## 2 Materials and Methods
### Data Analysis and Modelling  
The images of the droplets captured by the camera are analyzed using a Convolutional Neural Network (CNN), which detects spherical droplets in a series of images to ensure statistical significance as depicted in Figure 4. The CNN is based on a U-net architecture using PyTorch with pre- and post-processing by the corresponding OpenCV functions. The CNN is specially trained for this use case as described elsewhere [43]. For the training of the CNN, the synthetic dataset from [43] was augmented with real images of droplets to increase the detection quality. In previous work, the detection of droplets with the CNN was validated up to \(\varphi=25\) vol.-% with an average error of 4.26% for the Sauter mean diameter. The CNN was used without any additional training for phase fractions \(\varphi\geq 25\) vol.-% and images were manually crosschecked to ensure accurateness. The evaluated images show a precise detection of the droplets, whereas strongly overlapping droplets were not evaluated. Overall, more droplets were detected in the image at low phase fractions than at high phase fractions. In particular, Figure 4 shows that at 50 vol.-% only about half of the droplets were analyzed. However, since almost all detections are accurate, the network can be used for the evaluation of all phase fractions investigated. Overall, 15,000 to 300,000 droplets were detected per experiment, which is on average 100,000 droplets per experiment ensuring a statistic significance. Crosschecking of the images revealed a few false detections for large droplets (diameters from 2 mm to 8 mm). Since these erroneous detections lead to false droplet sizes, they falsify the volume distribution and the Sauter mean diameter in particular. Therefore, 1% of droplets with the largest diameters were systematically excluded from the evaluation and not considered further. The measured droplet diameters were converted to a number and volume distribution. The following relationship was used for the number distribution \(q_{0,i}\):  
\[q_{0,i}=\frac{\Delta Z_{i}}{Z\cdot\Delta d_{i}}\text{ with }\Delta d_{i}=d_{i}-d_{1-i} \tag{11}\]  
The number distribution \(q_{0,i}\) describes the number of particles, \(\Delta Z_{i}\), of all measured particles, \(Z\), that are in a specific diameter range, \(\Delta d_{i}\), the so-called class width, which was set to 20 \(\upmu\)m for all classes. The number distribution is suitable for showing phenomena such as unwanted emulsification, but has limited use for the description of mass transfer processes. The volume distribution, \(q_{3,i}\), is calculated from the number distribution without considering any shape factor as follows:  
\[q_{3,i}=\frac{\overline{d}_{i}^{3}\cdot q_{0,i}}{\sum_{i=1}^{n}\left(\overline {d}_{i}^{3}\cdot q_{0,i}\cdot\Delta d_{i}\right)}\text{ with }\overline{d}_{i}=\frac{d_{i}+d_{i-1}}{2} \tag{12}\]  
The volume distribution is more relevant for the description of mass transfer processes than the number distribution, since very small droplets contain almost no transfer component, and therefore have almost no contribution to mass transfer. Although a complete DSD is decisive for a detailed description of processes, in many cases the Sauter mean diameter, \(d_{32}\), is sufficient. It is calculated from the second moment, \(M_{2,0}\) and third moment, \(M_{3,0}\) of the number distribution as follows:  
\[d_{32}=\frac{M_{3,0}}{M_{2,0}}=\frac{\sum_{i=1}^{n}\left(d_{i}^{3}\cdot q_{0} \cdot\Delta d_{i}\right)}{\sum_{i=1}^{n}\left(d_{i}^{2}\cdot q_{0}\cdot\Delta d _{i}\right)} \tag{13}\]  
Figure 4: CNN analysis at different phase fractions at \(N=325\) rpm. (**a**) 10 vol.-%, (**b**) 30 vol.-% and (**c**) 50 vol.-%. The green circles represent the detected droplet circumference. No shape factor was used, as the drops in the images are perfect circles (shape factor equals 1).