Two-stage dynamics of droplet oscillation under alternating-current electrowetting-on-dielectric

The canonical view in alternating-current electrowetting-on-dielectric (AC EWOD) holds that droplets oscillate at twice the driving frequency (the frequency of the applied voltage). Here, we show that this doubling relationship persists only over a certain frequency range. We developed an ultrahigh-speed electrowetting-on-dielectric imaging system with an order-adaptive Fourier fitting method that enables accurate, noise-robust contact-angle extraction at high frequencies. Experiments reveal two stages of droplet dynamics in both time and frequency domains. In the time domain, the droplet transitions from irregular deformation to a stable, periodic oscillation dominated by a single frequency, with the transition time governed by inertia. In the frequency domain, the dominant frequency is strictly at twice the applied frequency below a threshold, but becomes irregular once the applied frequency exceeds that threshold. The threshold increases with applied amplitude and is insensitive to waveform, which is explained by a spectral analysis on the electrowetting driving force. These findings provide new insight into droplet oscillation and control under AC-EWOD.