Evolution of Clouds of Migrating Micro-particles with Hydrodynamic and Electrostatic Interactions

Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China

^* e-mail: lishuiqing@tsinghua.edu.cn

Published online: 30 June 2017

Abstract

The evolution of a migrating cloud of particles with electrohydrodynamic interactions is numerically investigated. The hydrodynamic interaction is modelled by Oseen dynamics in the limit of small-but-finite particle Reynolds number. The effects of external field and the particle-particle Coulomb repulsion, calculated through pairwise summation, are quantified by a charge parameter, κ_q. With a small or zero κ_q, the cloud is seen to flatten into a toroidal configuration and eventually breaks up into two small clouds, indicating that the external electrostatic field has a similar effect with gravity. Increasing the long-range Coulomb repulsion can delay or even totally prevent the breakup. With sufficiently strong repulsion, the cloud undergoes a self-similar expansion. Finally, we show that the breakup of the cloud is strongly related to the initial inhomogeneity of the particle concentration. This chaotic characteristic, however, is dramatically depressed by the long-range Coulomb repulsion.