Use of dynamic schlieren interferometry to study fluctuations during free diffusion

We used a form of schlieren interferometry to measure the mean-squared amplitude and temporal autocorrelation function of concentration fluctuations driven by the presence of a gradient during the free diffusion of a urea solution into water. By taking and processing sequences of images separated in time by less than the shortest correlation time of interest, we were able to simultaneously measure dynamics at a number of different wave vectors. The technique is conceptually similar to the shadowgraph method, which has been used to make similar measurements, but the schlieren method has the advantage that the transfer function is wave-vector independent rather than oscillatory.