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

Abstract:

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 value 0.1547 above which beads get pinned inside the packing . They move in this regime at a constant mean velocity decreasing with the ratio d/D. We analyse dispersion parallel and transverse to the mean velocity by studying the bead distribution in the x-y plane at the exit of the packing (radial dispersion) 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 spreading 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.