## 2 Materials and Methods
### Selection of Voxel Size  
A preliminary study was conducted to investigate the effect of the voxel size on the qualitative and quantitative estimations. The motivation was to determine whether larger voxel sizes could safely be used which would result in larger lengths of the channels being investigated. Figure 3 shows the analysis of the same section of the channel \(D_{nom}\) = 6 mm A, conducted with voxel sizes of 9 \(\upmu\)m, 20 \(\upmu\)m, 60 \(\upmu\)m, and 120 \(\upmu\)m. To fit the external diameter of the entire sample (i.e., 15 mm) within the detector field of view, leaving sufficient lateral space for acquiring information on the background grey values, voxel sizes below 9 \(\upmu\)m were not taken into account. It must be noted that no bandwidth matching was conducting for the quantitative comparison of average \(Pa\)-values in this section.  
Figure 2: Cropped cross-sectional view of the \(D_{nom}\) = 3 mm channel.  
Firstly, the quality of the cross-sectional views is greatly diminishing with the increasing voxel size. Secondly, the qualitative surface deviation maps indicate that a larger voxel size could be used in situations where only the significant surface texture patterns are of interest. The qualitative difference between a voxel size of 9 \(\upmu\)m and 20 \(\upmu\)m is only observable in how the smallest particles and agglomerations are not captured at a voxel size of 20 \(\upmu\)m. This difference means little for the qualitative evaluation and overall surface texture pattern but influences the quantitative evaluation. In this case, a difference of approximately 20% is found between the estimations of the average _Pa_-values of the channel (see Section 2.3 for the definition of _Pa_). The larger average _Pa_-value is due to the profile extraction methodology, wherein the profiles are generated similar to a stylus being dragged across the surface. The same \"probe size\" was used for extracting the profiles. Having a larger voxel size and lower resolution leads to each profile representing a \"broader\" area of the surface. Therefore, a larger percentage of the extracted profiles will have larger deviation values, resulting in an overestimation of the average _Pa_-value. The broadening effect is compensated by the \"smoothening\" of the surface texture that occurs when the voxel size is increased further. This can be seen for the 60 \(\upmu\)m and 120 \(\upmu\)m cases in Figure 3, which follow the general trend of voxel size effects on areal surface texture parameters [14]. The large negative deviation observed on the top part of the 60 \(\upmu\)m case is associated with how the nominal element is created by locally fitting an ellipse to each of the image slices used to create the 3D point cloud. The surrounding peaks of dorsal on both sides of the blue area in the 60 \(\upmu\)m case have a significant influence on the fit. Therefore, the general shape deviation from the nominal geometry is being captured, resulting in negative values at the top. This tendency is even more apparent for the 120 \(\upmu\)m case where, primarily, only the shape deviation from the nominal geometry is being captured.  
Since the purpose of this work was to investigate the characterization possibilities of using different surface texture parameters, it was decided to use a voxel size of 9 \(\upmu\)m to ensure a high enough resolution at the cost of the investigated channel length.