Physics-based Maxwell Model with Variable Accommodation Coefficient

The Maxwell model is one of the most popular gas-surface interaction models, which serves as boundary conditions at solid surfaces in the simulation of rarefied gas flows. However, the classic Maxwell model treats the accommodation coefficient sigma as a constant, which contradicts the observations of molecular dynamics (MD) simulations. In this paper, we propose a physics-based Maxwell model with a variable sigma that takes into account the velocity and mass of the gas molecule and the surface temperature. Based on a physical model of the gas-surface interaction layer, we theoretically analyze the evolution of the gas distribution function, and associate sigma with the time scales of gas-surface interaction. With the binary collision assumption, we evaluate the mean time of gas-surface collisions, and consequently establish a physical model (with one fitting parameter) to correlate sigma with the properties of gas molecule and the surface temperature. The proposed model is systematically validated against MD simulations for the argon-platinum system under varying properties of gas molecule and surface temperature. Its broad applicability is further demonstrated for the argon-carbon and nitrogen-silicon carbide systems.