## 2 Research Preparation
### Design of Micro Reacting Pipe  
As shown in Figure 3, the internal structure designed in this study is composed of the obstacles with the shape of quadrilateral pyramid table. The dimension of the outer circle is 10 mm. Fluid will turn into several strands by the front edges and the gaps between obstacles when it passes through the obstacles. Then, the split fluid will converge along the slope, so the fluid will collide and form swirls at the back of the obstacles. This process will break down the laminar pattern, turn the flow pattern into turbulence, and promote convection diffusion so as to improve the mixing efficiency. During manufacturing, out of consideration of process constraints of L-PBF, the axis of the micro reacting pipe should be vertical to the substrate. At the same time, the angle between the suspended structure and the wall in the channel should be not smaller than 45\({}^{\circ}\) to avoid building support inside the channel  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**Material** & **Cr** & **Fe** & **Mo** & **Si** & **Mn** & **Ni** & **Ti** & **Al** & **P** & **Nb** & **N** & **Cu** & **O** & **C** \\ \hline IN718 & 19.20 & 17.32 & 3.17 & 0.33 & 0.23 & 52.91 & 0.65 & 0.54 & 0.10 & 5.16 & 0.14 & 0.13 & - & - \\
316 LSS & 17.5 & Bal & 2.06 & 0.86 & 0.3 & 12.06 & - & - & - & - & - & 0.09 & 0.03 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Compositions of the IN718 and 316L Stainless Steel (wt. %).  
Figure 2: The flow chart of the research: (**a**) overall process; (**b**) test platform model.  
which cannot be removed after forming [28]. So, the first design principle is obtained: the angle of inclination of the internal structure is more than or equal to 45\({}^{\circ}\).  
The flow field model used in this simulation is shown in Figure 4a below. The entrance part was modeled according to the actual measurement of the tee coupling joint used in the chemical experiment. The mixing area was composed of 10 groups of internal structure units with the total length of 40 mm.  
The characteristic cross-section of the flow field is shown in Figure 4b. The size represented by x in the diagram is called the determining size and is denoted as \(\mathrm{J}\mathrm{xx}\) (indicating that the length of the gap is \(\mathrm{xx}\times 0.1\) mm). By geometrical analysis, the area, the circumference, and the critical dimension of the cross-section can be calculated. By the laws of geometry, the equations are as follows:  
The relationship between the area and the determining size:  
\[\mathrm{A}=\mathrm{ax}+\frac{\left(\mathrm{a}-\mathrm{x}\right)^{2}}{2\tan \theta}. \tag{1}\]  
The relationship between circumference and determining size:  
Figure 4: Flow field model in simulation: (**a**) whole reacting pipe model; (**b**) shape of the cross-section.  
Figure 3: The internal structure designed for the reaction pipe: (**a**) the isometric view; (**b**) the elevation view.  
\[\mathrm{C}=4a+\frac{2(a-x)(1-\cos\theta)}{\sin\theta}. \tag{2}\]  
The equation of the critical dimension of the cross-section:  
\[\mathrm{d}=\frac{4A}{C}=\frac{2 axsin\theta+(a-x)^{2}cos\theta}{2 as\theta+(a-x)(1 -\cos\theta)}. \tag{3}\]  
In this study, \(\theta\) was equal to 45\({}^{\circ}\), and a was equal to 2 mm. Therefore, the relationship between the critical dimension and the determining size is as follows:  
\[\mathrm{d}=\frac{4+x^{2}}{\big{(}1-\sqrt{2}\big{)}x+2\big{(}1+\sqrt{2}\big{)}}. \tag{4}\]  
In this paper, the simulation analysis and experimental verification were conducted with the determining size of 0.2, 0.4, 0.6, 0.8, 1.0 mm, which corresponded to the critical dimension of 0.85, 0.89, 0.95, 1.03, 1.13 mm.