Nonlinear electrohydrodynamics of particles and drops in strong electric fields

Department of Mechanical and Aerospace Engineering, University of California San Diego

Weakly conducting dielectric solid particles and liquid droplets in strong electric fields are known to undergo symmetry-breaking bifurcations leading to steady electrorotation. This so-called Quincke effect, which results from the antiparallel electrostatic dipole induced by the applied field inside the particles, is well described by the classic Taylor-Melcher leaky dielectric model. Yet, its impact on collective dynamics in colloidal suspensions and on the shape and dynamics of deformable droplets remains poorly understood from a theoretical standpoint. In this talk, I first discuss the effect of Quincke rotation in large collections of colloidal particles free to roll on the surface of a planar electrode. In agreement with recent experiments, our numerical simulations and theoretical model predict the emergence of a polar liquid state with large vortical patterns in circular confinement above a critical density, which is driven by a combination of electrostatic and hydrodynamic interactions between rollers. Our analysis uncovers the basic interactions leading to such patterns and also reveals a surprising self-similar structure to the emergent vortices. I then turn my attention to the dynamics of deformable liquid drops, which is analyzed numerically using a novel three-dimensional boundary-element formulation. Unlike previous studies that have neglected interfacial charge transport or assumed axisymmetric shapes, our simulations include nonlinear charge convection by the fluid flow and are the first to capture the three-dimensional transition to electrorotation. Our numerical results show excellent agreement with existing experimental data and with an improved small deformation theory. They also reveal the existence of interfacial charge shocks in low viscosity drops, for which we also propose a simple theoretical model.