Electrically modulated relaxation dynamics of pre-stretched droplets post switched-off uniaxial extensional flow

Droplets are known to elongate in extensional flow and exhibit capillary instabilities following flow cessation. Under several practical scenarios, where the deformed drops are exposed to electrified environments, the interplay between capillary and electric forces can further modulate the capillary-driven instability that may lead to novel drop evolution, which has not yet been explored. In the present study, we probe the transient droplet deformation under combined electrohydrodynamic and extensional flows, with a particular focus on the relaxation dynamics in a post-elongation phase, as the external flow field is withdrawn while the electric field remains on. Based on pre-relaxed droplet morphology and electric field strength, the drops appear to relax faster or slower, leading to a steady-state or a plethora of breakup events. The slightly deformed drops relax into stable prolate or oblate shape depending on the electrophysical properties of the fluid pairs. On the other hand, under large deformation limit, our results reveal that in the post-elongation phase, the electric field may either stabilize the droplet or may enforce its breakup primarily via two modes: mid-pinching and end-pinching. We have shown that the post-relaxation events can be mapped into the relevant parametric phase space as a function of the relative strengths of the various forcing parameters as well as geometric parameters. These results present new avenues of droplet manipulation in industrial and microfluidic applications by utilizing unique connectivity between the relaxation kinematics and imposed electrical forcing, a paradigm that has hitherto remained unaddressed.