## 2 Materials and Methods
### Experimental Details
In every case, the milling strategy for the pockets was a zig-zag i.e., straight paths with alternating directions under the same nominal traverse feed rate. The nominal dimensions of the pockets were 30 mm in length and 9.6 mm in width. Given the relatively lower hardness of the abrasive material in comparison to the hardness of common abrasives, e.g., garnet, Al\({}_{2}\)O\({}_{3}\), and silicon carbide, it was anticipated that the wear of the nozzle could be rather minimal; however, the nozzle diameter was checked before the experiment and after some passes in order to verify this assumption. Finally, the workpiece material was Ti-6 Al-4V alloy (titanium grade 5), with its composition presented in Table 3. It is worth noting that this material has already been used in AWJ experiments [41; 42] but research on the machining of pockets with an eco-friendly abrasive on this material is limited. After the experiments were conducted, several measurements were performed on the produced pockets. At first, the depth of the pockets was estimated by repeated measurements on a coordinate measuring machine (CMM), namely a Mitutoyo CMM Crysta Plus M443 (Mitutoyo, Kawasaki, Japan). The measurement of surface quality indicators was performed by using a VHX-7000 ultra-deep-field microscope (KEYENCE, Mechelen, Belgium), which is a focus variation microscope with the capability of zooming up to \(2000\times\). Its function is comparable to that of confocal microscopes and a white light LED source is employed that passes through a semi-transparent mirror and a lens before eventually reaching the surface of the measured object. A mirror-like component termed a beam splitter redirects the light that bounces back from the focal points to an optical sensor, where it is recorded both spatially and in terms of brightness using a light-sensitive device. Figure 3: Abrasive particle diameter distribution. Figure 2: Waterjet machine tool employed for the experiments. By combining the narrow depth of field typical of traditional optical systems with vertical scanning, FV (focus variation) technology is able to produce high-resolution, colorful 3D surface measurements at a lower cost. Since a 4K camera was employed, the resulting images had a resolution of 4096 \(\times\) 2160 pixels. Using these 2D images, it was possible to measure the various surface quality indicators along multiple lines in order to obtain averaged values. More specifically, for every pocket the following indicators were recorded: Ra, Rz, Rp, Rv, Rsk, Rku, and Wa. Ra represents the average surface roughness, which is defined as the arithmetic average of the profile height deviations from the mean line, whereas Rz is defined as the maximum peak-to-valley height of the profile. Moreover, Rp and Rv represent the maximum peak height above the mean and maximum valley depth below the main line, respectively, while Rsk represents the skewness, e.g., asymmetry of the profile about the mean line and Rku represents the kurtosis e.g., intensity of features of the profile about the mean line. Finally, Wa is the average surface waviness, which is a higher order deviation (i.e.,a longer wavelength) than the surface roughness. For each indicator of surface roughness, the measurement was conducted on a sufficiently long path on the pocket surface including multiple evaluation lengths in order to achieve a reliable result, as the measurement of a restricted part of the surface, as was conducted in other studies, may lead to misleading results without generality. The cutoff (denoted as \(\lambda\)c) for the filtering of the roughness profile was selected based on the ISO 4288-1996 standard [43] determined by the Ra values. As the Ra exceeded 10 \(\mu\)m in every case, \(\lambda\)c was selected as 8 mm and the evaluation length 40 mm. For every quantity, average values are presented as well as the values of the coefficient of variation (CV), defined as the ratio of the standard deviation of the measurement \(\sigma\) to the average value \(\mu\).