# Density = f(Particle Size Distribution)

January 23, 2012 9:21 AM Subscribe

Sphere packing problem: for a distribution of sphere sizes?

Sphere packing has been of interest for many years, notably since Kepler conjectured the maximum packing efficiency for spheres of a single size.

Wikipedia tells me that for a sphere size

So, given a continuous particle size distribution function (e.g. a log-normal distribution), how can I estimate the maximum (or even typical or likely) packing efficiency and make comparisons between different distributions?

(My eventual goal is to correlate density of a real particulate substance to its PSD, but I though I'd phrase the question more generally.)

Sphere packing has been of interest for many years, notably since Kepler conjectured the maximum packing efficiency for spheres of a single size.

Wikipedia tells me that for a sphere size

*distribution*the problem quickly becomes untractable, but I have found references in some papers for estimation methods – however these go a bit too deep for me to gain usable knowledge.

So, given a continuous particle size distribution function (e.g. a log-normal distribution), how can I estimate the maximum (or even typical or likely) packing efficiency and make comparisons between different distributions?

(My eventual goal is to correlate density of a real particulate substance to its PSD, but I though I'd phrase the question more generally.)

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posted by demiurge at 9:35 AM on January 23, 2012