Shape evolution of compound droplet in combined presence of electric field and extensional flow

Studies on compound droplet are of emerging importance in biology and engineering. Here, we bring out unique morphodynamics of a compound droplet as a consequence of interplay between an imposed electric field and an extensional flow. As compared to the deformation characteristics of compound droplet reported in the sole presence of extensional flow [Stone and Leal, J. Fluid Mech. 211, 123 (1990)], our results implicate several nonintuitive findings on the dynamical evolution of the droplet. These exclusive new features include the interconversion of shape-evolution patterns of the compound droplet system contingent on the strength of background flow, electric field strength, electrophysical properties, and hitherto-unveiled post-breakup dynamics. Depending on these key parameters, in addition to three steady-state configurations, two new modes of droplet pinch-off are observed: Mode I: polar pinch-off; Mode II: equatorial pinch-off. Interestingly, the pinch-off time is found to vary nonmonotonically with the strength of the electric field. In sharp contrast to the extensional viscosity of a compound droplet in absence of other external fields [Stone and Leal, J. Fluid Mech. 211, 123 (1990)], we show that the additional presence of electric field brings in an intricate dependence on the electrical properties of the inner droplet; a paradigm that is not prevalent in pure extensional flow.