Electrowetting-induced parametric instability of a merged micro-droplet

Numerical simulations are employed to investigate the electrowetting-induced parametric instability in merged micro-droplets. By subjecting two merged droplets to an alternating current voltage (AC voltage) in open electrowetting-on-dielectric microfluidics, we observe the triggering of parametric instability at specific frequencies and amplitudes, manifesting as periodic lateral and upper waves. The work aims to delineate the characteristics and onset conditions of this instability in electrowetting devices. Notably, the droplet assumes a star-like shape due to the lateral wave formation, with both lateral and upper waves sharing the same oscillating frequency and being sub-harmonic to the driving frequency. The dispersion relation for resonance mode is enhanced with a modification parameter. The modified phase diagram, derived from parametric theorem, aligns well with numerical results for various cases. The interplay between lateral and upper waves is theoretically analyzed using the theory of Dong et al. for star-shaped liquid puddles. Our study reveals that low aspect ratio droplets may not exhibit parametric instability despite excitation parameters aligning with phase diagram predictions. Geometric constraints and surface tension play a limiting role in the activation of sub-harmonic modes. This study has implications for optimizing droplet shape and size in electrowetting-based devices to manage parametric instabilities, potentially leading to more efficient and reliable designs.