Asymptotic analysis and reaction-diffusion approximation forBGK kinetic models of chemical processes in multispecies gas mixtures

A BGK-type model is derived to describe the interaction between transport and chemical reactions in multispecies gas mixtures, at the kinetic level. The underlying kinetic process is modelled by a Fokker-Planck-type equation, in the Kramers-Smoluchowski limit. When the reaction terms in the kinetic equation are properly scaled, an expansion in powers of a small parameter related to the mean collison time yields a reaction-diffusion equation for the densities of the chemical species involved. For different scalings of the reaction terms, the related macroscopic equations describe the prevailing of transport processes on chemical reactions, orvice versa. The spatially homogeneous case with its own peculiarities is addressed, and the Selkov model is considered as an example.