Non-equilibrium concentration fluctuations in binary liquids with realistic boundary conditions

TL;DR

This paper derives explicit analytical expressions for the intensity of non-equilibrium concentration fluctuations in binary liquids with realistic boundary conditions, highlighting their spatial dependence and implications for the non-equilibrium Casimir effect.

Contribution

It provides the first explicit analytical formulas for fluctuation intensity considering boundary effects in binary liquids with large Lewis numbers.

Findings

Analytical expressions for fluctuation intensity as a function of frequency and wave number.

Demonstration of the spatial dependence of fluctuations related to the non-equilibrium Casimir effect.

Insights into boundary condition effects on long-range fluctuations in non-equilibrium systems.

Abstract

Because of the spatially long-ranged nature of spontaneous fluctuations in thermal non-equilibrium systems, they are affected by boundary conditions for the fluctuating hydrodynamic variables. In this paper we consider a liquid mixture between two rigid and impervious plates with a stationary concentration gradient resulting from a temperature gradient through the Soret effect. For liquid mixtures with a large Lewis number, we are able to obtain explicit analytical expressions for the intensity of the non-equilibrium concentration fluctuations as a function of the frequency $\omega$ and the wave number $q$ of the fluctuations. In addition we elucidate the spatial dependence of the intensity of the non-equilibrium fluctuations responsible for a non-equilibrium Casimir effect.