Scaling laws for the contact time of impacting nanodroplets: From hydrophobic to superhydrophobic surfaces

Nanodroplet impacts have attracted significant attention, while the effect of surface wettability on contact time is evaluated poorly. Utilizing molecular dynamics simulations, the current work with a special focus on the contact time studies nanodroplets impacting solid surfaces in a wide range of static contact angles (θ₀ = 105°-175°) and the Weber number (We = 0.1-200). The complete trends in contact time and restitution coefficient with surface wettability are analyzed and reported for the first time. For surfaces with θ₀ > 160°, four different regimes are identified for the contact time and restitution coefficient as a function of the Weber number. For surfaces with 110° < θ₀ < 160°, the fourth regime is not observed. The restitution coefficient is employed to analyze the contact time of distinct rebound patterns in the individual wettability range. Intriguingly, surface wettability has a remarkable influence on the contact time of nanodroplets even for superhydrophobic surfaces. The main reason for the difference between the macroscale and nanoscale is attributed to the significantly enhanced viscous effect and interfacial effect of the nanoscale impact. Considering the different effects of surface wettability on spreading and retraction dynamics, the theoretical models for the maximum spreading factor, spreading velocity, and retraction velocity are established. Finally, scaling laws of the spreading time τ_spr ∼ (R₀/V_i)We^2/3Re^-1/3 and retraction time τ_ret ∼ (R₀/V_i)We^2/3Re^-1/3(1 - cos θ₀)^-1/2 are proposed. An excellent agreement with both the current data sources and the results in the literature verifies the universality of the current scaling law from hydrophobic to superhydrophobic surfaces.