Effect of reaction heat on Maxwellian distribution functions and rate of reactions

A binary gaseous mixture undergoing a reversible reaction of type A + A reversible arrow B + B is modeled with the chemical kinetic Boltzmann equation, assuming hard sphere cross sections for elastic collisions, and two different models with activation energy for reactive interactions, namely the line-of-centers and step cross-section models. The Chapman-Enskog method and Sonine polynomial representation of the distribution functions are used to obtain the solution of the Boltzmann equation in a chemical regime for which the reactive interactions are less frequent than the elastic collisions, i.e. in the early stage of the reaction when the constituent A is in a large amount with respect to B and the affinity of the reaction tends to infinity. The aim of this paper is twofold: (i) to evaluate the effect of the reaction heat on the Maxwellian distribution functions and on the production terms of both particle number densities and mixture energy density; (ii) to analyze spatially homogeneous solutions for the particle number density and temperature of the reactants when the chemical reaction advances. It is shown that the reaction heat changes the Maxwellian distribution functions, the production terms and hence the trend to equilibrium of the particle number density and temperature of the reactants. Moreover, these changes differ for exothermic and endothermic reactions.