Evolution of Clouds of Migrating Micron-particles with Hydrodynamic and Electrostatic Interactions.

The evolution of dilute clouds of charged micron-sized particles during the migration in an external electric field is numerically investigated. The hydrodynamic interaction is modeled employing the Oseen dynamics in the limit of small-but-finite particle Reynolds number. The effects of external field and inter-particle Coulomb repulsion are accounted by a pairwise summation. As a result, with a dominant external electrostatic force, the cloud is seen to flatten into a planar configuration with particle leakage in the tail and eventually breaks up into two small clouds. Decreasing the external force or increasing the pairwise Coulomb repulsion has a similar effect on the dynamics of the cloud, i.e., decreases the scaled migrating velocity of the cloud and makes the cloud steady in its spherical shape. While this behavior bears some similarity with the transition from the Stokes regime to the micro-scale inertia dominant regime, the underlying physical mechanisms differ. Finally, the variation of the typical aspect ratio of the cloud, as a function of a scaled radial velocity of particles, is used to quantify the effect of Coulomb repulsion on the stability of the shape of the cloud.