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Knudsen's pioneering experimental and theoretical work performed more than acentury ago pointed to the fact that the Navier-Stokes-Fourier (NSF) paradigmis inapplicable to compressible gases at Knudsen numbers (Kn) beyond thecontinuum 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 remainapplicable. Surprisingly, this belief appears never to have been criticallytested; rather, most tests of the viability of the NSF equations for continuumflows have, to date, effectively been limited to incompressible fluids, namelyliquids. Given that bivelocity hydrodynamic theory has recently raisedfundamental questions about the validity of the NSF equations for compressiblecontinuum gas flows, we deemed it worthwhile to test the validity of the NSFparadigm for the case of continua. Although our proposed NSF test does not,itself, depend upon the correctness of the bivelocity model that spawned thetest, the latter provided motivation. This Letter furnishes molecular dynamics(MD) simulation evidence showing, contrary to current opinion, that the NSFequations are not, in fact, applicable to compressible gaseous continua, nor,presumably, either to compressible liquids. Importantly, this conclusionregarding NSF's inapplicability to continua, is shown to hold independently ofthe viability of the no-slip boundary condition applied to fluid continua, thusseparating the issue of the correctness of the NSF differential equations fromthat of the tangential velocity boundary condition to be imposed upon theseequations when seeking their solution. Finally, the MD data are shown to befunctionally consistent with the bivelocity model that spawned the presentstudy.

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