Two-dimensional packing in prolate granular materials

Abstract

We investigate the two-dimensional packing of extremely prolate (aspect ratio = L/D > 10) granular materials, comparing experiments with Monte-Carlo simulations. In experimental piles of particles with aspect ratio = 12 we find the average packing fraction to be 0.68±0.03. Both experimental and simulated piles contain a large number of horizontal particles, and particle alignment is quantified by an orientational order correlation function. In both simulation and experiment the correlation between particle orientation decays after a distance of two particle lengths. It is possible to identify voids in the pile with sizes ranging over two orders of magnitude. The experimental void distribution function is a power law with exponent − = −2.37 ± 0.05. Void distributions in simulated piles do not decay as a power law, but do show a broad tail. We extend the simulation to investigate the scaling at very large aspect ratios. A geometric argument predicts the pile number density to scale as −2. Simulations do indeed scale this way, but particle alignment complicates the picture, and the actual number densities are quite a bit larger than predicted.