Mathematical Modeling of Water Uptake Through Diffusion in 3D Inhomogeneous Swelling Substrates

Diffusion-driven water uptake in a substrate (imbibition) is a subject of great interest in the field of food technology. This is a particular challenge for rice grains that are preprocessed to accelerate the water uptake, i.e., to reduce the cooking time. Rice preprocessing disrupts the mesostructural order of starch and induces a microporous structure in the grains. The mesoand microstructural length scales have not been considered in joint approach until now. The (re)hydration of rice grains can be modeled by free (concentration-driven) diffusion or by water demand-driven diffusion. The latter is driven by the ceiling moisture content related to the extent of gelatinization of the rice substrate network. This network can be regarded as a fractal structure. As the spatial resolution of our models is limited, we choose to model the apparent water transport by a set of coupled partial differential equations (PDEs). Current models of water uptake are often limited to a single dimension, and the swelling of the substrate is not taken into account. In this article, we derive a set of PDEs to model water uptake in a three-dimensional (3D) inhomogeneous substrate for different types of water diffusion as well as the swelling of the substrate during water uptake. We will present simulation results for different 3D (macroscopic) structures and diffusion models and compare these results, qualitatively, with the experimental results acquired from magnetic resonance imaging. VC 2009 American Institute of Chemical Engineers AIChE J, 55: 1834–1848, 2009