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

Jason M. Reese, Yonghao Zhang

Research output: Contribution to journalArticle

15 Citations (Scopus)
231 Downloads (Pure)

Abstract

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 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
Volume6
Issue number10
DOIs
Publication statusPublished - Oct 2009

Keywords

  • microfluidics
  • nanofluidics
  • rarefied gas dynamics
  • non-equilibrium fluid dynamics
  • slip flow
  • Knudsen Layer
  • micro-scale flows
  • nano-scale flows
  • extended hydrodynamics
  • lattice Boltzmann

Fingerprint Dive into the research topics of 'Simulating fluid flows in micro and nano devices: the challenge of non-equilibrium behaviour'. Together they form a unique fingerprint.

  • Cite this