# Fluid Dynamics in a Continuous Pump-Mixer
## 3 Results
### Experimental Results
#### 3.1.2 DSD at Different Measurement Positions  
The most suitable measurement position was found to be \(MP_{1}\) where the droplet size at every combination of impeller speed, phase ratio, and flow rate could be measured. The droplet size measurement at position \(MP_{2}\) could only be measured at low feed phase ratios because droplets accumulated at the glass windows and would lead to erroneous droplet size measurements. However, measurement position \(MP_{3}\) was capable of reliably measuring the droplet size, except at feed phase ratios of \(\varphi_{F}\) = 25 and 30 vol.-\(\%\) with an impeller speed of \(N\) = 425 rpm. The main reasons for droplet adhesion are the usage of simple borosilicate glasses without any coating and the local flow rate in the measurement gap was too low to tear off the droplets. The measured DSDs for all measurement positions are exemplarily depicted for \(N\) = 400 rpm and \(\varphi_{F}\) = 10 vol.-\(\%\) in Figure 6a. It shows identical, almost normally distributed DSDs for every measurement position. Hence, it can be assumed that the DSD generated by the impeller does not change until it leaves the pump-mixer, which indicates an axial-flow regime throughout the vessel. This is reasonable and is caused by the low off-bottom clearance \(C\). = 10 mm, leading to a single-loop pattern [28; 29; 36; 37] in a comparable batch vessel. This was also observed in pump-mixers by other authors using a low off-bottom clearance [7; 10].  
The normal distributed shape, slightly shifted to a log-normal distribution of the DSD, can be observed in a good approximation for all measured droplet sizes. This indicates a weak coalescence tendency that was already observed in our previous work using the same chemicals [22]. Hence, the DSD is well represented by the Sauter mean diameter, \(d_{32}\), being depicted for \(N\) = 425 rpm and feed phase ratios of \(\varphi_{F}\) = 10 and 20 vol.-\(\%\) in Figure 6b. It can be seen that the Sauter mean diameters were almost identical at different measurement positions and the deviations were within the typical error range of \(\pm\) 20 um, which is consistent with our previous studies [22; 32]. A consistent DSD between impeller and pump-mixer outlet could only be confirmed for \(\varphi_{F}\) = 10 vol.-\(\%\) because of the effects of droplet adhesion at higher values as mentioned above. However, it can be assumed that this is also valid for higher feed phase fractions. The measured Sauter mean diameters for all measurement positions are listed in the supplementary material in Table S2. Since the measured DSDs and Sauter mean diameters are almost equal, it can be assumed that at all measurement positions \(MP_{1-3}\) the DSDs are equal. Since measurement position \(MP_{1}\) was the only measurement position at which the DSD could always be measured, the following results and effects are discussed on the Sauter mean diameters measured at \(MP_{1}\).  
Figure 5: (**a**) Measured heads and flow rates for \(N\) = 400 rpm. (**b**) Measured heads and flow rates of the continuous phase for \(N\) = 375, 400, and 425 rpm for all measured feed phase ratios. The lines are the pumping curves calculated as quadratic polynomials as a guide for the eye.