Gas dynamics at the micro-scale: a review of progress in hydrodynamic modelling

Jason Reese, Duncan A. Lockerby, David Emerson

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We review some recent developments in the modelling of non-equilibrium (rarefied) gas flows at the micro- and nano-scale using extended hydrodynamic models. Following a brief exposition of the challenges that non-equilibrium poses in micro- and nano-scale gas flows, we outline the field of extended
hydrodynamics, describing the effective abandonment of Burnett-type models in favour of high-order regularised moment equations. We then review the boundary conditions required if the conventional Navier-Stokes-Fourier (NSF) fluid dynamic model is applied at the micro scale, describing how 2nd-order Maxwelltype conditions can be used to compensate for some of the non-equilibrium flow behaviour near solid surfaces. While extended hydrodynamics is not yet widely-used for real flow problems because of its
inherent complexity, we finish with an outline of recent ‘phenomenological extended hydrodynamics’ (PEH) techniques — essentially the NSF equations scaled to incorporate non-equilibrium behaviour close to solid surfaces — which offer promise as engineering models.
Original languageEnglish
Number of pages8
Publication statusUnpublished - 2 Sep 2009
Event2nd Micro and Nano Flows Conference, MNF2009 - Uxbridge, UK
Duration: 1 Sep 20092 Sep 2009


Conference2nd Micro and Nano Flows Conference, MNF2009
CityUxbridge, UK


  • microfluidics
  • nanofluidics
  • rarefied gas dynamics
  • non-equilibrium fluid dynamics
  • slip flow,
  • Knudsen layer
  • micro- and nano-scale flows
  • extended hydrodynamics


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