Transition in the scaling laws of droplet-impact contact time

Contact time has become a central focus in recent studies of droplet impact dynamics because of its relevance to anti-icing and self-cleaning. At the macroscale and nanoscale, distinct scaling laws for contact time have been proposed; however, the transition between them remains unresolved because of a lack of systematic investigations at the intermediate microscale. In this work, many-body dissipative particle dynamics simulations are employed to explore droplet impacts at the microscale. The results reveal two regimes of contact-time evolution: a velocity-dependent regime consistent with the Hertz elasticity theory, and a velocity-independent regime exhibiting pronounced scale effects. By decoupling the contributions of slip and viscous effects to the scale effects, it is found that varying slip length does not significantly alter the contact time, whereas increasing the Ohnesorge number markedly and nonlinearly prolongs it. When Oh > 0.3, viscous effects begin to significantly affect the contact time, and it can increase to more than 1.5 times that of droplets in the velocity-independent regime. These findings clarify that the change in bouncing dynamics induced by decreasing droplet size is mediated by viscous effects. To describe such scale effects, a full-scale scaling law for contact time is proposed, achieving an average error of <10% over the parameter range involved in this paper. Moreover, a boundary equation between the velocity-dependent and velocity-independent regimes is further established based on the insights into these regimes. By bridging the microscale gap, this study provides cross-scale insight into the bouncing dynamics of droplets impacting solid surfaces.