Abstract
With numerous applications prevailing in science and engineering, the dynamics of charged droplets coupled together via electrostatics is of great interest to many researchers. In this study, the liquid droplets are assumed to be inviscid, incompressible, and electrically conductive. The boundary integral method is used to solve the three Laplace equations governing the dynamics of the two axisymmetric, inviscid charged droplets (two for hydrodynamic problems with interior domains and one for the electrostatic problem with exterior domains). Time integration of the associated dynamical system is achieved by using the fourth order Runge-Kutta method. The present results suggest that the electrostatic interaction has only a localized effect on the motions of the two coupled droplets. Global analysis based upon Legendre modes may not be a meaningful approach in the current study. Consequently, some interesting aspects of the dynamics of two electrostatically coupled charged droplets are illustrated via various examples.
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