Fickian Diffusion Equation—an Unsolved Problem

Two forms of diffusion equation are discussed: (1) the conventional Fick’s law with concentration-independent diffusion coefficient and (2) the flux as proportional to the chemical potential gradient with the proportional constant independent of concentration (which is, in most cases, equivalent to the application of Fick’s law with a diffusion coefficient inversely proportional to concentration). It is shown that appropriate empirical form of the resistant forces could validate both forms thermodynamically. It is concluded that the ideal form of diffusion equation is absent. It is also shown that the second form of the flux equation might describe the self-diffusion flux better.