A Diffusion Model to Describe Water Absorption by Red Rice during Soaking: Variable Mass Diffusivity, Variable Volume, Use of Boundary-Fitted Coordinates

Abstract

This article aims to carry out experiments on water absorption by husked red rice at constant temperatures of 28, 40, and 50 °C. The description of the absorption kinetics and the analyses of the water distribution and volumetric expansion of each grain, at a given instant, were carried out using a diffusion model. In order for the model to be as close as possible to the real physical situation, the mesh necessary to numerically solve the diffusion equation was generated from the photograph of a grain. Thus, the diffusion equation was written in Boundary-Fitted Coordinates (BFCs). The solution of the diffusion equation written in generalized coordinates was then discretized in space and time, using the Finite Volume method, with a fully implicit formulation, considering the variable volume and variable mass diffusivity as functions of the local moisture content. Optimizations based on the Levenberg–Marquardt algorithm make it possible to determine the parameters of an exponential function relating mass diffusivity and the local moisture content for each temperature. Statistical indicators (chi-square, determination coefficient, and Student’s t-test) allowed us to conclude that the proposed model was very satisfactory for all temperatures, making it possible to simulate the water absorption, water distribution, and volumetric expansion of the grain over time.