Journal of food science and technology(Iran)

Journal of food science and technology(Iran)

Development and Simulation of a Coupled Salt and Moisture Transfer Model in Cheese Considering the Effects of Temperature and Osmotic Forces

Document Type : Original Article

Authors
1 Associate Professor of Department of Food Science and Technology, Faculty of Agriculture, Jahrom University, Jahrom, Fars, Iran, P.O. Box 74135-111
2 Biosystems Engineering Department, Jahrom University
10.48311/fsct.2026.119858.83108
Abstract
Salting is a critical step in cheese production, contributing to microbial safety, shelf life, texture, and flavor development. In this study, salt uptake during the brining process was investigated using both experimental measurements and modeling approaches. The chemical composition of cheese samples was first determined. The effective diffusion coefficient of salt at different temperatures was then calculated using Fick’s second law. To more accurately describe the brining process, an extended numerical model incorporating simultaneous salt and water transport as well as osmotic effects was developed and simulated. Results showed that salt concentration in cheese increases over time, with the highest rate of uptake occurring in the early stages due to strong concentration gradients. As brining progresses, the rate of diffusion decreases. Temperature had a significant impact: increasing the temperature from 6 to 20 °C led to higher effective diffusion coefficients and greater overall salt uptake. The temperature dependence of diffusivity followed the Arrhenius relationship, yielding an activation energy of 53.32 kJ/mol. Numerical simulations demonstrated that incorporating osmotic forces provides a more realistic prediction of moisture loss and the coupled spatial distribution of salt and water within the cheese matrix. Two dimensional concentration maps further confirmed that higher temperatures promote deeper salt penetration over a fixed brining duration.
Keywords
Subjects

[1] Bisig W., Arias-Roth, E., Fröhlich-Wyder, M. T., Guggisberg, D., Jakob, E., Sheehan, J. J., & Skeie, S. (2025). Chapter 13 - Salt in Cheese: Physical, Chemical, Biological, and Sensory Aspects—Water Activity☆☆This is a revised and partly newly written version of the previous 4th edition by Timothy P. Guinee and Patrick F. Fox. In P. L. H. McSweeney, P. D. Cotter, D. W. Everett & R. Govindasamy-Lucey (Eds.), Cheese (Fifth Edition) (pp. 349-406). San Diego: Academic Press.
[2] Guinee T. P. (2004). Salting and the role of salt in cheese. International Journal of Dairy Technology, 57(2-3), 99-109.
[3] Luo J., Pan, T., Guo, H. Y., & Ren, F. Z. (2013). Effect of calcium in brine on salt diffusion and water distribution of Mozzarella cheese during brining. Journal of Dairy Science, 96(2), 824-831.
[4] Melilli C., Barbano, D. M., Licitra, G., Tumino, G., Farina, G., & Carpino, S. (2003). Influence of Presalting and Brine Concentration on Salt Uptake by Ragusano Cheese1. Journal of Dairy Science, 86(4), 1083-1100.
[5] Marchetti M. D., Gomez, P. L., Yeannes, M. I., & Garcia Loredo, A. B. (2021). Mathematical modeling of mass transfer kinetics during salting procedures of hake fillets. Journal of Food Processing and Preservation, 45(1), e15002.
[6] Graiver N., Pinotti, A., Califano, A., & Zaritzky, N. (2009). Mathematical modeling of the uptake of curing salts in pork meat. Journal of Food Engineering, 95(4), 533-540.
[7] Torres-Baix E., Illana, A., Gou, P., Olmos, A., Arnau, J., & Fulladosa, E. (2024). Modelling of salt uptake for salt content standardization in dry-cured ham. Meat Science, 214, 109523.
[8] Pajonk A. S., Saurel, R., & Andrieu, J. (2003). Experimental study and modeling of effective NaCl diffusion coefficients values during Emmental cheese brining. Journal of Food Engineering, 60(3), 307-313.
[9] Velázquez-Varela J., Fito, P. J., & Castro-Giráldez, M. (2014). Thermodynamic analysis of salting cheese process. Journal of Food Engineering, 130, 36-44.
[10] Santapaola J., Maldonado, S., & Medina, J. L. (2013). NaCl diffusion kinetics in dry salting of goat cheese. Journal of Food Engineering, 118(2), 172-177.
[11] Dalvi M., & Hamdami, N. (2011). Characterization of Thermophysical Properties of Iranian Ultrafiltrated White Cheese: Measurement and Modeling. Journal of Agricultural Science and Technology, 13(1), 67-78.
[12] Izady L., Hamdami, N., & Mohamadi, A. (2009). Determination of Moisture Diffusivity in Iranian White Cheese During Brining. JSTNAR, 13(47), 15. [In Persian]
[13] Illescas-Chavez E., & Vélez-Ruiz, J. F. (2009). Effect of the Salting Process on the Mass Transfer Kinetics of Manchego-type Cheese. International Journal of Food Properties, 12(4), 791-807.
[14] Dalvi-Isfahan M. (2023). Mathematical modeling for investigating the effect of single-sided flipping on moisture, fat content, and safety of hamburger patty. Journal of Food Process Engineering, 46(12), e14450.
[15] Costa R., Gomes, V., & Gândara, J. F. M. (2021). Modeling mass transfer in brine salting of chickpea. Heat and Mass Transfer, 57(9), 1439-1452.
[16] Nourani M., Hamdami, N., & Nasirpour, A. (2014). Modeling of Involved Phenomena in UF White Cheese Ripening after Dry Salting. Iranian Journal of Biosystem Engineering, 45(1), 61-72. [In Persian]
[17] Floury J., Rouaud, O., Le Poullennec, M., & Famelart, M.-H. (2009). Reducing salt level in food: Part 2. Modelling salt diffusion in model cheese systems with regards to their composition. LWT - Food Science and Technology, 42(10), 1621-1628.
[18] Simal S., Sánchez, E. S., Bon, J., Femenia, A., & Rosselló, C. (2001). Water and salt diffusion during cheese ripening: effect of the external and internal resistances to mass transfer. Journal of Food Engineering, 48(3), 269-275.
[19] Hofmeister L. C., Souza, J. A. R., & Laurindo, J. B. (2005). Use of dyed solutions to visualize different aspects of vacuum impregnation of Minas cheese. LWT - Food Science and Technology, 38(4), 379-386.