  For more than 150 years the Navier-Stokes equations for thermodynamically
quasi-equilibrium flows have been the cornerstone of modern computational fluid
dynamics that underpins new fluid technologies. However, the applicable regime
of the Navier-Stokes model in terms of the level of thermodynamic
non-equilibrium in the local flowfield is not clear especially for hypersonic
and low-speed micro/nano flows. Here, we re-visit the Navier-Stokes model in
the framework of Boltzmann statistics, and propose a new and more appropriate
way of assessing non-equilibrium in the local flowfield, and the corresponding
appropriateness of the Navier-Stokes model. Our theoretical analysis and
numerical simulations confirm our proposed method. Through molecular dynamics
simulations we reveal that the commonly-used Knudsen number, or a parametric
combination of Knudsen and Mach numbers, may not be sufficient to accurately
assess the departure of flowfields from equilibrium, and the applicability of
the Navier-Stokes model.
