Electrohydrodynamics of drops in strong uniform dc electric fields

Abstract

Drop deformation in an uniform dc electric field is a classic problem. The pioneering work of Taylor demonstrated that for weakly conducting media, the drop fluid undergoes a toroidal flow and the drop adopts a prolate or oblate spheroidal shape, the flow and shape being axisymmetrically aligned with the applied field. However, recent studies have revealed a nonaxisymmetric rotational flow in strong fields, similar to the rotation of solid dielectric particles observed by Quincke in the 19th century. We present a systematic experimental study of this phenomenon, which highlights the importance of charge convection along the drop surface. The critical electric field, drop inclination angle, and rate of rotation are measured. We find that for small, high viscosity drops, the threshold field strength is well approximated by the Quincke rotation criterion. Reducing the viscosity ratio shifts the onset for rotation to stronger fields. The drop inclination angle increases with field strength. The rotation rate is approximately given by the inverse Maxwell–Wagner polarization time. Novel features are also observed such as a hysteresis in the tilt angle for large low-viscosity drops.