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arXiv · 0912.0852

Close packing density of polydisperse hard spheres

Robert S. Farr·Robert D. Groot
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Abstract

The most efficient way to pack equally sized spheres isotropically in 3D is known as the random close packed state, which provides a starting point for many approximations in physics and engineering. However, the particle size distribution of a real granular material is never monodisperse. Here we present a simple but accurate approximation for the random close packing density of hard spheres of any size distribution, based upon a mapping onto a one-dimensional problem. To test this theory we performed extensive simulations for mixtures of elastic spheres with hydrodynamic friction. The simulations show a general (but weak) dependence of the final (essentially hard sphere) packing density on fluid viscosity and on particle size, but this can be eliminated by choosing a specific relation between mass and particle size, making the random close packed volume fraction well-defined. Our theory agrees well with the simulations for bidisperse, tridisperse and log-normal distributions, and correctly reproduces the exact limits for large size ratios.

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Robert S. Farr, Robert D. Groot. 2009-12-04. Close packing density of polydisperse hard spheres. https://doi.org/10.1063/1.3276799

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