# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1907.13097