Mixing and segregation of granular matter: Multi-lobe formation in time-periodic flows

We study size segregation in two classes of granular systems in time-periodically forced quasi-two-dimensional tumblers. In dry granular systems (DGS), particles are immersed in air, whereas in liquid granular systems (LGS) or slurries, particles are wholly immersed in a less dense liquid. Experimental results show lobe formation and classical radial segregation, depending on the frequency of the forcing and fill fraction of the system. Both DGS and LGS exhibit similar multi-lobe patterns when subjected to the same forcing. A simple model captures the experimental results and suggests that the symmetry of the forcing plays a crucial role in the emergence of the patterns. Lobes form via a reinforcement mechanism that depends on the period of the regular islands in the Poincaré map. The mechanism can be controlled by changing the forcing period and/or fill fraction.