## 1 Introduction
The permeability of the GDL was measured by [PERSON] et al. [20], and its impact on the fuel cell efficiency was analyzed. The focus in the studies mentioned above was on GDLs, in particular their material properties and the mass flow in the microstructure. The simulation of entire fuel cells and stacks spans more than such small components. The consideration of all components covers multiple scales. Continuum-based approaches are often used in cell and stack modeling [21; 22; 23]. Such methods use effective volumetric properties of porous materials, e.g., the permeability. Surface characteristics can be found in experimental work; for instance, the roughness of the GDL surface was analyzed by [PERSON] et al. [24]. Interfaces between the regions of different properties have been investigated by several researchers. [PERSON] et al. [25] presented a review of the membrane/catalyst layer interface. The interface between the electrode and GDL was also addressed by [PERSON] et al. [26]. The relevance of the interface between the GDL and channels is reflected by experimental and modeling work. In the measurements of [PERSON] et al. [27], effective properties of the GDLs were investigated, as well as the mass flow at the GDL/channel interface. Many investigations of this interface focus on the liquid water transport in low-temperature PEFCs. [PERSON] et al. [28] observed in their experiments the behavior of droplets on a GDL surface. They studied the removal of liquid water droplets in a channel from the surface of different types of GDL. [PERSON] et al. [29], meanwhile, identified the GDL surface near the channel as a topic of high interest for the simulation of gas flow on the channels of the flow field of a fuel cell. [PERSON] et al. [30] simulated two-phase flow in fuel cell channels, assuming a static contact angle at the GDL surface. [PERSON] et al. [31], in turn, simulated the hydrodynamics of water droplets in the gas channels. They investigated droplets leaving the GDL surface at two distinct positions. [PERSON] and [PERSON] [32] simulated the inhibition of oxygen transport in flow channels in the presence of liquid water. They worked with regular patterns at the GDL interface where the water was entering the channel. The position of liquid water transported from the GDL into the gas channel can be inherently transferred by coupling the simulation domains of both spatial scales, as was done by [PERSON] et al. [33]. They found that such tight coupled simulations can require enormous computational resources. Two adjacent regions of a fuel cell are sometimes simulated on different spatial scales. From a macroscopic view, the interface is a 2D element. The role of the GDL/channel interface in this scenario is illustrated in Figure 1. The GDL/channel interface was investigated by [PERSON] et al. [34], who analyzed irregular contact angles of water droplets at the GDL surface and their pattern when they passed the GDL/channel interface at several positions. The relevance of the interface for multi-scale simulations was shown by [PERSON] et al. [35; 36] and [PERSON] et al. [37], who used pore network modeling (PNM) to bridge the scales (still on water transport in low temperature PEFCs). [PERSON] et al. [38] coupled the LBM in the porous GDL structure with OpenFOAM simulations in the air channel. The relevance of the characterization of the interface for multi-scale simulations still holds for other types of fuel cells, e.g., HT-PEFCs. [PERSON] et al. [39] analyzed the gas flow in a channel over a regular porous structure for different Reynolds numbers. The interface was included in the comprehensive analytical studies of [PERSON] [40]. The studies of [PERSON] et al. [41] showed that the Peclet number at the GDL/channel interface is relevant for the current density profile along the channel. They focused their studies on oxygen transport in the GDL and channel, as well as on charge transport in the membrane. In this manuscript, through-plane transport in GDLs is simulated with the LBM.