Critical and Optimal Wall Conditions for Coalescence-Induced Droplet Jumping on Textured Superhydrophobic Surfaces

The effectiveness of coalescence-induced jumping of microdroplets on superhydrophobic surfaces is critical to a wide range of applications such as self-cleaning surfaces, anti-icing/frosting, water harvesting, phase-change heat transfer, and hotspot cooling. Introducing textures on the surfaces can readily enlarge the effective contact angle, while an overlarge texture spacing may unfavorably lead to droplet penetration into the gaps in droplet coalescence processes. To clarify the effect of surface textures on the droplet jumping dynamics, we simulated the coalescence of droplets on textured superhydrophobic surfaces with various surface wettability and texture spacings and theoretically derived the critical conditions of jumping and the optimal condition of maximum jumping velocity. The results show that the nonmonotonic emergence of "nonjumping"-"jumping"-"nonjumping" with decreasing solid fraction is synergistically controlled by the surface adhesion and the effective impinging pressure. At a large solid fraction, the transition from "nonjumping" to "jumping" is caused by the reduction of the dimensionless surface adhesion energy below a critical value, which is determined to be 0.035 for Oh = 0.02 and 0.01 for Oh = 0.12. At a small solid fraction, the transition from "jumping" to "nonjumping" is dominated by the reduction of the dimensionless effective impinging pressure, the critical value of which is identified to be 0.14 and is independent of Oh. Moreover, jumping velocity maximizes when wetting critically transits from the Cassie-Baxter (CB) state to the partial-wetting state, and a penetration index is proposed from the wetting theory to predict such transition, which shows good agreement with both present simulations and previous experiments. The present findings are helpful for the design of superhydrophobic surfaces that pursue robust and efficient jumping of droplets.