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Research Papers

# Multiscale Study of Gas Slip Flows in Nanochannels

[+] Author and Article Information
Quy Dong To

Laboratoire Modélisation et
Simulation Multi Échelle,
UMR-CNRS 8208,
Université Paris-Est,
5 Boulevard Descartes,
Marne-la-Vallée Cedex 2 77454, France
e-mail: quy-dong.to@univ-paris-est.fr

Thanh Tung Pham, Vincent Brites, Céline Léonard, Guy Lauriat

Laboratoire Modélisation et
Simulation Multi Échelle,
UMR-CNRS 8208,
Université Paris-Est,
5 Boulevard Descartes,
Marne-la-Vallée Cedex 2 77454, France

1Present address: Université d'Evry Val d'Essonne, Laboratoire Analyse et Modélisation pour la Biologie et l'Environnement, LAMBE CNRS UMR 8587, Boulevard F. Mitterrand, Evry Cedex 91025, France.

Manuscript received January 6, 2014; final manuscript received March 17, 2014; published online May 14, 2015. Assoc. Editor: Yogesh Jaluria.

J. Heat Transfer 137(9), 091002 (Sep 01, 2015) (8 pages) Paper No: HT-14-1009; doi: 10.1115/1.4030205 History: Received January 06, 2014; Revised March 17, 2014; Online May 14, 2015

## Abstract

A multiscale modeling of the anisotropic slip phenomenon for gas flows is presented in a tree-step approach: determination of the gas–wall potential, simulation and modeling of the gas–wall collisions, simulation and modeling of the anisotropic slip effects. The density functional theory (DFT) is used to examine the interaction between the Pt–Ar gas–wall couple. This potential is then passed into molecular dynamics (MD) simulations of beam scattering experiments in order to calculate accommodation coefficients. These coefficients enter in an effective gas–wall interaction model, which is the base of efficient MD simulations of gas flows between anisotropic surfaces. The slip effects are quantified numerically and compared with simplified theoretical models derived in this paper. The paper demonstrates that the DFT potential is in good agreement with empirical potentials and that an extension of the Maxwell model can describe anisotropic slip effects due to surface roughness, provided that two tangential accommodation parameters are introduced. MD data show excellent agreement with the tensorial slip theory, except at large Kundsen numbers (for example, Kn $≃$0.2) and with an analytical expression which predicts the ratio between transverse and longitudinal slip velocity components.

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## Figures

Fig. 1

Pt(111)–Ar interaction potentials

Fig. 2

Nanotextured surface with strips and gas beaming direction θ, ϕ in cartesian coordinate system. The geometric parameters are l1 = 11.76 Å, l2 = 19.6 Å, l3 = 7.84 Å, h = 0-5.88 Å.

Fig. 3

σtdir computed for striped walls versus azimuth angle ϕ for different roughnesses (Tw = 300 K, θ=45 deg). The solid, dashed, dashed-dotted lines are the analytical expressions (7) used to fit the present numerical results.

Fig. 4

Collision between gas atoms and a solid wall. The number of gas atoms going downward (velocity v') and upward (velocity v) within one time unit are denoted N and N+, respectively. If there is no gas accumulation at the wall, N+ = N-.

Fig. 5

Longitudinal and transverse velocity profiles un, um for different values of ϕ and Kn = 0.104. The velocities are normalized with umax—the velocity at z = 0 for case ϕ = 90 deg.

Fig. 6

Dimensionless slip length Ls/H as a function of ϕ at different Kn. Points are MD data which are fitted with solid lines corresponding to the analytical expression (30). The dashed lines represent quantitative estimation (31) based on αx,αy.

Fig. 7

Ratio of transverse and longitudinal components of fitted slip velocity as a function of ϕ for various Kn. Points are MD data, the solid and dashed lines are analytical expressions (32) and (33).

Fig. 8

Ratio of transverse and longitudinal components of real slip velocity as a function of ϕ for different Kn. Points are MD data and the dashed line is for the analytical expression (33).

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