2008, Fuhrmann, Jürgen, Zhao, H., Holzbecher, E., Langmach, H., Chojak, M., Halseid, R., Jusys, Z., Behm, R.J.

We describe first measurement in a novel thin-layer channel flow cell designed for the investigation of heterogeneous electrocatalysis on porous catalysts. For the interpretation of the measurements, a macroscopic model for coupled species transport and reaction, which can be solved numerically, is feasible. In this paper, we focus on the limiting current. We compare numerical solutions of a macroscopic model to a generalization of a Leveque-type asymptotic estimate for circular electrodes, and to measurements obtained in the aforementioned flow cell. We establish, that on properly aligned meshes, the numerical method reproduces the asymptotic estimate. Furthermore, we demonstrate, that the measurements are partially performed in the sub-asymptotic regime, in which the boundary layer thickness exceeds the cell height. Using the inlet concentration and the diffusion coefficient from literature, we overestimate the limiting current. On the other hand, the use of fitted parameters leads to perfect agreement between model and experiment.

2008, Ehrhardt, Matthias, Fuhrmann, J., Holzbecher, E., Linke, A.

In proton exchange membrane (PEM) fuel cells, the transport of the fuel to the active zones, and the removal of the reaction products are realized using a combination of channels and porous diffusion layers. In order to improve existing mathematical and numerical models of PEM fuel cells, a deeper understanding of the coupling of the flow processes in the channels and diffusion layers is necessary. After discussing different mathematical models for PEM fuel cells, the work will focus on the description of the coupling of the free flow in the channel region with the filtration velocity in the porous diffusion layer as well as interface conditions between them. The difficulty in finding effective coupling conditions at the interface between the channel flow and the membrane lies in the fact that often the orders of the corresponding differential operators are different, e.g., when using stationary (Navier-)Stokes and Darcy's equation. Alternatively, using the Brinkman model for the porous media this difficulty does not occur. We will review different interface conditions, including the well-known Beavers-Joseph-Saffman boundary condition and its recent improvement by Le Bars and Worster.