Molecular Simulations of Knudsen Wall-slip: Effect of Wall Morphology

Abstract

This work involves a molecular simulation study of the phenomena of wall slip occurring in rarefied gases flowing through micro- and nano-channels. A simulation strategy that mimics a scattering experiment is developed in order to compute the tangential momentum accommodation coefficient (f) which governs the degree of slip at the wall surface. Noninteracting gas molecules are bombarded at an atomic wall composed of rigid atoms with suitably distributed velocities and a tangential drift velocity that simulates flow. The accommodation coefficient is computed from the loss in the tangential momentum of these molecules. The accommodation coefficient is observed to be strongly dependent on the physical roughness of the wall, as characterized by the parameter sgr wg/L, and the attractiveness of the wall to the fluid, as characterized by the parameter ε wg/k B T, where sgr wg and ε wg are the Lennard–Jones interaction parameters of the wall and gas atoms while L is the lattice unit length. The accommodation coefficient is found to be independent of the tangential drift velocity at small drift velocities commensurate to those observed in micro devices. The accommodation coefficient is also found to be independent of the inertial mass of the gas molecules. The dependence of f on the two main governing factors has been presented in convenient “phase diagrams” plots. We also show a means of separating gases based on the differences in the accommodation coefficients of the various components in the mixture. Using molecular dynamics simulations, we show that separation factors higher than 20 are achieved for gases flowing through nanometer wide channels in the Knudsen regime. We also present a simple analytical model to determine the lower bound on the separation factor of the two gases.