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Scaling laws for migrating cloud of low-Reynolds-number particles with Coulomb repulsion

Published online by Cambridge University Press:  28 November 2017

Sheng Chen ,
Wenwei Liu  and
Shuiqing Li Open the ORCID record for Shuiqing Li [Opens in a new window]
Sheng Chen
Affiliation:
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China
Wenwei Liu
Affiliation:
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China
Shuiqing Li*
Affiliation:
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China
*
†Email address for correspondence: lishuiqing@tsinghua.edu.cn
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Abstract

We investigate the evolution of spherical clouds of charged particles that migrate under the action of a uniform external electrostatic field. Hydrodynamic interactions are modelled by Oseen equations and the Coulomb repulsion is calculated through pairwise summation. It is shown that strong long-range Coulomb repulsion can prevent the breakup of the clouds covering a wide range of particle Reynolds number $Re_{p}$ and cloud-to-particle size ratio $R_{0}/r_{p}$ . A dimensionless charge parameter $\unicode[STIX]{x1D705}_{q}$ is constructed to quantify the effect of the repulsion, and a critical value $\unicode[STIX]{x1D705}_{q,t}$ is deduced, which successfully captures the transition of a cloud from hydrodynamically controlled regime to repulsion-controlled regime. Our results also reveal that, with sufficiently strong repulsion, the cloud undergoes a universal self-similar expansion. Scaling laws of cloud radius $R_{cl}$ and particle number density $n$ are obtained by solving a continuum convection equation.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Multiphase and Particle-laden Flows: Particle/fluid flow Complex Fluids: Suspensions

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 835 , 25 January 2018 , pp. 880 - 897
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Copyright
© 2017 Cambridge University Press 

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