Giant fluctuations in a free diffusion process

Macroscopic concentration gradients in physical systems relax towards equilibrium by diffusion1,2,3, in the absence of bulk motion. This is normally regarded as a spatially homogeneous mixing process. Here, however, we show that unexpectedly large spatial fluctuations in concentration can occur during a free diffusion process. We set up an initially sharp interface between two miscible fluids by letting a mixture phase-separate below the critical consolution temperature and then raising the temperature quickly to the single-phase region. Shadowgraph images and low-angle light scattering show evidence for large fluctuations in composition, orders of magnitude larger in amplitude than those seen in the equilibrium state. We show that these pronounced inhomogeneities are due to a coupling between velocity and concentration fluctuations in the non-equilibrium state4,5,6. Gravity cuts off the fluctuations above a certain wavelength, and the amplitude of the fluctuations at longer wavelengths does not depend on any relevant thermodynamic property of the fluid. As a consequence, these giant fluctuations should be observable in any mixture undergoing mixing by diffusion.