Theoretical derivation of slip boundary conditions for single-species gas and binary gas mixture

A theoretical derivation of slip boundary conditions for single-species gas and binary gas mixture based on two typical gas-surface scattering kernels is presented. If the Maxwell model is assumed, then the derived slip boundary conditions are consistent with the previous conclusions. Considering the limitation of the Maxwell model in describing the complexity of gas-surface scattering behavior, we further perform theoretical analyses based on the Cercignani-Lampis-Lord (CLL) model, where separate accommodation coefficients in the tangential and normal directions are defined. Our results demonstrate that for both single-species gas and binary gas mixture, the velocity slip predicted by the CLL model is only dependent on the tangential accommodation coefficient, while the temperature jump determined by the CLL model is related to the accommodation coefficients in both tangential and normal directions. To account for the collision effect in the Knudsen layer, we propose to add correction terms to the theoretical models, and the corrected slip coefficients agree well with the previous numerical results obtained by solving Boltzmann equation for single-species gas. Moreover, the slip boundary conditions for binary gas mixture based on the CLL model are determined theoretically for the first time. Since at most situations the tangential and normal accommodation coefficients are not equal, the temperature jump boundary condition based on the CLL model is expected to give more accurate predictions about temperature distribution and heat flux at the boundaries, particularly for hypersonic gas flows with strong nonequilibrium effect.