## 2 Materials and Methods
### Definition of Surface Profile Parameters of Interest and Fractal Dimension  
The surface topography characterization inside channels performed in this study was based on the methodology proposed by [PERSON] et al. [29], which uses 3D point cloud data generated from 3D voxel-based data to extract surface profiles along the length of channels and at 360\({}^{\circ}\) around the channel periphery. The surface profiles are obtained similar to running a contact stylus across the surface of the channel. For a detailed description of the  
Figure 3: Investigation of the effect of voxel size on qualitative and quantitative evaluation of surface texture. The shown case is for \(D_{nom}\) = 6 mm (sample A). The top row of images shows the quality of cross-sections at different voxel sizes. The bottom row shows 3D color plots of the investigated channel at different voxel sizes. profile extraction methodology and subsequent profile preparation and analysis, the reader is referred to the aforementioned work. The in-house Python code used in the former work was expanded in terms of the computed surface profile parameters. In particular, the 12 calculated parameters are briefly described below. All the parameters (i.e., \(P\)-parameters) were computed on the primary profiles, obtained after removing the form error (e.g., mean line) of the original profiles. The height at a given point along the profile length \(x\) is described as \(Z(x)\) and the sampling length in this work was equivalent to the profile length \(l\). _Amplitude surface profile parameters_  
* \(Pa\) is the arithmetical mean deviation of the assessed profile [9]: \[Pa=\frac{1}{l}\int_{0}^{l}\lvert Z(x)\rvert dx\] (2)
* \(Pq\) is the root mean square deviation of the profile, representing the variation of the profile [9]: \[Pq=\sqrt{\frac{1}{l}\int_{0}^{l}Z(x)^{2}dx}\] (3)
* \(Pp\) is the maximum profile peak height [9]: \[Pp=\max(Z(x))\] (4)
* \(Pz\) is the maximum height of a profile [9]: \[Pz=\max(Z(x))-\min(Z(x))\] (5)
* \(P10z\) is the average of the 10 largest heights of a profile [30]: \[P10z=avg(max10(Z(x))-min10(Z(x)))\] (6)
* \(Psk\) is the skewness of the profile, representing mass distribution around the mean line or _bias_ of the profile [9]: \[Psk=\frac{1}{Pq^{3}}(\frac{1}{l}\int_{0}^{l}Z(x)^{3}dx)\] (7)
* \(Pku\) is the kurtosis of the profile, representing the spikiness of the profile [9]: \[Pku=\frac{1}{Pq^{4}}(\frac{1}{l}\int_{0}^{l}Z(x)^{4}dx)\] (8)  
_Functional parameters_  
Profile versions of the void and material volume parameters according to ISO 25178-2:2012 [21] and similar to the linear material ratio curve parameters [31] were implemented. The void and material volume parameters defined in ISO 25178-2:2012 [21] are typically used to analyze the fluid flow over a surface, wear potential of the surface, lubrication properties, and debris entrapment [32]. In this work, such parameters are computed using the linear material ratio curve (see Figure 4) generated from the surface profiles. * \(Pmp\) (\(Vmp\)) is the peak material volume;
* \(Pmc\) (\(Vmc\)) is the difference in material volume between \(p\) and \(q\) material ratios (by default \(p=10\%\) and \(q=80\%\)[33]);
* \(Pvc\) (\(Vvc\)) is the difference in void volume between \(p\) and \(q\) material ratios (\(p=10\%\), \(q=80\%\));_Prextal dimension of profiles_  
Fractal dimensions can describe the complexity of natural phenomena where similar structures that are repeating at different scales are called self-affine structures [34]. Highly self-affine structures can be considered complex or \"rough\". The basic concept of fractal dimensions is that the more self-affine or self-similar a profile is, the higher its fractal dimension becomes, and this has led to the idea that it could be used as a measure for the roughness of a profile or area [35]. This measure is inherently different from classic profile parameters and was therefore included in the current work as an alternative parameter for characterizing surface texture.