Competition between randomizing impacts and inelastic collisions in granular pattern formation

The flow and mixing of granular materials occur during handling of a wide variety of substances, from pharmaceuticals to cement to cereal grains1,2. The understanding of such flows is, however, considerably more limited than it is for fluids3; even basic processes such as tumbling4,5, simple shear6,7,8 and shaking9,10,11,12 give rise to unexpected results. A case in point is granular pattern formation. A rich variety of patterns, including stripes, squares, hexagons and solitary structures, has been observed in vertically shaken, shallow granular beds13,14. The vertical dynamics responsible for these patterns have been explored15,16,17,18,19, but the role of horizontal motions of the grains is less well understood. Here I present a model of these motions that identifies two aspects as central to pattern formation: the randomization of horizontal velocities20 by shaking, and the inelastic nature of grain collisions. These two elements alone, even without the influence of gravity, are sufficient to produce organized patterns in the horizontal plane — both those observed and others not yet seen experimentally.