Phyllotactic Description of Hard Sphere Packing in Cylindrical Channels - CHAN, HO-KEI; WEAIRE, DENIS (My University, 2011)
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?(?/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 various competing phases.
PUBLISHED
For the densest packings of identical hard spheres inside a cylinder, all the spheres will be in contact with the cylindrical surface if the cylinder-to-sphere diameter ratio is below the critical value 2.7013. This paper shows that such structures can be understood in terms of a distorted triangular lattice that describes the spheres' positions on the unrolled cylindrical surface.
Keywords: Fluids and plasma physics; sphere packings; disk packings; Nanoscience & Materials