Electrohydrodynamic flows inside a neutrally buoyant leaky dielectric drop

Abstract: We present for the first time an experimental investigation of electrohydrodynamic (EHD) flows within a neutrally buoyant drop with initial radius of 2.25 mm. Utilizing particle image velocimetry (PIV) and high-speed shadowgraphy, we measure the internal circulation and reported velocity profiles in the bulk and at the interface of the drop. Two leaky dielectric liquids, Silicone and Castor oils, are employed as the drop and external phase, allowing for the analysis of two shape configurations: oblate and prolate. The strength of the applied uniform electric field, $E_o$, spans from 0.125 to 1.75 kV/cm, enabling the analysis covering the small-deformation limit, where the leaky dielectric model (LDM) is applicable. Drops with larger deformations, for which no analytical velocity field is available, are also investigated. Our measurements show a good agreement with the LDM theory for the small-deformation cases. The flows begin at the interface as a result of jump in the electric stresses, leading then to four counter-rotating vortices inside the drop. At permanent regime, the analytical solutions adequately predicts the radial and tangential velocity components both in the bulk and at the interface of the drop. However, a nuanced behavior is noticed for larger deformations, where the LDM theory underpredicts the internal circulation. Moreover, due to the increased deformation, a non-uniform azimuthal profile is observed for the velocity at the interface. Transient measurements of this velocity component enlighten the dynamic response of the EHD flows of the drop. Following the currently available analytical solutions, the dynamic response is governed by the time-scale of its deformation. We propose a critical value of electric capillary number of roughly 0.1 below which the LDM adequately describes the velocity field in both quasi steady-state and transitory regimes.