The Restitution Coefficient of Impacting Low-Viscosity Nanodroplets on Solid Surfaces

The restitution coefficient of a bouncing droplet is determined by energy conversion during impact on superhydrophobic surfaces, including both the spreading and retraction. The energy conversion mechanism during retraction remains poorly understood at the nanoscale, thereby limiting the understanding of nanodroplet bouncing dynamics. In this study, molecular dynamics simulations are performed to investigate the retraction dynamics of low-viscosity nanodroplets impacting superhydrophobic solid surfaces with particular emphasis on the corresponding energy conversion mechanism. At the macroscale, the retraction of low-viscosity droplets consists of an inertial stage with decreasing surface energy and increasing kinetic energy followed by a capillary stage with decreasing kinetic energy and increasing surface energy. However, the retraction of nanodroplets exhibits an additional crossover stage between the inertial and capillary stages, in which both the kinetic and surface energies decrease simultaneously. Although the surface energy continues to be released and is converted into kinetic energy during this stage, the corresponding conversion rate becomes lower than the rate at which the kinetic energy is dissipated through viscous dissipation, identified as a distinctive feature of nanoscale retraction induced by scale effects. By extracting velocity contours in different stages during nanodroplet retraction, it is found that the deformation-induced bulk dissipation persists throughout the entire retraction process, whereas the rim dissipation from the violent velocity gradient near the rim entrance exists only in the inertial and crossover stages. Based on the revealed energy conversion mechanism during retraction, together with literature on spreading, a theoretical model of the restitution coefficient is established, which is validated against both the present data and previously reported data over a wide range of Weber numbers from 17 to 108, across different liquids. These findings provide physical insights into the bouncing of nanodroplets and offer a basis for future cross-scale modeling of droplet impact dynamics.