Kinetic Equations and Method of Small Parameter

Abstract

In the present monograph, on the basis of the methods of kinetic theory, we study non-equilibrium flows of multi-component mixtures consisted of molecular gases with translational, rotational, and vibrational degrees of freedom. Collisions between particles can result in the translational energy exchange, internal energy transitions, bimolecular chemical reactions, dissociation, and recombination. Our consideration is restricted by the conditions when electronic excitation, ionization, and radiation can be neglected. A quasi-classical approach is applied. In the framework of this approach, the translational degrees of freedom of gas particles are treated classically whereas the rotational and vibrational energy spectra are assumed to be quantized; the pure quantum effects of the diffraction and particles collective are neglected. The gas description is based on one-particle distribution functions of molecules over the velocity, internal energy and chemical species. The quasi-classical method is well suited for the solution of molecular supersonic aerodynamic problems in a wide temperature and pressure range. The quantum description becomes necessary for low temperatures and rapid processes in strong fields, as well as for light gases. Such conditions are not considered in the monograph.