Beyond fick: How best to deal with non-fickian behavior in a fickian spirit

Abstract

Starting from Fick’s train of thought, which led to the formulation of his law governing diffusion in a solid or liquid medium, we first consider the limits of applicability of this law to solid medium-single penetrant systems. We then take up the question of proper formulation, in combination with simple but physically meaningful modeling, of diffusion behavior deviating from this law, because of (i) concentration dependence (ii) time dependence or (iii) space dependence, of the relevant transport parameters (which include the sorption, no less than the diffusion, coefficient). Examples of application to real systems are offered in each case. We conclude that progress in such studies depends on following Fick’s mode of thinking rather than on adhering to the formalism of his law.