Singular behaviour of time-averaged stress fluctuations on surfaces

TL;DR

This paper develops a theoretical method to calculate surface stress fluctuations in viscous fluids at equilibrium, revealing inverse proportionality to the distance between plates.

Contribution

It introduces a novel approach combining Gaussian assumptions and large deviation theory to analyze time-averaged stress fluctuations on surfaces.

Findings

Surface stress fluctuations are inversely proportional to plate separation.

The method applies Green-Kubo formula and saddle-point approximation.

Results provide insight into stress behavior in confined viscous fluids.

Abstract

We provide a method for calculating time-averaged stress fluctuations on surfaces in a viscous incompressible fluid at equilibrium. We assume that (i) the time-averaged fluctuating stress is balanced in equilibrium at each position and that (ii) the time-averaged fluctuating stress obeys a Gaussian distribution on the restricted configuration space given by (i). Using these assumptions with the Green-Kubo formula for the viscosity, we can derive the large deviation function of the time-averaged fluctuating stress. Then, using the saddle-point method for the large deviation function, we obtain the time-averaged surface stress fluctuations. As an example, for a fluid between two parallel plates, we study the time-averaged shear/normal stress fluctuations per unit area on the top plate at equilibrium. We show that the surface shear/normal stress fluctuations are inversely proportional to the distance between the plates.