## 3 Results
### Impact of the Compression  
The through-plane transport was simulated under 30% compression. Figure 5 shows the velocity extracted at the GDL/channel interface with contour levels according to the mass-related quantiles \(z\) \begin{table}
\begin{tabular}{l c c c c} \hline  & \(s_{\text{tot}}(50)\) & \(s_{\text{tot}}(20)\) & \(\kappa\) & \(\tau\) \\ \hline \(s_{\text{tot}}(70)\) & \(0.833\) & \(0.48\) & \(0.113\) & \(-0.053\) \\ \(s_{\text{tot}}(50)\) & & \(0.593\) & \(0.12\) & \(-0.087\) \\ \(s_{\text{tot}}(20)\) & & & \(-0.127\) & \(-0.133\) \\ \(\kappa\) & & & & \(-0.593\) \\ \hline \end{tabular}
\end{table} 
Table 3: Correlation coefficients, uncompressed GDL. \(q\) in %. The velocity is colored in the same range as is used in Figure 4. Although the transport properties--permeability and tortuosity--changed under compression according to the Kozeny-Carman equation, the distribution of the relative total quantile areas at the interface did not change. The permeability and tortuosity are shown in Figure 6a. Compared to the uncompressed properties in Figure 3a, the tortuosity increased and the permeability decreased under compression, which is consistent with earlier studies [4]. Related to the quantiles of the total mass flow, Figure 6b,c shows the relative total quantile areas of the gas flow and the largest of these. The overall picture of the diagrams in Figure 4 looks very similar to that in Figure 6, but with reduced absolute values. It is noticeable that also the permeability and tortuosity in Figure 6 changed their absolute values compared to the numbers in Figure 3, which was already discussed by [PERSON] et al. [4; 5]. Detailed surface characteristics of the compressed GDL are shown in Table 4. The GDL was compressed here by 30%. Figure 5: Velocity at the GDL/channel interface for realization Nos. 5 and 15. Mass-related quantiles for \(q=70\%\), \(50\%\), and \(20\%\). Figure 6: Impact of compression, 30% compressed, slip condition at walls: (**a**) permeability and tortuosity; (**b**) relative total quantile areas of the gas flow; total area where \(u_{q}(z)>0\). (**c**) The largest area from (**b**). The size of the total area \(s_{\text{tot}}\) was smaller under compression, i.e., the average value was reduced from 167,000 \(\upmu\)m\({}^{2}\) (Table 2) to 150,000 \(\upmu\)m\({}^{2}\) for the 70% quantile level. The percentage of \(s_{\text{tot}}\) related to the total surface of 590,000 \(\upmu\)m\({}^{2}\) is shown in Table 5. The upper limit of the total quantile area was roughly the porosity of the GDL, which was 78% in the representations of the geometric model [4; 8]. In particular, \(s_{\text{tot}}\) was limited by the local porosity of the upper fiber layer, which may vary slightly from the average. A similar trend can be observed on the other average values in the tables. The reduced porosity of a compressed porous structure leads (on average) to a higher absolute velocity under the condition of a fixed total amount of gas to be transported through the GDL. The higher velocity is caused by smaller pore sizes. The correlation between the surface characteristics of the compressed and uncompressed material is presented in Table 6. Because the range of the values changed under compression, [PERSON]'s test was again chosen as the test method. The entries in the table are the correlation coefficients of the given property, i.e., \(s_{\text{tot}}\) for the 70% quantile in the first line, first column, obtained from simulation results on uncompressed and compressed microstructures. As before, the value of 0.593--the correlation between \(\kappa\) and \(\tau\) from Table 3--was taken as a lower limit for judging two characteristics as being related to each other or not. On the basis of this value, the total quantile area \(s_{\text{tot}}\) was evaluated as being correlated under compression for all quantile levels, as well as the average sizes \(s_{\varnothing}\) for the quantile levels of 70% and 50%.