Electrohydrodynamics of cones on the surface of a liquid

Stationary structures formed on the surface of a liquid under the action of an electric field have been studied. With the use of the equations of electrohydrodynamics, it has been shown that cones are formed in a dynamic regime when the current of surface ions, which is induced by the tangential component of the electric field, dominates over the conductivity current in the bulk of a cone and the surface current induced by the flow of the liquid. The electric field strength both inside and outside the cone, as well as the velocity field inside the cone, has been determined. It has been shown that the angle of the cone depends on the current flowing on its surface. The characteristic size of the cone has been determined.