Reaction-diffusion models from the Fokker-Planck formulation ofchemical processes

Abstract

A Fokker-Planck-type model is proposed to describe the kinetics of certain chemical reactions. In particular, the competition between transport and reaction processes is analysed. The study is carried out considering various scalings of interaction, measured by the exponent of a small parameter related to the mean free path. In the most significant case of competition between both effects, the lowest-order density in the asymptotic expansion obeys a reaction-diffusion equation. Such an equation was earlier considered as the starting point in the study of these processes by other authors (e.g. by Schlögl). For other interaction scalings, the prevalence of chemical processes implies that the lowest-order density is determined by the (algebraic) equations of chemical equilibrium. In contrast, when transport prevails, the reaction terms affect only higher-orderdensities.