Drop and Bubble Deformation in an Electric Field

A steady problem of drop (bubble) shape in a uniform electric field is considered when the drop and the surrounding medium are immiscible. The electric-charge transport includes both the ohmic current across the interphase boundary and convective transport over the interface. If there is no convective transport, the drop (bubble) may be transformed into either an elongated or a flattened spheroid. Under these conditions, the sign of the deformation remains unchanged for arbitrary values of the problem parameters. Convective charge transport along the surface initiates additional motion in both the drop and the surrounding medium. However, with increase in the convective-transport intensity the deformed drops display different behavior. The compression of a flattened drop slows and, under certain conditions, compression is replaced by extension. However, an elongated spheroid cannot be transformed into a flattened spheroid. The calculations were performed under the assumption that the drop is convex. It was found that, for both an elongated and a flattened drop, the maximum ratio of the major and minor spheroid axes is 2:1. In experiments with oils, the possibility of both a decrease in the drop compression rate and deformation sign reversal was demonstrated.