Studies in Electrohydrodynamics. I. The Circulation Produced in a Drop by Electrical Field

TLDR: In this article, it is shown that equilibrium can only be established in a drop when circulations are set up both in the drop and its surroundings, and the streamlines of the circulation for this case are shown and criteria are given for distinguishing between circulations which carry the surface of the drop towards or away from the poles and for predicting whether the drop will become prolate or oblate.

Abstract: The elongation of a drop of one dielectric fluid in another owing to the imposition of an electric field has previously been studied assuming that the interface is uncharged and the fluids at rest. For a steady field this is unrealistic, because however small the conductivity of either fluid the charge associated with steady currents must accumulate at the interface till the steady state is established. It is shown that equilibrium can only be established in a drop when circulations are set up both in the drop and its surroundings. A relation is found between the ratios of the conductivity, viscosity and dielectric constant for the drop and surrounding fluid which permits the drop to remain spherical when subjected to a uniform field. The streamlines of the circulation for this case are shown and criteria are given for distinguishing between circulations which carry the surface of the drop towards or away from the poles and for predicting whether the drop will become prolate or oblate. Experiments by S. G. Mason and his co-workers are compared with the theoretical predictions and agreement is found in all cases for which the necessary data are given.