Generalized Hydrodynamics and Analysis of Current Correlation Functions

Abstract

A generalization of the Navier-Stokes equation, valid for wavelengths and times of a molecular order of magnitude, is discussed on the basis of viscoelastic behavior of simple classical liquids. In this theory, transport coefficients are replaced by appropriate viscoelastic memory functions. The theory is verified by analyzing the data on current-correlation functions obtained from computer experiments. Three different models for the time dependence of the viscoelastic memory are investigated, namely, a single-exponential decay, a modified-exponential decay, and a Gaussian decay. It is obsrved that the memory functions are approximately Gaussian, at least for times of the order of one or two relaxation times. This is in agreement with a conjecture of Forster, Martin, and Yip. The wave-number dependence of the half-width of the Gaussian decay, and of the longitudinal- and shear-viscosity coefficients, are found from computer experiments. The extrapolated values of these transport coefficients, in the limit $k\ensuremath{\rightarrow}0$, are in good agreement with experiments on liquid argon.