How dense can one pack spheres of arbitrary size distribution?

Details How dense can one pack spheres of arbitrary size distribution? How dense can one pack spheres of arbitrary size distribution?

2011-09-05

arxiv.org/abs/1109.0966v2

EPL 97,18004 (2012)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 5 figures

Scientific paper

10.1209/0295-5075/97/18004

We present the first systematic algorithm to estimate the maximum packing density of spheres when the grain sizes are drawn from an arbitrary size distribution. With an Apollonian filling rule, we implement our technique for disks in 2d and spheres in 3d. As expected, the densest packing is achieved with power-law size distributions. We also test the method on homogeneous and on empirical real distributions, and we propose a scheme to obtain experimentally accessible distributions of grain sizes with low porosity. Our method should be helpful in the development of ultra-strong ceramics and high performance concrete.

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