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

Extraction of the translational Eucken factor from light scattering by molecular gas

“…For example, in thermal transpiration where the gas automatically moves from a cold region to a hot region in the absence of a pressure gradient (Maxwell 1879; Reynolds 1879), the mass flow rate is proportional to , rather than (Porodnov, Kulev & Tuchvetov 1978; Loyalka & Storvick 1979; Loyalka, Storvick & Lo 1982). Although can be measured in thermal transpiration flows (Mason 1963; Gupta & Storvick 1970), the result cannot be accurate as it is hampered by the inaccurate gas–surface interaction (Sharipov 2011; Wu & Struchtrup 2017).…”

Variational derivation of thermal slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules and Cercignani–Lampis boundary conditions: Comparison with experimental results

“…Several attempts have been made to extract, for different gases, both the tangential momentum, α t , and the normal energy, α n , accommodation coefficients simultaneously, see Refs. [ 22], [ 23]. The author of Ref.…”

“…The authors of Ref. [ 23] solved numerically the linearized Boltzmann equation with the Lennard-Jones intermolecular potential and the Cercignani-Lampis boundary conditions, to calculate the temperaturedriven mass flow rate and the thermomolecular pressure difference, and compared their outputs with the experimental data provided in Ref. [ 25].…”

A high-order hybridizable discontinuous Galerkin method with fast convergence to steady-state solutions of the gas kinetic equation

“…Other type of boundary conditions, such as the Maxwell diffuse-specular boundary condition with given tangential momentum accommodation coefficient, symmetry boundary, periodic boundaries, as well as far-pressure inlet/outlet boundary could be incorporated straightforwardly [38,52].…”