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

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 kappa(q) is constructed to quantify the effect of the repulsion, and a critical value kappa(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.