Diffusive mass transfer by nonequilibrium fluctuations: Fick's law revisited

Recent experimental and theoretical works have shown that giant fluctuations are present during diffusion in liquid systems. We use linearized fluctuating hydrodynamics to calculate the net mass transfer due to these nonequilibrium fluctuations. Remarkably, the mass flow turns out to coincide with the usual Fick's one. The renormalization of the hydrodynamic equations allows us to quantify the gravitational modifications of the diffusion coefficient induced by the gravitational stabilization of long wavelength fluctuations.