(214b) The Effects of Charge Relaxation and Charge Convection on Nonlinear Electrohydrodynamic Drop Deformation

We quantify the nonlinear transient deformation of a weakly conductive ("leaky dielectric") drop under the influence of a uniform DC electric field. An axisymmetric boundary integral method, which accounts for surface charge convection and a finite relaxation time scale over which the interface charges, is implemented to calculate the transient droplet deformation. The simulations show that as the time scale for interfacial charging increases, a shape transition from prolate (parallel to the applied field) to oblate (normal to the applied field) occurs at intermediate times. Our work identifies the scaling that characterizes the magnitude and duration of this transition. Additionally, convection of charge towards the equator of the drop is shown to weaken the steady oblate deformation as the applied field is increased. The numerical results are then compared with an experimental system consisting of a silicone oil droplet suspended in a castor oil medium. Although agreement is observed for moderate electric field strengths, the experiments exhibit an onset of rotation and three-dimensional flow as higher fields are attained.