# Study of Deformation and Breakup of Submillimeter Droplets' Spray in a Supersonic Nozzle Flow
## 3 Results
### Droplets Size, Shape Oscillations, and Breakup
Distributions for some of the regions are presented in Figure 7 and the evolution of the fraction of droplets of different sizes over the regions--in Figure 8. In addition, more detailed information on the fraction of droplets over the different regions in the form of a table and additional figures, showing the evolution of the normalized droplets fraction \(F\)/\(  
A fraction of droplets in size range of 15-23 \(\upmu\)m gradually increased along the \(x\)-axis up to the SW front. Around the average position of the SW front and 3 mm downstream of it, the fraction of such droplets decreased due to coalescence. Such droplets did not exhibit breakup nor upstream nor downstream of the SW front. \(We_{max}\) for such droplets is 9.6. For the droplets in the size range of 23-27 \(\upmu\)m, their fraction remained almost constant along the whole path of the spray. On the bases of this observation, a size of 27 \(\upmu\)m (\(We_{max}=11.2\)) can be interpreted as a threshold for the droplets that do not disrupt. A _We_ number of 10-12 is a classical value for the transition to bag breakup regime, reported in many papers [1,25]. This allows concluding that in described conditions, the main physical mechanisms governing the droplets' breakup remain the same for small droplets. A fraction of droplets of larger size decreased, reaching the minima at the distance of 3 mm downstream of the SW front. For larger droplets, the decrease was faster. A fraction of droplets with the size \(d>50\)\(\upmu\)m (\(We_{max}\) 22.2) was almost negligible. The total amount of such droplets was about 2% at the beginning of the measurement area (\(x=-15\) mm) and fell to 0.1% at a distance of 3 mm downstream of the SW front. Due to a small number of such droplets, the evolution of normalized fraction for the droplets in this size range, shown in Figure 11 may be biased. Interesting to note that a slight decrease in the fraction of larger droplets starts at the beginning of the measurement area. In addition, despite exceeding the bag breakup regime _We_ threshold, some of the larger droplets did not exhibit breakup or exhibited significantly delayed breakup least, as they persisted, although in small quantities, in the flow upstream and downstream of the SW front. The observed trends for gradual increase and decrease of the fraction of droplets allow to suggest that empirical approximation can be derived to predict the evolution of droplets size distribution using the initial (measured at the single point or region) distribution and known gas flow parameters. Still, to achieve this goal, more data, statistics and validation cases for various experimental conditions are required. Regarding the droplets' morphology, most of the droplets observed in a state of disruption resembled bag breakup at different stages (Figure 9), described in [14,25]. Larger droplets tended to disrupt through dual-bag and multi-bag formations, described in [26]. For the bag breakup in many events, a collapse of an underdeveloped bag was noticed. In this case, instead of explosive bag disruption with the formation of a cloud of small drops, the bag used to collapse into several fibers attached to the rim or shrink to the deformed droplet shape (also shown in Figure 9). Currently, there is no developed theory that would fully describe a process of bag rupture. Arguably, initial bag rupture may be explained through instability growth at the thin liquid sheet separating two gaseous media [27]. [PERSON] and [PERSON] [28] performed a numerical simulation of the bag breakup of the droplet at different _Bo_ numbers and connected the results with the mentioned assumption. They found that an  
Figure 8: Evolution of the normalized droplets fraction \(F/F_{x=-15}\) along the centerline of the nozzle. For each coordinate, the fraction of droplets is normalized by the fraction of droplets in the same size range in the first visualization region at \(x=-15\).