Title: Spherocylinder Packings and Wedge Hoppers: Life with Straight Lines

Author (Invited): Scott Franklin, Rochester Institute of Technology

Abstract:

A love of symmetry often influences our choice of systems to study. Grains are spherical or, when not, ellipsoids, easily represented analytically. Hoppers or silos have circular openings, the single length scale characterized simply in terms of the particle diameter. Motivated by the extremely rigid jammed state of large aspect ratio particles (L/d > 35), we study packings of spherocylinders --- cylinders with hemispherical endcaps --- using energy minimization techniques. While many of the characteristics (e.g. average contact number, packing fraction, and vibrational modes) mirror those of ellipsoids, the energy spectrum of the modes appears quite different. The absence of sidewall curvature facilitates translational, and inhibits rotational, modes. In a separate experimental study, we look at the flow of granular particles through wedge-shaped hoppers. The second length scale of the hopper aperture (width and length) results in a crossover from exponential to power-law in the exit-mass probability distribution function. Put simply, when the hopper length is much larger than its width, abnormally large amounts of particles can exit without jamming. We have since confirmed that this behavior is independent of particle aspect ratio and is indeed a property of the hopper geometry. As I will show, the straight lines in these problems result in fundamentally different behaviors that we are only beginning to understand. I'll present preliminary theoretical and experimental data, and lay out a plan for the coming months' investigations.