Stochastic Reaction-Diffusion Phenomena in Porous Media with Nonlinear Kinetics: Effects of Quenched Porosity Fluctuations

Abstract

We study the effects of quenched porosity fluctuations in the presence of nonlinear kinetics in a reaction-diffusion porous system. Adopting a weak-noise approximation and a mean-field assumption, a renormalized equation of motion for the average concentration of a chemical species is obtained. It is characterized by a smaller effective diffusion coefficient and by the presence of supplementary nonlinear reactive terms. Explicit results are given for a Gaussian porosity distribution and for a long-ranged one. Comparisons with simulations in one dimension are presented.