Singular perturbation techniques in the study of a diatomic gas with reactions of dissociation and recombination

Model equations for the description of chemical reactions of dissociation and recombination through a transition state constitute necessarily singular perturbation problems because of the very short lifetime of the excited molecules, compared to all other characteristic times. Asymptotic solutions are derived and tested versus an accurate numerical solution by resorting to different expansion algorithms, taking initial layer corrections into account. Since the singular problem turns out to be also singularly perturbed, techniques like Hilbert and Chapman–Enskog expansions, typical of the Boltzmann equation for gas kinetic theory, have been considered. The simple stationary state approximation, very popular in chemistry, is shown to provide very good results out of the initial layer if equipped with the proper initial conditions, as obtained from the present analysis.