A kinetic model for chemical reactions without barriers

Abstract

A system of coupled Boltzmann equations (BE) is here proposed for a binary gaseous mixture undergoing elastic and reactive collisions. Reactive cross sections without activation energy, i.e. without barriers, are adopted to model the chemical process, whereas differential cross sections of rigid spheres are assumed for elastic scattering. The possibility of a pair of molecules to collide through an elastic mechanism or a reactive process is described by means of probability coefficients which are introduced in the collision terms. The rate of reaction and temperature exchange rate are explicitly computed using the non-equilibrium solution of the BE obtained through the Chapman-Enskog method in a chemical regime such that the reactive process is in its initial stage. Spatially homogeneous solutions are examined for the number density of reactants and mixture temperature.