Random loose packings of uniform spheres and the dilatancy onset

TLDR

The structure corresponds to a sphere packing at its rigidity‑percolation threshold. The random‑loose‑packing fraction of uniform spheres is 0.555 ± 0.005, with dilatancy onset at the same density, and preliminary evidence suggests shear thickening and a hard‑sphere glass transition may occur between 0.555 and 0.645.

Abstract

The random-loose-packing fraction of uniform spheres at the limit of zero gravitational force is determined to be 0.555\ifmmode\pm\else\textpm\fi{}0.005. This structure corresponds to a sphere packing at its rigidity-percolation threshold. The onset of dilatancy was also measured to be at approximately the same packing fraction. Preliminary evidence also indicates that shear thickening of suspensions with macroscopic spheres and a negative pore liquid pressure develops at the rigidity threshold. These provide further evidence that a hard-sphere glass transition could exist in the packing fraction range of 0.555 to 0.645.