Impact and freezing coupling processes of supercooled water droplets on cold superhydrophobic spheres at low Weber numbers

While the previous studies discussed the impact and freezing coupling processes of supercooled water droplets on cold superhydrophobic convex spheres at medium or high Weber numbers (We > 10), the cases on convex and concave spheres at low Weber numbers (We <= 10) are numerically studied. A numerical model using the VOF (Volume of Fluid) method and solidification-melting model is established and validated by comparing the calculated results with the experimental data in reference. The influences of the Weber number, supercooling degree, and sphere diameter (characterized by the sphere-to-droplet diameter ratio) on the dynamic behaviors, including the droplet profile, the spreading area and arc angle, and the final outcomes, are explored. As the Weber number increases and the supercooling degree decreases, the impact droplet yields a higher retraction speed and tends to rebound from the cold spheres more easily. The influence of the diameter ratio at low Weber numbers is distinct from that at medium Weber numbers. With the increase of the diameter ratio, the maximum spreading area factor on the convex sphere increases while that on the concave sphere decreases. The final droplet outcome transits from adhesion to rebound when the surface shape continuously changes from concave to convex. The rebound-adhesion morphology maps in terms of the Weber number and diameter ratio are obtained at various supercooling degrees. The rebound region of the convex sphere in the morphology map is wider than that of the concave sphere, and the adhesion region of the morphology map expands with a greater supercooling degree. A smaller diameter ratio yields a smaller critical Weber number between rebound and adhesion regions on the convex sphere but a greater one on the concave sphere. The innovation and optimization of the anti-icing surface may obtain theoretical reference and guidance from the above findings.