Shape and stability of electrostatically levitated drops

An investigation is presented of the shape and stability of an electrically conducting drop held together by surface tension and statically levitated in an insulating medium by accumulating a net charge on its surface and applying a dc field in the direction of gravity. Asymptotic analysis for small electric fields is used to show the coupling at O(E sub 0, super 3) between the second and third Legendre functions that describe the characteristic three-lobed drop shapes. A Galerkin finite element scheme is employed to calculate drops with large deformations, resulting in the simultaneous determination of shape stability. The locus of Q and E sub 0 are obtained which indicates the loss of existence of static drops. It is determined that the end points corresponding to no field and no charge agree well with the calculations of Rayleigh (1882) and Taylor (1964), respectively. Shapes predicted by the perturbation analysis are found to be within 2 percent of the finite element calculations for almost the entire accessible ranges of Q and E sub 0.