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A unified description of gravity- and kinematics-induced segregation forces in dense granular flows

Published online by Cambridge University Press:  26 August 2021

Lu Jing Open the ORCID record for Lu Jing [Opens in a new window] ,
Julio M. Ottino Open the ORCID record for Julio M. Ottino [Opens in a new window] ,
Richard M. Lueptow Open the ORCID record for Richard M. Lueptow [Opens in a new window]  and
Paul B. Umbanhowar Open the ORCID record for Paul B. Umbanhowar [Opens in a new window]
Lu Jing
Affiliation:
Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA
Julio M. Ottino
Affiliation:
Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA Northwestern Institute on Complex Systems (NICO), Northwestern University, Evanston, IL 60208, USA
Richard M. Lueptow*
Affiliation:
Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA Northwestern Institute on Complex Systems (NICO), Northwestern University, Evanston, IL 60208, USA
Paul B. Umbanhowar
Affiliation:
Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA
*
†Email address for correspondence: r-lueptow@northwestern.edu
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Abstract

Particle segregation is common in natural and industrial processes involving flowing granular materials. Complex, and seemingly contradictory, segregation phenomena have been observed for different boundary conditions and forcing. Using discrete element method simulations, we show that segregation of a single particle intruder can be described in a unified manner across different flow configurations. A scaling relation for the net segregation force is obtained by measuring forces on an intruder particle in controlled-velocity flows where gravity and flow kinematics are varied independently. The scaling law consists of two additive terms: a buoyancy-like gravity-induced pressure gradient term and a shear rate gradient term, both of which depend on the particle size ratio. The shear rate gradient term reflects a kinematics-driven mechanism whereby larger (smaller) intruders are pushed toward higher (lower) shear rate regions. The scaling is validated, without refitting, in wall-driven flows, inclined wall-driven flows, vertical silo flows, and free-surface flows down inclines. Comparing the segregation force with the intruder weight results in predictions of the segregation direction that match experimental and computational results for various flow configurations.

JFM classification

Granular media: Dry granular material Mixing: Granular mixing

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JFM Papers
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Journal of Fluid Mechanics , Volume 925 , 25 October 2021 , A29
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© The Author(s), 2021. Published by Cambridge University Press

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