Close packing density of polydisperse hard spheres

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 p...

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Bibliographic Details
Published in:arXiv.org 2009-12
Main Authors: Farr, Robert S, Groot, Robert D
Format: Article
Language:English
Subjects:
Dependence
Granular materials
Mapping
Packing density
Particle size
Particle size distribution
Simulation
Spheres
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0912.0852