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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 196, Number 3, Pages 503–516
DOI: https://doi.org/10.4213/tmf9464 (Mi tmf9464) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Construction of exact solutions for equilibrium configurations of the boundary of a conducting liquid deformed by an external electric field

N. M. Zubarevab, O. V. Zubarevaa

a Institute for Electrophysics, Urals Branch, RAS, Ekaterinburg, Russia
b Lebedev Physical Institute, RAS, Moscow, Russia
Full-text PDF (461 kB) Citations (1)
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DOI: https://doi.org/10.4213/tmf9464
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.
Keywords: equilibrium configuration, exact solution, free surface, conductive fluid, surface tension, electrostatic force, conformal map method.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0389-2015-0023
2
11
Russian Foundation for Basic Research 16-08-00228
17-08-00430
Ural Branch of the Russian Academy of Sciences 18-2-2-15
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).
Received: 18.09.2017
English version:
Theoretical and Mathematical Physics, 2018, Volume 196, Issue 3, Pages 1380–1391
DOI: https://doi.org/10.1134/S0040577918090106
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: N. M. Zubarev, O. V. Zubareva, “Construction of exact solutions for equilibrium configurations of the boundary of a conducting liquid deformed by an external electric field”, TMF, 196:3 (2018), 503–516; Theoret. and Math. Phys., 196:3 (2018), 1380–1391
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9464
  • https://doi.org/10.4213/tmf9464
  • https://www.mathnet.ru/eng/tmf/v196/i3/p503
    • This publication is cited in the following 1 articles:
    1. O. V. Zubareva, N. B. Volkov, N. M. Zubarev, “Equilibrium configurations of an uncharged liquid jet in a transverse electric field: conditions for existence”, Interfacial Phenom. Heat Transf., 9:2 (2021), 1–13  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:36
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