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

Segregation of granular materials composed of different-sized particles has important repercussions in various industrial processes and natural phenomena, but predicting size segregation remains a challenging problem. To address this problem, we have developed 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 earlier models for segregation, our model uses parameters based on kinematics 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 and circular rotating tumblers. The model yields two dimensionless control parameters, both of which are only functions of control parameters (feed rate, particle sizes, and system size) and kinematic parameters (diffusion coefficient, flowing layer depth, and percolation velocity). The Péclet number, Pe, captures the interplay of advection and diffusion, and the second dimensionless parameter, Λ, describes the interplay between segregation and advection. A parametric study of Λ and Pe demonstrates how particle segregation configuration depends on the interplay of advection, segregation, and diffusion. In bounded heap flow, the particle segregation configurations are determined by advection, segregation, and diffusion depending on flow conditions and particle properties. In contrast, in circular tumbler flow, the final particle segregation configurations depend primarily on the competition between segregation and diffusion, and segregation rates are determined by advection and the flowing layer thickness. ACKNOWLEDGEMENTS We gratefully acknowledge financial support from The Dow Chemical Compan