## 3 Results  
### Impact of the Water Droplet  
Table 2 summarizes the results from the experiments with the water droplet falling on the molten Rose's alloy surface. The droplet volume was very well controlled by the experimental procedure of droplet generation, however, perturbations that developed during the droplet's fall in the air resulted in distortion of its spherical shape, and some scatter was observed in the impact velocities. The pre-impact droplet size indicated in Table 2 was measured as the horizontal droplet size visible on the last frame before the droplet's contact with the melt surface. As the baseline case, Case D1 from Table 2 elucidates all the typical features of the interaction observed in all the free-falling droplet experiments. After the droplet touches the melt surface, it starts to disturb it so that a cavity develops, which is surrounded by a circular \"crown\" into which the melt material is displaced. For each frame, the visible diameter of the crown was obtained; for most of the frames, it was easily detected thanks to the high contrast between the water (looking dark) and the melt (highly reflective). Along with the experimental photos, it is also useful to analyze the time dependence of the crown diameter, which is presented in Figure 2; the time is plotted on the logarithmic scale. Three distinct stages of cavity development can be seen in the graph, denoted by the linear pieces of the plot, and separated by points A and B where the slope of the lines changes abruptly. Note that once the cavity diameter \(d(t)\) is described by a linear function in the coordinates of Figure 2, it can be represented by  
\[d(t)=d_{0}\log_{10}(t/t_{0})+d_{1}, \tag{1}\]  
where \(d_{0}\) and \(d_{1}\) are characteristic diameters, and \(t_{0}\) is a characteristic time found for each stage from the best fit of the experimental data. Since the radial velocity of the crown top is \(v=dr/dt\) (where \(r=d/2\)), it follows from (1) that the cavity velocity decays proportionately to \(d_{0}/t\), and the constant in the velocity decay law changes abruptly from one stage to another. The best-fit linear regression lines are shown in Figure 2 for each stage, and they will be further discussed below in comparison with other water impact experiments. The flow corresponding to each above-mentioned stage is shown in Figure 3; the field of view in each frame is 26 \(\times\) 17.5 mm and the resolution is 800 \(\times\) 600 pixels. Immediately after the droplet touches the hot melt, high-velocity water streamers are ejected from the contact zone, almost parallel to the melt surface (Figure 3a). The video record clearly shows that water boiling occurs on the water-melt interface, where small-scale bubbles are seen (Figure 3b). It is not clear from the video if a continuous vapor film is formed to completely separate water from the melt, however, liquid water definitely remains in the cavity for long time (Figure 3c-h). \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Case** & **Drop Height, mm** & **Water Volume, mL** &
\begin{tabular}{c} **Pre-Impact Droplet** \\ **Size, mm** \\ \end{tabular} & **Impact Velocity, m/s** & **Melt Temperature, \({}^{\circ}\)C** \\ \hline D1 & 58 & 0.0388 & 4.56 & 3.17 & 200 \\ D2 & 58 & 0.0388 & 4.45 & 3.08 & 200 \\ D3 & 58 & 0.0388 & 4.48 & 2.9 & 200 \\ D4 & 58 & 0.0388 & 4.38 & 3.46 & 200 \\ D5 & 58 & 0.0388 & 3.95 & 3.14 & 200 \\ D6 & 58 & 0.0388 & 4.26 & 3.05 & 200 \\ D7 & 58 & 0.0388 & 4.03 & 3.24 & 200 \\ D8 & 58 & 0.0388 & 4.2 & 3.45 & 200 \\ D9 & 58 & 0.0388 & 4.04 & 3.1 & 280 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of free-falling droplet impact experiments. Figure 3: Snapshots of Case 1 video at the instances indicated in Figure 2 (the dimensions are in millimeters). (**a**) t = 0 ms; (**b**) t = 1 ms; (**c**) t = 2.8 ms; (**d**) t = 6.2 ms; (**e**) t = 10 ms; (**f**) t = 13.2 ms; (**g**) t = 15.4 ms; (**h**) t = 20 ms.  
Figure 2: Time dependence of the cavity diameter (Case D1). Dots: experimental data, solid line: approximation.