Mathematical Model and Experimental Validation of Free Surface Size Segregation for Polydisperse Granular Materials

 A mathematical model of free surface size segregation of granular matter is proposed. The material is assumed to be dry, cohesionless and to consist of several populations with distinct diameter ranges. It is not necessary that one population is predominant. The extent of segregation depends mainly on the relative amount of small and large particles and on the diameter ratios but not on their absolute values. The model predicts how the fractions of these populations change from the position where the material is fed onto a heap to its bottom. It is based on ideas of L. Prigozhin} to treat binary mixtures. Introducing a new scheme to interpolate the local deposition rates from situations with one predominant population it becomes possible to handle mixtures with three and more diameters. The model may be applied to storage systems of any kind, such as bunkers, hoppers, silos or mixing beds, provided the source is sufficiently weak and concentrated. Numerical simulations are discussed for conical and ramp-like geometries and for ternary mixtures. In order to validate the model a few experiments were conducted. As measured by the natural variability of the problem and the simplicity of the model, which is sufficiently easy to be used in an industrial controller, good agreement between theory and experiment is found.