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

Lei Wu, Henning Struchtrup

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.
LanguageEnglish
Pages511-537
Number of pages27
JournalJournal of Fluid Mechanics
Volume823
Early online date21 Jun 2017
DOIs
Publication statusPublished - 1 Jul 2017

Fingerprint

Kinetic theory of gases
Boltzmann equation
Boundary conditions
boundary conditions
kinetics
gases
slip
transpiration
Transpiration
coefficients
surface reactions
Fluids
fluids
Lennard-Jones potential
rarefied gases
mass flow rate
Gases
gas flow
Flow of gases
unity

Keywords

  • gas kinetic boundary
  • Boltzmann equations
  • thermal transpiration flows
  • mass flow rates
  • Epstein boundary condition
  • Cercignani-Lampis boundary condition
  • Maxwell boundary condition

Cite this

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title = "Assessment and development of the gas kinetic boundary condition for the Boltzmann equation",
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.",
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Assessment and development of the gas kinetic boundary condition for the Boltzmann equation. / Wu, Lei; Struchtrup, Henning.

In: Journal of Fluid Mechanics, Vol. 823, 01.07.2017, p. 511-537.

Research output: Contribution to journalArticle

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