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Collision rate of bidisperse spheres settling in a compressional non-continuum gas flow

Published online by Cambridge University Press:  08 January 2021

Johnson Dhanasekaran Open the ORCID record for Johnson Dhanasekaran [Opens in a new window] ,
Anubhab Roy Open the ORCID record for Anubhab Roy [Opens in a new window]  and
Donald L. Koch Open the ORCID record for Donald L. Koch [Opens in a new window]
Johnson Dhanasekaran
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY14853, USA
Anubhab Roy
Affiliation:
Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, Tamil Nadu600036, India
Donald L. Koch*
Affiliation:
Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY14853, USA
*
†Email address for correspondence: [email protected]
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Abstract

Collisions in a dilute polydisperse suspension of spheres of negligible inertia interacting through non-continuum hydrodynamics and settling in a slow uniaxial compressional flow are studied. The ideal collision rate is evaluated as a function of the relative strength of gravity and uniaxial compressional flow and it deviates significantly from a linear superposition of these driving terms. This non-trivial behaviour is exacerbated by interparticle interactions based on uniformly valid non-continuum hydrodynamics, that capture non-continuum lubrication at small separations and full continuum hydrodynamic interactions at larger separations, retarding collisions driven purely by sedimentation significantly more than those driven purely by the linear flow. While the ideal collision rate is weakly dependent on the orientation of gravity with the axis of compression, the rate including hydrodynamic interactions varies by more than $100\,\%$ with orientation. This dramatic shift can be attributed to complex trajectories driven by interparticle interactions that prevent particle pairs from colliding or enable a circuitous path to collision. These and other important features of the collision process are studied in detail using trajectory analysis at near unity and significantly smaller than unity size ratios of the interacting spheres. For each case analysis is carried for a large range of relative strengths and orientations of gravity to the uniaxial compressional flow, and Knudsen numbers (ratio of mean free path of the media to mean radius).

JFM classification

Drops and Bubbles: Breakup/coalescence Low-Reynolds-number flows: Stokesian dynamics Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 910 , 10 March 2021 , A10
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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