Departure from Navier-Stokes hydrodynamics in confined liquids

Abstract

In this work we use nonequilibrium molecular dynamics (NEMD) to simulate an atomic liquid undergoing gravity-fed flow down a narrow channel. We compare the simulation results against the predictions of classical Navier-Stokes theory for two different channel widths. For a channel width of 5.1 molecular diameters, we find that the velocity profile deviates significantly from the hydrodynamic prediction. The shape of this velocity profile is found to be independent of the applied field (pressure gradient). We find that the heat flux profile does not agree with the cubic profile predicted by Navier-Stokes hydrodynamics, but shows significant oscillations located about one molecular diameter from the walls. This result differs from the earlier work of Todd and Evans [B. D. Todd and D. J. Evans, J. Chem. Phys. 103, 9804 (1995)], in which an assumption of a purely quadratic velocity profile resulted in very weak oscillations in the heat flux. We find that in narrow channels the viscosity cannot be described by a linear, local constitutive relation. However, classical Navier-Stokes behavior is approached for a channel width of g\ensuremath{\sim}10 molecular diameters.