  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.
