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A slip model for micro/nano gas flows induced by body forces

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Abstract

A slip model for gas flows in micro/nano-channels induced by external body forces is derived based on Maxwell’s collision theory between gas molecules and the wall. The model modifies the relationship between slip velocity and velocity gradient at the walls by introducing a new parameter in addition to the classic Tangential Momentum Accommodation Coefficient. Three-dimensional Molecular Dynamics simulations of helium gas flows under uniform body force field between copper flat walls with different channel height are used to validate the model and to determine this new parameter.

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Abbreviations

λ:

Mean free path

H, B, L:

Channel height, width and length

Kn:

Knudsen number

n, ρ:

Number density, mass density

d :

Molecular diameter

L s , L* s :

Slip length, dimensionless slip length

x, y, z:

Cartesian coordinate

\(\hat{z}\) :

Normalized coordinate

σ v :

Tangential Momentum Accommodation Coefficient

\(v,\hat{v}\) :

Tangential velocity, normalized tangential velocity

\(v_{\rm slip},\hat{v}_{\rm slip}\) :

Slip velocity, normalized slip velocity

v ref :

Reference velocity

N  ±  :

Molecules going upward N + and downward N − with respect to the control surface s

N :

Total number of molecules passing through s

\( < v^\pm_x > \) :

Average velocity of molecules going upward \( < v_x^+ > \) and downward \( < v_x^- > \) with respect to s

v s , v w :

Gas velocity near the wall, velocity of the wall

\( < \tau >,\bar{c}\) :

Mean collision time, thermal speed

k B , T:

Boltzmann constant, absolute temperature

m, γ x :

Molecular mass, acceleration along x-axis

α, β:

Slip parameters of the present model

v λ :

Gas velocity at distance λ from the wall

\(\mu,\mu^*,\bar{\mu}\) :

Gas viscosity, scaled viscosity, kinetic theoretical viscosity

V i :

Potential energy of atom i

F, ρ e , ϕ:

Potential functions of Embedded Atom Model

\(\sigma _{{a - b}} , \epsilon _{{a - b}}\) :

Parameters of Lennard Jones potential between molecules a and b

r ij :

Distance between two molecules i and j

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Acknowledgments

The authors acknowledge the French National Institute for Advances in Scientific Computations (IDRIS) for computational support of this project through grant No.i2009092205. We also wish to thank the reviewers for their helpful comments that help to improve the quality of this article.

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Authors and Affiliations

  1. Université Paris-Est, Laboratoire Modelisation et Simulation Multi Echelle, FRE 3160 CNRS, 5 Boulevard Descartes, 77454, Marne-la-Vallée Cedex 2, France

    Q. D. To, C. Bercegeay, G. Lauriat, C. Léonard & G. Bonnet

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  1. Q. D. To
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  2. C. Bercegeay
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  3. G. Lauriat
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  4. C. Léonard
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  5. G. Bonnet
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Correspondence to Q. D. To.

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To, Q.D., Bercegeay, C., Lauriat, G. et al. A slip model for micro/nano gas flows induced by body forces. Microfluid Nanofluid 8, 417–422 (2010). https://doi.org/10.1007/s10404-009-0532-4

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  • DOI: https://doi.org/10.1007/s10404-009-0532-4

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