Molecular hydrodynamic theory of the velocity autocorrelation function

TL;DR

This paper develops a hydrodynamic theory for the velocity autocorrelation function (VACF) in fluids, bridging molecular and continuum descriptions, and accurately predicts VACF for various fluids including gases and supercritical fluids.

Contribution

It introduces a hydrodynamic model using linear equations and kinetic energy spectra to accurately describe the VACF, extending applicability to low-density gases.

Findings

Quantitative VACF predictions for noble gases and alkali metals.

Hydrodynamic VACF as a superposition of quasinormal modes.

Extended model applicability to gases and supercritical fluids.

Abstract

The velocity autocorrelation function (VACF) encapsulates extensive information about a fluid's molecular-structural and hydrodynamic properties. We address the following fundamental question: How well can a purely hydrodynamic description recover the molecular features of a fluid as exhibited by the VACF? To this end, we formulate a bona fide hydrodynamic theory of the tagged-particle VACF for simple fluids. Our approach is distinguished from previous efforts in two key ways: collective hydrodynamic modes are modeled by \emph{linear} hydrodynamic equations; the fluid's static kinetic energy spectrum is identified as a necessary initial condition for the momentum current correlation. Our formulation leads to a natural physical interpretation of the hydrodynamic VACF as a superposition of quasinormal hydrodynamic modes weighted commensurately with the static kinetic energy spectrum, which appears to be essential to bridging continuum hydrodynamical behavior and discrete-particle kinetics. Our methodology yields VACF calculations quantitatively on par with existing approaches for liquid noble gases and alkali metals; moreover, our hydrodynamic model for the self-intermediate scattering function extends the applicable domain to low densities where the Schmidt number is of order unity, enabling calculations for gases and supercritical fluids.