Onset of mechanical stability in random packings of frictional spheres

Using sedimentation to obtain precisely controlled packings of noncohesive spheres, we find that the volume fraction ${\varphi }_{\mathrm{R}\mathrm{L}\mathrm{P}}$ 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, ${\varphi }_{\mathrm{R}\mathrm{L}\mathrm{P}}=0.550\pm 0.001$.