Long-Ranged Correlations in Sheared Fluids

TL;DR

This paper investigates long-range correlations in sheared fluids, revealing a crossover from $1/r$ decay to faster decay, challenging simple mode coupling theory predictions, with implications for understanding fluid behavior under shear.

Contribution

It provides an exact relation between correlation functions and demonstrates a crossover in decay behavior through analytic and numerical methods.

Findings

Density autocorrelation decays faster than $1/r$ at large distances.

A crossover from $1/r$ to stronger decay occurs at a characteristic length scale.

The length scale depends on sound damping and shear rate, $\, ext{approximately} \, \, ext{sqrt}(rac{ ext{sound damping}}{ ext{shear rate}})$.

Abstract

The presence of long-ranged correlations in a fluid undergoing uniform shear flow is investigated. An exact relation between the density autocorrelation function and the density-mometum correlation function implies that the former must decay more rapidly than $1/r$, in contrast to predictions of simple mode coupling theory. Analytic and numerical evaluation of a non-perturbative mode-coupling model confirms a crossover from $1/r$ behavior at ''small'' $r$ to a stronger asymptotic power-law decay. The characteristic length scale is $\ell \approx \sqrt{\lambda_{0}/a}$ where $% \lambda_{0}$ is the sound damping constant and $a$ is the shear rate.