Liquid Water Transport in Polymer Electrolyte Fuel Cells With Multi ...

shown that highly hydrophobic MPLs usually exhibit betterperformance (Wilson et al. 1995, Qi and Kaufman 2002 andKong et al. 2002). Although the exact mechanisms are yet to befully elucidated, the performance enhancement is usuallyassociated with better water management capabilities of MPLs.The two main effects of improvement with MPLs are due toenhancement of water management by better humidifying themembrane, consequently decreasing the ohmic losses andreducing the flooding in cathode, consequently improving thegas phase diffusion.Although several studies have been carried out to modelthe two-phase transport in PEFCs, only a few has discussed theeffects of MPL on water management and two-phase transport.Nam and Kaviany (2003) have modeled the two-phasetransport in multi-layered cathode GDM using the unsaturatedflow theory (UFT), which assumes the gas pressure in the GDLis constant, therefore neglects the gas flow counter to the liquidflow. They have optimized the MPL properties according to thetotal liquid water in the cathode GDM, and concluded that thereis an optimum for thickness and porosity of the MPL. Mostrecently, Pasaogullari and Wang (2004a), elucidated the effectof MPL, using the more complete two-phase model i.e. M 2formulation, which relaxes the constant gas phase pressureassumption, hence accounts for the gas flow counter to thecapillarity-induced liquid flow. It was indicated for the firsttime that the build-up in liquid pressure in the cathode due tothe presence of MPL creates a hydraulic pressure differential todrive water flow back to the anode. This water back flow canbe controlled by the pore size and wettability of MPL followingthe capillary flow theory developed by Pasaogullari and Wang(2004b). In addition, the study of Pasaogullari and Wang(2004a) revealed a capillary-driven enhancement of oxygentransport once the two-phase zone is formed. This newenhancement mechanism is, however, over-dominated by theincrease in the diffusion resistance, yielding an overallreduction in the oxygen transport limitation in most cases offlooding. In a meeting abstract, Weber and Newman (2003)also mentioned the positive role played by MPL to promotewater back flow through the membrane, improving thehumidification of the membrane as well as the anode catalystlayer, reducing the overall ohmic losses, hence improving theperformance.The aim of the present work is to present a two-phase flowmodel for the entire membrane-GDM assembly, based on theM 2 formulation (Wang and Cheng, 1997) and analyze the liquidwater transport in PEFCs with MPLs. The effects of porous andwetting structure of MPL are also analyzed. The paper isorganized as follows: The development of the mathematicalmodel for multi-layered GDM and polymer electrolytemembrane (PEM) is presented based on the theory of liquidwater flow in hydrophobic gas diffusion layers presented byPasaogullari and Wang (2004a). Then, the liquid watertransport with MPL is compared with the conventional PEFCconfigurations and the effects of MPL properties are examined.MATHEMATICAL MODELThe present study focuses on liquid water transport inporous gas diffusion anode and cathode and across themembrane. The cell is considered to be isothermal as a firstapproximation. The gas channels are excluded from themodeling domain by specifying boundary conditions at the gasdiffusion media/channel interfaces. Furthermore, catalyst layersare taken to be infinitely thin; and hence the anode hydrogenoxidation reaction (HOR) and cathode oxygen reductionreaction (ORR) are assumed to take place at the PEM-GDMinterfaces. Within these assumptions, the domain considered isconfined to porous anode GDL, PEM and cathode GDM,consisting of MPL and GDL, as shown in Figure 1 along withthe associated transport processes. Although the present modelis developed in 1-D, it can be readily implemented in a multidimensionalCFD model with the channel incorporated asshown in Pasaogullari and Wang (2004c).In this study, the multi-phase, mixture model (M 2 ) isemployed to describe the two-phase transport processes in theporous media. M 2 model is an exact reformulation of classicaltwo-phase, two-fluid models into a single equation. Unlike theunsaturated flow theory (UFT) utilized in some of the earliertwo-phase PEFC models (He et al. 2000 Nam and Kaviany2003) M 2 model does not require the assumption of a constantgas phase pressure across the porous medium, hence it alsoaccounts for the gas flow counter to the capillarity driven liquidflow. Furthermore, M 2 modeling does not require explicitlytracking of phase interfaces; consequently simplifiesmathematical modeling of two-phase transport in porousmedium, where both single- and two-phase regions coexist. Thereader is referred to Wang and Cheng (1997) for details of themultiphase mixture model and its applications to a number ofmultiphase transport problems in porous media.Mass conservation for the two-phase mixture in steadystateas given by M 2 formulation is:∇ ⋅ ( ρ u ) = 0(1)In the above equation; u is the superficial mixture velocity andρ is the mixture density and given as:ρ = ρl⋅ s + ρg⋅ ( 1−s)(2)where s is the liquid saturation and represents the fraction ofopen pore space of porous media occupied by liquid.When Eq. (1) is integrated along the GDM in steady-state: ρ u =(3)where jmj mindicates the net mass flux through the porous media,and corresponding expressions for each individual layers aregiven in Table 1.The species conservation equation of M 2 formulation, whenwritten in terms of molar concentrations is (Pasaogullari andWang, 2004a):⎡⎛i i⎞ ⎤ieff iC ∇ ⋅ ( ) = ∇ ⋅ ( i ,∇ ) − ∇ ⋅ ⎢⎜mflgγ− ⎟cuCDgCgjil ⎥(4)⎢⎣⎝ M ρg⎠ ⎥⎦where the advection correction factor is:⎧ ⎛H 2Oρ⎞⎪ ⎜λlCsat+ λ ⎟ for waterH O⎪H O g22C= ⎝ M ρ ⎠(5)gγi ⎨⎪ ρλg⎪for other species⎩ρ( 1−s)In Eq. (4), C i denotes the total molar concentration of species iin liquid and gas phases, defined as:ii iC = ( 1 − s) Cg+ sC(6)lThe gas-phase diffusion coefficient,i effD , is corrected forgtortuosity and reduction in the open pore space due to presenceof liquid water via Bruggeman correlation, i.e.:2 Copyright © 2004 by ASME