Poiseuille flow of molecular fluids

Abstract

We examine a generalised Navier-Stokes theory applicable to fluids composed of non-spherical molecules. We compare the theoretical predictions for flow velocity and viscosity with results obtained from nonequilibrium molecular dynamics (NEMD) simulations of a fluid undergoing gravity fed flow down a rectangular channel. We study two different fluids: one composed of spherical particles and the other composed of uniaxial molecules at two different channel widths, W = 5.1 and 10.2 molecular diameters. Our results show that aside from boundary effects due to the roughness of the atomistic walls, the generalised Navier-Stokes theory gives a reasonable qualitative account of a fluid composed of molecules that possess spin, even in a channel that is only 10.2 molecular diameters wide. In the simple fluid case, we find that classical behaviour is behaviour is approached at this same channel width ( W = 10.2) but in the W = 5.1 channel, Navier-Stokes theory begins to break down. For both channel widths we find that the assumption of a constant shear viscosity is incorrect and, further, that the viscosity in the narrow channel of 5.1 molecular diameters is probably non-local.