Transition regime analytical solution to gas mass flow rate in a rectangular micro channel

Kokou Sename Enyonam Dadzie, Nishanth Dongari

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)
45 Downloads (Pure)

Abstract

We present an analytical model predicting the experimentally observed gas mass flow rate in rectangular micro channels over slip and transition regimes without the use of any fitting parameter. Previously, Sone reported a class of pure continuum regime flows that requires terms of Burnett order in constitutive equations of shear stress to be predicted appropriately. The corrective terms to the conventional Navier-Stokes equation were named the ghost effect. We demonstrate in this paper similarity between Sone ghost effect model and newly so-called 'volume diffusion hydrodynamic model'. A generic analytical solution to gas mass flow rate in a rectangular micro channel is then obtained. It is shown that the volume diffusion hydrodynamics allows to accurately predict the gas mass flow rate up to Knudsen number of 5. This can be achieved without necessitating the use of adjustable parameters in boundary conditions or parametric scaling laws for constitutive relations. The present model predicts the non-linear variation of pressure profile along the axial direction and also captures the change in curvature with increase in rarefaction.

Original languageEnglish
Title of host publication28th International Symposium on Rarefied Gas Dynamics 2012
EditorsMichel Mareschal, Andrés Santos
PublisherAIP Publishing
Pages720-726
Number of pages7
ISBN (Print)9780735411159
DOIs
Publication statusPublished - 27 Nov 2012
Event28th International Symposium on Rarefied Gas Dynamics 2012 - Zaragoza, Spain
Duration: 9 Jul 201213 Jul 2012

Publication series

NameAIP Conference Proceedings
PublisherAIP Publishing
Number1
Volume1501
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference28th International Symposium on Rarefied Gas Dynamics 2012
CountrySpain
CityZaragoza
Period9/07/1213/07/12

Keywords

  • Knudsen paradox
  • Mass diffusion
  • microchannel gas flow
  • pressure distribution
  • slip flows
  • volume diffusion hydrodynamics

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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  • Cite this

    Dadzie, K. S. E., & Dongari, N. (2012). Transition regime analytical solution to gas mass flow rate in a rectangular micro channel. In M. Mareschal, & A. Santos (Eds.), 28th International Symposium on Rarefied Gas Dynamics 2012 (pp. 720-726). (AIP Conference Proceedings; Vol. 1501, No. 1). AIP Publishing. https://doi.org/10.1063/1.4769613