Mixing of granular materials: a test-bed dynamical system for pattern formation

Abstract

Mixing of granular materials provides fascinating examples of pattern formation and self-organization. More mixing action - for example, increasing the forcing with more vigorous shaking or faster tumbling - does not guarantee a better-mixed final system. This is because granular mixtures of just barely different materials segregate according to density and size; in fact, the very same forcing used to mix may unmix. Self-organization results from two competing effects: chaotic advection or chaotic mixing, as in the case of fluids, and flow-induced segregation, a phenomenon without parallel in fluids. The rich array of behaviors is ideally suited for nonlinear-dynamics-based inspection. Moreover, the interplay with experiments is immediate. In fact, these systems may constitute the simplest example of coexistence between chaos and self-organization that can be studied in the laboratory. We present a concise summary of the necessary theoretical background and central physical ideas accompanied by illustrative experimental results to aid the reader in exploring this fascinating new area.