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Collision rate of bidisperse, hydrodynamically interacting spheres settling in a turbulent flow

Published online by Cambridge University Press:  04 February 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: dlk15@cornell.edu
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Abstract

The collisions in a dilute polydisperse suspension of sub-Kolmogorov spheres with negligible inertia settling in a turbulent flow and interacting through hydrodynamics including continuum breakdown on close approach are studied. A statistically significant decrease in ideal collision rate without gravity is resolved via a Lagrangian stochastic velocity-gradient model at Taylor microscale Reynolds number larger than those accessible by current direct numerical simulation capabilities. This arises from the difference between the mean inward velocity and the root-mean-square particle relative velocity. Differential sedimentation, comparable to the turbulent shear relative velocity, but minimally influencing the sampling of the velocity gradient, diminishes the Reynolds number dependence and enhances the ideal collision rate i.e. the rate without interactions. The collision rate is retarded by hydrodynamic interactions between sphere pairs and is governed by non-continuum lubrication as well as full continuum hydrodynamic interactions at larger separations. The collision efficiency (ratio of actual to ideal collision rate) depends on the relative strength of differential sedimentation and turbulent shear, the size ratio of the interacting spheres and the Knudsen number (defined as the ratio of the mean-free path of the gas to the mean radius of the interacting spheres). We develop an analytical approximation to concisely report computed results across the parameter space. This accurate closed form expression could be a critical component in computing the evolution of the size distribution in applications such as water droplets in clouds or commercially valuable products in industrial aggregators.

JFM classification

Drops and Bubbles: Breakup/coalescence Low-Reynolds-number flows: Stokesian dynamics Turbulent Flows: Isotropic turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 912 , 10 April 2021 , A5
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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