Nonequilibrium Casimir pressures in liquids under shear

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.