Phyllotactic description of hard sphere packing in cylindrical channels

TL;DR

This paper presents an analytical theory linking dense sphere packings in cylinders to disk packings on their surface, identifying the densest arrangements and phase competition for specific diameter ratios.

Contribution

It introduces a simple analytical model that describes sphere packings in cylinders and clarifies the nature of competing phases within a certain size ratio range.

Findings

Densest packings involve spheres in contact with the cylinder boundary.

The theory applies for diameter ratios up to 1+1/sin(pi/5).

Identifies phases and their competition through comparison with numerical simulations.

Abstract

We develop a simple analytical theory that relates dense sphere packings in a cylinder to corresponding disk packings on its surface. It applies for ratios R=D/d (where d and D are the diameters of the hard spheres and the bounding cylinder, respectively) up to R=1+1/sin(pi/5). Within this range the densest packings are such that all spheres are in contact with the cylindrical boundary. The detailed results elucidate extensive numerical simulations by ourselves and others by identifying the nature of all competing phases.