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Because of the spatially long-ranged nature of spontaneous fluctuations inthermal non-equilibrium systems, they are affected by boundary conditions forthe fluctuating hydrodynamic variables. In this paper we consider a liquidmixture between two rigid and impervious plates with a stationary concentrationgradient resulting from a temperature gradient through the Soret effect. Forliquid mixtures with a large Lewis number, we are able to obtain explicitanalytical expressions for the intensity of the non-equilibrium concentrationfluctuations as a function of the frequency $\omega$ and the wave number $q$ ofthe fluctuations. In addition we elucidate the spatial dependence of theintensity of the non-equilibrium fluctuations responsible for a non-equilibriumCasimir effect.

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