Radial segregation of granular mixtures in rotating cylinders

Simultaneous mixing and segregation of granular materials is of considerable practical importance; the interplay among both processes is, however, poorly understood from a fundamental viewpoint. The focus of this work is radial segregation - core formation - due to density in a rotating cylinder. The flow regime considered is the cascading or continuous flow regime where a thin layer of solids flows along a nearly flat free surface, while the remaining particles rotate as a fixed bed along with the cylinder. The essence of the formation of a central segregated core of the more dense particles lies in the flow, mixing, and segregation in the cascading layer. The work involves experiments and analysis. A constitutive model for the segregation flux in cascading layers is proposed and validated by particle dynamics and Monte Carlo simulations for steady flow down an inclined plane. The model contains a single parameter, the dimensionless segregation velocity (β), which is treated as a fitting parameter here. Experimental results for the equilibrium segregation of steel balls and glass beads are presented for different fractions and different extents of filling. There is a good match between theoretical predictions and all experimental results when the value of dimensionless segregation velocity is taken to be β=2. The extent of segregation is found to increase with increase in the dimensionless segregation velocity and dimensionless diffusivity but is independent of the level of filling. Lagrangian simulations based on the theory and experiments demonstrate the competition between segregation and mixing. In the case of slow mixing, the intensity of segregation monotonically decreases to an equilibrium value; for fast mixing, however, there exists an optimal mixing time at which the best mixing is obtained.