Modeling Two-Phase Behavior in PEFCs Adam Z. Weber, a, * ,z Robert M. Darling, b, ** and John Newman a, *** a Department of Chemical Engineering, University of California, Berkeley, California 94720-1462, USA b UTC Fuel Cells, South Windsor, Connecticut 06074, USA A model is developed to examine quantitatively the effects of flooding on the operation of polymer-electrolyte fuel cells PEFCs. Specifically, the change in the maximum power as a function of the structural properties of the diffusion media, including the bulk porosity, wettability, thickness, and pore-size distribution, is described. The porous-medium model developed includes analytic expressions and a modeling methodology for handling both liquid and gas flow. The model is used in combination with our previous membrane model to simulate transport in typical gas diffusion layers and examine the effect of layer hydrophobicity on the maximum power. © 2004 The Electrochemical Society. DOI: 10.1149/1.1792891 All rights reserved. Manuscript submitted November 3, 2003; revised manuscript received March 24, 2004. Available electronically September 27, 2004. Polymer-electrolyte fuel cells PEFCs show great promise in becoming energy-delivery devices for a variety of technologies in the future. However, there are still some issues that have to be re- solved before PEFCs can realize their potential. 1 It is well known that their operation is a balance between flooding and membrane dehydration. In the former case, liquid water either saturates the gas diffusion layers GDLs or it covers the catalytic sites, which in either case blocks transport of reactants to the reaction sites. In the latter, the resistance through the membrane, including that embed- ded in the catalyst layer, increases because the lower water content reduces the ionic conductivity. In either case, the efficiency of the fuel cell FC decreases due to higher mass-transfer and ohmic over- potentials, as seen in Fig. 1, which is an example FC polarization curve. In the figure, the three main types of overpotential regions are shown, as well as the location of the maximum power and the lim- iting current. To understand FC behavior and optimize FC design and operating conditions, a model is needed that can predict both types of behavior. Membrane dehydration mainly affects the ohmic region in Fig. 1, causing a lower power and voltage for a given current. A previous paper by us describes the functional forms for the conductivity as a function of temperature and water content. 2 These forms are valid for both vapor- and liquid-equilibrated membranes i.e., those in contact with water vapor and liquid water, respectively. Many mod- els have adopted a varying conductivity as a function of water con- tent in the membrane for examples, see Ref. 3-5, but not many models consider flooding effects as well. In PEFCs, liquid water is produced at the cathode. This water evaporates and moves by diffusion through the gas phase. If the vapor is already saturated, the water moves as a liquid down its pressure gradient through either the membrane or the cathode diffu- sion medium cDM. As the current density increases, more water is generated, and the liquid is at a higher pressure. This higher pressure has the effect of filling up more of the void volume of the cDM. In the extreme case, all the pore pathways from the gas channel to the catalyst layer become blocked, and a limiting current due to oxygen diffusion is observed. 6-9 Such a case causes the sharp drop in poten- tial and power in Fig. 1. Water flooding and the subsequent low oxygen diffusion are not the only cause for a limiting current, 10-12 but they provide the best explanation when the feeds are saturated air and hydrogen. 9,13-15 Along with flooding of the cDM, there is the possibility of lim- iting behavior occurring within the catalyst layers. These effects include diffusional limitations due to ionomer layer thickness on the platinum particles and water film formation. 12,16-22 In this paper, such effects are ignored, although the polarization and ohmic effects in the catalyst layers are taken into account. The main reason for ignoring the catalyst layers in terms of water transport is that the focus of this paper is to develop a model for determining the water effects in the GDLs and coupling them to a membrane model. The previous omission implicitly assumes that the catalyst layers do not significantly alter the water transport and that they can be treated as uniform regions. The justification is that the catalyst layers are very thin, water is produced at hydrophilic reaction sites throughout the layer, and the properties of the layer do not cause a large impedi- ment to water flow. Finally, all effects and results described in this paper occur in FCs, and although they may not be the whole story, they are definitely a large part. In other words, although the actual numerical results may change upon the inclusion of a detailed catalyst-layer model, the general trends and conclusions remain valid. Early PEFC models handled flooding phenomena by assuming a constant void volume for the gas phase that was less than the bulk porosity of the medium for examples, see Ref. 8, 23, and 24. Later, Baschuk and Li 25 allowed the void volume to vary across the cDM; however, they used it as a fitting parameter at each location. Gurau et al. 26,27 had a similar approach where they took into account liquid water in the membrane, catalyst layers, and diffusion media. How- ever, they separated the cDM into regions with different void vol- umes, tortuosities, and lengths, which were used essentially as fitting * Electrochemical Society Student Member. ** Electrochemical Society Active Member. *** Electrochemical Society Fellow. z E-mail: aweber@uclink.berkeley.edu Figure 1. Example polarization and power curves showing the locations of the limiting current and the maximum power. The kinetic, ohmic, and mass- transfer regions of the polarization curve are shown; the dotted lines repre- sent parts of the curve not normally measured experimentally. Journal of The Electrochemical Society, 151 10 A1715-A1727 2004 0013-4651/2004/15110/A1715/13/$7.00 © The Electrochemical Society, Inc. A1715