Universal Model for the Maximum Spreading Factor of Impacting Nanodroplets: From Hydrophilic to Hydrophobic Surfaces

Using molecular dynamics (MD) simulations, we investigate impact behaviors of water nanodroplets on hydrophilic to hydrophobic surfaces with static contact angles ranging from 21 to 148 degrees in a wide Weber number range of 15-90, aiming to understand how the surface wettability influences the maximum spreading factor of nanodroplets. We show that the existing macroscale and nanoscale models cannot capture the influence of surface wettability on the maximum spreading factor. We demonstrate that the failure is attributed to the rough estimation of the spreading velocity during the spreading stage, which is assumed to be a constant value in these models. We show that the spreading velocity strongly depends on both the surface wettability and the Weber number. After scaling with the impact velocity, we obtain a universal function of the spreading velocity with respect to the static contact angle and the Weber number. We employ this function to modify the expression of viscous dissipation and develop a new model of the maximum spreading factor. We verify that the model is in excellent agreement with the MD simulations regardless of hydrophilic and hydrophobic surfaces, with the mean relative deviation ranging from 0.88 to 4.75%. We also provide evidence to support the fact that incorporating the influence of surface wettability by modifying viscous dissipation is more reasonable than by modifying surface energy for nanodroplet impact.