Coalescence induced self-propulsion of droplets on superomniphobic surfaces.

We utilized superomniphobic surfaces to systematically investigate the different regimes of coalescence-induced self-propulsion of liquid droplets with a wide range of droplet radii, viscosities and surface tensions. Our results indicate that for all the liquids studied, the transition from the inertial-capillary regime to the visco-capillary regime occurs over a narrow range of Ohnesorge number \textit{Oh} $\approx $ 0.02 to 0.05. The non-dimensional jumping velocity $V_{j}^{\ast }$ is nearly constant ($V_{j}^{\ast }$ $\approx $ 0.2) in the inertial-capillary regime and decreases in the visco-capillary regime as the Ohnesorge number \textit{Oh} increases, in agreement with prior work. Within the visco-capillary regime, decreasing the droplet radius $R_{0}$ results in a more rapid decrease in the non-dimensional jumping velocity $V_{j}^{\ast }$ compared to increasing the viscosity $\mu $. This is because decreasing the droplet radius $R_{0}$ increases the inertial-capillary velocity $V_{ic}$ in addition to increasing the Ohnesorge number \textit{Oh}.