The random packing density of nearly spherical particles

TL;DR

This paper develops an analytical and numerical approach to estimate the packing density of nearly spherical particles, extending understanding from spherical packings to more complex shapes.

Contribution

It introduces a perturbative method based on spherical packings to estimate densities of nearly spherical particles, providing both analytical and simulation-based results.

Findings

All sufficiently spherical shapes pack more densely than spheres.

The method accurately estimates packing densities for nonspherical particles.

Simulation data supports the analytical predictions.

Abstract

Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials. By leveraging existing understanding of the random packing of spherical particles, we estimate the random packing density for all sufficiently spherical shapes. Our method uses the ensemble of random packing configurations of spheres as a reference point for a perturbative calculation, which we carry to linear order in the deformation. A fully analytic calculation shows that all sufficiently spherical shapes pack more densely than spheres. Additionally, we use simulation data for spheres to calculate numerical estimates for nonspherical particles and compare these estimates to simulations.