Numerical and asymptotic analysis of the three-dimensional electrohydrodynamic interactions of a drop and a nearby planar boundary

We study the interaction of a drop with a planar wall under an applied uniform DC electric field using the leaky dielectric model framework. We develop three-dimensional numerical simulations using the boundary integral method and an analytical theory assuming small drop deformations. By integrating numerical simulations with theoretical analysis, we examine the electrohydrodynamic interactions as a function of separation distance and fluid properties. Specifically, we focus on a drop near an insulating wall, where the electric field is tangential to the wall surface. Our results show that the drop migrates away or towards the wall, depending on the relative conductivities and permittivities of the drop and the suspending fluid. For instance, a drop that is more conducting than the suspending fluid experiences electrohydrodynamic attraction but electrostatic repulsion—due to the interaction with the image dipole—by the insulating wall, leading to a stable hovering state. We compare our simulations with experiments, particularly in cases where the drop is less conducting than the suspending fluid, resulting in electrohydrodynamic and electrostatic repulsion.