Abstract
In a two-dimensional plane-symmetric formulation, we consider the problem of the equilibrium configurations of the free surface of a conducting capillary liquid placed in an external electric field. We find a one-parameter family of exact solutions of the problem according to which the fluid takes the shape of a blade. Such a configuration provides formally unlimited local field amplification: the field strength is maximum at the edge of the blade and drops to zero at the periphery. For a given potential difference between the liquid and the flat electrode located above it, we find threshold values of the electric field strength at the edge of the liquid blade, the radius of curvature of the edge, and the distance from the edge to the electrode limiting the region of existence of the solutions.
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This research was performed in the framework of the theme of state assignment No. 0389-2015-0023 with support by the Russian Foundation for Basic Research (Project Nos. 16-08-00228 and 17-08-00430), the Presidium of the Russian Academy of Sciences (Programs 2 and 11), and the Presidium of the Ural Branch, RAS (Project No. 18-2-2-15).
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 196, No. 3, pp. 503–516, September, 2018.
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Zubarev, N.M., Zubareva, O.V. Construction of Exact Solutions for Equilibrium Configurations of the Boundary of a Conducting Liquid Deformed By an External Electric Field. Theor Math Phys 196, 1380–1391 (2018). https://doi.org/10.1134/S0040577918090106
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DOI: https://doi.org/10.1134/S0040577918090106