Three-dimensional clogging structures of granular spheres near hopper orifice

The characteristic clogging structures of granular spheres blocking three-dimensional granular flow through hopper outlet are analyzed based on packing structures reconstructed using magnetic resonance imaging techniques. Spheres in clogging structures are arranged in a way with typical features of load-bearing, such as more contacting bonds close to the horizontal plane and more mutually-stabilized contact configurations than packing structures away from the orifice. The requirement of load-bearing inevitably leads to the cooperativity of clogging structures with a correlation length of several particle diameters. This correlation length being comparable with the orifice diameter suggests that a clogging structure is composed of several mutually-stabilized structural motifs to span the orifice perimeter, instead of a collection of independent individual spheres to cover the whole orifice area. Accordingly, we propose a simple geometric model to explain the unexpected linear dependence of the average size of three-dimensional clogging structures on orifice diameter.