A numerical test of stress correlations in fluctuating hydrodynamics

TL;DR

This study uses molecular dynamics simulations to measure stress correlations in a Lennard-Jones liquid, confirming some fluctuating hydrodynamics assumptions in bulk but revealing complex behavior near rigid boundaries.

Contribution

It introduces a numerical method to compute stress correlation functions in space and time, and explores boundary effects on stress correlations and viscosities.

Findings

Stress correlations match hydrodynamics assumptions in bulk.

Near a rigid wall, five viscosities emerge instead of two.

Stress relaxation times are significantly longer near walls.

Abstract

The correlations of the fluctuating stress tensor are calculated in an equilibrium molecular-dynamics simulation of a Lennard--Jones liquid. We define a coarse-grained local stress tensor which can be calculated numerically and which allows for the first time to determine the stress correlation function both in time and in space. Our findings corroborate the assumptions made in fluctuating hydrodynamics as long as the liquid is isotropic, that is in bulk. In the vicinity of a rigid plate, however, the isotropy is restricted, and major modifications must be done with respect to the usual theory. Among these are the appearance of five different viscosities instead of two and a non-trivial dependence of the distance from the wall. We determine these viscosities from the simulation data and find that their values are very different from the bulk values. We further find much longer relaxation times of the stress correlations than in bulk.