Mathmatical formulations of the basic diffusion equation: a discussion

Abstract

A discussion is made on the possible forms of mathematical formulations for the basic diffusion equation. The formulations have been derived from the law of motion. It is shown that the assumption of Stokes resistance leads to paradoxical conclusions in some specific cases of diffusion processes. It is argued that the expression for resistant forces in transport processes is empirical, and hence the form of the diffusion equation depends on the expression chosen in describing the resistant forces. Evidences are collected from literature in favor of both thermodynamic and Fickian formulation of the diffusion equation. It is concluded that ideal form of diffusion equation is absent, and the choice of the form of diffusion equation would depend on the specific circumstances being studied.