The gas dynamics equations of slow flows of polyatomic gas mixtures, non-uniform in temperature and concentrations

Abstract

The formulation of the system of equations of the mechanics of a gas as a continuous medium is completed. This describes the non-stationary slow laminar flow of a mixture of gases (the Mach number being much less than unity), for a Reynolds number and relative drops in temperature and molar fractions of the order of unity. The distribution with respect to the internal energies of the molecules is close to Boltzmann (the case of rapid exchanges of translational and internal energies of the molecules). The difference from the similar system of equations in the Navier–Stokes approximation is the fact that in the equation of motion the Burnett stresses, expressed in terms of the second differential and paired products of the first derivatives with respect to the temperature and molar fractions (concentrations) are taken into account. A consequence of the action of these stresses is thermal-stress and concentration-stress convection. Special cases and possible extensions are considered.