## 2 Experimental Devices and Methods
### Experimental Parameters  
The aerodynamic force acting on the droplet's surface, the interfacial tension between the droplet and the ambient gas, and the viscous force inside the droplet are the main factors affecting the deformation and breakup of the droplet under the action of gas flow. The Weber number _We_ and Ohnesorge number _Oh_ are crucial dimensionless numbers related to droplet deformation and breakup. _We_ is the ratio of the aerodynamic force from the ambient gas and the interfacial tension, which plays a dominant role in the deformation and breakup of the droplet. And _Oh_ relates the viscosity to the aerodynamic force and interfacial tension [2]. The equations for _We_ and _Oh_ are as follows:  
\[We=\frac{\rho_{\mathrm{g}}u_{\mathrm{g}}{}^{2}d_{0}}{\sigma} \tag{1}\]  
\[Oh=\frac{\mu_{\mathrm{I}}}{\sqrt{\rho_{\mathrm{I}}\sigma d_{0}}} \tag{2}\]  
where \(d_{0}\) is the initial droplet diameter, \(\sigma\) is the interfacial tension, \(u_{\mathrm{g}}\) is the gas velocity behind the wave, \(\rho_{\mathrm{g}}\) is the gas density behind the wave, \(\mu_{\mathrm{I}}\) is the dynamic viscosity of the droplet, and \(\rho_{\mathrm{I}}\) is the droplet density.  
The diameter of the water droplets generated by the pneumatic droplet generator is around 240 \(\upmu\)m. The diameter error between different droplets is less than 5% due to the inherent error of the pixel dot size. The relative errors of both gas velocity and density were less than 1% (averaged over multiple calculations). The table of relevant parameters of the experiment is shown in Table 1.  
In the definition of thermodynamic or aerodynamic parameters, which involve temperature or temperature-dependent physical quantities, the temperature before the shock wave is usually used to define them. Therefore, for the temperature-dependent physical quantities involved in calculating _We_ and _Oh_, the temperature before the shock wave, which is the ambient temperature, is used. As a result, the dynamic viscosity of the droplet is 1.00160 \(\times\) 10\({}^{-3}\) Pa-s, the density of the liquid droplet is 997.07 kg/m\({}^{3}\) and the interfacial  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \(d_{\mathrm{g}}\)/ & \(p_{\mathrm{I}}\)/ & \(p_{\mathrm{Z}}\)/ & \(Ma\) & \(u_{\mathrm{g}}\)/ & \(\rho_{\mathrm{g}}\)/ & \(T_{\mathrm{g}}\)/ & \(W\) & \(Oh\) \\ (mm) & (Pa) & (Pa) & & (m/s) & (kg/m\({}^{3}\)) & (K) & & \\ \hline
0.24 & 101325 & 128198 & 1.11 & 58.01 & 1.41 & 318.9 & 15 \(\pm\) 1 & 0.00764 \(\pm\) 0.00018 \\
0.24 & 101325 & 130597 & 1.12 & 62.73 & 1.44 & 320.6 & 19 \(\pm\) 1 & 0.00764 \(\pm\) 0.00018 \\
0.24 & 101325 & 200960 & 1.36 & 175.69 & 1.93 & 366.1 & 184 \(\pm\) 13 & 0.00764 \(\pm\) 0.00018 \\
0.24 & 101325 & 298847 & 1.63 & 289.32 & 2.50 & 421.2 & 696 \(\pm\) 30 & 0.00764 \(\pm\) 0.00018 \\ \hline \end{tabular} Note. \(d_{0}\) is the initial droplet diameter; \(p_{\mathrm{I}}\) is the pressure of the low-pressure chamber of the shock tube; \(p_{\mathrm{Z}}\) is the gas pressure behind the shock wave; \(Ma\) is the propagation Mach number of the shock wave; \(u_{\mathrm{g}}\) is the gas velocity behind the shock wave; \(\rho_{\mathrm{g}}\) is the gas density behind the shock wave; \(T_{\mathrm{g}}\) is the gas temperature behind the shock wave.  
\end{table}
Table 1: Experimental operating conditions parameters.  
tension is 0.0728 N/m (at a temperature of 293.2 K and a pressure of 101,325 Pa). When \(Oh\) is low enough (\(Oh\) < 0.1), the viscous force inside the droplet can be ignored, and \(We\) is the main parameter dominating droplet breakup [21].