On the physical regularities of the instability of charged spheroidal droplets

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Abstract

Asymptotic methods study the conditions for the implementation of electrostatic instability of oscillating highly charged flattened and elongated spheroidal droplets depending on the values of their eccentricities. It turned out that the electrostatic stability of the flattened spheroidal droplet with respect to axisymmetric deformations increases with an increase in eccentricity, and the elongated spheroidal droplet decreases. It is shown that the electrostatic instability of the flattened charged droplet itself is realized at its equator, where the surface density of the charge reaches the maximum value, and for the elongated droplet at its vertices.

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About the authors

A. I. Grigoriev

Ishlinsky Institute for Problems in Mechanics of the RAS

Author for correspondence.
Email: grigorai@mail.ru
Russian Federation, Moscow

S. O. Shiryaeva

Yaroslavl State University named after P.G. Demidov

Email: shir@uniyar.ac.ru
Russian Federation, Yaroslavl

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2. Fig. 1. Graph of the dependence of the dimensionless surface density of the proper electric charge on a spheroidal drop of an incompressible conductive liquid on the value of its eccentricity e and its polar angle: a flattened drop; b elongated drop.

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