## 3 Results and Discussion
### Entrance Section
#### 3.1.2 Parameter Case Study  
The four case studies that are shown in Table 4 were carried out to test the influence of velocity, channel height, particle diameter, and ratio between channel height and particle diameter. Table 5 shows the parameter ratios that are varied in the different cases. The results for a 30% bulk particle volume fraction are shown in Figure 6; the concentration at the center of the channel increases with an increasing channel length till it reaches a maximum, while the concentration at the wall decreases, which is indicative of shear induced diffusion taking place. Taking case 1 as our base case, an increase in channel height (case 2), and thus a change in H/D\({}_{\text{p}}\) ratio, results in reaching a different fully developed profile, as was also reported by [PERSON] and coworkers [16]. Although the average particle volume fraction stays the same, the absolute number of particles is higher in case 2, which allows for more particle migration, leading to more particles in the center, and less particles near the wall. Besides, we see that the length needed to develop the SID profile changes, because particles need to travel further in case 2, which is in line with findings by [PERSON] et al. [16]. Interestingly, at an equal channel height/particle diameter ratio (comparison between case 1 and 3), the entrance length changes while the fully developed profile does not differ, indicating the relative importance of these factors. Last, we checked the change in velocity but this did not influence the profile (case 1 and 4 in Figure 6 overlap), and indicates that the total number of interactions determines the concentration profile that is formed. Furthermore, if we compare different bulk particle volume fractions (Figure 7), we conclude that the profiles develop faster at higher concentrations, and the differences in concentration at the centerline decrease with an increasing bulk particle volume fraction, while the opposite is true for the region near the wall. We believe this is caused by the limited freedom of movement that particles have at higher particle volume fractions; the increase in particle concentration that can be achieved in the center is a function of the initial particle concentration, as illustrated in Figure 8. At high volume fractions, the particle concentration in the center may be very close to the maximum packing density (\(\alpha_{max}=0.68\)), while the concentration at the wall is considerably reduced when compared to the average concentration. Both effects are beneficial for the novel process that we investigate, but they are only useful if the concentration profile re-establishes fast after being disturbed by a pore, as is investigated next. It is good to mention that these effects are directly related to pore placement design, which is discussed in the concluding section. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{\begin{tabular}{c} **Channel Height** \\ **(H) (\(\mu\)m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Velocity (mm/s)** \\ **(D\({}_{\text{p}}\)) (\(\mu\)m)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Particle Diameter** \\ **(D\({}_{\text{p}}\)) (\(\mu\)m)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Ratio H/D\({}_{\text{p}}\)** \\ **Length (cm)** \\ \end{tabular} } \\ \hline
1 & 50 & 1.0 & 2 & 25 & 4 \\
2 & 100 & 1.0 & 2 & 50 & 10 \\
3 & 100 & 1.0 & 4 & 25 & 8 \\
4 & 50 & 0.5 & 2 & 25 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Four different case studies to look at the influence of different parameters. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Comparison between Cases**} & \multicolumn{2}{c}{**Parameters Compared**} \\ \hline
1 and 2 & Difference in H/D\({}_{\text{p}}\) ratio \\
1 and 3 & Difference in H and D\({}_{\text{p}}\) at equal H/D\({}_{\text{p}}\) ratio \\
1 and 4 & Difference in velocity \\ \hline \hline \end{tabular}
\end{table}