Effect of intermolecular potential on compressible Couette flow in slip and transitional regimes

Abstract

The effect of intermolecular potentials on compressible, planar flow in slip and transitional regimes is investigated using the direct simulation Monte Carlo method. Two intermolecular interaction models, the variable hard sphere (VHS) and the Lennard-Jones (LJ) models, are first compared for subsonic and supersonic Couette flows of argon at temperatures of 40, 273, and 1,000 K, and then for Couette flows in the transitional regime ranging from Knudsen numbers (Kn) of 0.0051 to 1. The binary scattering model for elastic scattering using the Lennard-Jones (LJ) intermolecular potential proposed recently [A. Venkattraman and A. Alexeenko, “Binary scattering model for Lennard-Jones potential: Transport coefficients and collision integrals for non-equilibrium gas flow simulations,” Phys. Fluids 24, 027101 (2012)] is shown to accurately reproduce both the theoretical collision frequency in an equilibrium gas as well as the theoretical viscosity variation with temperature. The use of a repulsive-attractive instead of a purely repulsive potential is found to be most important in the continuum and slip regimes as well as in flows with large temperature variations. Differences in shear stress of up to 28% between the VHS and LJ models is observed at Kn=0.0051 and is attributed to differences in collision frequencies, ultimately affecting velocity gradients at the wall. For Kn=1 where the Knudsen layer expands the entire domain, the effect of the larger collision frequency in the LJ model relative to VHS diminishes, and a 7% difference in shear stress is observed.