Nonequilibrium fluctuations in time-dependent diffusion precesses

A fluctuating hydrodynamics approach is presented for the calculation of the structure factor for time-dependent nonequilibrium diffusive processes in binary liquid mixtures. The hydrodynamic equations are linearized around the time-dependent macroscopic state given by the usual phenomenological diffusion equation. The cases of free diffusion, thermal diffusion, and barodiffusion are considered in detail. The results are used to describe the low-angle scattered intensity distributions from the time-dependent concentration profiles during the approach to steady state. The theoretical predictions are found to be in agreement with experimental data from thermal diffusion and free diffusion experiments. It is shown that in general the presence of nonequilibrium concentration fluctuations yields a substantial increase in the static structure factor over the equilibrium value, at least for the cases of free diffusion and thermal diffusion. As in the case of nonequilibrium fluctuations at steady state, the static structure factor displays a fast k(-4) divergence at larger wave vectors k, and saturation to a constant value for k smaller than a critical wave vector k(RO) It is also shown that the static structure factor from a sedimenting mixture is actually temporarily lowered below the equilibrium value for k smaller than k(RO). As the steady state is approached, the structure factor loses any k dependence and it attains the equilibrium value. [S1063-651X(98)14910-3].