## 3 Results and Discussions
### Simulation Results of Micro Reacting Pipe and Selection of Model Parameters
#### 3.2.2 Simulation Results of Micro Reacting Pipe  
The simulation data were substituted in Equations (5) and (6) to obtain the mixing index under the corresponding determining size, as shown in Figure 9.  
Based on the theories and experiment results above, concrete measures were put forward for the design of the micro reacting pipe, including:  
* Reducing the micromixing distance and improving the mixing efficiency by means of sudden contraction and sudden enlargement of the cross-section of the micro reacting pipe;
* The fluid can be separated by means of a structure with a sharp edge;
* The fluid confluence can be guided by an inclined plane with a certain angle between the wall of the tube and the surfaces of the obstacles. With these measures, the fluid can collide in the radial direction and greatly enhance the convection diffusion of the components in the radial direction. It can be seen from Figure 9a that the mixing index decreases first and then become larger with the increase of the determining size, and then decreases rapidly after an extreme value, where the extreme value appears when the determining size is 0.8 mm. Refer to the previous analysis of the design principles of micro reacting pipes, it is the result of the combination of the second design principle (reducing the size, enhancing the free diffusion) and the third design principle (creating turbulence and enhancing convection-diffusion) in Figure 9b. According to the analysis of the second design principle, with the increase of the determining size, the critical dimension of the channel as well as the longest distance between the fluid components is also increasing. Therefore, the mixing efficiency caused by free diffusion decreases with the increasing of the determining size, and the mixing index caused by free diffusion decreases monotonously with the increase of the determining size. With the increase of the determining size, the critical dimension of the channel is also increasing. According to Equation (16), this accelerates the increase of the actual Reynolds number in the channel. However, the increase of the determining size also reduces the volume of the obstacle and the interference to the flow. Due to the existence of this pair of contradictions, the mixing efficiency caused by convection-diffusion exhibits an \"inverted U-shaped\" change as the critical dimension to increase. Figure 9: Mixing index and diffusion types in the reacting pipe: (**a**) mixing index of the micro reacting pipe with different determining size; (**b**) interaction of free diffusion and convection diffusion. To explain the disturbance effect of the designed obstacle on the fluid flow, and according to Figure 9a, the best determining size is 0.2 mm. The micro reacting pipe without obstacles and the micro reacting pipe with the determining size of 0.2 mm were simulated, as shown in Figure 10 below. The mixing index of the obstacle free micro reacting pipe was calculated to be 0.315734242. As shown in Figure 10a,c, the state of flow flowing in an unobstructed channel is laminar, the fluid flows completely along the axial direction, and there is a lack of transverse mass and momentum exchange between the fluid microspheres. So, the diffusion of components depends on the random motion of molecules. In the channel with obstacles, the fluid is squeezed at the square frame, which reduces the distance between the two sides of the fluid boundary, shortens the maximum displacement of the two components, and enhances the free diffusion efficiency of the components. At the circle, the velocity vectors round in layers of circles, indicating that a swirl is formed there, which indicates that the fluid flow changes into turbulence. Figure 10d,e is respectively two velocity vector diagrams of the fluid formed after passing through one set of orthogonal obstacles. In Figure 10d, four strands of fluid, upper left, upper right, lower left, and lower right, are guided by obstacles to move towards the circle in the graph and converge into two strands.