# Study of Deformation and Breakup of Submillimeter Droplets' Spray in a Supersonic Nozzle Flow
## 1 Introduction
The most common approaches to the experimental study of liquid drops deformation and breakup processes can be roughly divided into two categories: shock-tube experiments and experiments in continuous flows. Shock-tubes provide supersonic flow speed and controllable conditions, though instant aerodynamic loads can alter the behavior of the droplets comparing to the gradual acceleration case. Shock-tube approach was adopted, for example, in the works [12; 13], and many others. Experiments with droplets in the continuous flow often provide more close resemblance to the practical application cases but also introduce additional parameters and effects to consider [14; 15; 16]. For example, in the paper by [PERSON] [14] experiments on the bag type breakup of 2.2-3.9 mm size droplets in the continuous flow at near-critical \(We\) were reported. The main aim was to accurately determine the critical conditions necessary to complete the bag breakup. The author reported that five significantly different modes of droplet deformation and breakup were observed within the range of \(11\sim<\) We \(\sim<14\). [PERSON] concluded that breakup of droplets at nearly critical \(We\) is very sensitive to fluctuations of the flow conditions. Similarly, in the review [3], the authors concluded that the transition between breakup regimes is a continuous process, while a single transitional _We_ is an over-simplification. The paper by [PERSON] and [PERSON] [15] covered many issues, including droplets trajectory prediction and droplets morphology at different stages of a breakup for the bag, shear stripping and catastrophic regimes. Through scaling down the size of the droplet from 200 \(\upmu\)m to 70 \(\upmu\)m while preserving _We_, the authors showed that similar bag breakup regime occurred in both cases. Interesting to note, that in [15] authors observed the bag breakup regime at _We_ = 56, while multimode or bag and stamen regime is considered to occur at such _We_ numbers. The physical mechanisms behind the bag and multimode breakup regimes are still a matter of discussion that primarily provides two different explanations. The first one attributes the bag breakup purely to the aerodynamic effects, while the second assumes that the bag breakup occurs due to the initial disturbance of the flattened droplet's surface, caused by Rayleigh-Taylor (RT) instability. The work by [PERSON] et al. [17] showed, among other results, that the second theory neatly explains the transition from bag to multimode breakup. In the majority of the papers, droplets of size about 1 mm and larger are considered (see, for example, reviews [2; 3]). For such droplets, low and medium Weber numbers at normal ambient conditions are achieved only at low, strongly subsonic gas velocities. At the same time, droplets of smaller size, usually produced in a primary jet, liquid film or a large droplet breakup at the atomizer, are also subjected to considerable aerodynamic loads in high-speed flow. While relative gas and droplets' velocity can be high, up to supersonic, the Weber number for small droplets remains in the moderate or low range, resulting in a combination of dimensionless parameters, significantly different from those observed in experiments with large droplets. Another aspect is the change of flow conditions--rapid acceleration of small droplets, as well as the rapid change of velocity and density in supersonic flow--may lead to multiple switching of the _We_ number range associated with specific breakup modes. Examples of works in which the breakup of small droplets in high-speed continuous flows is considered are few, some of those being [18; 19]. In both works droplets in a converging-divergent nozzle were investigated. Other examples are [8; 20], in which high-speed vaporizing droplets of the size of about 200 \(\upmu\)m, injected into the cross-flow, were studied. The work by [PERSON] [18] did not provide insight into the processes of droplets' breakup.