Shape and stability of electrostatically levitated drops

Abstract

Abstract An electrically conducting drop held together by surface tension is statically levitated in an insulating medium by accumulating a net charge on its surface and applying a d. c. field in the direction of gravity. Asymptotic analysis for small electric fields shows the coupling at O(E30) between the second and third Legendre functions that describe the characteristic three-lobed drop shapes. Drops with large deformations are calculated by a Galerkin finite element scheme that leads to simultaneous determination of shape stability. The locus of Q̃ and Ẽ0 marking the loss of existence of static drops is determined; end points corresponding to no field (Ẽ0 = 0) and no charge (Q̃ = 0) agree well with calculations of Rayleigh and Taylor, respectively. Shapes predicted by the perturbation analysis are within two percent of the finite element calculations for almost the entire accessible ranges of Q̃ and Ẽ0.