Ordered packing of uniform spheres via random packing protocol

The packing structure of granular materials is crucial to their performance. Uniform granular spheres always form a disordered packing when randomly fed into a container, which is considered as a natural consequence and a prototype of glass transition. This paper presents a method to design containers to promote ordered packings. In a particular container, mono-sized granular spheres can self-assemble into a single crystal without human interventions when randomly fed at a small rate, and hence achieve much higher packing density than the normally obtained random packings. The container is designed to achieve the consistency of ordered structures formed on the boundary and at the centre, so that a new particle can always be assembled into a crystal lattice node simply by gravity. Such container is generally effective for the self-assembly of uniform size spheres of different material properties (density, friction coefficients, size, etc.). Similarly designed containers can also be very effective to achieve ordered packings under vibration, which provides a method to densify packed beds of granular particles. Moreover, the finding indicates that glass transition or crystallisation could result from boundary symmetry in addition to other factors. It also suggests a way to design boundaries to promote the self-assembly of particles in general.