Dynamics of Segregation, Mixing, and Coarsening of Granular Matter

Julio M. Ottino, R. R. McCormick School of Engineering and Applied Sciences, Northwestern University, Evanston, IL

Mixing and segregation of granular materials is so pervasive in industry and natural processes that one would think that a theoretical framework would have been developed long ago. However, in contrast to mixing of liquids, flow and mixing of granular materials is poorly understood. A significant complicating factor is the tendency for materials to segregate or demix as a result of differences in particle properties. Mixing-segregation processes involving mixture of large/small (S-systems) or dense/less-dense particles (D-systems) often lead to baffling results. However, understanding is beginning to emerge. We review recent results focusing on analogies and differences. We consider dry materials and slurries (two-phase systems of dense particles and liquids). Superficially, quasi-2D systems are relatively well understood and it is now possible to target specific segregated structures; the 2D+1 case, however, corresponding to long-rotating cylinders, is still far from clear. In light of this, one might imagine that full 3D cases, e.g., a sphere of a cube rotating and rocking on two orthogonal axes, may be out of reach. This, however, is not the case. For example, even though the frequency/amplitude phase diagram of modes of segregation in a sphere shows rich behavior, the final segregation patterns are relatively independent of the properties of the materials used, and simple models provide considerable insight. On the other hand, the long-term dynamics of the segregated systems in long cylinders over long periods of time are considerably more complex, often showing structures that do not settle down. However, the rate of coarsening, when it exists, shows that the domain-size growth is logarithmic in all cases studied, including circular and square cross section cylinders filled with dry material and slurries with fluids of different viscosities.

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