## 2 Experimental Procedure  
The experimental facility (Figure 3) is composed of four main parts: image acquisition, impact surface, droplet dispensing system, and impact site illumination. For image acquisition, we used a high-speed digital camera Photron FASTCAM mini UX50 with 1.3 Megapixel resolution at frame rates up to 2000 fps (frames per second) and at reduced image resolution for frame rates up to 160,000 fps. We used a Macro Lens Tokina AT-X M100 AF PRO D with a minimum focus distance of 0.3 m, a focal length of 100 mm, a macro ratio of 1:1, and a filter size of 55 mm. The image resolution at first was \(1280\times 1024\), the exposure time was \(1/5120\) s, and the frame rate was 2000 fps. A topless right-angled perspex container was the impact surface and its dimensions were calculated based on the maximum droplet diameter (edge equal to \(40D_{0,max}\)). To release the droplets, a syringe pump NE-1000 was used at a pumping rate of 0.5 mL/min. To vary the droplet diameter, five stainless steel precision tips were used. They had straight tips and their inner diameters were: 1.5 mm, 0.84 mm, 0.51 mm, 0.25 mm,and 0.10 mm. The illumination of the impact site is crucial, and the only light source in the room was a 20 W LED in front of the camera to provide backlighting. A piece of diffusion glass was placed between the impact site and the LED. The physical properties of the three fuels used were measured to increase the precision of the study (density, surface tension, and dynamic viscosity) and can be seen in Table 2. It is possible to see that both the densities and the surface tensions of the three fluids are very similar, the major differences being in the dynamic viscosity values. As mentioned, pure water was also tested as a reference since its properties are well defined in the literature. The experimental procedure has two parts. In the first part, the camera was kept parallel to the droplet falling plane and the droplet diameters and impact velocities were measured through the impact upon the dry surface to allow the determination of the liquid film thickness. In the second part, the camera was leaned 10\({}^{\circ}\) with the horizontal plane to improve visualization. In this part, the droplet impinged upon a liquid film with dimensionless thicknesses (\(\delta\)) of 0.1, 0.5, and 1. Since perspex is a hydrophobic surface, it was not possible to produce the thinner films for water. Water and perspex are a non-wetting system. In this way, the thinner films produced for H\({}_{2}\)O were defined by the minimum volume that allowed the production of a homogeneous liquid film and it was then calculated for every droplet diameter. Table 11 in the Appendix A shows the values for the thinner dimensionless thicknesses for H\({}_{2}\)O. To measure the droplet diameter and the impact velocity, a MATLAB algorithm was created to subtract the background and the binarization of the image; the number of pixels corresponding to the droplet diameter were counted. By multiplying that by the pixel size, the droplet diameter was then determined. The maximum pixel size was 49.2 \(\upmu\)m/pixel providing a maximum error of 24.6 \(\upmu\)m. For the impact velocity, the image treatment was similar, but in this case, it was chosen the last droplet before impact and the droplet 5 ms before and again by pixel counting the values were determined. A more detailed description of the experimental work can be seen in [PERSON] [27]. In terms of the experimental conditions explored in this work, the five different inner diameters of the needle used resulted in the droplet diameters varying from, approximately, \(D_{0}\) = 1.7 to 4.0 mm (see Table 12 in the Appendix A for the details). The differences between the three fuels are negligible, and water registered the largest diameters due to the higher surface tension. Table 13 in Appendix A