Model of random packings of different size balls

TL;DR

This paper presents an analytical model for the properties of random packings of polydisperse spheres, predicting packing densities and coordination based on size distribution and friction, with potential applications to non-spherical particles.

Contribution

It introduces a novel analytical framework linking free volume, coordination numbers, and species concentration in polydisperse sphere packings.

Findings

Predicts density of random close and loose packings for polydisperse systems.

Provides analytical expressions for coordination numbers based on size distribution.

Applicable to systems with varying interparticle friction coefficients.

Abstract

We develop a model to describe the properties of random assemblies of polydisperse hard spheres. We show that the key features to describe the system are (i) the dependence between the free volume of a sphere and the various coordination numbers between the species, and (ii) the dependence of the coordination numbers with the concentration of species; quantities that are calculated analytically. The model predicts the density of random close packing and random loose packing of polydisperse systems for a given distribution of ball size and describes packings for any interparticle friction coefficient. The formalism allows to determine the optimal packing over different distributions and may help to treat packing problems of non-spherical particles which are notoriously difficult to solve.