Impurities in a fluid, including solid particles, bubbles and droplets, are separated by gravity and dispersed by turbulence. Understanding the diffusion of these impurities in turbulent flows is important in predicting many phenomena like volcanic eruptions, oil slicks and breaking waves and splashing rain form air bubbles etc. The objective of this study is to understand and model the dispersion of small fuel droplets in turbulent water flow. It was motivated by a series of puzzling phenomena that we had observed in previous experiments, including rise velocity exhibiting complex dependence on the turbulence level and the Stokes number (Friedman, P. D. et al 2002). We consider the case in which turbulence is isotropic which is a resonalbe approximation to many natural phenomena and to aid (by means of comparison) in the develoment of modelling tools which are being simultaneously developed.

Taylor's (1921) pioneering work on turbulent dispersion showed that diffusivity of a "fluid point" could be calculated from the Lagrangian autocorrelation function. We also wish to broden the scope of analysis using the process followed by Cushman and Mororni (2002) which enables us to accommodate various processes, including Fickian, convolution-Fickian, as well fractional-Fickian fluxes.This requires a three dimensional time history of droplet tracks.

Holographic particle image velocimetry is the only technique to-date that can measure 3-D instantaneous velocity distribution over a sample volume with an extended depth. In order to obtain a time series of images over an extended period of time we use digital holography in which the images are recorded in digital format and processed numerically to obtain the reconstructed image .In holography there is lower resolution in the optical direction (depth), compared to the lateral spatial resolution. We overcome this problem by imaging the field of interest in two perpendicular direction.

We developed an algorithm for automatically detecting the droplet trajectories from each view, for matching the two views to obtain the three-dimensional tracks, and for calculating the time history of velocity. Details of this alogorithm can be found in our paper in the Proceedings of ASME 2005.