Limitations and Generalizations of the Classical Model for Diffusion In Fluids

It is shown that the classical diffusion model is based on two incompatible assumptions:1) the diffusion coefficient, D = (1/3)VL , is assumed to be finite (V is a characteristic velocity and L is the mean-free path); but 2) the flux is approximated in the limit of L going 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 terms of finite differences, not gradients. Relaxing this second assumption gives a new type of diffusion equation for fluids which reveals a qualitatively new, more complex diffusion paradigm than the classical “propagation of chaos” concept [1, 2].

1. Aranovich G.L., and Donohue M.D., Molecular Physics, 105 (2007) 1085.

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