Moment method and non-equilibrium thermodynamics of rarefied gas mixture

Abstract

The problem of the kinetic justification of the extended irreversible thermodynamics on the basis of Grad's moment method for multicomponent rarefied gas mixture is discussed. The examination is carried out of linearized kinetic Boltzmann equation which is used to obtain an infinite chain of linked equations (moment equations) for the coefficients of expansion of the distribution function in a system of tensor polynomials. Using these equations generalized expressions are obtained for the entropy density, entropy flux density and entropy production as functions of an arbitrary number of state variables, which allow different variants of the relations between fluxes and thermodynamic forces to be considered. For spatially homogeneous systems these relations correspond to the Onsager version of the linear non-equilibrium thermodynamics. In a more general case thermodynamic forces involved in the transport equations are significantly redefined to include, besides the usual gradients of the initial macroscopic parameters, derivatives of the dissipative fluxes with respect to time and coordinates. Some consequence and physical effects, following from the obtained equations are analyzed.