## 3 Results and Discussion  
### Numerical Simulations  
Figure 4 shows contour profiles of the dimensionless fraction of tracer in the T-reactor. It can be seen that the difference in the mixing of citric and formic acid in the T-type reactor is hardly discernible as both acid mixtures have similar densities and viscosities. As the flow velocity of the reactants increases, the agitation rate does not increase. The differencein mixing citric acid and formic acid in the S-type reactor is almost imperceptible (Figure 5). As the reactor flow rate increases, the agitation rate increases significantly in contrast to the T-reactor. This is a positive effect as the S-type reactor allows the process to be controlled by the reactor flow rate. The homogeneous precipitation of molybdenum disulfide is an almost instantaneous process [28,29]. Therefore, to limit secondary precipitation and agglomeration processes, intensive mixing of the inlet streams is required. In order to demonstrate the difference between T-type and S-type reactors, we decided to determine areas of high mixing intensity, defined as areas above 70% of the maximum value for turbulence intensity. The volume of these areas is shown in Table 2 and their shape in Figure 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Reactor Type**} & **Flow Velocity** & **Volume of Mixing Zones with** & **Maximum Intensity of Turbulence** \\  & **[mL/min]** & **the Highest Intensity \({}^{*}\) [m\({}^{3}\)]** & **[\%]** \\ \hline \multirow{2}{*}{T} & 20 & \(1.49\times 10^{-9}\) & 13 \\  & 40 & \(1.78\times 10^{-9}\) & 24 \\  & 60 & \(1.80\times 10^{-9}\) & 34 \\ \hline \multirow{2}{*}{S} & 20 & \(1.89\times 10^{-9}\) & 13 \\  & 40 & \(3.40\times 10^{-9}\) & 24 \\  & 60 & \(4.10\times 10^{-9}\) & 35 \\ \hline \hline \end{tabular} \({}^{*}\)Zones were defined as areas above 70% of the maximum value for mixing intensity.  
\end{table} 
Table 2: The volume of mixing zones with the highest intensity and maximum intensity of turbulence for T- and S-type reactors. Figure 4: Contour profiles of dimensionless fraction of tracer in the T-reactor with citric acid (scale from 0 to 1) for various flow velocities (**a**) 20, (**b**) 40, and (**c**) 60 mL/min and for formic acid for flow velocities (**d**) 20, (**e**) 40, and (**f**) 60 mL/min. Figure 5: Contour profiles of the dimensionless fraction of tracer in the S-reactor for citric acid (scale from 0 to 1) for various flow velocities (**a**) 20, (**b**) 40, and (**c**) 60 mL/min and for formic acid for flow velocities (**d**) 20, (**e**) 40, and (**f**) 60 mL/min. Figure 6: Mixing zones with turbulence intensity above 70% in the T-reactor for various flow velocities of CA (**a**) 20, (**b**) 40, and (**c**) 60 mL/min and in the S-reactor for (**d**) 20, (**e**) 40, and (**f**) 60 mL/min. The maximum value of the turbulence intensity is equal in both reactors (Table 2). Only the sizes of the zones where mixing is most intense differ. A comparison of these values shows that in the S-reactor the volume of high mixing intensity is 27% greater than in the T-reactor for the lowest flow and increases by up to 228% for the highest flow. Figure 6 shows these zones for both T- and S-type reactors for different flow velocities. Differences in the shape of these areas can be clearly observed. In the T-type reactor, the maximum turbulence intensity values occur in the collision area of the inlet streams and in the outlet pipe axis (especially for higher flows). The situation is different in the S-type mixer, where the shift of the inlet tubes creates a vortex that intensely mixes the streams and creates a zone that is difficult for the inlet fluid elements to bypass. These conclusions are consistent with the literature [30; 31; 32]. The effect discussed can be clearly seen in Figure 5, where there is a faster homogenization of the tracer concentration in the S-reactor than in the T-reactor. Due to the lack of significant differences between FA and CA, the results are presented only for citric acid.