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Soft Matter and Biological Physics

Eur. Phys. J. E 3, 227-236

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

I. Ippolito1 - L. Samson1 - S. Bourlès1 - J.-P. Hulin2

1 Groupe Matière Condensée et Matériaux (UMR CNRS 6626), Université de Rennes 1, Bâtiment 11A, Campus de Beaulieu, 35042 Rennes Cedex, France
2 Laboratoire Fluides Automatiques et Systèmes Thérmiques (UMR CNRS 7608), Université de Paris Sud, 91405 Orsay Cedex, France
irene.ippolito@univ-rennesl.fr

Received 5 November 1999 and Received in final form 30 March 2000

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.

PACS
81.05.Rm Porous materials; granular materials - 45.70.Mg Granular flow: mixing; segregation and stratification - 05.40.Fb Random walks and Levy flights

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