A wall-function approach to incorporating Knudsen-layer effects in gas micro flow simulations

Duncan A. Lockerby, Jason Reese, Michael A. Gallis

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)
113 Downloads (Pure)

Abstract

For gas flows in microfluidic configurations, the Knudsen layer close to the wall can comprise a substantial part of the entire flow field and has a major effect on quantities such as the mass flow rate through micro devices. The Knudsen layer itself is characterized by a highly nonlinear relationship between the viscous stress and the strain rate of the gas, so even if the Navier-Stokes equations can be used to describe the core gas flow they are certainly inappropriate for the Knudsen layer itself. In this paper we propose a "wall-function" model for the stress/strain rate relations in the Knudsen layer. The constitutive structure of the Knudsen layer has been derived from results from kinetic theory for isothermal shear flow over a planar surface. We investigate the ability of this simplified model to predict Knudsen-layer effects in a variety of configurations. We further propose a semi-empirical Knudsen-number correction to this wall function, based on high-accuracy DSMC results, to extend the predictive capabilities of the model to greater degrees of rarefaction.
Original languageEnglish
Title of host publicationRarefied Gas Dynamics
Pages731-736
Volume762
DOIs
Publication statusPublished - 10 Jul 2004
Event24th International Symposium on Rarefied Gas Dynamics, Bari, Italy -
Duration: 1 Jan 1900 → …

Publication series

NameAIP Conference Proceedings
PublisherAmerican Institute of Physics
Number1
Volume762

Conference

Conference24th International Symposium on Rarefied Gas Dynamics, Bari, Italy
Period1/01/00 → …

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Keywords

  • knudsen layer
  • wall-function
  • gas microflows

Cite this

Lockerby, D. A., Reese, J., & Gallis, M. A. (2004). A wall-function approach to incorporating Knudsen-layer effects in gas micro flow simulations. In Rarefied Gas Dynamics (Vol. 762, pp. 731-736). (AIP Conference Proceedings; Vol. 762, No. 1). https://doi.org/10.1063/1.1941622