Binary Water Droplet Impact Dynamics on Flat and Micropillared Hydrophobic Substrates

We experimentally investigate the binary droplet impact dynamics on flat and square-micropillared hydrophobic polydimethylsiloxane (PDMS) substrates. The primary droplet is initially impacted on the substrate and allowed to achieve static conditions, which may be characterized by the Cassie-Baxter or Wenzel state, depending on the droplet impact velocity and pitch of micropillars. Following this, a secondary droplet is introduced, which impacts on the primary droplet as a vertical head-on collision. We examine how surface wettability (by varying the solid fraction of substrates from 1-0.069) and Weber number (1.41-11.21) influence the dynamic interaction of droplets and their resulting fate. High-speed visualization is utilized to capture the transient evolution of binary droplet impact. Different interaction regimes are observed, namely, no lift-off, lift-off, partial lift-off, direct coalescence, and conglutination with droplet breakup. When the vertical head-on collision of droplets occurs, at a given Weber number, the lift-off probability on micropillared substrates increases in comparison to that of no lift-off on flat substrates, which further transits to partial lift-off/direct coalescence/conglutination based on variations in solid fraction and Weber number. An energy-based analysis is presented to model the maximum spreading ratio of secondary droplets and maximum axial height attained during the receding phase of binary droplets, which agrees with present measurements. Our results show that, in the Cassie-Baxter state, the maximum height does not depend on solid fraction. Instead, it is governed by the Weber number and increases with Weber number. Finally, to replace the complex form of the energy equation, simplified empirical correlations are proposed for the maximum spreading ratio of secondary droplets and the maximum axial height. Insights from this study can be used to modify surface morphology for desired droplet impact, benefiting applications such as spray cooling, self-cleaning, and energy harvesting.