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

Jason M. Reese*, Yingsong Zheng, Duncan A. Lockerby

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 (provided 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 less than or similar to 0.1 and acceptable results up to Kn approximate to 0.25. This is much better than the traditional NSF model with non-scaled constitutive relations.

Original languageEnglish
Pages (from-to)807-813
Number of pages7
JournalJournal of Computational and Theoretical Nanoscience
Volume4
Issue number4
Publication statusPublished - Jun 2007
EventEuropean Conference on Computational Fluid Dynamics - Egmond, Netherlands
Duration: 5 Sep 20068 Sep 2006

Keywords

  • Knudsen layer
  • rarefied gas flows
  • microfluidics
  • nanofluidics
  • constitutive relations
  • LINEARIZED BOLTZMANN-EQUATION
  • HARD-SPHERE MOLECULES
  • TEMPERATURE-JUMP PROBLEM
  • COLLISION FREQUENCY MODEL
  • RAREFIED-GAS
  • NUMERICAL-ANALYSIS
  • SURFACE INTERACTION
  • KRAMERS PROBLEM
  • PLANE WALL
  • MOTION

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