Droplet bouncing enhancement via substrate vibration on nanopillar-arrayed surfaces

The interplay between the surface nanostructure and the mechanical vibration in governing nanodroplet impact dynamics remains poorly understood in fluid mechanics. This study systematically investigates the impact dynamics of nanodroplets on vertically vibrating nanopillar-arrayed surfaces, revealing the amplitude-frequency decoupling phenomena on nanostructured surfaces through molecular dynamics simulation. Our results demonstrate an amplitude-dominated phase transition threshold mechanism in droplet bouncing dynamics. When the applied amplitude exceeds a dimensionless critical threshold A*crit, which is correlated with surface solid fraction ϕs, the complete rebound occurs independently of the frequency. Notably, in the subcritical amplitude regime (A* < Acrit*), droplet bouncing exhibits pronounced frequency dependence. Specifically, the droplet bouncing only occurs at the low- and high-frequency regimes, while the intermediate frequency would suppress rebound probability. Importantly, we present a theoretical derivation of the spreading time ts and the maximum spreading factor βmax via a vibration-coupled energy framework, resolving the competition among the vibrational energy, interfacial energy, and viscous dissipation. This work advances the fundamental understanding of the fluid–structure–vibration interactions and provides strategies for anti-icing, thermal management, and energy harvesting applications.