Nonlinear dynamics of the interface of dielectric liquids in a strong electric field: Reduced equations of motion

摘要

The evolution of the interface between two ideal dielectric liquids in astrong vertical electric field is studied. It is found that a particular flowregime, for which the velocity potential and the electric field potential arelinearly dependent functions, is possible if the ratio of the permittivities ofliquids is inversely proportional to the ratio of their densities. Thecorresponding reduced equations for interface motion are derived. In the limitof small density ratio, these equations coincide with the well-known equationsdescribing the Laplacian growth.