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Granular segregation in circular tumblers: theoretical model and scaling laws

Published online by Cambridge University Press:  28 January 2015

Conor P. Schlick ,
Yi Fan ,
Paul B. Umbanhowar ,
Julio M. Ottino  and
Richard M. Lueptow
Conor P. Schlick
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
Yi Fan
Affiliation:
Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA The Dow Chemical Company, Midland, MI 48667, 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 address for correspondence: r-lueptow@northwestern.edu
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Abstract

We model bidisperse size segregation of granular material in quasi-two-dimensional circular tumbler flow using the advection–diffusion transport equation with an additional term to account for segregation due to percolation. Segregation depends on three dimensionless parameters: the ratio of segregation to advection, ${\it\Lambda}$; the ratio of advection to diffusion, $\mathit{Pe}$; and the dimensionless flowing layer depth, ${\it\epsilon}$. The degree of segregation in steady state depends only on the ratio of segregation effects to diffusion effects, ${\it\Lambda}\,\mathit{Pe}$, and the degree of segregation increases as ${\it\Lambda}\mathit{Pe}$ increases. The transient time to reach steady-state segregation depends only on advection, which is manifested in ${\it\epsilon}$ and $\mathit{Pe}$ when ${\it\Lambda}\mathit{Pe}$ is constant. This model is also applied to unsteady tumbler flow, where the rotation speed varies with time.

JFM classification

Complex Fluids: Complex Fluids Granular media: Granular media Mixing: Granular mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 765 , 25 February 2015 , pp. 632 - 652
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Copyright
© 2015 Cambridge University Press 

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Schlick et al. supplementary movie

A movie of the theoretical prediction of a rotating tumbler with ε=0.1, Λ=1.5, and Pe=30 over 1.5 rotations.

Download Schlick et al. supplementary movie(Video)
Video 3 MB

Schlick et al. supplementary movie

A movie of the theoretical prediction of a rotating tumbler with ε=0.1, Λ=1.5, and Pe=30 over 1.5 rotations.

Download Schlick et al. supplementary movie(Video)
Video 1.6 MB