Diffusion of a single particle in a 3D random packing of spheres

We report an experimental study of the dispersion properties of individual spherical particles of size d! moving under gravity in a dry random packing of large spheres of size D. The diameter ratio d/D is below the critical v alue 0.1547 above which beads get pinned inside the packing. They move in t his regime at a constant mean velocity decreasing with the ratio d/D. We an alyse dispersion parallel and transverse to the mean velocity by studying t he bead distribution in the x-y plane at the exit of the packing (radial di spersion) and the transit time distribution (longitudinal dispersion) while varying the height H of the bed. Diffusion in both directions is found to be governed essentially by the diameter D of packed spheres and not by the size d of the small beads. A dispersivity length characterising the spreadi ng amplitude is determined. Comparisons between transverse and longitudinal dispersion demonstrate that both processes have similar properties. A key parameter is the diameter D which controls the path length of the particles .