Gas-surface interaction in rarefied gas flows through long capillaries via the linearized Boltzmann equation with various boundary conditions

Abstract

Reliable gas–surface interaction modeling is of major importance in consistent simulation of rarefied gas flows with applications in vacuum technology and micro-electromechanical systems. The effectiveness of the most prominent kinetic boundary conditions, namely the ones by Maxwell, Cercignani-Lampis and Epstein, is elaborated by numerically solving the classical plane Poiseuille and thermal creep flows via the linearized Boltzmann equation, subject to these boundary conditions. The flow rates are provided in a wide range of the gas rarefaction for many values of the accommodation coefficients of each scattering kernel, identifying in parallel, the sensitivity of the flow rates in small variations of the free parameters. A comparison with available experimental data is performed to deduce that the Cercignani-Lampis and Epstein scattering kernels, compared to the Maxwell one, are more suitable to characterize coupled momentum and energy accommodation modes. With these boundary conditions, the accommodation coefficients may be extracted by fitting computations with measurements, in the Poiseuille flow in a wide range of gas rarefaction, but in the thermal creep flow, experimental data under rarefied conditions, as high as possible, are recommended. The present work may be useful in determining the measurement conditions and uncertainties, allowing accurate extraction of the accommodation coefficients.