  Predicting segregation of granular materials composed of different-sized
particles is a challenging problem. In this paper, we develop and implement a
theoretical model that captures the interplay between advection, segregation,
and diffusion in size bidisperse granular materials. The fluxes associated with
these three driving factors depend on the underlying kinematics, whose
characteristics play key roles in determining particle segregation
configurations. Unlike previous models for segregation, our model uses
parameters based on kinematic measures from discrete element method simulations
instead of arbitrarily adjustable fitting parameters, and it achieves excellent
quantitative agreement with both experimental and simulation results when
applied to quasi-two-dimensional bounded heaps. The model yields two
dimensionless control parameters, both of which are only functions of
physically control parameters (feed rate, particle sizes, and system size) and
kinematic parameters (diffusion coefficient, flowing layer depth, and
percolation velocity). The P\'eclet number, $Pe$, captures the interplay of
advection and diffusion, and the second dimensionless parameter, $\Lambda$,
describes the interplay between segregation and advection. A parametric study
of $\Lambda$ and $Pe$ demonstrates how the particle segregation configuration
depends on the interplay of advection, segregation, and diffusion. The model
can be readily adapted to other flow geometries.
