## 2 Materials and Methods
### Spray Parameters Calculation  
The images with the droplets were processed with the ImageJ analysis software, ver. 1.52a [43]. They were first converted in 8-bit gray scale images and then segmented to detect the droplets with respect to the background. After segmentation, the watershed binary filter was applied to separate some touching particles. Particles up to 4 contiguous pixels were considered as noise and then ignored.  
Among the numerous characteristic parameters provided by the software for the \(i\)-th identified particle, only the area \(A_{i}^{\prime}\) (pixel) was considered. Assuming that the droplet was a sphere and that it was not deformed by the silicone oil, its diameter \(D_{i}^{\prime}\) (pixel) was calculated according to Equation (1)  
\[D_{i}^{\prime}=\sqrt{\frac{4A_{i}^{\prime}}{\pi}} \tag{1}\]  
The distance in pixel provided by Equation (1) was then converted in real world distance by applying the measured calibration factor \(C_{f}\) (\(\upmu\)m/pixel)  
\[D_{i}(\upmu)=C_{f}(\upmu\text{m/pixel})\cdot D_{i}^{\prime}(\text{pixel}) \tag{2}\]  
Knowing the diameter of all the \(N\) droplets detected in each repetition, the following mean diameters were calculated:  
Arithmetic mean diameter  
\[D_{10}=\frac{\sum_{i=1}^{N}D_{i}}{N} \tag{3}\]  
Surface mean diameter  
\[D_{20}=\sqrt{\frac{\sum_{i=1}^{N}D_{i}^{2}}{N}} \tag{4}\]  
Volume mean diameter  
\[D_{30}=\sqrt[3]{\frac{\sum_{i=1}^{N}D_{i}^{3}}{N}} \tag{5}\]  
Sauter mean diameter (SMD)  
\[D_{32}=\frac{\sum_{i=1}^{N}D_{i}^{3}}{\sum_{i=1}^{N}D_{i}^{2}} \tag{6}\]  
Other diameters, usually adopted to classify agricultural nozzles in terms of spray quality, were computed with reference to the volume of liquid carried by the droplets. Given a droplet with diameter \(D_{i}\) (\(\upmu\)m), its volume \(V_{i}\) (\(\upmu\)m\({}^{3}\)) was calculated according to Equation (7)  
\[V_{i}=\frac{\pi}{6}D_{i}^{3} \tag{7}\]  
Sorting the droplets in increasing order by their diameter, the cumulative volume \(CV_{D_{k}}\) (%) corresponding to the diameter \(D_{h}\) was calculated according to Equation (8)  
\[CV_{D_{h}}=\frac{\sum_{i=1}^{h}V_{i}}{V_{T}}\times 100 \tag{8}\]  
\(V_{T}\) being the total volume carried by all the \(N\) droplets. Knowing the cumulative volume, the following volumetric diameters were computed:  
\(D_{v10}\): the diameter such that \(CV_{D_{v10}}=10\%\);  
\(D_{v50}\): the diameter such that \(CV_{D_{v50}}=50\%\), also known as Volumetric Median Diameter (VMD);  
\(D_{v90}\): the diameter such that \(CV_{D_{v90}}=90\%\).  
In general, the volumetric diameter \(D_{v\alpha}\) is the diameter such that the \(\alpha\%\) of the total volume is carried by droplets with diameter lower than \(D_{v\alpha}\). These diameters, especially the VMD, are used to classify the nozzles in terms of drop pulverization. An index of uniformity of the spray is provided by the Relative Span Factor (RSF, %)  
\[\text{RSF}=\frac{D_{v90}-D_{v10}}{D_{v50}}\times 100 \tag{9}\]  
All diameters were calculated for each repetition, considering the three Petri dishes together in such a way to have a significant drop sample (at least 2000 droplets), and mean values were reported. The calculations were carried out by means of custom functions written in R language, ver. 3.6.3 [44].