A geometric probabilistic approach to random packing of hard disks in a plane

Abstract

In this paper the random packing fraction of hard disks in a plane is analyzed, following a geometric probabilistic approach. First, the random close packing (RCP) of equally sized disks is modelled. Subsequently, following the same methodology, a simple, statistical geometric model is proposed for the random loose packing (RLP) of monodisperse disks. This very basic derivation of RLP leads to a packing value (~ 0.66) that is in very good agreement with values that have been obtained previously for 2D disk packings. The present geometrical model also enables closed-form expression for the contact (coordination) number as function of the packing density at different states of compaction. These predictions are thoroughly compared with empirical and simulation results, among others the R\'enyi parking model, yielding good agreement.