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

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