Transient dynamics and stability of Newtonian and viscoelastic sessile droplets under a uniform electric field

The electrohydrodynamic (EHD) deformation of Newtonian and viscoelastic sessile droplets under a uniform electric field is investigated through finite-volume simulations based on a Volume-of-Fluid formulation with adaptive mesh refinement. The study focuses on the subcritical regime, characterized by bounded oscillatory deformations reaching a steady state, and on the transition to the supercritical regime, where the interface becomes unstable and may lead to breakup. The dynamics is governed by the competition between electric, capillary, viscous, and elastic stresses. The results indicate that increasing the Ohnesorge number, reflecting the relative importance of viscous effects compared to inertial and capillary forces, from 0.1 to 10 strongly damps oscillations and shifts the instability threshold toward higher electric forcing, with variations of approximately 10% in the critical electric capillary number over the investigated Ohnesorge-number range. Viscoelasticity introduces an additional relaxation timescale that enhances oscillation amplitudes and delays relaxation, but does not significantly modify either the steady-state deformation or the instability threshold. Conductive droplets exhibit larger deformations than dielectric ones due to interfacial charge accumulation. These findings provide a quantitative characterization of the distinct roles of viscous dissipation and elastic stress in governing droplet dynamics and stability.