Dense packings of spheres in cylinders

We develop a simple analytical theory that relates dense hard 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=2.738. 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 others and ourselves by identifying the nature of various competing phases. We also present results for the regime R greater than 2.738. These preliminary results explore packings that include internal spheres (i.e. spheres that do not contact the cylinder). This is done through a combination of experiments and numerical simulation (simulated annealing). Our experiments involve the packing of monodisperse bubbles in narrow micron-sized capillaries. Such ``wet foams'' are an excellent model of the hard sphere packing problem and are analyzed by X-ray tomography to provide structural information.