Predicting and controlling droplet splashing is important for industrial applications such as inkjet printing and spray coating. Two dimensionless parameters, the capillary number Ca and the splashing parameter K, are typically used to explain splashing behavior. But those dimensionless numbers only describe the approaching droplet—including its size, viscosity, surface tension, and speed—and not its interaction with the impinged upon surface. Previous research has investigated the role of surface wettability on splashing by looking at static and dynamic contact angles, but a universal criterion that can predict splashing has so far remained elusive.
Through a systematic study of impacting droplets, Miguel Quetzeri-Santiago and Rafael Castrejon-Pita at Queen Mary University of London and their collaborators at Cardiff and Oxford Universities have identified two other parameters that, unlike Ca and K, can predict whether a droplet will splash. The first parameter is the contact angle, which has also been investigated in previous studies. Using a high-speed camera, the researchers recorded the impacts of three types of droplets—water, ethanol, and aqueous glycerol—on surfaces ranging from hydrophilic to superhydrophobic. The images, taken at 23 000 frames per second, showed both static and dynamic contact angles.
The researchers then looked at whether the contact angle, in conjunction with either Ca or K, could predict the onset of splashing. As shown in the left plot for Ca and the maximum dynamic contact angle θmax, combining those variables separated droplets that splashed (empty symbols) from those that did not (filled symbols). But the boundaries were not the same for the different liquids.
For their second parameter, the researchers turned to the splashing ratio, β. As an impacting droplet spreads, the leading edge of the thin liquid sheet that forms during the expansion lifts off the surface. Unlike Ca and K, β depends on the angle of that lifting.
Plotting the data in terms of β and θmax, as shown in the right plot, effectively divided the data into splashing and nonsplashing regions with a boundary that was not liquid dependent. The data deviate from the previously reported splashing threshold (dashed line) for β at larger values of θmax because that is where the effect of wettability on splashing becomes more important. (M. A. Quetzeri-Santiago et al., Phys. Rev. Lett. 122, 228001, 2019.)