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Physics of Fluids / Volume 24 / Issue 2 / ARTICLES / Micro- and Nanofluid Mechanics

Phys. Fluids 24, 022001 (2012); http://dx.doi.org/10.1063/1.3680873 (14 pages)

Velocity slip coefficients based on the hard-sphere Boltzmann equation

Livio Gibelli

Dipartimento di Matematica, Politecnico di Milano, Milan 20133, Italy

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(Received 24 June 2011; accepted 30 December 2011; published online 3 February 2012)

We present a kinetic theory derivation of higher-order slip boundary conditions. The situation studied is that of a pressure driven isothermal gas flowing through a plane microchannel. The distribution function is expanded in terms of half-range Hermite polynomials and the system of moment equations in the expansion coefficients is analytically solved. The velocity slip coefficients, as well as their Knudsen-layer corrections, are obtained by evaluating the solution in the near continuum limit. The proposed approach is accurate and easy to implement. The results are presented for the hard-sphere Boltzmann equation and Maxwell's diffuse-specular boundary conditions, but can be extended to arbitrary intermolecular interactions and more general scattering kernels.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. FORMULATION OF THE PROBLEM
  3. HALF-RANGE POLYNOMIAL SOLUTION
  4. NEAR CONTINUUM SOLUTION AND VELOCITY SLIP COEFFICIENTS
  5. RESULTS AND DISCUSSION
  6. CONCLUSION

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KEYWORDS and PACS

Keywords

aerodynamics, Boltzmann equation, computational fluid dynamics, kinetic theory, Knudsen flow, method of moments, microchannel flow, Poiseuille flow, slip flow

PACS

  • 47.45.Gx

    Slip flows and accommodation

  • 47.60.Dx

    Flows in ducts and channels

  • 47.11.-j

    Computational methods in fluid dynamics

  • 47.15.Rq

    Laminar flows in cavities, channels, ducts, and conduits

  • 47.40.-x

    Compressible flows; shock waves

  • 47.45.Ab

    Kinetic theory of gases

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3680873

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
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