Conditions for the applicability and molecular-kinetic derivation of the equations of multitemperature multivelocity gas dynamics

The properties of the solutions of the system of Boltzmann equations as the Knudsen number $\mathrm K\to0$ are considered for a binary mixture of monatomic gases with arbitrary ratios of the component molecular masses, and arbitrary concentrations and collision cross-sections. The conditions are found for the hydrodynamic description of the flows of such mixtures in general, and of the multitemperature description in particular, to be applicable. The desirability of introducing multivelocity gas dynamics is discussed. The equations are given in the Navier-Stokes approximation, valid in the case of strongly differing component molecular masses for any ratio between their concentrations, and any ratio between their interaction crosssections.