We investigate leaky dielectric droplet dynamics in a superposed electric field consisting of alternating and constant electric fields using both analytical and numerical approaches. In the present study, an analytical formulation is developed within the framework of small deformation theory to describe the mean and amplitude of the steady-state-time-periodic droplet deformation. In addition, a phase field interface tracking numerical method is employed to accurately capture the droplet interface evolution and to explore the parametric space governing the oscillatory response of the droplet subjected to the superposed electric field. The influence of the mixing ratio of the alternating and constant electric field components on both the mean deformation and oscillation amplitude is systematically examined. It is shown that the frequency of the mechanical response of the droplet is twice the frequency of the alternating electric field and corresponds to the base frequency of the superposed electric field. The droplet deformation exhibits a phase difference to the applied superposed electric field, and the effects of electrical relaxation and mechanical response on this phase difference are established. The dependence of mean droplet deformation on the mixing ratio is analyzed for low forcing frequencies and for frequencies at which surface charge polarization remains unaffected. The present work bridges droplet dynamics in alternating and constant electric fields and identifies conditions where superposed fields produce larger mean deformation and oscillation amplitude than a pure ac electric field.

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• Low Reynolds number flows
• Binary fluids
• Drops & bubbles