Growth of nonlinear structures on the interface between dielectric liquids in a strong vertical electric field

Abstract

Abstract Nonlinear dynamics of the interface between dielectric liquids exposed to a strong vertical electric field is studied. Two types of exact solutions for quadratically nonlinear equations of motion (periodic solutions involving a finite number of Fourier harmonics and spatially localized rational solutions) are analyzed. Description of the interfacial evolution reduces to solving a finite number of ordinary differential equations either on amplitudes of harmonics, or, through the analytical continuation into the complex plane from the interface, for the poles motion. The common property of the solutions is a tendency for the growth of interface perturbations in the direction of the liquid with a lower permittivity.