Nonequilibrium Casimir pressures in liquids under shear

TL;DR

This paper derives explicit expressions for shear-induced nonequilibrium Casimir pressures in liquids, highlighting the dominant role of viscous heating over thermal fluctuations and correcting previous theoretical results.

Contribution

It provides corrected and complete formulas for shear-induced Casimir pressures in liquids, emphasizing the importance of viscous heating and long-range hydrodynamic mode coupling.

Findings

Shear-induced pressures are mainly caused by viscous heating.

Short-range fluctuation contributions are negligible in shear nonequilibrium.

Computer simulations of molecular correlations do not directly probe shear-induced Casimir pressures.

Abstract

In stationary nonequilibrium states coupling between hydrodynamic modes causes thermal fluctuations to become long ranged inducing nonequilibrium Casimir pressures. Here we consider nonequilibrium Casimir pressures induced in liquids by a velocity gradient. Specifically, we have obtained explicit expressions for the magnitude of the shear-induced pressure enhancements in a liquid layer between two horizontal plates that complete and correct results previously presented in the literature. In contrast to nonequilibrium Casimir pressures induced by a temperature or concentration gradient, we find that in shear nonequilibrium contributions from short-range fluctuations are no longer negligible. In addition, it is noted that currently available computer simulations of model fluids in shear observe effects from molecular correlations at nanoscales that have a different physical origin and do not probe shear-induced pressures resulting from coupling of long-wavelength hydrodynamic modes. Even more importantly, we find that in actual experimental conditions, shear-induced pressure enhancements are caused by viscous heating and not by thermal velocity fluctuations. Hence, isothermal computer simulations are irrelevant for the interpretation of experimental shear-induced pressure enhancements.