Transient Deformation and Charge Evolution during Alternating Current-Electrohydrodynamic Oscillations of Confined Droplets

This study investigates the transient electrohydrodynamic behavior of a confined, neutrally buoyant droplet subjected to a cyclic electric field, focusing on the coupled evolution of interfacial charge, deformation, and flow. Both the droplet and the surrounding medium are modeled as Newtonian, immiscible leaky-dielectric fluids under creeping-flow and small-deformation conditions. Confinement is shown to significantly dampen droplet oscillations by enhancing viscous dissipation in thin fluid gaps, restricting internal and external circulation, and increasing hydrodynamic resistance that opposes electrically induced Maxwell stresses. The transient response is decomposed into mean and time-periodic components to examine two conductivity configurations, in which the droplet is either more or less conductive than the surrounding medium. The effects of confinement ratio, oscillation frequency, and electrical property contrasts are systematically analyzed to quantify their influence on deformation amplitude, flow-field strength, and interfacial stress balance. Increasing the confinement suppresses time-dependent deformation by limiting flow development and amplifying viscous resistance, leading to a marked reduction in oscillation amplitude. The role of the relaxation frequency in governing the electrical response is examined by distinguishing conduction- and displacement-dominated regimes. At low frequencies, rapid charge relaxation promotes strong interfacial charge accumulation and enhanced electrohydrodynamic forcing, resulting in pronounced deformation and circulation. At higher frequencies, displacement currents dominate, interfacial charge weakens, and both deformation and flow are attenuated, particularly under confinement. Phase lags between the applied electric field, interfacial charge, and electric fields inside and outside the droplet are quantified and shown to depend on confinement, fluid properties, and excitation frequency. The results provide physical insight into frequency-dependent electrohydrodynamic droplet dynamics in confined environments relevant to microfluidic and droplet-based technologies.