Relation of shear viscosity and self-diffusion coefficient for simple liquids

A Stokes-Einstein-type relation is derived for the potential part of the shear viscosity of a simple liquid by means of statistical mechanics. The product of the shear viscosity and the self-diffusion coefficient is shown to be expressible in terms of the pair correlation function and the intermolecular force as well as the density. The shear viscosity formula, consisting of kinetic and potential parts and given in terms of the self-diffusion coefficient, is tested against experimental data with regard to the temperature and density dependence of the shear viscosity. Given the self-diffusion coefficient determined by experiment or simulations, the viscosity formula involving the Stokes-Einstein relation obtained produces the shear viscosity of argon, krypton, and xenon, in good agreement with experiment in the case of temperatures well away from the triple point. However, in the neighborhood of the triple point of argon examined, a cutoff parameter, which is a measure of the range of density variation, is needed to account for the experimental data. The applicability of the Stokes-Einstein relation to molecular particles is assessed, and it is found to remain applicable in the range of density and temperature examined.