# Fluid Dynamics in a Continuous Pump-Mixer
## 3 Results
### Experimental Results
#### 3.1.4 Effects of the Process Parameters on the DSD
Additionally, while the values for \(\varphi_{F}\) = 10, 15, and 30 vol.-% were close to their least square lines, the values for the feed phase ratios \(\varphi_{F}\) = 20 and 25 vol.-% were scattered. Figure 9: (a) Measured Sauter mean diameters for \(N\) = 425 rpm at measurement position \(MP_{1}\) at different feed phase ratios \(\varphi_{F}\) and total flow rates \(\dot{V}_{tot}\). The dashed lines are linear least square lines as a guide for the eye. (b) Measured Sauter mean diameters at all impeller speeds \(N\) = 375, 400, and 425 rpm at different feed phase ratios and flow rates. The dashed lines are linear fits as a guide for the eyes. All Sauter mean diameters are measured at measurement position \(MP_{1}\). The impeller speed had a low impact on the Sauter mean diameter at different feed phase ratios \(\varphi_{F}\) = 10, 20, and 30 vol.-%. The cases for \(\varphi_{F}\) = 10 and 20 vol.-% are depicted in Figure 10a,b. Increasing the impeller speed at \(\varphi_{F}\) = 10 vol.-% led to smaller Sauter mean diameters, as expected from literature [23; 24] and previous studies in batch vessels [22]. Generally, a higher impeller speed leads to a higher energy dissipation and thus smaller droplets (see Figure 10a). This trend is present for the feed phase ratio \(\varphi_{F}\) = 10 vol.-%. In addition, the influence of the flow rate increased for lower impeller speeds, because the slopes of the dashed lines are flatter at lower impeller speeds. From Figure 10b, it can be seen that this behavior changes at a feed phase ratio of \(\varphi_{F}\) = 20 vol.-% because all Sauter mean diameters were more or less on one line. This indicates that the Sauter mean diameter at this feed phase ratio was mostly independent of the impeller speed. However, as long as the volume flow at the operating point is the same, the impeller speed has little to no significance on the Sauter mean diameter. It can be assumed that in the transition region, where collision and therefore coalescence suddenly increase (around \(\varphi_{F}\) = 20 vol.-%), the additional energy dissipation caused by the impeller speed is compensated. This indicates that the impeller speed has no impact, but this is only true for this specific feed phase ratio. Investigating this for the feed phase ratio \(\varphi_{F}\) = 30 vol.-% gives the Sauter mean diameter depicted in Figure 11a, where at a \(\varphi_{F}\) = 30 vol.-% the impeller speed \(N\) = 400 rpm produces the smallest Sauter mean diameters. This is counterintuitive, as a larger impeller speed generally lead to smaller droplets. However, the DSD at \(N\) = 400 rpm depicted in Figure 11b showed a large peak at around \(d\) = 40-60 \(\upmu\)m, which are fine emulsified droplets. We assume that this emulsification is a result of an increased energy dissipation. Since the most emulsification was found at \(N\) = 400 rpm compared with the other impeller speeds, we assume the highest energy dissipation is at \(N\) = 400 rpm. Additionally, data for \(\varphi_{F}\) = 15 and 25 vol.-% are shown in the supplementary material in Figure S4. Figure 10: Sauter mean diameter at measurement position \(MP_{1}\) at a feed phase ratio of (**a**) 10 and (**b**) 20 vol.-%. The dashed lines are least square lines as a guide for the eye.