during the warm water blanching of potatoes," Journal of Food Science, 1983, vol. 48, pp. 220-225.
[3] P. Tomasula, and M. F. Kozempel, "Diffusion coefficients of glucose, potassuin and magnesium in Maine Russet Burbank and Maine Katahdin potatos from 45 to 90 ┬░C," J. of Food Science, 1989, vol. 54, pp. 985- 989.
[4] M. F. Kozempel, J. F. Sullivan, E. S. DellaMonica, M. J. Egoville, E. A. Talley, W. J. Jones, and J. C. Craig, "Application of leaching model to describe potato nutrient losses in hot water blanching," J. of Food Science, 1982, vol. 47, pp. 1519-1523.
[5] H. E. Wistreich, R. E. Morse and L. J. Kenyon, "Curing of ham: a study of sodium chloride accumulation. I: Methods, effect of temperature, cations, muscles and solution concentration," Food Technology, 1959, vol. 13, pp. 441-443.
[6] H. E. Wistreich, R. E. Morse and L. J. Kenyon, "Curing of ham: a study of sodium chloride accumulation. II: Combined effects of time, solution concentration and solution volume," Food Technology, 1960, vol. 14, pp. 549-551.
[7] R. Stahl, and M. Loncin, "Prediction of diffusion in solid foodstuffs," J. of Food Processing and Preservation, 1979, vol. 3, pp. 213-223.
[8] W. C. Wang, and S. K. Sastry, "salt diffusion into vegetable tissue as a pretreatment for ohmic Heating: determination of parameters and mathematical model verification," J. of Food Engineering, 1993, vol. 20, pp. 311-323.
[9] J. Crank, "The Mathematics of Diffusion," Oxford Clarendon Press, 1975
[10] R. Nikazar and M. Kharrat, "Mathematic application in chemical engineering, part 2,"Amirkabir Press, 2002.