Computing the near-wall region in gas micro- and nanofluidics: critical Knudsen layer phenomena

Jason M. Reese, Yunlong Zheng, Duncan A. Lockerby

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

In order to capture critical near-wall phenomena in gas micro- and nanoflows within conventional CFD codes, we present scaled Navier-Stokes-Fourier (NSF) constitutive relations. Our scaling is mathematically equivalent to applying an 'effective' viscosity to the original constitutive relations. An expression for this 'effective' transport coefficient is obtained from the half-space Kramer's flow problem. The advantage of our model over the traditional NSF equations is that the non-equilibrium flow near to the wall (the momentum Knudsen layer) can be described. Its advantage over higher-order hydrodynamic models for gas micro and nanoflows is that the boundary conditions remain the same as required for the traditional NSF equations, so modifications to current CFD codes (pro-vided they are already capable of modelling slip at solid surfaces) would be minimal. As an application example, we apply our model to the isothermal problem of a micro-sphere moving through a gas: we show that our model gives excellent results in the Knudsen number range Kn . 0:1 and acceptable results up to Kn ¼ 0:25. This is much better than the traditional NSF model with non-scaled constitutive relations.
LanguageEnglish
Pages807-813
Number of pages7
JournalJournal of Computational and Theoretical Nanoscience
Volume4
Issue number4
DOIs
Publication statusPublished - Jun 2007

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Nanofluidics
Microfluidics
Navier-Stokes
Constitutive Relations
Gases
Computing
gases
charge flow devices
Computational fluid dynamics
Knudsen number
Microspheres
Transport Coefficients
Hydrodynamic Model
nonequilibrium flow
Knudsen flow
Model
Slip
Half-space
Non-equilibrium
Viscosity

Keywords

  • Knudsen layer
  • rarefied gas flows
  • microfluidics
  • nanofluidics
  • constitutive relations

Cite this

Reese, Jason M. ; Zheng, Yunlong ; Lockerby, Duncan A. / Computing the near-wall region in gas micro- and nanofluidics : critical Knudsen layer phenomena. In: Journal of Computational and Theoretical Nanoscience. 2007 ; Vol. 4, No. 4. pp. 807-813.
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Computing the near-wall region in gas micro- and nanofluidics : critical Knudsen layer phenomena. / Reese, Jason M.; Zheng, Yunlong; Lockerby, Duncan A.

In: Journal of Computational and Theoretical Nanoscience, Vol. 4, No. 4, 06.2007, p. 807-813.

Research output: Contribution to journalArticle

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AB - In order to capture critical near-wall phenomena in gas micro- and nanoflows within conventional CFD codes, we present scaled Navier-Stokes-Fourier (NSF) constitutive relations. Our scaling is mathematically equivalent to applying an 'effective' viscosity to the original constitutive relations. An expression for this 'effective' transport coefficient is obtained from the half-space Kramer's flow problem. The advantage of our model over the traditional NSF equations is that the non-equilibrium flow near to the wall (the momentum Knudsen layer) can be described. Its advantage over higher-order hydrodynamic models for gas micro and nanoflows is that the boundary conditions remain the same as required for the traditional NSF equations, so modifications to current CFD codes (pro-vided they are already capable of modelling slip at solid surfaces) would be minimal. As an application example, we apply our model to the isothermal problem of a micro-sphere moving through a gas: we show that our model gives excellent results in the Knudsen number range Kn . 0:1 and acceptable results up to Kn ¼ 0:25. This is much better than the traditional NSF model with non-scaled constitutive relations.

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