Nondiffusive decay of gradient-driven fluctuations in a free-diffusion process

We report the results of an experimental study of the static and dynamic properties of long wavelength concentration fluctuations in a mixture of glycerol and water undergoing free diffusion. The shadowgraph method was used to measure both the mean-squared amplitude and the temporal correlation function of the fluctuations for wave vectors so small as to be inaccessible to dynamic light scattering. For a fluid with a stabilizing vertical concentration gradient, the fluctuations are predicted to have a decay rate that increases with decreasing wave vector q, for wave vectors below a cutoff wave vector qC, determined by gravity and the fluid properties. This behavior is caused by buoyant forces acting on the fluctuations. We find that for wave vectors above ~qC, the decay rate does vary in the normal diffusive manner as Dq2, where D is the mass diffusion coefficient. Furthermore, for qqC we find that longer wavelength fluctuations decay more rapidly than do shorter wavelength fluctuations, i.e., the behavior is nondiffusive, as predicted.