Onset of mechanical stability in random packings of frictional spheres

TL;DR

This study investigates the minimum volume fraction for mechanically stable random packings of frictional spheres, revealing how it varies with pressure and friction, and establishing a new lower bound for loose packings.

Contribution

It introduces a precise operational definition of the loosest stable packing and quantifies how it depends on pressure and friction, providing a new lower bound.

Findings

Loosest stable packing volume fraction decreases with pressure and friction.

A new lower bound for random loose packing is established at 0.550.

Boundary effects are corrected using X-ray tomography.

Abstract

Using sedimentation to obtain precisely controlled packings of noncohesive spheres, we find that the volume fraction $\phi_{\rm RLP}$ of the loosest mechanically stable packing is in an operational sense well defined by a limit process. This random loose packing volume fraction decreases with decreasing pressure $p$ and increasing interparticle friction coefficient $\mu$. Using X-ray tomography to correct for a container boundary effect that depends on particle size, we find for rough particles in the limit $p \to 0$ a new lower bound, $\phi_{\rm RLP} = 0.550 \pm 0.001$.