Applicability of the hydrodynamic description of classical fluids

TL;DR

This study uses numerical simulations to determine the limits of hydrodynamic descriptions in classical fluids, showing that the interaction range sets the applicability limit, except for Coulomb interactions where it fails entirely.

Contribution

It establishes a universal relation between microscopic interaction range and the maximum wavenumber for hydrodynamic validity, independent of many-body correlations.

Findings

Hydrodynamics applies up to a wavenumber inversely proportional to interaction range.

For Coulomb potentials, hydrodynamics is never valid.

The applicability limit is independent of correlation degree.

Abstract

We investigate using numerical simulations the domain of applicability of the hydrodynamic description of classical fluids at and near equilibrium. We find this to be independent of the degree of many-body correlations in the system; the range r_c of the microscopic interactions completely determines the maximum wavenumber k_{max} at which the hydrodynamic description is applicable by k_{max}r_c ~ 0.43. For the important special case of the Coulomb potential of infinite range, we show that the ordinary hydrodynamic description is never valid.