Title: From the simple reacting sphere kinetic model to the reaction-diffusion system of Maxwell-Stefan type,
Abstract: In this paper we perform a formal asymptotic analysis on a kinetic model for
reactive mixtures in order to derive a reaction-diffusion system of
Maxwell-Stefan type. More specifically, we start from the kinetic model of
simple reacting spheres for a quaternary mixture of monatomic ideal gases that
undergoes a reversible chemical reaction of bimolecular type. Then, we consider
a scaling describing a physical situation in which mechanical collisions play a
dominant role in the evolution process, while chemical reactions are slow, and
compute explicitly the production terms associated to the concentration and
momentum balance equations for each species in the reactive mixture. Finally,
we prove that, under isothermal assumptions, the limit equations for the scaled
kinetic model is the reaction diffusion system of Maxwell-Stefan type.