Eur. Phys. J. E (2015) 38: 99
https://doi.org/10.1140/epje/i2015-15099-x

Regular Article

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

¹ Departamento de Fısica Aplicada I, Facultad de Fısica, Universidad Complutense, 28040, Madrid, Spain
² Institute for Physical Science and Technology, University of Maryland, 20742, College Park, Maryland, USA
³ Department of Physics, University of Maryland, 20742, College Park, Maryland, USA

^* e-mail: jmortizz@fis.ucm.es

Received: 6 May 2015
Revised: 18 August 2015
Accepted: 20 August 2015
Published online: 21 September 2015

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 large Lewis and Schmidt numbers, we are able to obtain explicit analytical expressions for the intensity of the non-equilibrium concentration fluctuations as a function of the frequency ω 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.