On inelastic reactive collisions in kinetic theory of chemically reacting gas mixtures

A kinetic theory for a simple reversible reaction–characterized by a binary mixture of ideal gases whose constituents denoted by A and B undergo a reaction of the type A+A⇌B+B–is developed by considering the reactive collisions as inelastic ones. The geometry of the collision is taken into account in the line-of-centers differential cross section by allowing that a chemical reaction may occur only when the energy of the relative velocity in the direction of the line which joins the centers of the molecules at collision is larger than the activation energy. It is shown that the restitution coefficients: (i) depend explicitly on the reaction heat and on the relative translational energy in the direction of the line which joins the centers of the molecules during an inelastic collision; (ii) vanish when the reaction heat is zero; (iii) are larger or smaller than one depending on the direction of the reaction and on the sign of the reaction heat. First approximations to the distribution functions are determined from the system of Boltzmann equations for the last stage of a chemical reaction. It is shown that the deviations from the Maxwellian distribution functions and the production terms of the particle number densities: (i) vanish when the reaction heat is zero provided that the affinity is close to zero and (ii) are negative or positive depending on the sign of the reaction heat and on the direction of the reaction.