Influence of surface viscosities on the electrodeformation of a prolate viscous drop.

Contaminants and other agents are often present at the interface between two fluids, giving rise to rheological properties such as surface shear and dilatational viscosities. The dynamics of viscous drops with interfacial viscosities has attracted greater interest in recent years, due to the influence of surface rheology on deformation and the surrounding flows. We investigate the effects of shear and dilatational viscosities on the electro-deformation of a viscous drop using the Taylor-Melcher leaky dielectric model. We use a large deformation analysis to derive an ordinary differential equation for the drop shape. Our model elucidates the contributions of each force to the overall deformation of the drop and reveals a rich range of dynamic behaviors that show the effects of surface viscosities and their dependence on rheological and electrical properties of the system. We also examine the physical mechanisms underlying the observed behaviors by analyzing the surface dilatation and surface deformation.

Electrohydrodynamics of a viscous drop with inertia.

Most of the existing numerical and theoretical investigations on the electrohydrodynamics of a viscous drop have focused on the creeping Stokes flow regime, where nonlinear inertia effects are neglected. In this work we study the inertia effects on the electrodeformation 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.

Equilibrium electrodeformation of a spheroidal vesicle in an ac electric field.

In this work, we develop a theoretical model to explain the equilibrium spheroidal deformation of a giant unilamellar vesicle (GUV) under an alternating (ac) electric field. Suspended in a leaky dielectric fluid, the vesicle membrane is modeled as a thin capacitive spheroidal shell. The equilibrium vesicle shape results from the balance between mechanical forces from the viscous fluid, the restoring elastic membrane forces, and the externally imposed electric forces. Our spheroidal model predicts a deformation-dependent transmembrane potential, and is able to capture large deformation of a vesicle under an electric field. A detailed comparison against both experiments and small-deformation (quasispherical) theory showed that the spheroidal model gives better agreement with experiments in terms of the dependence on fluid conductivity ratio, permittivity ratio, vesicle size, electric field strength, and frequency. The spheroidal model also allows for an asymptotic analysis on the crossover frequency where the equilibrium vesicle shape crosses over between prolate and oblate shapes. Comparisons show that the spheroidal model gives better agreement with experimental observations.