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.

Coupled non-equilibrium fluctuations in a polymeric ternary mixture

“…1 and 2 , are independent. The corresponding diffusion fluxes 1 and 2 in the centre-of-mass frame of reference have thermodiffusion and Fickean components, as expressed by [51]:…”

“…At the stationary state, the diffusion fluxes become zero and, following Ortiz de Zárate [51], the Soret coefficients can be expressed by:…”

“…The introduction of the matrix concentration pre-factors in Eqs. 4 and 5 forces the thermodiffusion coefficients and the Soret coefficients to display the same frameinvariance properties of the single or of a binary mixture, that is, they are numerically the same irrespective of whether mass fractions or mole fractions are used to express the composition [51]. Here, for simplicity, we display the equations only in the mass fraction framework.…”

Frame-invariant Fick diffusion matrices of multicomponent fluid mixtures

“…For the purpose of the present paper it is important to note that, in a binary mixture, the relationship between the gradient of mass fraction and the gradient of mole fraction can be expressed as 6,19,22 =w…”

“…In a previous paper one of us has shown how the procedure for binary mixtures can be generalized to obtain frame-independent thermodiffusion coefficients of multicomponent mixtures. 19 In the present paper we consider the case of isothermal diffusion that was not considered in the previous paper. Specifically, we shall show how a simple similarity transformation of frame-dependent Fick diffusion matrices yields Fick diffusion matrices that are indeed independent of the reference frame.…”