On the modelling of isothermal gas flows at the microscale

Duncan A. Lockerby*, Jason M. Reese

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper makes two new propositions regarding the modelling of rarefied (non-equilibrium) isothermal gas flows at the microscale. The first is a new test case for benchmarking high-order, or extended, hydrodynamic models for these flows. This standing time-varying shear-wave problem does not require boundary conditions to be specified at a solid surface, so is useful for assessing whether fluid models can capture rarefaction effects in the bulk flow. We assess a number of different proposed extended hydrodynamic models, and we find the R13 equations perform the best in this case.

Our second proposition is a simple technique for introducing non-equilibrium effects caused by the presence of solid surfaces into the computational fluid dynamics framework. By combining a new model for slip boundary conditions with a near-wall scaling of the Navier-Stokes constitutive relations, we obtain a model that is much more accurate at higher Knudsen numbers than the conventional second-order slip model. We show that this provides good results for combined Couette/Poiseuille flow, and that the model can predict the stress/strain-rate inversion that is evident from molecular simulations. The model's generality to non-planar geometries is demonstrated by examining low-speed flow around a micro-sphere. It shows a marked improvement over conventional predictions of the drag on the sphere, although there are some questions regarding its stability at the highest Knudsen numbers.

Original languageEnglish
Pages (from-to)235-261
Number of pages27
JournalJournal of Fluid Mechanics
Volume604
Issue numbern/a
DOIs
Publication statusPublished - 10 Jun 2008

Keywords

  • HARD-SPHERE MOLECULES
  • BOLTZMANN-EQUATION
  • NUMERICAL-ANALYSIS
  • rarefied gas dynamics
  • micro gas flows
  • extended hydrodynamics
  • boundary conditions
  • Knudsen layer

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