Non-Equilibrium Thermodynamics of Boundary Conditions for Slightly Rarefied Gases

A procedure for deriving the boundary conditions for slightly rarefied gases is proposed. This procedure is based on the decomposition of the bulk and the Knudsen layer distribution functions. As will be shown, the boundary conditions can be referred to the gas-solid interface and include the discontinuities of the mass, momentum and energy fluxes. These discontinuities are due to the surface fluxes associated with the Knudsen distribution function. In proving this, the thickness of the Knudsen layer was assumed to be finite, i.e. different zero! By means of Non-equilibrium Thermodynamics the Knudsen layer fluxes are expressed by the bulk parameters of the gas and some kinetic coefficients. The correspondence between the retained terms in the Chapman-Enskog expansion of the bulk distribution function and the boundary conditions is established. The boundary conditions obtained differ from Waldmann's ones already at the first-order Chapman-Enskog approximation. Introduction Transport processes in slightly rarefied gases often are treated by means of generalized hydrodynamics with appropriate boundary conditions [1,2]. Waldmann [3], proposed a procedure for deriving the boundary conditions from the principles of irreversible thermodynamics. Using this technique, the boundary conditions for temperature, velocity, etc. are obtained from the interfacial entropy production Α£Σ and in fact are some linear phenomenological combinations of thermodynamic "fluxes" and "forces". The kinetic coefficients in these combinations satisfy Ons ger's symmetry relation and characterize the transport processes in the boundary layer. The interfacial entropy production was defined in [3] as the difference of the entropy fluxes in the gas and the condensed phase. The ordinary hydrodynamic expressions for the entropy fluxes were used in [3]. It was shown later [4,5], that J. Non-Equilib. Thermodyn., Vol. 16, 1991, No. 1 Copyright © 1991 Walter de Gruyter · Berlin New York