Effect of a Surrounding Liquid Environment on the Electrical Disruption of Pendant Droplets

The effect of a surrounding, dielectric, liquid environment on the dynamics of a suddenly electrified liquid drop is investigated both numerically and experimentally. The onset of stability of the droplet is naturally dictated by a threshold value of the applied electric field. While below that threshold the droplet retains its integrity, reaching to a new equilibrium state through damped oscillations (subcritical regime), above it electrical disruption takes place (supercritical regime). In contrast to the oscillation regime, the dynamics of the electric droplet disruption in the supercritical regime reveals a variety of modes. Depending on the operating parameters and fluid properties, a drop in the supercritical regime may result in the well-known tip streaming mode (with and without whipping instability), in droplet splitting (splitting mode), or in the development of a steep shoulder at the elongating front of the droplet that expands radially in a sort of "splashing" (splashing mode). In both splitting and splashing modes, the sizes of the progeny droplets, generated after the breakup of the mother droplet, are comparable to that of the mother droplet. Furthermore, the development in the emission process of the shoulder leading to the splashing mode is described as a parametrical bifurcation, and the parameter governing that bifurcation has been identified. Physical analysis confirms the unexpected experimental finding that the viscosity of the dynamically active environment is absent in the governing parameter. However, the appearance of the splitting mode is determined by the viscosity of the outer environment, when that viscosity overcomes a certain large value. These facts point to the highly nonlinear character of the drop fission process as a function of the droplet volume, inner and outer liquid viscosities, and applied electric field. These observations may have direct implications in systems where precise control of the droplet size is critical, such as in analytical chemistry and "drop-on-demand" processes driven by electric fields.