SymmetryBreaking Bifurcations of Charged Drops
 Marco A. Fontelos,
 Avner Friedman
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It has been observed experimentally that an electrically charged spherical drop of a conducting fluid becomes nonspherical (in fact, a spheroid) when a dimensionless number X inversely proportional to the surface tension coefficient γ is larger than some critical value (i.e., when γ<γ_{ c }). In this paper we prove that bifurcation branches of nonspherical shapes originate from each of a sequence of surfacetension coefficients ), where γ_{2}=γ_{ c }. We further prove that the spherical drop is stable for any γ>γ_{2}, that is, the solution to the system of fluid equations coupled with the equation for the electrostatic potential created by the charged drop converges to the spherical solution as tρ∞ provided the initial drop is nearly spherical. We finally show that the part of the bifurcation branch at γ=γ_{2} which gives rise to oblate spheroids is linearly stable, whereas the part of the branch corresponding to prolate spheroids is linearly unstable.
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 Title
 SymmetryBreaking Bifurcations of Charged Drops
 Journal

Archive for Rational Mechanics and Analysis
Volume 172, Issue 2 , pp 267294
 Cover Date
 20040501
 DOI
 10.1007/s002050030298x
 Print ISSN
 00039527
 Online ISSN
 14320673
 Publisher
 SpringerVerlag
 Additional Links
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 Authors

 Marco A. Fontelos ^{(1)}
 Avner Friedman ^{(2)}
 Author Affiliations

 1. Departamento de Matemática Aplicada, Universidad Rey Juan Carlos, C/ Tulipán S/N, 28933Móstoles, Madrid, Spain
 2. Department of Mathematics, The Ohio State University, 231 18th Ave, W Columbus, OH 43210, U.S.A