## 2 Experimental Setup and Methods
### Film Thickness Measurement  
The film thickness sensor used for the presented experiments was developed in previous work [39] and is based on the Beer-Lambert Law (Equation (2)), which relates the attenuation of light of intensity I to the incident light intensity I\({}_{0}\); the path length through an absorbing medium, which is geometrically related to the film thickness \(\delta\); the absorption coefficient \(\kappa\), which is a function of wavelength \(\
u\); the film temperature T and wavelength-independent transmission losses Tr. The indices I and k represent the different wavelengths.  
\[\mathrm{I}(\
u_{\mathrm{i}})=\mathrm{I}_{0}(\
u_{\mathrm{i}})\cdot\mathrm{exp }[-\kappa(\
u_{\mathrm{i}},\ \mathrm{T})\cdot\delta]\cdot\mathrm{Tr}(\mathrm{i}=\mathrm{I},\mathrm{k}) \tag{2}\]  
The robustness of the sensor is increased using a second wavelength. In this way, it is ensured that wavelength-independent transmission losses (Tr) do not influence the measurement. The absorption coefficient \(\kappa\) is a wavelength-dependent material-specific  
\begin{table}
\begin{tabular}{c c c c c c c} \hline No. & \(\alpha\) & \(T^{\prime\circ}C\) & \(\overset{\rightarrow}{\
u}I\frac{\mathrm{m}}{\mathrm{s}}\) & \(\hat{m}_{Air}\frac{k\mathrm{g}}{\mathrm{h}}\) & \(\hat{m}_{DEF}\frac{\mathrm{\delta}}{\mathrm{h}}\) & Reynolds Number \\ \hline C1 & 1 & 180 & 6.5 & 129 & 697 & \(17.6\times 10^{3}\) \\ C2 & 1 & 250 & 3 & 51 & 278 & \(6.8\times 10^{3}\) \\ C3 & 1 & 250 & 6.5 & 111 & 604 & \(14.8\times 10^{3}\) \\ C4 & 1 & 250 & 10 & 171 & 929 & \(22.3\times 10^{3}\) \\ C5 & 1 & 350 & 6.5 & 94 & 507 & \(11.0\times 10^{3}\) \\ C6 & 2 & 250 & 6.5 & 111 & 1208 & \(14.8\times 10^{3}\) \\ C7 & 3 & 250 & 6.5 & 111 & 1812 & \(14.8\times 10^{3}\) \\ \hline \end{tabular}
\end{table}
Table 1: Operating conditions considered in this study.  
constant that varies with temperature and concentration differences. Therefore, \(\kappa\) is replaced by the calibration constants a and b determined by a previous, one-time calibration measurement. In this way, a direct relation between the intensities before and after passing the film, I and I\({}_{0}\), and the liquid film thickness \(\delta\) can be established (Equation (3)).  
\[\delta=\text{a}\cdot\ln\frac{\text{I}_{\text{I}}\cdot\text{I}_{\text{k},0}}{ \text{I}_{\text{I},0}\cdot\text{I}_{\text{k}}}+\text{b} \tag{3}\]  
In a previous work wavelengths of 1441 and 1654 nm were selected, which ensure that cross-sensitivities to temperature and urea concentration only have minimal influence on the measurement [40].  
The sensor used in the present study is depicted in Figure 3b. Since the sensor is a single-ended transceiver, it requires only one optical access from opposite the wetted wall. This allows the film to be deposited on a stainless-steel surface, comparable to the system walls of a real SCR system. The measurement point is located in the center of the channel, 13 cm downstream from the injection nozzle (see Figure 3a). As seen in Figure 3b, light of both wavelengths is time-multiplexed and guided through a glass fiber directly to the optical access. In this way, the free path of the beam is minimized. It is decoupled with a graded index (GRIN) lens and passed through the film and reflected at the bottom wall of the channel, and the returned beam is detected by a photodiode, delivering the intensity I\({}_{\text{x}}\). A prior splitting of 1% of the signal allows measurement of reference intensity I\({}_{0}\) that quantifies the intensity before the beam passes the film. Together with the calibration, the four measured intensities allow computation of the thickness of the investigated liquid film.  
To ensure comparability between the individual measurements, the injection of AdBlue was started 30 s after the start of the measurement and continued at 1 Hz repetition rate for 330 s. The measurements were stopped after all liquid was evaporated and solid deposits had formed.