Scaling laws for the droplet rebound with lateral motion after impacting on heterogeneous surfaces

After droplet impacting onto solid surfaces, various outcomes such as deposition, rebound and splashing are possible, which greatly depend on the surface wettability. In this paper, the spontaneous rebound with lateral motion of a water droplet impacting on a hydrophobic substrate decorated with the hydrophilic pattern is studied numerically and theoretically. The effects of multiple parameters on the droplet lateral motion are investigated, including the initial droplet diameter and impact velocity, the arrangement of hydrophilic patterns, and the surface energy gradient. The numerical results show that the dimensionless lateral velocity obeys some simple scaling laws. Moreover, the theoretical analysis of droplet impact is performed, and the same relationship between the lateral motion and the impact conditions is derived. The reliability of the proposed relationship is validated by some testing cases and previous experimental data. The results obtained here may strengthen our understanding of droplet manipulation and achieve the controllable rebound of impacting droplets.