Phys. Rev. E 76, 041112 (2007)

http://journals.aps.org/pre/abstract/10.1103/PhysRevE.76.041112

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

Fabrizio Croccolo, Doriano Brogioli, Alberto Vailati, Marzio Giglio and Dave S. Cannell

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 q≲qC we find that longer wavelength fluctuations decay more rapidly than do shorter wavelength fluctuations, i.e., the behavior is nondiffusive, as predicted.