Non-equilibrium phenomena in gas mixture flow through a plane channel in near-continuum regime

Non-equilibrium phenomena in the flow of a binary gas mixture between two parallel plates, driven by gradients of the pressure, temperature and concentration, are studied. The phenomenological relationships that describe the energy and mass transfer in the flow of a gas mixture through a channel are analyzed by using methods of the non-equilibrium thermodynamics of discontinuous systems. The solution of the linearized moment equations in the 13-moments approximation of the Grad’s method and the relation for the slip velocity previously found in Zhdanov (Phys. Rev. E95 (2017), 033106) are applied to deduce the expression for the mass-average velocity of the mixture flowing in a plane channel in the near-continuum regime. Expressions for the diffusion and heat fluxes are determined from the initial third-order moment equations for the gas mixture, averaged over the channel cross-section, with the subsequent evaluation of several moments of the distribution function at the channel wall by using the modified Maxwell method. It is shown that the employed approach automatically ensures the validity of the reciprocal relations for the cross terms in the Onsager matrix. Analytical formulas for kinetic coefficients of the Onsager matrix, expressed in terms of known transport coefficients of the gas mixture and slip coefficients at the channel wall, are obtained. The results of calculations of the matrix coefficients for several binary mixtures of noble gases (Ne–Ar and He–Xe) and their comparison with the results of the numerical calculations on the basis of the linearized Boltzmann equation with the McCormack model are presented.