Hydrodynamic time correlation functions for a Lennard-Jones fluid

Abstract

Four time correlation functions of a Lennard-Jones (LJ) fluid at a reduced density of $n^{\mathrm{*}}$=n${\sigma }_{\mathrm{LJ}{}^3=0.845\mathrm{}}$ and a reduced temperature of $T^{\mathrm{*}}$=$k_{\mathrm{B}\mathrm{T}/{\varepsilon }_{\mathrm{LJ}=1.71\mathrm{}}}$ have been determined numerically using molecular dynamics. They were computed as a function of wave number k for reduced wave numbers 0≤k${\sigma }_{\mathrm{LJ}<15\mathrm{}}$ and for reduced times 0≤t/${\tau }_{\sigma }$${\tau }_{\sigma }$ is an average collision time. From these four, all 25 correlation functions can be derived between three conserved and two nonconserved quantities: the number density, energy density, longitudinal velocity, momentum flux, and energy flux, respectively. They can be fitted consistently by five exponentials that correspond to the five eigenmodes of a 5×5 k-dependent, but not t-dependent, matrix based on the above-mentioned five quantities. Three of these eigenmodes are extensions of the usual hydrodynamic modes and suffice to describe the density-density correlation function alone. A comparison with previous work on Lennard-Jones, noble-gas, and hard-sphere fluids is made.