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Physics of Fluids / Volume 22 / Issue 10 / ARTICLES / Micro- and Nanofluid Mechanics

Phys. Fluids 22, 102001 (2010); http://dx.doi.org/10.1063/1.3500686 (22 pages)

Diffusion model for Knudsen-type compressor composed of periodic arrays of circular cylinders

Satoshi Taguchi

Organization of Advanced Science and Technology, Kobe University, Kobe 657-8501, Japan

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(Received 28 February 2010; accepted 10 September 2010; published online 27 October 2010)

A rarefied gas flow in a long porous channel having a periodic structure that is consisting of alternately arranged porous media and gaps, the former of which contains a periodic array of parallel circular cylinders, is considered for the case in which the channel is infinitely wide. The cylinder arrays have a periodic temperature distribution with the same period as the structure. Under the assumption that the length of each cylinder array and that of each gap are much larger than the period of the cylinders in the array, a fluid-dynamic system describing the overall behavior of the gas in the channel is derived from the kinetic system composed of the Bhatnagar–Gross–Krook equation and the diffuse reflection boundary condition. The derived system is composed of a diffusion model for each cylinder array, whose isothermal version has been reported previously [ S. Taguchi and P. Charrier, Phys. Fluids 20, 067103 (2008) ], a set of fluid-dynamic equations for each gap, and the macroscopic connection conditions at each junction between an array and a gap. Then, the fluid-dynamic system is applied to a long channel consisting of many cylinder arrays and gaps. Some numerical results demonstrating the pumping effect of the flow are presented.

© 2010 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. FLOW PAST A SQUARE ARRAY OF CIRCULAR CYLINDERS AND ITS FLUID-DYNAMIC MODEL
    1. Problem and basic equations
    2. Scaling
    3. Homogenization
      1. Problem for ϵ0 order
      2. Problem for ϵ1 order
      3. Problem for ϵ2 order and diffusion model
  3. FLOW ACROSS A GAP AND ITS FLUID-DYNAMIC EQUATIONS
    1. Problem
    2. Asymptotic analysis and fluid-dynamic equations
  4. CYLINDER ARRAY IN CONTACT WITH A HALF SPACE
    1. Connection problem
    2. Condition at junction
  5. FLOW AROUND PARALLEL CIRCULAR CYLINDERS INDUCED BY SMALL PRESSURE AND TEMPERATURE GRADIENTS
    1. Problem and relevant equations
    2. Transport coefficients
  6. FLUID-DYNAMIC SYSTEM FOR A KNUDSEN-TYPE COMPRESSOR COMPOSED OF CYLINDER ARRAYS AND GAPS
  7. NUMERICAL RESULTS AND DISCUSSION
  8. CONCLUDING REMARKS

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KEYWORDS and PACS

Keywords

channel flow, diffusion, flow through porous media, Knudsen flow, pulsatile flow, pumps

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3500686

PUBLICATION DATA

ISSN

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

Publisher

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

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    References

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