## 3 Results and Discussion  
Figure 7 shows a raw image captured in the bubbly flow. The raw image shows two identical particles because the laser was emitted twice while the camera shutter was open, causing the particle to be captured twice. The bubble is located in the top and bottom parts of the image, and the particles around the bubble were able to be measured accurately because the laser wavelength band was blocked using a notch filter. The [PERSON] (LaVision, Germany) program was used for velocity calculation, with auto-correlation used as the velocity calculation algorithm. The auto-correlation has three correlation values and two correlation values that are symmetrical around the center value, which causes flow direction ambiguity. Thus, the flow direction needs to be determined prior to experimenting [34,35]. In this research, the flow direction was established by varying the brightness of the first and second lasers and pre-setting the camera direction before the experiment. The N\({}_{2}\) representations in the image were marked as obstacles and excluded from the calculation area. The reflectance of the notch filter was not 100%, so it was possible to distinguish the N\({}_{2}\) bubbles from the calculation area due to laser reflection on the N\({}_{2}\) surface. The interrogation window used was \(32\times 32\) pixels\({}^{2}\), and the overlap was 50%. The details of the image capture and vector calculation method are described in a supplementary.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Manufacture, Model** & **Specifications** \\ \hline
1 & Thorlabs, LA1252-A, Plano convex lens & F * 25.4 mm, D ** 25 mm \\
2 & Thorlabs, LA1540-A, Plano convex lens & F 15 mm, D 12.5 mm \\
3 & Thorlabs, LA1484-A, Plano convex lens & F 300 mm, D 25.4 mm \\
4 & Thorlabs, LA1805-A, Plano convex lens & F 30 mm, D 25.4 mm \\
5 & Edmund Optics, 43–473, Full fan angle laser line generator lens & 30 degree \\
6 & Mitutoyo, Plan Apo infinity corrected long working distance(WD) objective lens & 10\(\times\), N.A. 0.28, WD 34 mm \\
7 & Thorlabs, MRA25-P02, F9911, Right angle prism + right angle prism mirror & 25 mm \\
8 & Thorlabs, CCM1-E02/M, Cube-mounted turning prism mirror with 50:50 beam & 565 nm \\  & splitter and prism mirror & 100 \\
9 & Thorlabs, LA1509-A, Plano convex lens & F 100 mm, D 25.4 mm \\
10 & Thorlabs, VA100C/M, Adjustable mechanical slits & 30 mm \\
11 & Thorlabs, LA1433-A, Plano convex lens & F 150 mm, D 25.4 mm \\
12 & Thorlabs, CDFW5/M, Manual dichroic filter wheel & 30 mm, 5 filters \\
13 & Thorlabs, LA1461-A, Plano convex lens & F 250 mm, D 25.4 mm \\
14 & Thorlabs, BB1-E02 Broadband dielectric mirror & D 25.4 mm \\
15 & Thorlabs, MRAK25-P01, Knife-edge right prism & 25 mm \\
16 & Semrock, NFD01-532, Notch filter & 532 nm \\ \hline \hline \end{tabular}
\end{table}
Table 2: A list of the optical parts used in the LIF-PIV setup.  
Figure 6: The timing chart for the LIF-PIV.  
The vorticity is considered to be a physical quantity that can be used to determine the degree to which \(\theta\) is close to 0 in Equation (2). The nonrotating property can be determined by the vorticity of particles. The \(xy\)-vorticity and the vorticity magnitude were calculated using Equations (3) and (4), as follows:  
\[[\omega_{z}]\ =\ \left[\frac{\partial v}{\partial x}-\frac{\partial u}{\partial y }\right], \tag{3}\]  
\[\|\omega\|\ =\ \sqrt{\omega_{z}^{2}}. \tag{4}\]