Granular Matter Instability: a Structural Rigidity Point of View

Granular materials are ubiquitous in nature and very common in industrial processes, but it is only recently that their unusual properties have begun to receive detailed attention from the physicists community [1, 2]. The earliest documented studies of granular matter date back to Faraday [3], who discovered the convective behavior of vibrated sand, and Reynolds [4], who noted that compactified granular matter cannot undergo shear without increasing its volume. The behavior of vibrated granular matter in some aspects resembles that of a fluid, although there are crucial differences. Size segregation [5], for example, at first sight defies intuition. When a mixture of particles of different sizes is subject to vibration, the larger ones migrate to the top, irrespective of density. Also interesting is the layering instability [6] of a binary mixture under pouring. Instead of a homogeneously mixed pile, under certain conditions an alternation of layers of both kinds of particles can be obtained. Similar demixing phenomena occur in granular materials subject to various kinds of external excitation. These seem to contradict the naive expectation that shaking should favor mixing, or take the system to a low-energy state. Many of the unusual properties of vibrated granular matter are in fact due to the dissipative character of interparticle collisions. An interesting example of the consequences of dissipation is inelastic clustering [7], by which particles tend to cluster together as their relative kinetic energy is completely lost during collisions.