(374o) On a Least-Squares Finite Element Method for Multicomponent Diffusion and Reaction Processes

Although Fick's law of diffusion is commonly used to model the diffusion process of binary mixtures, it must be used with caution for multicomponent systems because of the interaction effects of osmotic diffusion, diffusion barrier and reverse diffusion. The phenomenological model for multicomponent diffusion is the Maxwell-Stefan (M-S) equations. For one-dimensional (1-D) diffusion processes, it is rather easy to obtain numerical solutions for the M-S equations. However, for 2-D and 3-D transport processes, the M-S equations are not easily amenable to numerical solutions because they form a set of complicated and nonlinear partial differential equations. In this work, we show that the Least-Squares Finite Element Method lends itself naturally to the M-S equations. We provide numerical solutions for a variety of 1-D and 2-D diffusion/reaction processes.