Electric field-dependent scaling law for overdamped (di)electrowetting and dewetting on dielectric

Equilibrium droplet shape and transient dynamics during (di)electrowetting and dewetting on dielectric are electric field–dependent. We present a lubrication model incorporating the Young–Lippmann law that accurately predicts the equilibrium droplet shape and its transient dynamics. The droplet contact line position 𝑥𝑐⁢𝑙 follows a field-dependent power law 𝑥𝑐⁢𝑙∝𝑡ⁿ, where the magnitude of 𝑛 increases with the applied electric field. When the field strength equals the critical value required for complete wetting, the electrospreading dynamics reduce to the classical Tanner's law (𝑛=1/7), in agreement with past experiments. The magnitude of 𝑛 for electrodewetting is shown to be greater compared with wetting, attributed to a lesser viscous dissipation in the former case. Despite a difference in the power-law exponent 𝑛, the transient dynamics for both (di)electrowetting and electrodewetting are shown to follow the Cox–Voinov law. These observations qualitatively extend beyond the lubrication regime to large contact-angle droplets as well, as confirmed using Navier–Stokes simulations.