During drying, heat and mass transfer is commonly observed along with a change in volume (i.e. Shrinkage). Which tool should be chosen to model this process?
Thank you in advance.
For theoretical considerations of shrinkage during drying and models I recommend to you the following papers,
Hernández, J.A., Pavon, G., García, M.A. (2000). Analytical solution of mass transfer equation considering shrinkage. Journal of Food Engineering, 45 (1), 1-10. DOI: 10.1016/S0260-8774(00)00033-9
Ruiz-López, I.I., Cordova, A.V., Rodriguez-Jimenes, G.C., García-Alvarado, M.A. (2004). Moisture and temperature evolution during foods drying: effect of variable properties. Journal of Food Engineering, 63 (1), 117-124.
Ruiz-López, I.I., García-Alvarado, M.A. (2007). Analytical solution for food-drying kinetics considering shrinkage and variable diffusivity. Journal of Food Engineering, 79 (1), 208-216.
Ruiz-López, I.I., Ruiz-Espinosa, H., Arellanes-Lozada, P., Bárcenas-Pozos, M.E., García-Alvarado, M.A. (2012). Analytical model for variable moisture diffusivity estimation and drying simulation of shrinkable food products. Journal of Food Engineering, 108 (3), 427-435. http://dx.doi.org/10.1016/j.jfoodeng.2011.08.025 .
Ortiz-García-Carrasco, B.Yañez-Mota E., Pacheco-Aguirre, F.M., Ruiz-Espinosa, H., García-Alvarado, M.A., Cortés-Zavaleta, O., Ruiz-López, I.I. (2015). Drying of shrinkable food products: Appraisal of deformation behavior and moisture diffusivity estimation under isotropic shrinkage. Journal of Food Engineering, 144, 138-147. http://dx.doi.org/10.1016/j.jfoodeng.2014.07.022 .
Pacheco-Aguirre, F.M., García-Alvarado, M.A., Corona-Jiménez, E., Ruiz-Espinosa, H., Cortés-Zavaleta, O., Ruiz-López, I.I. (2015). Drying modeling in products undergoing simultaneous size reduction and shape change: Appraisal of deformation effect on water diffusivity. Journal of Food Engineering, 164, 30-39. http://dx.doi.org/10.1016/j.jfoodeng.2015.04.031 .
I can send privately to you the paper, but I need that you request.
You can find detailed description in Rahman's book Handbook of Food Properties.
Essentially you can take an empirical approach or a mechanistic. With the former, you can measure the change in volume and fit an empirical equation (beware of the functions domain) for further implementation. The shrinkage in mechanistic models results from a change in (negative) pressure (same as any other biological system in nature) which can be equated to the volume integral over the domain.
You may consider Stefan Problem approach to model shrinkage or swelling in a phenomenological mass or heat transfer model. In such approach one considers that one or two boundaries of the diffusion domain is free to move. This is physically observable and mass or heat balance equations may be written in order to describe the boundary movement. Here is an article where me and my colleagues applied and validated such approach to model hydration of soybean grains
Moving boundary modeling of conventional and transgenic soybean hydration: Moisture profile and moving front experimental validation
doi:10.1016/j.ijheatmasstransfer.2015.07.014
As plant-based food materials have hygroscopic, porous and anisotropy nature. It is very difficult to develop comprehensive theoretical model of shrinkage during food processing. Moreover, variable physical properties makes it more difficult.
The simple way it get a shrinkage velocity approach for your particular food product.
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