# Long-Term Dynamics of Water Droplet Impact on Rotating Hydrophilic Disk
###### Abstract
Due to the superhydrophobic nature of these surfaces, ethanol droplets displayed only spreading, with the initial spreading phase dominated by inertia and the later phase governed by centrifugal forces. [PERSON] et al. [39] experimentally studied the behavior of water droplets impacting a spinning aluminum disk, investigating the effects of impact velocity, rotating speed, and impact location on wetted area, finger formation, and secondary droplet generation. [PERSON] et al. [40] focused on the influence of liquid viscosity on radial and tangential spreading dynamics during eccentric droplet impacts on rotating stainless steel disks, defining four regimes to describe the dominant forces during spreading. [PERSON] et al. [41] systematically examined the effects of impact velocity, rotating speed, and radial impact position on impact phenomena such as asymmetric spreading, finger formation, and secondary droplet creation. In a subsequent study, [PERSON] et al. [42] further explored the influence of rotating speed, surface tension, and liquid viscosity on splashing phenomena, both with and without liquid filament formation. Concurrently, [PERSON] et al. [43] investigated how liquid properties influence the dynamics of a droplet that impacts a rotating aluminum disk with 3 cm off-axis. To summarize, after eccentric impact on rotating hydrophilic surfaces, the droplet undergoes asymmetric spreading dynamics, with both radial and tangential components. The inner and outer edges experience centrifugal acceleration, triggering wave propagation from the inner to the outer edge. This results in fingering and secondary droplet generation--phenomena characteristic of eccentric impact dynamics. However, for droplets impacting the center of a rotating hydrophilic surface, symmetric spreading dynamics occur, a phenomenon that remains less investigated. Recently, [PERSON] et al. [44] conducted a detailed experimental study on the spreading and retraction dynamics of water droplets impacting the center of both rotating hydrophilic and hydrophobic surfaces. They also proposed a simplified model to predict tangential velocity induced by the surface shear force and established a quantitative description for the maximum spreading factor in the spreading regime, as well as deriving the critical conditions for the transition from spreading and retraction to spreading and breakup. However, the long-term evolution of droplets has not been fully explored, and explicit scaling laws for spreading parameters are still lacking. In this study, we aim to investigate the long-term dynamics of water droplets impacting the center of a commonly used hydrophilic rotating stainless steel disk under varying impact velocities and rotating speeds. The evolution of droplet diameter over time will be quantitatively measured, and the effects of impact velocity and rotating speed on the spreading and retraction dynamics will be analyzed. Additionally, we will discuss the equilibrium stages in detail, search for empirical scaling laws for maximum and equilibrium spreading diameters, and present a special phenomenon involving ring-like droplet formation.