A second-order slip model for arbitrary accomodation at the wall

Abstract

We present a kinetic-theory derivation of second-order slip boundary conditions for a plane isothermal pressure driven gas owing through a microchannel. In the proposed approach, the distribution function is expanded in terms of orthogonal polynomials and the system of moment equations in the expansion coefficients is analytically solved. The velocity slip coefficients, as well as their Knudsen layer corrections, are obtained by evaluating the solution in the near continuum limit. In comparison with other methods, the present approach is accurate and easy to implement. The results are presented for the Bhatnagar-Gross-Krook-Welander (BGKW) kinetic model equation and Maxwell's boundary conditions, but can be extended to more general collision integral and different scattering kernels.