Electrohydrodynamic Drop Deformation: Inertial Overshoot and Long-Time Tail

In 1966, GI Taylor introduced the Leaky Dielectric Model to explain the unexpected oblate deformation of a dielectric droplet suspended in a weakly conductive fluid under a DC electric field. In this poster, we extend Taylor’s calculation to quantify the transient deformation of a drop exposed to a suddenly imposed DC field. Previous analytical work has suggested that the drop deformation grows monotonically to Taylor's classic result, approaching steady-state with an exponentially decaying transient. However, we show that this is a consequence of the neglect of linear (or transient) fluid inertia, the inclusion of which (via the unsteady Stokes equations) leads to an overshoot in the deformation at intermediate times, in agreement with existing numerical simulations that utilize the full Navier-Stokes equations. Moreover, a long-time algebraic tail now describes the approach towards the steady deformation. Lastly, we present preliminary results for transient deformation of a linear viscoelastic droplet suspended in a Newtonian medium under an electric field.