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