Breakup behavior of a conducting drop suspended in a viscous fluid subject to an electric field

Abstract

The slow axisymmetric deformation of a conducting drop surrounded by a viscous insulating fluid subject to a uniform electric field is considered. Numerical computations, based on a boundary integral formulation, are used to follow the behavior of relatively inviscid and viscous drops right up to breakup. The type of breakup seen depends on the ratio of the viscosity of the drop to that of the surrounding fluid, and on the electric field strength. The different types of breakup possible are small droplets being emitted from the ends of the drop with a charge greater than the Rayleigh limit, the formation of what appear to be pointed ends with the subsequent ejection of thin jet-like structures, or the formation of thin jet-like structures without the pointed ends. The different types of breakup are examined and the different regions of the parameter space where each occurs is determined. Also, by considering different stress balances, local equilibrium solutions that allow for a conical drop end are derived. Several sets of solutions, corresponding to different stress balances, are found. However, none of the conical end solutions appear to be compatible with the pointed ends seen in the numerical results.