J. Phys. France 51, 2673-2680 (1990)
DOI: 10.1051/jphys:0199000510230267300

Simulation of small particle penetration in a random medium

Paul Meakin¹ et Rémi Jullien<sup>2

1</sup>  Experimental Station, E. I. du Pont de Nemours and Co., Wilmington, DE 19898, U.S.A.
²  Physique des Solides, Bât. 510, Université Paris-Sud, Centre d'Orsay, 91405 Orsay, France

Abstract
Random packings of identical spheres of unit diameter were built according to a procedure in which spheres are released one after another along randomly positionned vertical trajectories and then follow the path of steepest descent on the others until they reach a stable position under gravity. Once a packing has been built, smaller spheres, of diameter d < 1, are allowed to penetrate into it, also following the path of steepest descent and their penetration depth ΔZ is studied as a function of the parameter ε = (1 - d)/(1 + d). Previous results that demonstrate the existence of a treshold εc = 31/2 - 1 (corresponding to the « apollonian » ratio of diameters 2/31/2 - 1), above which Δ Z is infinite, are confirmed. New results are presented concerning the behavior of ΔZ when the threshold is approached from below : the mean value <ΔZ> does not diverge but saturates to <Δ Z>c ~ 11 and the histogram N <ΔZ> reaches an exponential shape whose large ΔZ tail is well fitted by N <ΔZ> a exp (- 0.103 ΔZ). It is shown that such behavior is due to a non zero proportion of equilateral triangles of tangent spheres in the random packing.

PACS
0540 - Fluctuation phenomena, random processes, noise, and Brownian motion.

Key words
random processes