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Weakly conducting dielectric liquid drops suspended in another dielectricliquid and subject to an applied uniform electric field exhibit a wide range ofdynamical behaviors contingent on field strength and material properties. Thesephenomena are best described by the Melcher-Taylor leaky dielectric model,which hypothesizes charge accumulation on the drop-fluid interface andprescribes a balance between charge relaxation, the jump in Ohmic currents fromthe bulk and charge convection by the interfacial fluid flow. Most previousnumerical simulations based on this model have either neglected interfacialcharge convection or restricted themselves to axisymmetric drops. In this work,we develop a three-dimensional boundary element method for the complete leakydielectric model to systematically study the deformation and dynamics of liquiddrops in electric fields. The inclusion of charge convection in our simulationspermits us to investigate drops in the Quincke regime, in which experimentshave demonstrated a symmetry-breaking bifurcation leading to steadyelectrorotation. Our simulation results show excellent agreement with existingexperimental data and small-deformation theories.

Electrohydrodynamics of viscous drops in strong electric fields: Numerical simulations