A molecular dynamics test of the Navier-Stokes-Fourier paradigm for compressible gaseous continua

TL;DR

This study uses molecular dynamics simulations to critically test the applicability of the Navier-Stokes-Fourier equations to compressible gaseous continua, challenging the assumption that these equations are valid in the continuum limit.

Contribution

It provides the first molecular dynamics evidence indicating the NSF equations are not valid for compressible gaseous continua, independently of boundary condition assumptions.

Findings

NSF equations are not applicable to compressible gaseous continua.

MD data aligns with the bivelocity model.

Validity of no-slip boundary condition is independent of NSF applicability.

Abstract

Knudsen's pioneering experimental and theoretical work performed more than a century ago pointed to the fact that the Navier-Stokes-Fourier (NSF) paradigm is inapplicable to compressible gases at Knudsen numbers (Kn) beyond the continuum range, namely to noncontinua. However, in the case of continua, wherein Kn approaches zero asymptotically, it is nevertheless (implicitly) assumed in the literature that the compressible NSF equations remain applicable. Surprisingly, this belief appears never to have been critically tested; rather, most tests of the viability of the NSF equations for continuum flows have, to date, effectively been limited to incompressible fluids, namely liquids. Given that bivelocity hydrodynamic theory has recently raised fundamental questions about the validity of the NSF equations for compressible continuum gas flows, we deemed it worthwhile to test the validity of the NSF paradigm for the case of continua. Although our proposed NSF test does not, itself, depend upon the correctness of the bivelocity model that spawned the test, the latter provided motivation. This Letter furnishes molecular dynamics (MD) simulation evidence showing, contrary to current opinion, that the NSF equations are not, in fact, applicable to compressible gaseous continua, nor, presumably, either to compressible liquids. Importantly, this conclusion regarding NSF's inapplicability to continua, is shown to hold independently of the viability of the no-slip boundary condition applied to fluid continua, thus separating the issue of the correctness of the NSF differential equations from that of the tangential velocity boundary condition to be imposed upon these equations when seeking their solution. Finally, the MD data are shown to be functionally consistent with the bivelocity model that spawned the present study.