Self-similar solutions for conic cusps formation at the surface of dielectric liquids in electric field.

The nonlinear dynamics is studied for the free surface of an ideal dielectric fluid in an electric field. Self-similar solutions of electrohydrodynamic equations describing the formation of surface conic cusps are revealed. The behavior of physical quantities (field strength, fluid velocity, and surface curvature) near the singularity is established. The threshold value of the fluid dielectric constant required for the proposed mechanism of a cusp development is found.