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Continuum theory for rapid cohesive-particle flows: general balance equations and discrete-element-method-based closure of cohesion-specific quantities

Published online by Cambridge University Press:  26 October 2017

Kevin M. Kellogg Open the ORCID record for Kevin M. Kellogg [Opens in a new window] ,
Peiyuan Liu ,
Casey Q. LaMarche Open the ORCID record for Casey Q. LaMarche [Opens in a new window]  and
Christine M. Hrenya
Kevin M. Kellogg
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, CO 80309, USA
Peiyuan Liu
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, CO 80309, USA
Casey Q. LaMarche
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, CO 80309, USA
Christine M. Hrenya*
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, CO 80309, USA
*
†Email address for correspondence: hrenya@colorado.edu
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Abstract

The continuum description of rapid cohesive-particle flows comprises the population balance, which tracks various agglomerate sizes in space and time, and kinetic-theory-based balances for momentum and granular energy. Here, fundamental closures are provided in their most general form. In previous population balances, the probability (‘success factor’) that a given collision results in agglomeration or breakage has been set to a constant even though it is well established that the outcome of a collision depends on the impact (relative) velocity. Here, physically based closures that relate the success factors to the granular temperature, a (continuum) measure of the impact velocity, are derived. A key aspect of this derivation is the recognition that the normal component of the impact velocity dictates whether agglomeration occurs. With regard to the kinetic-theory balances, cohesion between particles makes the collisions more dissipative, thereby decreasing the granular temperature. The extra dissipation due to cohesion is accounted for using an effective coefficient of restitution, again determined using the derived distribution of normal impact velocities. This collective treatment of the population and kinetic-theory balances results in a general set of equations that contain several parameters (e.g. critical velocities of agglomeration) that are cohesion-specific (van der Waals, liquid bridging, etc.). The determination of these cohesion-specific quantities using simple discrete element method simulations, as well as validation of the resulting theory, is also presented.

JFM classification

Granular media: Granular media Multiphase and Particle-laden Flows: Multiphase flow Multiphase and Particle-laden Flows: Particle/fluid flow

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Papers
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Journal of Fluid Mechanics , Volume 832 , 10 December 2017 , pp. 345 - 382
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© 2017 Cambridge University Press 

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