Mono-emulsion droplet stretching under direct current electric field

We study the mechanism of stretching and breaking of a mono-emulsion droplet under a direct current electric field using theoretical and experimental approaches aided by numerical simulation. Axisymmetric straining flow driven by an electric field results in the equilibrium deformation of the droplet along the direction of the electric field if the electric capillary number Ca-e that is the ratio of electric stresses to capillary stresses, is less than a critical value (Ca-e)(crit). At (Ca-e)(crit), the droplet breaks either before showing the slow deformation stage or rapidly. Furthermore, we developed a theoretical model to understand the mechanism of the transition from equilibrium deformation to non-equilibrium breaking. The Ca-e that can induce Taylor's deformation D = (alpha = beta)/(alpha + beta) approximate to 0.295; where a and b are the lengths of semi-major and semi-minor axes of the droplet, corresponds to (Ca-e) crit. At this stage, the maximum flow velocity shifts to the outside of the droplet along the electric field direction and large electric stresses are mainly concentrated at the droplet's side apex causing daughter droplet ejection. Finally, we compare the values of (Ca-e) crit obtained from the theoretical model ((Ca-e)(crit) approximate to 0.25) for which the conductivity ratio (R) between the droplet and ambient liquid i.e., R similar to O(10) with our experimental results ((Ca-e)(crit) approximate to 0.245) and realize that (Ca-e)(crit) decreases as R increases. We also observe that even though the viscosity ratio can alter the emulsion breakup modes, it has no effect on (Ca-e)(crit) for the onset of breaking.