Spatial correlations of hydrodynamic fluctuations in simple fluids under shear flow: A mesoscale simulation study

TL;DR

This study uses mesoscale simulations to demonstrate that hydrodynamic fluctuations in simple fluids under shear flow are spatially correlated, showing specific decay behaviors and long-range correlations unlike at equilibrium.

Contribution

It provides the first detailed comparison between mesoscopic simulation results and fluctuating hydrodynamic theory for fluids under shear, revealing the nature of spatial correlations.

Findings

Hydrodynamic correlations decay as k^{-4} and k^{-2} depending on direction.

Long-range correlations are present at small wave vectors.

Non-equilibrium pressure contributions depend quadratically on shear rate.

Abstract

Hydrodynamic fluctuations in simple fluids under shear flow are demonstrated to be spatially correlated, in contrast to the fluctuations at equilibrium, using mesoscopic hydrodynamic simulations. The simulation results for the equal-time hydrodynamic correlations in a multiparticle collision dynamics (MPC) fluid in shear flow are compared with the explicit expressions obtained from fluctuating hydrodynamic calculations. For large wave vectors $k$, the nonequlibrium contributions to transverse and longitudinal velocity correlations decay as $k^{-4}$ for wave vectors along the flow direction, and as $k^{-2}$ for the off-flow directions. For small wave vectors, a cross-over to a slower decay occurs, indicating long-range correlations in real space. The coupling between the transverse velocity components, which vanishes at equilibrium, also exhibits a $k^{-2}$ dependence on the wave vector. In addition, we observe a quadratic dependency on the shear rate of the non-equilibrium contribution to pressure.