## 3 Results and Discussion
### Qualitative Overview  
Figure 10 shows a surface deviation map overview of all the investigated channels. The sizes of the channels are scaled to the approximate relative sizes, enabling a qualitative comparison.  
Figure 10: Overview of the investigated channels showing dorsal formation and roughness.  
Figure 9: Prediction of \(D_{eq}\) for the \(D_{nom}\) = 3 mm channel. The length value on the x-axes corresponds to the length of a straight channel segment of which the equivalent diameter may be predicted. (**a**) Testing of the appropriate fitting; (**b**) normal stack size vs. large stack size.  
At around \(\beta=180^{\circ}\), it can be seen how dross formation is significantly reduced for all investigated channels except \(D_{nom}=1\) mm. This is likely due to the surface being identified as a down skin surface. A down skin surface is typically made with reduced power and scan speed to reduce the locally accumulated heat. A reduction in the locally accumulated heat could result in the observed reduction in sintered particles. The experimental and numerical work conducted by [PERSON] et al. on small circular LPBF geometries, made in AlSi10 Mg, supports this observation [37]. Their work showed a significant influence from changing down skin parameter settings such as laser power, scan rate, and hatch spacing on the dross formation in LBPF manufactured channels with a diameter of 0.5 mm and a build orientation perpendicular to the build direction.  
From the view through the channels, some qualitative deductions can be made. First, it can be seen how all channels, except the \(D_{nom}=1\) mm channel, follow a general dross formation pattern with regions of high dross formation on both sides of \(\beta=180^{\circ}\). This is in contrast to the dross formation pattern observed in steel LPBF channels [29; 38] where the dross formation was continuous from \(\beta=90^{\circ}\) to \(\beta=270^{\circ}\) and with maximum dross at \(\beta=180^{\circ}\). This discrepancy could be caused by the use of different process parameters at the down skin surfaces. The method of locally optimized process parameters might also be affecting steel and aluminum powder differently. The difference observed in the dross formation pattern could be due to the difference in thermal conductivity between aluminum and steel. The higher conductivity of aluminum allows for a larger degree of thermal diffusivity and could result in less heat accumulation at the top of the overhanging section, and thus less dross formation. The observed trend shows that in the range of \(\beta<90^{\circ}\) or \(\beta>270^{\circ}\), dross formation is generally minimal. A few scattered sintered particles and particle agglomerations are found on the upward facing surface. The sintered particles are mostly seen around \(\beta=45^{\circ}\), which could be due to the influence of the stair-casing effect, leading to further retainment of sintered particles [38]. The dross formation is seemingly increasing from \(\beta=90^{\circ}\) towards \(\beta=180^{\circ}\) until it abruptly reaches the onset of a low-dross area forming an upside-down \"valley\" between two \"hills\". While all investigated channels with \(D_{nom}\geq 2\) mm follow the same dross formation pattern, the \(D_{nom}=1\) mm channel is experiencing close to randomly distributed dross formation. This could be due to the small size of the channel and the possibility of increased local heat accumulation in the adjacent powder. Due to the size of the channel, this accumulated heat could be affecting every part of the channel contour leading to increased particle sintering. Finally, it can be seen how the angular widths (\(\beta\)) of the two dross formation \"hills\" are increasing with decreasing channel diameter.