Electrohydrodynamic interactions of droplets

The interaction of fluids and electric fields is at the heart of natural phenomena such as disintegration of raindrops in thunderstorms and many applications such as ink-jet printing, microfluidics, crude oil demulsification, and electrosprays. Many of these processes involve droplets and there has been a long-standing interest in understanding drop electrohydrodynamics. While an isolated drop in applied electric fields has been extensively studied, the behavior of many drops is largely unexplored. Even the pair-wise drop interactions have received scant attention and existing models are limited to axisymmetric and two-dimensional geometries. In three dimensions, the electrohydrodynamic interactions can be quite complex and non-trivial. For example, in an applied uniform electric field, instead of chaining along the field direction, drops can initially attract in the direction of the field and move towards each other, but then separate in the transverse direction [1]. Using a combination of numerical simulations based on a boundary integral formulation and an analytical theory assuming small drop deformations, we study the dynamics of a drop pair in an applied uniform electric field at arbitrary orientation of their line-of-centers relative to the applied field direction. For identical drops covered with insoluble surfactant [2], we find that the surfactant weakens the electrohydrodynamic flow and thus dielectrophoretic interactions play more prominent role in the dynamics of surfactant-covered drops compared to clean drops. If drop conductivity is the same as the suspending fluid, a nondiffusing surfactant can arrest the drops' relative motion thereby effectively preventing coalescence. Drop dissimilarity can also have profound effect on the pair dynamics: we find that in some cases droplets can form a stable pair (tandem) that “swims” either parallel or perpendicular to the applied field direction [3]. If time permits, I will discuss particle-particle and particle-wall interactions driven by electrohydrodynamic flows due to the Onsager effect.