Electrohydrodynamics of Lenticular Drops and Equatorial Streaming

As a result of their ability to induce stresses at fluid interfaces, electric fields can deform drops into shapes exhibiting pointed or sharp features. When exposed to a strong electric field, perfectly conducting drops immersed in perfectly insulating surroundings deform into prolate shapes and eventually develop spindle-like profiles capped by conical tips. The radius of curvature at the tip of the cone tends to zero, giving rise to the conic cusping singularity (Zubarev 2001). Were the drop not a perfect conductor and instead more conducting than its surroundings, the conical ends are destabilized at a finite value of the tip curvature and the instability engenders tip-streaming where fine jets issue from the conical tips (Collins et al. 2008, 2013). However, if the surroundings were more conducting, permittive, and viscous than the drop, the drop deforms into an oblate shape and adopts a lenticular profile at high field strengths (Brosseau and Vlahovska 2017, Wagoner et al. 2020, Marin 2020). At the incipience of instability, the equatorial cross section of the drop superficially resembles a wedge. In this talk, we examine the physics of the destabilization of the wedge and the equatorial streaming---the emission of a liquid sheet---from the unstable drop.