Mathematical model for dehydration and shrinkage. Prediction of eggplant's MRI spatial profiles

In the preceding work, Brasiello et al. (2013) developed a mathematical model for eggplant's dehydration taking into account the shrinkage effects. Although the model provided good results in predicting the total water weight loss of slices, at that time, no information was given about the capability of predicting water content profiles inside the material. This is a very important issue in order to catch some fundamental aspects of dehydration with shrinkage. In this paper, we analyze the evolution of the water content profiles inside cylindrical samples of eggplant during dehydration using a mathematical model which takes into account shrinkage effects. In particular, we show the good agreement between numerical derived spatial profiles and the Magnetic Resonance Imaging (MRI) data available in Literature. Model's parameters are calculated through a suitable simplified procedure, which uses experimental data from samples of a different shape. The numerical results are compared to those derived from the same procedure applied to Fick's diffusion equation.