(560f) Electrohydrodynamics of a Viscous Drop with and without Inertia

In this talk we present our recent work on electrohydrodynamics of a viscous drop in an external electric field. In the first half we present work on spheroidal modeling of a surfactant-laden viscous drop under an electric field in the Stokes flow regime. In the second half we present numerical results from a recent study of the inertia effects on the electro-deformation of a viscous drop under a DC electric field using a novel second-order immersed interface method. The inertia effects are quantified by the Ohnesorge number $Oh$, and the electric field is characterized by an electric capillary number $Ca_E$. Below the critical $Ca_E$, small to moderate electric field strength gives rise to steady equilibrium drop shapes. We found that, at a fixed $Ca_E$, inertia effects induce larger deformation for an oblate drop than a prolate drop, consistent with previous results in the literature. Moreover, our simulations results indicate that inertia effects on the equilibrium drop deformation are dictated by the direction of normal electric stress on the drop interface: Larger drop deformation is found when the normal electric stress points outward, and smaller drop deformation is found otherwise. To our knowledge, such inertia effects on the equilibrium drop deformation has not been reported in the literature.

Above the critical $Ca_E$, no steady equilibrium drop deformation can be found, and often the drop breaks up into a number of daughter droplets. In particular our Navier-Stokes simulations show that, for the parameters we use, (1) daughter droplets are larger in the presence of inertia, (2) the drop deformation evolves more rapidly compared to creeping flow, and (3) complex distribution of electric stresses for drops with inertia effects.
Our results suggest that normal electric pressure may be a useful tool in predicting drop pinch-off in oblate deformations.