Simulating fluid flows in micro and nano devices: the challenge of non-equilibrium behaviour

Jason M. Reese*, Yonghao Zhang

*Corresponding author for this work

Research output: Contribution to journalLiterature reviewpeer-review


We review some recent developments in the modelling of non-equilibrium (rarefied) gas flows at the micro- and nano-scale, concentrating on two different but promising approaches: extended hydrodynamic models, and lattice Boltzmann methods. Following a brief exposition of the challenges that non-equilibrium poses in micro- and nano-scale gas flows, we turn first to extended hydrodynamics, outlining the effective abandonment of Burnett-type models in favour of high-order regularised moment equations. We show that the latter models, with properly-constituted boundary conditions, can capture critical non-equilibrium flow phenomena quite well. 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 Maxwell-type 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 this section 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. Understanding non-equilibrium within the lattice Boltzmann (LB) framework is not as advanced as in the hydrodynamic framework, although LB can borrow some of the techniques which are being developed in the latter-in particular, the near-wall scaling of certain fluid properties that has proven effective in PEH. We describe how, with this modification, the standard 2nd-order LB method is showing promise in predicting some rarefaction phenomena, indicating that instead of developing higher-order off-lattice LB methods with a large number of discrete velocities, a simplified high-order LB method with near-wall scaling may prove to be just as effective as a simulation tool.

Original languageEnglish
Pages (from-to)2061-2074
Number of pages14
JournalJournal of Computational and Theoretical Nanoscience
Issue number10
Publication statusPublished - Oct 2009


  • microfluidics
  • nanofluidics
  • rarefied gas dynamics
  • non-equilibrium fluid dynamics
  • slip flow
  • Knudsen layer
  • micro- and nano-scale flows
  • extended hydrodynamics
  • lattice Boltzmann
  • non-continuum fluid dynamics
  • Navier-Stokes equations
  • gas micro flow
  • boundary conditions
  • transition-continuum regime
  • heat transfer
  • review
  • Knudsen number
  • moment equations
  • temperature jump
  • wall-scaling


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