Droplet Jumping: Effects of Droplet Size, Surface Structure, Pinning, and Liquid Properties

Coalescence-induced droplet jumping has the potential to enhance the efficiency of a plethora of applications. Although binary droplet jumping is quantitatively understood from energy and hydrodynamic perspectives, multiple aspects that affect jumping behavior, including droplet size mismatch, droplet-surface interaction, and condensate thermophysical properties, remain poorly understood. Here, we develop a visualization technique utilizing microdroplet dispensing to study droplet jumping dynamics on nanostructured superhydrophobic, hierarchical superhydrophobic, and hierarchical biphilic surfaces. We show that on the nanostructured superhydrophobic surface the jumping velocity follows inertial-capillary scaling with a dimensionless velocity of 0.26 and a jumping direction perpendicular to the substrate. A droplet mismatch phase diagram was developed showing that jumping is possible for droplet size mismatch up to 70%. On the hierarchical superhydrophobic surface, jumping behavior was dependent on the ratio between the droplet radius R-i and surface structure length scale L. For small droplets (R-i <= 5L), the jumping velocity was highly scattered, with a deviation of the jumping direction from the substrate normal as high as 80 degrees. Surface structure length scale effects were shown to vanish for large droplets (R-i > 5L). On the hierarchical biphilic surface, similar but more significant scattering of the jumping velocity and direction was observed. Droplet-size-dependent surface adhesion and pinning-mediated droplet rotation were responsible for the reduced jumping velocity and scattered jumping direction. Furthermore, droplet jumping studies of liquids with surface tensions as low as 38 mN/m were performed, further confirming the validity of inertial-capillary scaling for varying condensate fluids. Our work not only demonstrates a powerful platform to study droplet-droplet and droplet-surface interactions but provides insights into the role of fluid-substrate coupling as well as condensate properties during droplet jumping.