Microscopic model for granular stratification and segregation

– We study segregation and stratification of mixtures of grains differing in size, shape and material properties poured into two-dimensional silos using a microscopic lattice model for surface flows of grains. The model incorporates the dissipation of energy in collisions between rolling and static grains and an energy barrier describing the geometrical asperities of the grains. We study the phase diagram of the different morphologies predicted by the model as a function of the two parameters. We find regions of segregation and stratification, in agreement with experimental finding, as well as a region of total mixing. When mixtures of grains [1-8] of different sizes are poured on a heap, a size segregation of the mixture is observed; the large grains are more likely to be found near the base, while the small grains are more likely to be near the top [9-14]. If the grains differ not only in size but also in shape and roughness, a spontaneous periodic pattern arises upon pouring the mixture into a two-dimensional cell. When a mixture of large cubic grains and small rounded grains is poured into a vertical Hele-Shaw cell (two vertical slabs separated by a gap of approximately 5 mm) the mixture spontaneously stratifies into alternating layers of small rounded and large cubic grains [15]. Otherwise, the mixture only segregates when the large grains are more rounded than the small grains [15] with the large rounded grains being found near the bottom of the cell. The dynamical process leading to stratification was recently studied numerically and theoretically [16], using the set of continuum equations for surface flows of granular mixtures developed in [17-20]. The physical quantities defined in this phenomenological formalism are to be understood as an average over a certain coarse grain length on the surface of the sandpile (larger than the size of the grains), where hydrodynamic equations are valid, and any quantity defined below this scale is not well defined. Thus the relevant length scale appearing in this formalism is that of the coarse grain scale (≈ 5d) and not of the grain size (d). However, fluctuations may also occur at the level of the grains, so that a microscopic description of collisions and transport of grains may be needed to describe this situation. In this paper, we