Maximum and Minimum Stable Random Packings of Platonic Solids

Motivated by the relation between particle shape and packing, we measure the volume fraction $\phi$ occupied by the Platonic solids which are a class of polyhedron with congruent sides, vertices and dihedral angles. Tetrahedron, cube, octahedron, dodecahedron, and icosahedron shaped plastic dice were fluidized or mechanically vibrated to find stable random loose packing $\phi_{rlp} = 0.51, 0.54, 0.52, 0.51, 0.50$ and densest packing $\phi_{rcp} = 0.64, 0.67, 0.64, 0.63, 0.59$, respectively with standard deviation $\simeq \pm 0.01$. We find that $\phi$ obtained by all protocols peak at the cube, which is the only Platonic solid that can tessellate space, and then monotonically decrease with number of sides. This overall trend is similar but systematically lower than the maximum $\phi$ reported for frictionless Platonic solids, and below $\phi_{rlp}$ of spheres for the loose packings. Experiments with ceramic tetrahedron were also conducted, and higher friction was observed to lead to lower $\phi$

Shocks in sand flowing in a silo

We study the formation of shocks on the surface of a granular material draining through an orifice at the bottom of a quasi-two dimensional silo. At high flow rates, the surface is observed to deviate strongly from a smooth linear inclined profile giving way to a sharp discontinuity in the height of the surface near the bottom of the incline, the typical response of a choking flow such as encountered in a hydraulic jump in a Newtonian fluid like water. We present experimental results that characterize the conditions for the existence of such a jump, describe its structure and give an explanation for its occurrence.Comment: 5 pages, 7 figure

Dynamic wrinkling and strengthening of a filament in a viscous fluid

We investigate the wrinkling dynamics of an elastic filament immersed in a viscous fluid submitted to compression at a finite rate with experiments and by combining geometric nonlinearities, elasticity, and slender body theory. The drag induces a dynamic lateral reinforcement of the filament leading to growth of wrinkles that coarsen over time. We discover a new dynamical regime characterized by a timescale with a non-trivial dependence on the loading rate, where the growth of the instability is super-exponential and the wavenumber is an increasing function of the loading rate. We find that this timescale can be interpreted as the characteristic time over which the filament transitions from the extensible to the inextensible regime. In contrast with our analysis with moving boundary conditions, Biot's analysis in the limit of infinitely fast loading leads to rate independent exponential growth and wavelength

Spatial distribution functions of random packed granular spheres obtained by direct particle imaging

We measure the two-point density correlations and Voronoi cell distributions of cyclically sheared granular spheres obtained with a fluorescence technique and compare them with random packing of frictionless spheres. We find that the radial distribution function $g(r)$ is captured by the Percus-Yevick equation for initial volume fraction $\phi=0.59$. However, small but systematic deviations are observed because of the splitting of the second peak as $\phi$ is increased towards random close packing. The distribution of the Voronoi free volumes deviates from postulated $\Gamma$ distributions, and the orientational order metric $Q_6$ shows disorder compared to numerical results reported for frictionless spheres. Overall, these measures show significant similarity of random packing of granular and frictionless spheres, but some systematic differences as well.Comment: 4 pages, 4 figure