Effect of Gravity on the Dynamics of Nonequilibrium Fluctuations in a Free-Diffusion Experiment

摘要

Diffusion is commonly believed to be a homogeneous process at the mesoscopic scale, being driven only by the random walk of fluid molecules. On the contrary, very large amplitude, long wavelength fluctuations always accompany diffusive processes. In the presence of gravity, fluctuations in a fluid containing a stabilizing gradient are affected by two different processes: diffusion, which relaxes them, and the buoyancy force, which quenches them. These phenomena affect both the overall amplitude of fluctuations and their time dependence. For the case of free diffusion, the time-correlation function of the concentration fluctuations is predicted to exhibit an exponential decay with correlation time depending on the wave vector q. For large wave vector fluctuations, diffusion dominates, and the correlation time is predicted to be 1/Dq~2). For small wave vector fluctuations, gravitational forces have time to play a significant role, and the correlation time is predicted to be proportional to q~2. The effects of gravity and diffusion are comparable for a critical wave vector q_c determined by fluid properties and gravity. We have utilized a quantitative dynamic shadowgraph technique to obtain the temporal correlation function of a mixture of LUDOX~® TMA and water undergoing free diffusion. This technique allows one to simultaneously measure correlation functions achieving good statistics for a number of different wave vectors in a single measurement. Wave vectors as small as 70 cm~(-1) have been investigated, which is very difficult to achieve with ordinary dynamic light-scattering techniques. We present results on the transition from the diffusive decay of fluctuations to the regime in which gravity is dominant.