A continuum model of gas flows with localized density variations

S.K. Dadzie, J.M. Reese, C.R. McInnes

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Abstract

We discuss the kinetic representation of gases and the derivation of macroscopic equations governing the thermomechanical behavior of a dilute gas viewed at the macroscopic level as a continuous medium. We introduce an approach to kinetic theory where spatial distributions of the molecules are incorporated through a mean-free-volume argument. The new kinetic equation derived contains an extra term involving the evolution of this volume, which we attribute to changes in the thermodynamic properties of the medium. Our kinetic equation leads to a macroscopic set of continuum equations in which the gradients of thermodynamic properties, in particular density gradients, impact on diffusive fluxes. New transport terms bearing both convective and diffusive natures arise and are interpreted as purely macroscopic expansion or compression. Our new model is useful for describing gas flows that display non-local-thermodynamic-equilibrium (rarefied gas flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluid flows.
Original languageEnglish
Pages (from-to)6079-6094
Number of pages16
JournalPhysica A: Statistical Mechanics and its Applications
Volume387
Issue number24
DOIs
Publication statusPublished - 15 Oct 2008

Keywords

  • gas kinetic theory
  • Boltzmann equation
  • compressible fluids
  • Navier-Stokes equations
  • rarefied gas dynamics
  • constitutive relations

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