Transient Electrical Response Beyond Quasistatic Capacitance at Mechanically Excited Droplet--Dielectric Interfaces

Abstract

Dynamic electrowetting of conducting droplets under mechanical deformation is conventionally modeled as a quasi-static variable-capacitance system, in which the electrical response is assumed to be governed solely by the evolution of the droplet--electrode contact area. Under the assumption of instantaneous charge equilibration, this framework successfully describes the cyclic steady-state electromechanical response of the system. However, its validity for transient interfacial electrical dynamics remains largely unexplored. Here, the transient electrowetting response of mercury droplets confined between a polymeric dielectric-coated electrode (PTFE or PVDF) and an opposing copper electrode is investigated under periodic mechanical excitation with multiple waveforms at 2 Hz. The measured contact area and corresponding capacitance evolve closely as predicted from instantaneous surface-energy minimization, confirming that the liquid-interface mechanics remain quasi-static. In contrast, the measured transient current and instantaneous electrical power exhibit pronounced asymmetric excitation and relaxation phases that are independent of the excitation waveform, demonstrating that transient charge evolution cannot be inferred from the instantaneous geometric capacitance alone. This transient behavior is phenomenologically interpreted using constituent first-order interfacial dielectric charge-relaxation kinetics, indicating that the measured current arises from slow dielectric charging followed by dielectric relaxation over the timescale of the imposed periodic mechanical oscillations during discharging. These findings establish that transient electrowetting is governed by the coupled interplay of droplet electrohydrodynamics and dielectric interfacial polarization, requiring a constitutive description beyond quasi-static variable-capacitance models based solely on contact-line dynamics.