A phenomenological lubrication model for the entire Knudsen regime

Abstract

Rarefied gas flows in thin film slider bearings are studied in a wide range of Knudsen numbers (Kn) at low Mach number (Ma) with the objective of developing simple physics-based semi-analytical models. A recently developed modified slip boundary condition for steady plane Couette flows and a generalized high-order velocity slip boundary condition, developed and validated earlier for pressure-driven flows, are used to derive a modified slip-corrected Reynolds lubrication equation in the entire Knudsen regime. In particular, we present results of velocity profiles, pressure distribution and load capacity for various slider-bearing configurations. In addition, we outline a method to accurately predict the drag force induced by air resistance to the track-access-motion of the sliders. The new model is validated by comparisons with numerical solutions of the generalized lubrication equation based on the two-dimensional linearized Boltzmann equation and direct simulation Monte Carlo (DSMC) results available in the literature. The model predicts the velocity profiles, pressure distribution, load capacity and skin friction with good accuracy for a wide range of Knudsen numbers for low subsonic compressible flows.