Mixing and segregation of granular materials

Granular materials segregate. Small differences in either size or density lead to flow-induced segregation, a complex phenomenon without parallel in fluids. Modeling of mixing and segregation processes requires the confluence of several tools, including continuum and discrete descriptions (particle dynamics, Monte Carlo simulations, cellular automata computations) and, often, considerable geometrical insight. None of these viewpoints, however, is wholly satisfactory by itself. Moreover, continuum and discrete descriptions of granular flows are regime dependent, and this fact may require adopting different subviewpoints. This review organizes a body of knowledge that forms - albeit imperfectly - the beginnings of an expandable continuum framework for the description of mixing and segregation of granular materials. We focus primarily on noncohesive particles, possibly differing in size, density, shape, etc. We present segregation mechanisms and models for size and density segregation and introduce chaotic advection, which appears in noncircular tumblers. Chaotic advection interacts in nontrivial ways with segregation in granular materials and leads to unique equilibrium structures that serve as a prototype for systems displaying organization in the midst of disorder.