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

Wu, Lei and Struchtrup, Henning (2017) Assessment and development of the gas kinetic boundary condition for the Boltzmann equation. Journal of Fluid Mechanics, 823. pp. 511-537. ISSN 0022-1120 (https://doi.org/10.1017/jfm.2017.326)

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Abstract

Gas-surface interactions play important roles in internal rarefied 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 bound- ary condition (BC) has not been well studied. Here we assess the accuracy 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-C ́ardenas et al. [Phys. Fluids, 25, 072002 (2013)], and Yam- aguchi 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 effective viscous and thermal slip coefficients to match the experimental data. Among the three BCs, the Epstein BC has more flexibility to adjust the two slip coefficients, and hence in most of the time it gives good agreement with the experimental measurement. However, like the Maxwell BC, the viscous slip coefficient 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 approxi- mate analytical expressions for the viscous and thermal slip coefficients provide a useful guidance to choose these parameters.

  • Item type:Article
    ID code:60590
    Dates:
    Date
    Event
    1 July 2017
    Published
    21 June 2017
    Published Online
    2 May 2017
    Accepted
    Notes:This article has been published in a revised form in Journal of Fluid Mechanics [http://doi.org/10.1017/jfm.2017.326]. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © copyright holder.
    Subjects:Technology > Mechanical engineering and machinery
    Department:Faculty of Engineering > Mechanical and Aerospace Engineering
    Depositing user: Pure Administrator
    Date deposited:03 May 2017 11:43
    Last modified:19 Apr 2024 00:19
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/60590
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