Eur. Phys. J. E (2004) 15: 319-333
https://doi.org/10.1140/epje/i2004-10074-4

Nonequilibrium fluctuations in the Rayleigh-Bénard problem for binary fluid mixtures

¹ Departamento de Fısica Aplicada 1, Facultad de Ciencias Fısicas, Universidad Complutense, E-28040, Madrid, Spain
² via Emanuele Gianturco 31, I-80146, Napoli, Italy
³ Institute for Physical Science and Technology and Departments of Chemical and Mechanical Engineering, University of Maryland, College Park, MD 20742, USA

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

Received: 22 July 2004
Accepted: 27 October 2004
Published online: 18 November 2004

Abstract

We have employed a simple Galerkin-approximation scheme to calculate nonequilibrium temperature and concentration fluctuations in a binary fluid subjected to a temperature gradient with realistic boundary conditions. When a fluid mixture is driven outside thermal equilibrium, there are two instability mechanisms, namely a Rayleigh (stationary) and a Hopf (oscillatory) instability, causing long-ranged fluctuations. The competition of these two mechanisms causes the structure factor associated with the temperature fluctuations to exhibit two maxima as a function of the wave number q of the fluctuations, in particular, close to the convective instability. In the presence of thermally conducting but impermeable walls the intensity of the temperature fluctuations vanishes as q goes to zero, while the intensity of the concentration fluctuations remains finite in the limit of vanishing q. Finally, we propose a simpler small-Lewis-number approximation scheme, which is useful to represent nonequilibrium concentration fluctuations for mixtures with positive separation ratio, even close to (but below) the convective instability.