Identification of the potato moisture diffusion coefficient considering shrinkage: a nonlinear estimator approach to an inverse problem

Abstract

This study aimed to determine the moisture diffusion coefficients of potatoes by taking into account the shrinkage that occurs during the drying process. In addition, the study also considered the scenario where shrinkage was neglected for comparison purposes. The main objective of this study is to establish the importance of considering shrinking phenomena for proper modeling of the drying process and to highlight the advantages of a recently published methodology for estimating parameters. The potato samples, which were dried in a moisture balance, were prepared such that the moisture diffusion was unidimensional. The determination of the moisture diffusivity when shrinkage is neglected is based on the analytical solution of the diffusion equation when constant diffusivity is assumed. When shrinkage is considered, the diffusion coefficient is identified via a nonlinear estimator constructed based on a numerical solution to the diffusion equation. The shrinking rate and the drying kinetics are the information fed to the algorithm. Arrhenius-type expressions for the dependency of the diffusivity on temperature were obtained, and from them, activation energies were determined for both cases: considering and neglecting shrinkage. From the comparison of the effective diffusion coefficients obtained, we conclude that when shrinkage is neglected, the diffusion coefficients are underestimated. A model for the diffusion coefficient as a function of temperature and concentration is provided.