Onset of Mechanical Stability in Random Packings of Frictional Spheres

Abstract

Using sedimentation to obtain precisely controlled packings of noncohesive spheres, we find that the volume fraction ${\ensuremath{\phi}}_{\mathrm{RLP}}$ 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 $\ensuremath{\mu}$. Using x-ray tomography to correct for a container boundary effect that depends on particle size, we find for rough particles in the limit $p\ensuremath{\rightarrow}0$ a new lower bound, ${\ensuremath{\phi}}_{\mathrm{RLP}}=0.550\ifmmode\pm\else\textpm\fi{}0.001$.