Mean-field approach to diffusion with interaction: Darken equation and numerical validation

Abstract

A mean-field theory for diffusion with interaction was introduced in Phys. Rev. E 92, 062118 (2015)PLEEE81539-375510.1103/PhysRevE.92.062118. Interaction effects are represented with a mean-field potential. Here we show that the potential can be directly related to the activity coefficient. In this context, we obtain an alternative derivation of the Darken equation, that relates collective diffusion coefficient and single particle diffusion coefficient (generally different in the presence of interactions). We also carry out a validation test of the model using, as a case study, effective interactions that reproduce Bose-Einstein statistics.