Investigation of the density dependence of the shear relaxation time of dense fluids

Abstract

The shear relaxation time, a key quantity in the theory of viscosity, is calculated for the Lennard–Jones fluid and fluid krypton. The shear relaxation time is initially calculated by the Zwanzig–Mountain method, which defines this quantity as the ratio of the shear viscosity coefficient to the infinite shear modulus. The shear modulus is calculated from highly accurate radial distribution functions obtained from molecular dynamics simulations of the Lennard–Jones potential and a realistic potential for krypton. This calculation shows that the density dependence of the shear relaxation time isotherms of the Lennard–Jones fluid and Kr pass through a minimum. The minimum in the shear relaxation times is also obtained from calculations using the different approach originally proposed by van der Gulik. In this approach, the relaxation time is determined as the ratio of shear viscosity coefficient to the thermal pressure. The density of the minimum of the shear relaxation time is about twice the critical density and is equal to the common density, which was previously reported for supercritical gases where the viscosity of the gas becomes independent of temperature. It is shown that this common point occurs in both gas and liquid phases. At densities lower than this common density, even in the liquid state, the viscosity increases with increasing temperature.Key words: dense fluids, radial distribution function, shear modulus, shear relaxation time, shear viscosity.