A Critical Assessment of the Maxwell Slip Boundary Condition for Rarified Wall Bounded Flows

Abstract

The Maxwell slip boundary condition is widely used to compute the slip velocity at the wall under rarefied flow condition. In this paper, we apply the Direct Simulation Monte Carlo (DSMC) method on a Couette flow problem in order to evaluate this boundary condition. The computations are performed at different values of tangential momentum accommodation coefficient (between 0.1 and 1) and Knudsen numbers (Kn between 0.001 and 3), at 500 K for Argon, with the aim of comparing the ensuing slip length to that predicted by Maxwell's formula. It is found that the boundary condition is accurate up to a Kn = 0.1 but not at higher Knudsen numbers. Although it has been known that the slip boundary condition is valid only for small Knudsen numbers, the critical Knudsen number from where the deviation begins is not well documented. The present results indicate that such deviations occur at Kn = 0.1 in flows that are bounded by opposing walls. At higher Knudsen numbers, the Knudsen layers overlap and the collisions of molecules with walls dominate to change the boundary conditions significantly.