The Mechanical Basis for Fick’s Law and Its Generalizations

Abstract

In 1855 Fick [1] wrote about the problem of diffusion of one fluid species through another. After a rather long discussion of the basis for such diffusion in terms of molecular motion and the difficulties of careful analysis based on molecular theory, Fick proposed, by analogy to heat flow, that the concentration satisfies the differential equation

$$\frac{{\partial c}} {{\partial t}} = D{\nabla ^2}c$$

.