Mixing properties of bi-disperse ellipsoid assemblies: Mean-field behaviour in a granular matter experiment

TL;DR

This study investigates the packing properties of bi-disperse ellipsoid assemblies, demonstrating that their structure can be modeled as a mixture of uncorrelated mono-disperse packings, with implications for understanding granular matter.

Contribution

It introduces a mean-field model for bi-disperse ellipsoid packings based on mixture distributions, validated by experimental data, and highlights the insensitivity to compaction protocols.

Findings

Bi-disperse ellipsoid packings behave as a mixture of uncorrelated mono-disperse packings.

Local packing fraction shows no correlation beyond the first shell of neighbors.

The proposed model accurately describes experimental packing data.

Abstract

The structure and spatial statistical properties of amorphous ellipsoid assemblies have profound scientific and industrial significance in many systems, from cell assays to granular materials. This paper uses a fundamental theoretical relationship for mixture distributions to explain the observations of an extensive X-ray computed tomography study of granular ellipsoidal packings. We study a size-bi-disperse mixture of two types of ellipsoids of revolutions that have the same aspect ratio of alpha approximately equal to 0.57 and differ in size, by about 10% in linear dimension, and compare these to mono-disperse systems of ellipsoids with the same aspect ratio. Jammed configurations with a range of packing densities are achieved by employing different tapping protocols. We numerically interrogate the final packing configurations by analyses of the local packing fraction distributions calculated from the Voronoi diagrams. Our main finding is that the bi-disperse ellipsoidal packings studied here can be interpreted as a mixture of two uncorrelated mono-disperse packings, insensitive to the compaction protocol. Our results are consolidated by showing that the local packing fraction shows no correlation beyond their first shell of neighbours in the binary mixtures. We propose a model of uncorrelated binary mixture distribution that describes the observed experimental data with high accuracy. This analysis framework will enable future studies to test whether the observed mean-field behaviour is specific to the particular granular system or the specific parameter values studied here or if it is observed more broadly in other bi-disperse non-spherical particle systems.