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 Cae that is the ratio of electric stresses to capillary stresses, is less than a critical value (Cae)crit. At (Cae)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 Cae that can induce Taylor's deformation D = (α − β)/(α + β) ≈ 0.295; where α and β are the lengths of semi-major and semi-minor axes of the droplet, corresponds to (Cae)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 (Cae)crit obtained from the theoretical model ((Cae)crit ≈ 0.25) for which the conductivity ratio (R) between the droplet and ambient liquid i.e., R ∼ O(10) with our experimental results ((Cae)crit ≈ 0.245) and realize that (Cae)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 (Cae)crit for the onset of breaking.