Experiments on Random Packings of Ellipsoids

Abstract

Recent simulations indicate that ellipsoids can pack randomly more densely than spheres and, remarkably, for axes ratios near $1.25\ensuremath{\mathbin:}1\ensuremath{\mathbin:}0.8$ can approach the densest crystal packing (fcc) of spheres, with a packing fraction of 74%. We demonstrate that such dense packings are realizable. We introduce a novel way of determining packing density for a finite sample that minimizes surface effects. We have fabricated ellipsoids and show that, in a sphere, the radial packing fraction $\ensuremath{\phi}(r)$ can be obtained from $V(h)$, the volume of added fluid to fill the sphere to height $h$. We also obtain $\ensuremath{\phi}(r)$ from a magnetic resonance imaging scan. The measurements of the overall density ${\ensuremath{\phi}}_{\mathrm{avr}}$, $\ensuremath{\phi}(r)$ and the core density ${\ensuremath{\phi}}_{0}=0.74\ifmmode\pm\else\textpm\fi{}0.005$ agree with simulations.