Generalized hydrodynamics and Reynolds-number dependence of steady-flow properties in the cylindrical Couette flow of Lennard-Jones fluids.

Abstract

The Reynolds-number dependence is calculated for the shear stress, normal stress difference, velocity, effective viscosity, and effective normal stress coefficient by using the generalized hydrodynamic equations in the case of cylindrical Couette flow of a Lennard-Jones gas. The drag coefficient is shown to decrease more rapidly than the inverse Reynolds number and rapidly vanish on passing a critical Reynolds number. The shear stress and normal stress difference also vanish beyond the critical Reynolds number, and there is a region in space where the effective shear viscosity and normal stress coefficients become so small that the fluid behaves like an almost inviscid fluid in the region. These numerical results indicate that the generalized hydrodynamic equations tend to the Euler equations in the limit of sufficiently large Reynolds number at a rate faster than that for the Navier-Stokes equation and that the fluid is almost inviscid in some parts where the velocity changes steeply, and viscous in the rest.