Maximum Spreading Diameter of Bouncing Droplets at Ultralow Weber Numbers

In the present work, we study the maximum spreading of bouncing droplets in the capillary regime at ultralow Weber numbers with a fixed static contact angle. In the ultralow Weber number region, experiments reveal that existing spreading laws are inapplicable because of gravity exclusion and change in deformation shape. We propose a theoretical scaling law based on energy conservation, modeling the deformed droplet as an ellipsoid with gravity effects. The proposed scaling law indicates the competition between gravity and inertia at ultralow Weber numbers and distinguishes their dominant regimes. By integrating higher-Weber-number regions, we reveal that viscosity is prominent in the previously assumed inviscid regime. Furthermore, we devise a phase diagram to clarify different impact regimes on the basis of energy analysis.