Beyond the Knudsen number: assessing thermodynamic non-equilibrium in gas flows

TL;DR

This paper introduces a new method to evaluate thermodynamic non-equilibrium in gas flows, challenging the traditional reliance on the Knudsen number and enhancing the understanding of Navier-Stokes model applicability.

Contribution

It proposes a novel assessment approach based on Boltzmann statistics, improving the evaluation of flow non-equilibrium beyond traditional parameters.

Findings

The new method aligns with molecular dynamics simulations.

Knudsen number alone may not reliably indicate flow equilibrium.

The approach enhances the criteria for Navier-Stokes model validity.

Abstract

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.