Spatial distribution functions of random packed granular spheres obtained by direct particle imaging

TL;DR

This study investigates the spatial distribution functions of randomly packed granular spheres using direct imaging, revealing similarities and differences with frictionless sphere packings through correlation functions and Voronoi analysis.

Contribution

It provides detailed measurements of spatial correlations and Voronoi distributions in granular spheres, highlighting systematic deviations from idealized models.

Findings

Radial distribution function matches Percus-Yevick for initial volume fraction

Deviations increase with higher packing density, especially in second peak splitting

Voronoi volume distributions and orientational order differ from frictionless sphere models

Abstract

We measure the two-point density correlations and Voronoi cell distributions of cyclically sheared granular spheres obtained with a fluorescence technique and compare them with random packing of frictionless spheres. We find that the radial distribution function $g(r)$ is captured by the Percus-Yevick equation for initial volume fraction $\phi=0.59$. However, small but systematic deviations are observed because of the splitting of the second peak as $\phi$ is increased towards random close packing. The distribution of the Voronoi free volumes deviates from postulated $\Gamma$ distributions, and the orientational order metric $Q_6$ shows disorder compared to numerical results reported for frictionless spheres. Overall, these measures show significant similarity of random packing of granular and frictionless spheres, but some systematic differences as well.