Built upon sand: Theoretical ideas inspired by granular flows

Abstract

Granulated materials, like sand and sugar and salt, are composed of many pieces that can move independently. The study of collisions and flow in these materials requires new theoretical ideas beyond those in the standard statistical mechanics or hydrodynamics or traditional solid mechanics. Granular materials differ from standard molecular materials in that frictional forces among grains can dissipate energy and drive the system toward frozen or glassy configurations. In experimental studies of these materials, one sees complex flow patterns similar to those of ordinary liquids, but also freezing, plasticity, and hysteresis. To explain these results, theorists have looked at models based upon inelastic collisions among particles. With the aid of computer simulations of these models they have tried to build a “statistical dynamics” of inelastic collisions. One effect seen, called inelastic collapse, is a freezing of some of the degrees of freedom induced by an infinity of inelastic collisions. More often some degrees of freedom are partially frozen, so that there can be a rather cold clump of material in correlated motion. Conversely, thin layers of material may be mobile, while all the material around them is frozen. In these and other ways, granular motion looks different from movement in other kinds of materials. Simulations in simple geometries may also be used to ask questions like When does the usual Boltzmann-Gibbs-Maxwell statistical mechanics arise?, What are the nature of the probability distributions for forces between the grains?, and Might the system possibly be described by uniform partial differential equations? One might even say that the study of granular materials gives one a chance to reinvent statistical mechanics in a new context.