## 3 Results and Discussions
### Simulation Results of Micro Reacting Pipe and Selection of Model Parameters  
#### 3.2.1 Selection of Model Parameters and the Three Design Principles  
The fundamental reason for the high mass transfer performance of the micro reacting pipe is its small critical dimension of the channel. By reducing the critical dimension of the channel, the diffusion distance of the components reduces, and the mixing efficiency dominated by free diffusion is enhanced. The following formula (15) shows that the microscopic mixing time (t) of the micromixer is directly proportional to the square of the critical dimension (d) and inversely proportional to the component diffusion coefficient (D). Therefore, for the microscopic mixing process, the mixing efficiency decreases monotonously with the increase of the critical dimension [36]. Therefore, the second design principle of the micro reacting pipe is that the channel characteristic size should be reduced as much as possible to enhance the mixing efficiency dominated by free diffusion:  
\[\text{t}\propto\frac{\text{d}^{2}}{\text{D}}. \tag{15}\]  
Figure 8 shows the relationship between the intensity of segregation (Is) and the mixing time (t) in different flow states [2]. The intensity of segregation (Is) in turbulent flow decreases more rapidly than laminar flow, because turbulence can promote convective motion between micro-clusters of fluid, and shorten the distance between micro-clusters, thus enhancing the mixing efficiency dominated by \begin{table}
\begin{tabular}{c c} \hline \hline
**Chemical Constituents** & **Initial Concentration (mol/L)** \\ \hline H\({}^{+}\) & 0.05/0.06 \\ IO\({}_{3}\)\({}^{-}\) & 0.00233 \\ H\({}_{3}\)BO\({}_{3}\) & 0.1818 \\ I\({}^{-}\) & 0.01167 \\ NaOH & 0.0909 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Initial concentration of the chemical constituents in the experiment. Figure 7: Micromixedness ratio of the micro reacting pipe with different determining size. convective diffusion. Therefore, the third design principle of the micro reacting pipe is trying to put the fluid in a turbulent state to enhance the mixing efficiency dominated by convective diffusion. Combined with the application requirements of the micro reacting pipe and the process constraints of metal additive manufacture, three design principles of the micro reacting pipe based on the metal additive manufacture method are summarized:  
1. The tilt angle of the internal structure is greater than or equal to 45\({}^{\circ}\) to avoid warping during laser melting;
2. The critical dimension of the micro reacting pipe's channel should be reduced as much as possible to enhance the mixing efficiency dominated by free diffusion;
3. To enhance the convection-diffusion dominated mixing efficiency, the fluid in the micro reacting pipe channel should be put in a turbulent state. The critical Reynolds number (Re *) is related to the roughness of the wall and channel shape, and Re is defined by the following Equation [2]:  
\[\mathrm{Re}= \frac{\rho vd}{\mu}, \tag{16}\]  
where \(\rho,v,d,\mu\) represent the density, average rate, critical dimension (hydraulic diameter), and dynamic viscosity of a cross-section, respectively. When the actual Reynolds number (Re) on a cross-section exceeds the critical Reynolds number (Re *), the flow will begin to become unstable and gradually transform to complete turbulence as the difference between the two increases. As Equation (16) shows, when the critical dimension (d) of the micro reacting pipe is reduced to a low level, the actual Reynolds number (Re) will be so small that the critical Reynolds number (Re *) cannot be exceeded or the gap between Re * and Re cannot be enlarged, which makes it difficult for the flow to transfer from laminar flow to fully developed turbulence. That is also the reason why the flow state is usually laminar flow in ordinary micro reacting pipes.