Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Aug;88(2):023014. doi: 10.1103/PhysRevE.88.023014. Epub 2013 Aug 14.

Formation of curvature singularities on the interface between dielectric liquids in a strong vertical electric field.

Physical review. E, Statistical, nonlinear, and soft matter physics

Evgeny A Kochurin, Nikolay M Zubarev, Olga V Zubareva

PMID: 24032931 DOI: 10.1103/PhysRevE.88.023014

Abstract

The nonlinear dynamics of the interface between two deep dielectric fluids in the presence of a vertical electric field is studied. We consider the limit of a strong external electric field where electrostatic forces dominate over gravitational and capillary forces. The nonlinear integrodifferential equations for the interface motion are derived under the assumption of small interfacial slopes. It is shown in the framework of these equations that, in the generic case, the instability development leads to the formation of root singularities at the interface in a finite time. The interfacial curvature becomes infinite at singular points, while the slope angles remain relatively small. The curvature is negative in the vicinity of singularities if the ratio of the permittivities of the fluids exceeds the inverse ratio of their densities, and it is positive in the opposite case (we consider that the lower fluid is heavier than the upper one). In the intermediate case, the interface evolution equations describe the formation and sharpening of dimples at the interface. The results obtained are applicable for the description of the instability of the interface between two magnetic fluids in a vertical magnetic field.

Publication Types

• Journal Article
• Research Support, Non-U.S. Gov't