Phase diagram for nanodroplet impact on solid spheres: From hydrophilic to superhydrophobic surfaces

The impact of droplets on solid surfaces is a crucial fluid phenomenon in the additive industry, biotechnology, and chemistry, where controlling impact dynamics and duration is essential. While extensive research has focused on flat substrates, our understanding of impact dynamics on curved surfaces remains limited. This study seeks to establish phase diagrams for the process of droplet impact on solid spheres and further quantitatively describe the effect of curvature through theoretical analysis. It aims to determine the critical conditions between different impact outcomes and also establish a scaling relationship for the contact time. Here, the post-impact outcome regimes occurring for a wide range of Weber numbers (We) from 1.2 to 173.8, diameter ratio (λ) of solid spheres to nanodroplets from 0.25 to 2, and surface wettability (θ) from 21° to 160°, through the molecular dynamics simulation method (MD) and theoretical analysis. The MD simulations reveal that the phase diagrams of droplet impacts on hydrophilic, hydrophobic, and superhydrophobic spheres differ, with specific distinctions focusing on rebound and three different forms of dripping. Furthermore, a theoretical model based on the principle of energy conservation during impact on superhydrophobic surfaces has been developed to predict the critical conditions between rebound and dripping states, showing good agreement with simulation results. Additionally, a new scaling relationship of contact time for droplet impact on superhydrophobic spherical surfaces has also been established by extending and modifying the existing models, which also agrees well with the simulated results. These insights provide a foundational understanding for designing surface structures.