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

Published online by Cambridge University Press:  21 February 2014

Yi Fan*
Affiliation:
Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA The Dow Chemical Company, Midland, MI 48667, USA
Conor P. Schlick
Affiliation:
Department of Engineering Science and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
Paul B. Umbanhowar
Affiliation:
Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA
Julio M. Ottino
Affiliation:
Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA The Northwestern University Institute on Complex Systems (NICO), Northwestern University, Evanston, IL 60208, USA
Richard M. Lueptow*
Affiliation:
Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA The Northwestern University Institute on Complex Systems (NICO), Northwestern University, Evanston, IL 60208, USA
*
Email addresses for correspondence: yfan5@dow.com, r-lueptow@northwestern.edu
Email addresses for correspondence: yfan5@dow.com, r-lueptow@northwestern.edu

Abstract

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 control parameters (feed rate, particle sizes, and system size) and kinematic parameters (diffusion coefficient, flowing layer depth, and percolation velocity). The Péclet number, $\mathit{Pe}$, 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 $\mathit{Pe}$ 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.

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Papers
Copyright
© 2014 Cambridge University Press 

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