Catastrophic Drop Breakup in Electric Field

We report novel observations revealing the catastrophic breakup of water drops containing surfactant molecules, which are suspended in oil and subjected to an electric field of strength ∼10<sup>5</sup> V/m. The observed breakup was distinctly different from the gradual end pinch-off or tip-streaming modes reported earlier in the literature. There was no observable characteristic deformation of the drop prior to breakup. The time scales involved in the breakup and the resultant droplet sizes were much smaller in the phenomenon observed by us. We hypothesize that this mode of drop breakup is obtained by the combined effect of an external electric field that imposes tensile stresses on the surface of the drop, and characteristic stress−strain behavior for tensile deformation exhibited by the liquid drop in the presence of a suitable surfactant, which not only lowers the interfacial tension (and hence the cohesive strength) of the drop but also simultaneously renders the interface nonductile or brittle at high enough concentration. We have identified the relevant thermodynamic parameter, viz., the sum of interfacial tension, σ, and the Gibbs elasticity, ε, which plays a decisive role in determining the mode of drop breakup. The parameter (ε + σ) represents the internal restoration stress of a liquid drop opposing rapid, short-time-scale perturbations or local deformations in the drop shape under the influence of external impulses or stresses. A thermodynamic “state” diagram of (ε + σ) versus interfacial area per surfactant molecule adsorbed at the drop interface shows a “maximum” at a critical transition concentration (ctc). Below this concentration of the surfactant, the drop undergoes tip streaming or pinch off. Above this concentration, the drop may undergo catastrophic disintegration if the external stress is high enough to overcome the ultimate cohesive strength of the drop’s interface.