# Instability and Atomization of Liquid Cylinders after Shock Wave's Impacting
## 2 Experimental Devices  
Figure 1 shows the horizontal shock tube applied in our experiment, whose total length is about 12 m. The high-pressure gas tank 1 (nitrogen N2 gas), round cross low pressure section 5 and square cross low-pressure section 6 composes the shock wave generator. The experimental section 9 is connected to the square cross low-pressure section and vacuum chamber 14 by flanges and two pressure transducers 7 for measuring shock Mach number are set on the top of the square cross low-pressure section 6. Figure 2 is the enlarged schematic of the experimental section 8. The interior sectional dimension of the 500 mm long experimental section is 120 mm \(\times\) 120 mm. A highspeed camera (Photon Fastcam SA5) is set at one side of the experimental section 8 which is windowed by two transparent PMMA plates. If shadowgraph or schlieren optics is applied, the shock waves can also be visualized. On the upper and lower walls of the experimental section 8, square holes are machined respectively to arrange the water cylinder adapter 16, testing plate 17 and lower drainage board 18. The water cylinder adapter 16 is fixed on the testing plate 17 through screw structure. The outlet of the adapter 16 is machined carefully to ensure that a long smooth water cylinder can be obtained [23]. In Figure 2, it is also shown that the in-line double rows water columns can be obtained with 50 mm spacing distance. Using the shock tube, we already successfully conducted experiments on shock wave interaction with water droplet (see [13; 24]).  
Figure 1: Schemes follow the same formatting. 1. High pressure gas tank; 2. Gas valve; 3. High pressure section; 4. Aluminium foil; 5. Round cross low-pressure section; 6. Square cross low-pressure section; 7. Pressure transducer 8. Experimental section; 9. Water tank; 10. Water inlet valve; 11. Water tube; 12. Water container; 13. Vacuum chamber; 14. Trolley; 15. Support.  
After the shock wave's impact, the water cylinder (column) will experience processes of compression, RM instability, disintegration, atomization, etc. The RM instability will produce the so-called spike and bubble structures. Therefore, measurements of the spike height and bubble depth \(h_{\text{b}}\) are important to describe how the instability develops, which are shown in Figure 3. In Figure 3a, the two successive photos are overlapped each other so that the increment of the spike height \(\Delta h_{s}\) and increment of bubble depth \(\Delta h_{b}\) can be obtained. Then, the next time the spike height or bubble depth becomes \(h_{2}=h_{1}+\Delta h\). From Figure 3b,c, the displacement of the vertical axial base line \(\Delta s\) equals to that taken from high-speed photographs (e.g., Figures 4 and 5). By definition, if we consider the gas/liquid interface as a sinusoidal curve, the distance from the base line to the crest is \(h_{s}\); the distance from the base line to the trough is \(h_{b}\); then the turbulent mixing zone is that \(h=h_{s}+h_{\text{b}}\). Averaging the results along the axial direction of the cylinder, we have the global parameter:  
\[h_{i}=\frac{1}{m}\sum_{n=1}^{m}h_{lm}(i=s,b;\ m=1,2,3\ldots) \tag{1}\]  
Figure 3: Measurement of the spike height and bubble depth. (**a**) Definition of \(h_{s}\) and \(h_{b}\); (**b**,**c**) Definition of the vertical axial base line and \(\Delta s\).  
Figure 2: Sectional view of the experimental section. 16. Water cylinder adapter; 17. Testing plate; 18. Lower drainage board.  
Figure 4: High-speed photographs of RM instability of \(d_{0}=4.14\) mm diameter water cylinder at Mach number \(Ma=1.10\). Part 1-24 show the image at 0.25 ms interval.  
Figure 5: High-speed photographs of double \(d_{0}=3.38\) mm diameter water cylinders at Mach number \(Ma=1.10\). Part 1-24 show the image at 0.25 ms interval.