Droplet impact on a superhydrophobic surface under shear airflow: Lattice Boltzmann simulations and scaling analyses

Droplet impact in airflow environments is ubiquitous in nature and industry, making the understanding of this multiphase behavior crucial for technologies such as anti-icing and spray cooling. In this study, the dynamics of droplet impact on a superhydrophobic surface under shear airflow are numerically investigated using the pseudopotential multiphase lattice Boltzmann method. This three-dimensional model employs a non-orthogonal multiple-relaxation-time scheme to enhance numerical stability and a contact angle hysteresis window to effectively capture dynamic wetting. Specifically, the kinetic energy supplied by the airflow enhances streamwise spreading and significantly expands the final contact footprint due to continuous horizontal sliding. To describe the nonlinear dependence of these contact-line characteristics on the impact Weber number (We) and the airflow Reynolds number (Re), a set of composite scaling laws is developed based on a modified Weber number (We*) that incorporates the airflow contribution. Moreover, the aerodynamic effect leads to a higher velocity restitution coefficient and a deflected take-off angle. Based on an energy partition analysis at detachment, a refined power law is derived to scale the vertical restitution coefficient under shear airflow, while the streamwise restitution coefficient is formulated via the sliding velocity approximation. Integrating these two directional components enables accurate quantitative predictions of the total restitution coefficient and the take-off angle governed by the interplay of We and Re. Overall, this study clarifies the underlying mechanisms of droplet-airflow-surface interactions, providing practical insights for predicting droplet behaviors and guiding surface design under aerodynamic conditions.