Simulation of random packing of spheres

Abstract

PACKS simulates the very slow settling of rigid spheres (as in sedimentation) from a dilute suspen sion into a randomly packed bed. Spheres are intro duced one at a time in a potential field and fall or roll until they occupy one of the available sites. The position of an incoming sphere is calculated at each of the significant events in its history. Thus, probabilities for each site are assigned on a realis tic basis. Periodic boundary conditions eliminate wall effects (smooth walls induce partial ordering) and a rough floor reduces the disturbance at the bottom. These features make a greater proportion of simulated spheres truly random in final position and so available for analysis. A new search routine greatly reduces the time required to assemble a pack ing. Preservation of the addresses of supporting spheres simplifies the subsequent analysis for near est neighbors. Packings of 100 000 or more spheres are feasible. The simulation has potential applica tions in crystallography, soil engineering, biology, nuclear engineering, and petroleum engineering.