Thermal conductivity of fluids with steeply repulsive potentials

Abstract

We consider the thermal conductivity of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, φ(r) = ε(σ/r)n. The time correlation function for the heat flux, Cλ(t), and the time average, Cλ(0) are calculated numerically by molecular dynamics simulations, and accurate expressions for these are also derived for the SRP fluid. We show, by molecular dynamics simulations, that close to the hard-sphere limit this time correlation function has the same analytic form as for the shear and pressure correlation functions for the shear and bulk viscosity, i.e. Cλ(t)/Cλ(0) = 1 −T* (nt*)2 + 0((nt*)4), where T* = k B T/ε, is the reduced temperature, k B is Boltzmann's constant and t* = (ε/σ2)1/2 t is the reduced time. The thermal conductivity for the limiting case of hard spheres is numerically very close to that given by the traditional Enskog relation. At low densities the normalized relaxation times are typically largest for the thermal conductivity, followed by shear and then bulk viscosity. Close to the maximum fluid density, the latter two increase rapidly with density (especially for the shear) but continue a monotonic decline for the thermal conductivity. This reflects the relative insensitivity of the thermal conductivity to the approach to the fluid-solid phase boundary.