Validation of a Second-Order Slip Model for Dilute Gas Flows

Abstract

We present an extensive comparison between direct Monte Carlo simulations and the predictions of the Navier-Stokes description coupled to a recently proposed second-order slip model for hard sphere gases. Two one-dimensional, time-dependent channel flows are considered. In both cases excellent agreement is found between molecular simulation and the proposed model well into the transition regime for both the velocity and stress fields. The excellent quantitative agreement extends, approximately, to a Knudsen number based on the channel width of 0.4. The transient nature of the flows suggests that the slip model, despite its (quasi-) steady origins, remains reliable as long as the evolution timescale is long compared to the molecular collision time. Our discussion elucidates the effect of the Knudsen layer, a kinetic “boundary layer” in the vicinity of walls that needs to be superposed to the Navier-Stokes component of the flow in order to obtain the complete flow solution. The existence of this kinetic boundary layer, whose importance grows with increasing Knudsen number and which ultimately renders the Navier-Stokes component insufficient to describe the flow, implies that special care is needed in interpreting slip-flow flowfields.