Kinetic derivation of the gas-dynamic equation for multicomponent mixtures of light and heavy particles

Abstract

The gas-dynamic equations for multicomponent mixtures of particles with large mass disparity and frozen internal degrees of freedom are derived by means of the methods of the kinetic theory. It is found that the macroscopic description may be one-velocity and two-temperature. A special feature is the need to use a multivelocity solution of the Boltzmann equation for the heavy components and also the method of introducing their effective temperature. The corresponding modification of the generalized Chapman-Enskog method is given. The Stefan-Maxwell relations are shown to be meaningful as local relations for the diffusion velocities of the components in going over from the multivelocity solution of the kinetic equations to the one-velocity macroscopic description. The transport properties, the exchange terms, and the Stefan-Maxwell relations in the system of gas-dynamic equations written in the Navier-Stokes approximation are calculated in an arbitrary approximation in Sonine polynomials. A criticism of the generalized Chapman-Enskog method is considered and the necessary explanations are given.