Assessment and development of the gas kinetic boundary condition for the Boltzmann equation




Wu, Lei
Struchtrup, Henning

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Journal of Fluid Mechanics


Gas-surface interactions play important roles in internal rarefi ed gas flows, especially in micro-electro-mechanical systems with large surface area to volume ratios. Although great progresses have been made to solve the Boltzmann equation, the gas kinetic boundary condition (BC) has not been well studied. Here we assess the accuracy of the Maxwell, Epstein, and Cercignani-Lampis BCs, by comparing numerical results of the Boltzmann equation for the Lennard-Jones potential to experimental data on Poiseuille and thermal transpiration flows. The four experiments considered are: Ewart et al. [J. Fluid Mech. 584, 337-356 (2007)], Rojas-Cardenas et al. [Phys. Fluids, 25, 072002 (2013)], and Yamaguchi et al. [J. Fluid Mech. 744, 169-182 (2014); 795, 690-707 (2016)], where the mass flow rates in Poiseuille and thermal transpiration flows are measured. This requires the BC has the ability to tune the eff ective viscous and thermal slip coeffi cients to match the experimental data. Among the three BCs, the Epstein BC has more flexibility to adjust the two slip coeffi cients, and hence in most of the time it gives good agreement with the experimental measurement. However, like the Maxwell BC, the viscous slip coeffi cient in the Epstein BC cannot be smaller than unity but the Cercignani-Lampis BC can. Therefore, we propose to combine the Epstein and Cercignani-Lampis BCs to describe gas-surface interaction. Although the new BC contains six free parameters, our approximate analytical expressions for the slip coe fficients provide a useful guidance to choose these parameters.




Wu. Lei and Struchtrup, Henning. (2017). "Numerical heat transfer." J. Fluid Mechanics 823, 511-537