Dynamics of charged drop break-up

The nonlinear axisymmetric dynamics of an inviscid, charged drop near the Rayleigh limit were analyzed asymptotically. The dynamics of drop break-up are described based on the amplitude, initial drop shape deformation, and the net charge. Spheres with charges less than the Rayleigh limit were found to be unstable when the initial deformation was large enough to drive the motion beyond the separatrix surrounding the stable center. This precise criterion for drop instability corresponds directly to the estimate used to determine the Bohr-Wheeler saddle shape with the same amount of charge as the 'energy barrier' for fission of the drop. The result implies that instability of the spherical drop is initiated by a shape deformation substantially smaller than predicted using an unstable prolate form as the energy barrier. The drop shapes in the prolate and oblate families were calculated using finite-element methods. Asymptotic analysis of the static shapes was in good agreement with the numerical calculations for moderate amplitude and high-amplitude drop deformations.