Jumping number in the droplet jumping by resonant AC electrowetting

The droplet jumping by resonant AC electrowetting (DJ-RACE) is recently introduced to transport droplets to vertical direction, whereby three-dimensional digital microfluidics are envisioned. In DJ-RACE, the central mechanism of the droplet jumping is the conversion of the surface energy stored by resonant AC electrowetting to the kinetic energy for jumping. Here, we newly introduce the jumping number ($J_{u}$=\textit{$\gamma $/$\rho $gR}$^{2})$, measuring the energy conversion in the jumping process and, thus, the feasibility of droplet jumping. $J_{u}$ interprets that droplets having higher $J_{u}$ can make higher and easier jumping, and smaller and lighter droplets with higher surface tension can have higher $J_{u}$. Practically, $J_{u}$ should be greater than 1.5 for the droplet jumping, and active jumping was observed when $J_{u}$ is greater than 5. In addition, $J_{u}$ can predict the effect of diverse physicochemical changes in a system such as enzymatic additives or impurities on jumping, where it can also provide diverse strategies to compensate these changes. The newly introduced $J_{u}$ could be the fundamental and useful parameter in the three-dimensional digital microfluidic devices based on DJ-RACE.