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The Importance of Diffusion Mechanisms in High Temperature Polymer Electrolyte Fuel Cells

In the present work a three-dimensional computational model was developed to allow for calculations of conservation of mass, momentum, and energy transfer in both the liquid and gas regions of a HT-PEFC. The open source software OpenFOAM was employed for the development and application of the HT-PEFC model. The geometry used in this work is illustrated in figure 1 and corresponds to an in house testing cell. The active area of the cell is 16 cm^{2}. Experimental data on water distribution was used to validate the model.

A Maxwell-Stefan formulation for multi-component diffusion in the gas region was implemented. A matrix transformation was used to decouple the Maxwell-Stefan system. The results are compared to a Fick's-law type formulation. In the liquid region the phosphoric acid doped membrane is treated as a binary solution. A diffusion model based on Fick's law and Stokes-Einstein equation is used. Calculations were conducted to determine the diffusion flux of water from the cathode to the anode. Results in terms of the local concentration of phosphoric acid in the membrane are presented. The heterogeneous phosphoric acid distribution leads to local variations in the ionic conductivity of the membrane. A series of performance calculations is carried out to determine the impact of diffusion-effects on cell performance. Calculations based on Fick's law suggest the overall conductance to be about 20% higher than obtained with the Maxwell-Stefan formulation for these gas mixtures. Figure 2 shows the mass fraction of phosphoric acid on (a) the cathode and (b) the anode sides of the membrane. The non-homogeneous distribution suggests there are both through-plane and in-plane concentration gradients. These may be considered as the driving force for the motion of liquid water within the membrane. Initial comparisons of the results of the present authors’ calculations and those from experimental data, in terms of (i) polarization curve and (ii) water content at both anode and cathode outlets suggest the model is capable of being used predictively in the future.

[1] W. Maier, T. Arlt, C. Wannek, I. Manke, H. Riesemeier, P. Krüger, J. Scholta, W. Lehnert, J. Banhart, D. Stolten, "In-situ synchrotron X-ray radiography on high temperature polymer electrolyte fuel cells." *Electrochemistry Communications* **12** (2010) 1436-1438.

[2] K. Wippermann, C. Wannek, H.-F. Oetjen, J. Mergel,W. Lehnert, "Cell resistances of poly(2,5-benz-imidazole)-based high temperature polymer membrane fuel cell membrane electrode assemblies: Time dependence and influence of operating parameters" *Journal of Power Sources* **195** (2010) 2806–2809.