Nonequilibrium dissociation rates behind strong shock waves: classical model

Abstract

A model is suggested for the analytical calculation of dissociation rates behind shock waves where the vibrational temperature T v is less than the gas temperature T. The model is based on an analysis of the threshold translational energy for collision-induced dissociation as a function of initial vibrational and rotational energies. The threshold function method combined with a classical impulsive model for energy exchange yields explicit formulae for the rate coefficient k( T v, T) and the mean vibrational energy removed in dissociation. The mechanism of nonequilibrium dissociation is predicted to change during vibrational relaxation: dissociation from low vibrational levels dominates at low T v/ T, while dissociation from all levels contributes almost equally as T v/ T approaches unity. The formulae obtained exhibit an explicit dependence on the mass ratio of the dissociating molecule and its collision partner, the lighter mass of the partner making dissociation from high levels more favorable. Dissociation in a molecular gas at T > T v is demonstrated to occur predominantly via noncollinear collisions with simultaneous transfer of rotational and translational energy to the vibrational mode of the dissociating molecule.