Brief Communications

Exact partial solutions for the surface dynamics of a dielectric liquid with a charged surface in the gravitational field

N. M. Zubarev^a, O. V. Zubareva^a, G. A. Ruev<sup>b

a</sup> Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, Ekaterinburg
^b Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We study the evolution of instability in the boundary of a perfect dielectric liquid with a free surface charge in an external electric field. Conformal variables are used to find exact partial solutions to the equations of motion for the case when the charge completely shields the field above the liquid, the electrostatic and gravitational forces being taken into account. The solutions describe the development of instability of the initially planar boundary until sharp dimples are formed on it.

Received: 24.10.2009

 English version: Technical Physics, 2010, 55:7, 1068–1070

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