Disintegration of Water Drops in an Electric Field

TLDR: In this article, it was shown that a conical interface between two fluids can exist in equilibrium in an electric field, but only when the cone has a semi-vertical angle 49.3$^\circ$.

Abstract: The disintegration of drops in strong electric fields is believed to play an important part in the formation of thunderstorms, at least in those parts of them where no ice crystals are present. Zeleny showed experimentally that disintegration begins as a hydrodynamical instability, but his ideas about the mechanics of the situation rest on the implicit assumption that instability occurs when the internal pressure is the same as that outside the drop. It is shown that this assumption is false and that instability of an elongated drop would not occur unless a pressure difference existed. When this error is corrected it is found that a drop, elongated by an electric field, becomes unstable when its length is 1.9 times its equatorial diameter, and the calculated critical electric field agrees with laboratory experiments to within 1%. When the drop becomes unstable the ends develop obtuse-angled conical points from which axial jets are projected but the stability calculations give no indication of the mechanics of this process. It is shown theoretically that a conical interface between two fluids can exist in equilibrium in an electric field, but only when the cone has a semi-vertical angle 49.3$^\circ$. Apparatus was constructed for producing the necessary field, and photographs show that conical oil/water interfaces and soap films can be produced at the caloulated voltage and that their semi-vertical angles are very close to 49.3$^\circ$. The photographs give an indication of how the axial jets are produced but no complete analytical description of the process is attempted.