## 1 Introduction  
In all types of polymer electrolyte fuel cells (PEFC), also called proton exchange membrane (PEM) fuel cells, the gas diffusion layers (GDLs) are components with high relevance for efficient operation of fuel cells. Two major requirements can be identified. One is the electric contact to be provided between the bipolar plates and the catalyst layer (CL). This determines the choice of the material. The second requirement is to facilitate efficient mass transport. For this purpose, an appropriate microstructure is required. To meet the requirements, carbon fibers are typically used for the fabrication of different types of GDLs, e.g., paper, woven, or non-woven textiles. The lattice Boltzmann method (LBM) is widely used for the simulation of mass transport in GDLs. [PERSON] et al. [1] reviewed the many aspects of the modeling activities of PEM fuel cells. One topic that was identified as a critical issue to be investigated was the area between domains of different spatial scales; the interface between the GDL and channels is one of them. [PERSON] et al. [2] investigated multiphase modeling of PEFCs on the cell level. In their review, they highlighted the relevance of the GDL/channel interface. Various methods are available to obtain the microstructure of the GDL, e.g., X-ray synchrotron, focused ion beam (FIB)/SEM and stochastic reconstruction [3]. The gas transport in a GDL was simulated by [PERSON] et al. [4; 5; 6] and [PERSON] [7] by means of LBM. Uncompressed GDLs, as well as compressed GDLs were studied. In more detail, [PERSON] et al. [4; 5] simulated gas transport in paper-type GDL with its microstructure based on the stochastic geometry model of [PERSON] et al. [8]. The gas flow at the GDL exit was analyzed from a statistical viewpoint [5]. Furthermore, the macroscopic properties of permeability and tortuosity were analyzed statistically from the viewpoint of compression and the variation of the microstructure [4]. [PERSON] et al. [4] used the Kozeny-Carman equation to verify the calculated effective permeability and tortuosity. The Kozeny-Carman equation is widely used by researches investigating gas flow in porous structures, e.g., by [PERSON] et al. [9] in their experimental studies. [PERSON] et al. [10] used the LBM for their transport simulations in woven GDLs of high-temperature PEFCs (HT-PEFCs). The catalyst layer (CL) was reconstructed mimicking the clusterization of carbon particles statistically. [PERSON] et al. [11] reconstructed Toray GDL and investigated the addition of PTFE to the microstructure with varying total amount and spatial distribution. They studied the influence of the PTFE on surface area and volume and calculated the permeability from single-phase flow simulations using the LBM. Based on microstructures reconstructed from X-ray tomographic microscopy (XTM) scans, [PERSON] et al. [12] in turn simulated liquid transport, and they obtained effective properties of the GDL. [PERSON] et al. [13] completed the knowledge of the microstructure of a GDL with the distribution of binders. [PERSON] et al. [14] obtained the characteristics of the porous structure of paper-type GDL from transport simulations in geometries, which were reconstructed according to the distribution of the orientation of the fibers. Experimental investigations by several research groups complement the simulations mentioned above. The gas permeability of a GDL was measured by [PERSON] et al. [15]. They considered different levels of compression. Other properties of GDLs--diffusion, thermal, and electrical conductivity--were measured by [PERSON] and [PERSON] [16]. The in-plane diffusivity of several types of GDL was measured by [PERSON] and [PERSON] [17]. [PERSON] et al. [18], meanwhile, investigated the impact of compression on commercial GDLs. [PERSON] and [PERSON] [19] used two adjacent channels of a flow field as an application-oriented experimental setup. In order to obtain the in-plane permeability of the GDL, they analyzed the cross-flow under the ribs.