## 1 Introduction
### Morphological Considerations on the Hydrodynamics of Splashing  
The splashing mechanism is one of (if not) the most relevant and studied factors in the literature. On a typical vertical impact of a single droplet on a steady liquid film the droplet is initially spherical, and it does not suffer any deformation during the fall. A recent study [14], using precisely the same fluids, studied the effect of a droplet's initial deformation on the splashing dynamics. Due to the interaction between the droplet and an air flow before impact, the droplet deformed and assumed different shapes before impact. They reported that spherical droplets promote splashing, while deformed droplets promote spreading. The physical processes involved in fuel combustion include fuel atomization and impact, followed by the evaporation. The mixture preparation, including the impact upon dry and wetted surfaces, is recognized as of major importance. The secondary atomization produced by the splashing optimizes the fuel combustion efficiency. Considering this, a droplet falling vertically on a steady liquid film was studied for the fluids mentioned and the occurrence of splash was compared to the prediction of models presented in the literature. All models considered were designed for the impact of spherical droplets upon a liquid film. The morphology of this impact mechanism includes the formation of a crown with a rim in its upper bound, and from instabilities in this rim, the cusp can emerge, which disintegrates into droplets--thus, secondary atomization. [PERSON] et al. [15] were among the first to characterize the crown diameter, thickness, and maximum height. The authors noticed that higher values for the Weber number led to smaller secondary droplets. A few years later, [PERSON] et al. [16] focused their work on the time evolution  
Figure 2: Transition criteria between spread and splash after drop impact onto a liquid film. of the crown of water droplets impinging upon thin liquid films. They reached several conclusions related to the crown diameter, the non-dimensional crown height, and the mean secondary droplet size. However, since they used only one fluid, it is not possible to identify whether their conclusions could be extended to other fluids. [PERSON] and [PERSON] [17] studied experimentally and theoretically, the region of the fully developed splashing. They used water but also a 70% glycerol-water solution. They developed a model for the central jet formation at the cavity collapse. Some considerations were made about the viscosity of the fluids related to the cavity, the central jet, and the crown ejection. In fluids with low viscosity, the interaction between the capillary wave and the cavity wall has a major influence on the cavity shape, and by consequence, on the central jet speed. On the other hand, for fluids with high viscosity, the influence of capillary waves is minor. Understanding the roles of the fluid physical properties is essential to understanding how they influence the impact regimes. For example, [PERSON] and [PERSON] [18] reported that splashing is highly sensitive to surface tension values. A parameter particularly relevant to the impacts of droplets on wetted surfaces is the dimensionless thickness of the liquid film and its influence in the droplet dynamic behavior. [PERSON] et al. [19] studied droplets splashing upon liquid films of different depths. They reported that thinner liquid films decreased the critical Weber number, setting the transition between deposition and splash. They also found that the size and number of the splashed droplets depend upon the presence and thickness of the liquid film, and also on the fluid's viscosity and surface tension. For \(\delta<1\), both prompt and crown splash were spotted, but for \(\delta>1\), prompt splash was limited and crown splash inhibited. Moreover, the number of ejected droplets decreased while their mean size increased, an outcome attributed to the increase of the surface tension and viscosity.