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Papers, preprints, and talks Moderate Reynolds number particle interactions

The outcome of many important industrial and environmental processes (from sewage treatment to coal combustion) is determined by the hydrodynamic interaction between particles of moderate Reynolds number. Although significant progress has been made in the study of very low Reynolds number particles, the more complex interactions between particles that may have wakes, or may be actively shedding vortices, have, so far, found themselves absent the same level of attention. For example, one important issue involves how bulk quantities, like the hydrodynamic diffusion, depend on the particle Reynolds number and mean particle separation. We are actively working on a number of different experiments to investigate this question and many others.

The first step in analyizing three-dimensional particle interactions involves acquiring movies of the interactions simultaneously from at least a couple of different vantage points. These simple 2D representations of the particle dynamics can already lead to some very interesting observations.

Three-dimensional tracks are computed from multiple views of the particles much as our brains reconstruct a 3D picture of the world from the slightly different views seen by each eye. These different views can be achieved either by using mirrors or by using independent cameras. Traditional ray-tracing techniques are, then, used to determine the actual 3D particle positions. Finally, the particles are tracked between frames and quadratic fits made to the temporal evolution of the 3-space positions to extract velocity and acceleration information as well. In the linked image two particle tracks are shown with color representing the magnitude of the velocity at each point and the vectors representing the direction and magnitude of the acceleration.
The ejecta problem

Another interesting place where particles are interacting is in the laboratory analog of a meteorite impact. If you ever wondered exactly how those craters form you can see pretty conclusively how it happens from the following movie of a steel ball (the meteorite) impacting a bed of glass spheres (the ground). The entire collision takes place in air. The spray from the impact is quite dramatic!

In the above clip, particle interactions are essentially non-existent, both between the small particles and between small particles and the large one. The density, and hence inertia, of the surrounding fluid (air) is low enough that the the particles all behave essentially ballistically. One can, however, imagine surrounding the particles with a denser fluid .... water. The difference in the behavior of the ejected particles is stunning! At the earliest times the particles appear as if they will follow essentially the same trajectory as in air. Almost immediately, however, the wake of the large particle catches up and sweeps the ejected particles back down. The whole thing then appears to briefly explode, probably as the fluid entrained behind the large falling sphere slams into the particle bed.
One of the first steps in particle tracking (two or three dimensions) is determining the location of the particles. Sounds simple enough, but the task can be dramatically complicated by, for instance, overlapping particles (the red outline at left). After processing the original image using a deconvolution technique the largely overlapping particle images are well resolved into very distinct, very sharp, peaks.