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Predicting segregation of granular materials composed of different-sizedparticles is a challenging problem. In this paper, we develop and implement atheoretical model that captures the interplay between advection, segregation,and diffusion in size bidisperse granular materials. The fluxes associated withthese three driving factors depend on the underlying kinematics, whosecharacteristics play key roles in determining particle segregationconfigurations. Unlike previous models for segregation, our model usesparameters based on kinematic measures from discrete element method simulationsinstead of arbitrarily adjustable fitting parameters, and it achieves excellentquantitative agreement with both experimental and simulation results whenapplied to quasi-two-dimensional bounded heaps. The model yields twodimensionless control parameters, both of which are only functions ofphysically control parameters (feed rate, particle sizes, and system size) andkinematic parameters (diffusion coefficient, flowing layer depth, andpercolation velocity). The P\'eclet number, $Pe$, captures the interplay ofadvection and diffusion, and the second dimensionless parameter, $\Lambda$,describes the interplay between segregation and advection. A parametric studyof $\Lambda$ and $Pe$ demonstrates how the particle segregation configurationdepends on the interplay of advection, segregation, and diffusion. The modelcan be readily adapted to other flow geometries.

Modeling size segregation of granular materials: the roles of segregation, advection and diffusion