Swelling problems with two moving boundaries.

Abstract

The swelling of grease and whole grains are modelled by a nonlinear diffusion equation with two moving boundaries (a Stefan problem). In Cartesian coordinates interesting analytical solutions exist for some simplified cases, but in general the solution must be found numerically. In cylindrical coordinates only numerical solutions are possible and these need the Cartesian results. This article develops models of the swelling material, illustrates some of the analytic solutions, and demonstrates the numerical methods used to solve the problem in Cartesian and cylindrical coordinates.