Evolution of neutral and charged drops in an electric field

We study the evolution of drops of a very viscous and conducting fluid under the influence of an external electric field. The drops may be neutral or may be charged with some amount of electric charge. If both the external electric field and total drop charge are sufficiently small, then prolate spherical shapes develop according to Taylor’s observations. For sufficiently large charge and/or external field a selfsimilar cone-like singularity develops in a mechanism different from Taylor’s prediction. The opening semiangle of the cones both for uncharged and charged drops in a constant electric field is typically around 300.

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