Dynamics and maximum spreading of droplet impact on a stationary droplet on the surface

In numerous applications related to droplet impact, impacting droplets often interact with solid surfaces with adhesive droplets rather than dry surfaces, but the former is significantly less studied than the latter. Here, for the fundamental process of droplet impact on a stationary droplet on the surface, we investigate droplet dynamics and maximum spreading under various conditions. The spreading diameter and time are reasonably nondimensionalized as the spreading coefficient and dimensionless time by considering both the impacting and stationary droplets, and the complex influence of diameters of two droplets is reduced to the effect of a single droplet volume ratio. The proposed dimensionless framework provides a method to simplify influencing factors and facilitates the study of droplet dynamics under different Weber numbers, surface wettabilities, and droplet volume ratios. The maximum spreading coefficient increases with the increase of the Weber number or the droplet volume ratio, while it is nearly independent of surface wettability. A theoretical model of the maximum spreading diameter is established through energy analysis. By considering the coupled effects of various factors and modifying the viscous dissipation, the model has the merits of high prediction accuracy and broad applicability. Our findings can not only advance the basic understanding of the ubiquitous droplet impact phenomena, but also provide useful guidance for applications such as spraying cooling and inkjet printing.