Long-wavelength nonequilibrium concentration fluctuations induced by the Soret effect

In this paper we evaluate the enhancement of nonequilibrium concentration fluctuations induced by the Soret effect when a binary fluid layer is subjected to a stationary temperature gradient. Starting from the fluctuating Boussinesq equations for a binary fluid in the large-Lewis-number approximation, we show how one can obtain an exact expression for the nonequilibrium structure factor in the long-wavelength limit for a fluid layer with realistic impermeable and no-slip boundary conditions. A numerical calculation of the wave-number dependence of the nonequilibrium enhancement and of the corresponding decay rate of the concentration fluctuations is also presented. Some physical consequences of our results are briefly discussed.