A Class of Discrete Kinetic Solutions for Non-Boundary-Driven Gas Flow

Abstract

Discrete kinetic theory approach has been used to study dilute, monatomic, non-equilibrium gas flow between two walls in microdomains. A four-velocity coplanar model has been adopted, where the microscopic velocity-orientation angle and the Knudsen number are free parameters, which have to be prescribed. Diffusive reflection boundary condition has been incorporated to obtain the solution. A bounded range for the admissible orientation angle of the discrete velocity vectors for any given Knudsen number is identified. Consequently, the macroscopic velocity slip at the wall, the velocity profile across the walls and the volume flow rate is calculated as a function of the free parameters. The calculations based on a single model, 4-velocity, cover the transition flow regime between the continuum and the free-molecular flow. The calculated volume flow rate is compared with experimental data as well as with other theoretical models.