Numerical and theoretical modeling of water droplet impact on hydrophilic and superhydrophobic cones.

This article systematically investigates the dynamics of water droplet impacts on hydrophilic and superhydrophobic conical surfaces across a wide range of Weber numbers (We) and cone angles (φ). Three distinct phases of droplet behavior are identified for each surface type, with droplets ultimately depositing on hydrophilic cones and rebounding from superhydrophobic cones, often as toroidal shapes. The study quantifies spreading characteristics, contact times, and defines scaling laws relating maximum spreading area and characteristic times to We and φ. Two theoretical energy-based models are developed to predict the maximum spreading position on hydrophilic cones and the rebound position on superhydrophobic cones, incorporating gravitational potential energy and viscous dissipation; these models show good agreement with numerical simulations. The findings provide detailed insights into droplet impact phenomena relevant to engineering applications such as anti-icing and cooling systems.