(27b) Eliminating the Mean-Free-Path Inconsistency in Classical Phenomenological Model of Diffusion for Fluids

It is shown that the classical derivation of the diffusion equation uses two incompatible assumptions: 1) the diffusion coefficient, D=(1/3)LV, is assumed to be finite (V is characteristic velocity and L is mean-free path); but 2) the flux is approximated by the limit where L goes to zero. The second assumption results in unphysical instantaneous propagation which disappears as this assumption is relaxed and the flux term is represented exactly (in the framework of the classical model). Here, the mean-free-path inconsistency is corrected by relaxing the unnecessary assumption [1].

1. G.L. Aranovich and M.D. Donohue, Physica A 373 (2007) 119-141.