## 3 Results and Discussion  
### The Low Weber Number Conditions  
To eliminate the effects of droplet size, gas velocity/density, and droplet density, the dimensionless treatment of the droplet break-up time is shown in Equation (4):  
\[\tau=t\frac{u_{\mathrm{g}}}{d_{0}\sqrt{\rho_{\mathrm{g}}/\rho_{\mathrm{1}}}} \tag{4}\]  
where \(\tau\) is the dimensionless time, \(t\) is the dimensional time, \(u_{\mathrm{g}}\) is the gas velocity behind the wave, \(d_{0}\) is the initial droplet diameter, and \(\rho_{\mathrm{g}}/\rho_{\mathrm{1}}\) is the ambient-to-droplet density ratio. As shown in Figure 4(a), at \(We=15\), the non-uniform pressure distribution leads to an initial droplet deformation due to the acceleration of the ambient fluid around the droplet (\(\tau=0\)-\(1.285\)). The aforementioned deformation is resisted by interfacial tension, and the droplet ultimately adopts a disk-like morphology (\(\tau=1.285\)). The droplets subsequently undergo the breakup process due to the action of aerodynamic forces (\(\tau=1.285\)-\(2.687\)). As the gas flows through the droplet, it forms a hysteresis point on both the front and back surfaces, where a maximum velocity surrounds the droplet. Following the formation of the bag, expansion of the bag and the liquid ring occurs due to the pressure exerted upon them by the high-pressure stagnation inside the bag. The growth process of the bag corresponds to the development of R-T instability on the droplet surface. In Figure 4(b), it can be observed that at \(We=19\), the droplet experiences bag and stamen breakup. In a study by [PERSON] [22], the morphology of the bag, and bag and stamen breakup, were observed and analyzed. The results indicated the transition \(We\) between bag breakup, and bag and stamen breakup, was 16 while \(Oh\) tended to 0. The transition \(We\) in this experiment was 15 \(<We<\) 19, which is consistent with the range of \(We\) observed in [PERSON]'s study. Throughout the bag and stamen breakup process, an initial perturbation was formed on the droplet surface by R-T instability, which subsequently evolved into a stamen structure (\(\tau=0\)-\(1.228\)). The stamens are not in the droplet center during bag growth, which leads to different growth rates in different parts of the bag. During bag and stamen breakup, the stamens gradually become core droplets (\(\tau=1.228\)-\(2.021\)). The upper and lower edges of the initial droplet are pulled out into pockets, which indicates the presence of two R-T waves, and in this mechanism, droplet deformation leads to internal flow from the poles to the equator. At the time of bag breakup, the interfacial tension is  
Figure 5: Schematic of droplet breakup morphology characteristics. (**a**) bag breakup, (**b**) bag and stamen breakup. sufficient to resist this flow, resulting in the formation of a ring. However, as the rate of deformation increases, the interfacial tension is insufficient, and the droplets continue to elongate, reaching a critical point. Eventually, the edges of the droplets become particularly thin, and the plume droplets lose their liquid film connection with the nucleus and are carried away by the ambient gas flow, leaving only the nucleus portion to continue moving in the direction of the gas flow(\(\tau\) = 2.021-3.427). To further understand the effect of droplet diameter on deformation and breakup at identical _We_, we compared the submillimeter droplet images captured by [PERSON] [11] with our own experimental images, as illustrated in Figure 6. When droplets were subjected to close _We_, the submillimeter droplets did not undergo bag and stamen breakup, but bag breakup. This suggests that the reduction in droplet diameter at the same _We_ alters the breakup mode and typical characteristics of the droplets. Our analysis indicates that, holding _We_ constant, and decreasing the droplet diameter leads to an increase in the number of R-T waves, ultimately resulting in a change in droplet breakup mode. It is worth mentioning that this conclusion applies only to the _We_ = 19 condition.