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

Proceedings of IMECE042004 ASME International Mechanical Engineering Congress and ExpositionNovember 13-20, 2004, Anaheim, California USAIMECE2004-59283LIQUID WATER TRANSPORT IN POLYMER ELECTROLYTE FUEL CELLS WITH MULTI-LAYERDIFFUSION MEDIAUgur Pasaogullari, Chao-Yang WangElectrochemical Engine Center,Department of Mechanical and Nuclear EngineeringThe Pennsylvania State UniversityUniversity Park, PA 16802 USATel: +1-814-865-9768Fax: +1-814-863-4848E-mail: uyp101@psu.eduKen S. ChenEngineering Sciences CenterSandia National LaboratoriesP.O. Box 5800, MS 0834Albuquerque, NM 87185-0834 USAABSTRACTA two-phase, multi-component, full cell model isdeveloped in order to analyze the two-phase transport inpolymer electrolyte fuel cells with multi-layer cathode gasdiffusion media, consisting of a coarse gas diffusion layer(GDL) (average pore size ~10 µm) and a micro-porous layer(MPL) (average pore size ~0.2-2 µm). The relevant structuralproperties of MPL, including average pore size, wettability,thickness and porosity are examined and their effects on liquidwater transport are discussed. It is found that MPL promotesback-flow of liquid water across the membrane towards theanode, consequently alleviating cathode flooding. Furthermore,it is seen that unique porous and wetting characteristics of MPLcauses a discontinuity in the liquid saturation at MPL-GDLinterface, which in turn reduces the amount of liquid water incathode catalyst layer-gas diffusion medium interface in somecases. Our analyses show that the back-flow of liquid waterincreases with the increasing thickness and decreasing poresize, hydrophobicity and bulk porosity of the MPL.Keywords: PEFC, flooding, GDL, micro-porous layer,two-phase transport, polymer electrolyte membraneNOMENCLATUREC i Molar concentration of species i [mol·m -3 ]D g Gas phase diffusion coefficient [m 2 ·s -1 ]d Average pore size [m]F Faraday’s constant [96487 C·mol -1 ]I Local current density [A·cm -2 ]j m Mass flux [kg·m -2 ·s -1 ]j l Liquid flux [kg·m -2 ·s -1 ]j w Molar water flux [mol·m -2 ·s -1 ]K Absolute permeability [m 2 ]k rkRelative permeability of phase kM i Molar weight of species i [kg·mol -1 ]n d Electro-osmotic drag coefficientp c Capillary pressure [Pa]s Liquid saturationu Velocity [m·s -1 ]α Net water transport coefficientδ i Thickness of component iε Absolute porosityγ c Advection correction factorλ Membrane water content (#H 3 O + /#SO - 3 )λ k Relative mobility of phase kµ Dynamic viscosity [Pa·s]ν Kinematic viscosity [m 2 ·s -1 ]ρ Density [kg·m -3 ]INTRODUCTIONOne of the main limitations in polymer electrolyte fuel cell(PEFC) performance is governed by the transport of reactantsto the catalyst layer, referred as mass transport limitation. Thislimitation is further increased by the presence of liquid water inthe porous gas diffusion layer (GDL), which blocks some of theopen pores and thus reduces the available path for transport ofreactant species. This phenomenon is called flooding and it ismost problematic in cathode due to the slower electrochemicalkinetics of cathode oxygen reduction reaction. Lately, multilayergas diffusion media (GDM), consisting of a coarse GDLand a finer micro-porous layer (MPL) have been investigated toreduce the flooding in porous cathode and to enhance the watermanagement of PEFCs by increasing tendency of back-flow ofliquid water across the membrane towards anode. It has been1 Copyright © 2004 by ASME

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

shown in Figure 2. Therefore, the membrane water content iscalculated by:23⎧1.4089+ 11.263a−18.768a+ 16.209a⎪H O(23)2λ = ⎨if C ≤ Csat⎪H2O⎩10.1129( 1−s)+ 16sif C > CsatIn Eq. (21), K mem is the membrane hydraulic permeability andn d is the electro-osmotic drag coefficient. When integratedalong the membrane thickness, Eq. (21) becomes:Kmemw w I − ∇pl− Dm∇Cm+ nd= j(24)H Owνl⋅ M 2FThe values reported in the literature for hydraulicpermeability of membrane show a great variation. It is reportedbetween 1.8·10 -18 m 2 (Bernardi and Verbrugge, 1992) to 2·10 -20m 2 (Meier and Eigenberger, 2004), for Nafion® basedmembranes humidified with liquid water. In this work, we usethe latest available data from Meier and Eigenberger, which is2·10 -20 m 2 for a membrane fully humidified with liquid water at80ºC (i.e. λ=16).Here, the diffusion coefficient of water in the membrane istaken from Motupally et. al. (2000) and is given as:−70.28λ−1346 / T⎪⎧w3.1⋅10λ( e −1)e 0 < λ ≤ 3D = ⎨(25)m−8−λ−1346 / T⎪⎩ 4.17⋅10λ( 1+161e) e 3 ≤ λ < 17in m 2 /s.Boundary ConditionsIn this work, we assume that the gas channels are free ofliquid water. Furthermore, gas diffusion media for both anodeand cathode are saturated with water vapor; therefore the waterconcentration at the GDM-gas channel interface is equal to thesaturation concentration, therefore the liquid saturation at theseinterfaces is zero.s ( x = 0 ) = s A −GC/ GDL= 0(26)s( x = δMEA) = s C −GC/ GDL= 0(27)Consequently, the capillary pressures at these interfaces arealso zero, and the gas phase pressure is equal to the channelpressure.p x = 0 = p(28)gg( )A( xMEA) pCp = δ =(29)Numerical ProcedureThe given model is solved for three different regions,namely anode GDL, PEM and cathode GDM, simultaneously.As shown in Table 1, the fluxes are all function of net watertransport coefficient, α, which is not known initially. Therefore,an iterative procedure is used to determine α. An initial guess isprovided for α, and this guess is improved in consecutiveiterations using bisection method until water content of themembrane converges to the given accuracy. A relative errormargin of 10 -7 in water content is set for convergence criteria,which requires around 25 iterations for obtaining α up to 8-digit accuracy. The governing equations of water transport arenon-linear ordinary differential equations, which are solvedusing a 4 th order adaptive step Runge-Kutta method.RESULTS AND DISCUSSIONEffect of Micro-Porous LayerIn order to analyze the effect of MPL on liquid watertransport in PEFC, four different GDM configurations areanalyzed. These configurations are achieved by varying theanode and cathode GDM. Both of the anode and cathode GDLproperties are selected from values of carbon paper. Two of theconfigurations have hydrophobic GDL in the anode (wetproofed,θ c =110º), and the other two have hydrophilic GDL(not wet-proofed, θ c =70º). In all cases, cathode GDL is wetproofedand in two of the cases cathode GDL is coated withMPL. The MPL properties used here are taken from the basecase, as well as for the analyses in the next sections. Theproperties of the materials used here are given in Table 2, alongwith the associated transport parameters.In Figure 3, the variation of net water transport coefficientwith current density is given for all these cases. Note that, netwater transport coefficient, α is defined as the number of watermolecules transported per proton across the membrane,therefore when α is positive, the net water transport across themembrane is towards cathode.Hj 2 Omem⋅ Fα =(30)IIt is seen that the net water transport coefficient profiledoes not follow a single trend across the entire current densityrange. Around α=0, a change in the trend is visible and this isdue to the change in the anode water transport phenomena atα=0. When α is less than zero, there is a net water transporttowards the anode, and since the anode is already humidified,there is liquid water in the anode GDL and water transport inthe anode GDL is governed by the capillary force. However,when α is positive, net water transport across the anode GDL istowards the membrane, and it is governed by the gas phasediffusion of the water vapor, which is much stronger than thecapillary transport of water.It is clearly seen in all cases that, the use of a hydrophilicGDL in anode side decreases the water flux towards anode onlywhen α0,since the gas diffusion is the only mode of water transport inthe anode GDL, no effect of anode GDL wettability is seen.It is also evident from Figure 3 that the net water transportcoefficient increases with increasing current density. Inmembrane, the electro-osmotic drag of water is in counterdirectionto convective and diffusive transport of water.Electro-osmotic drag is towards cathode due to proton flux, andconvective and diffusive transport of water is towards anode4 Copyright © 2004 by ASME

since liquid pressure and water content is higher in the cathodeside of the membrane than the anode side. Therefore, withincreasing current density, the electro-osmotic drag increasesand starts to dominate over the convective and diffusivetransport of water across the membrane, resulting in increasingnet water transport coefficient with increasing current density.When cathode GDL is coated with MPL, it is seen that watertransport towards anode is significantly increased and thisincrease is clearly visible at the entire current density range.In Figure 4, the liquid pressure profiles in all fourconfigurations are shown at a current density of 0.1 A/cm 2 . Inthis current density, all four configurations result in two-phasetransport in both the anode and the cathode GDM. The inset ofthe figure shows the details of liquid pressure across themembrane. As stated above, the liquid pressure differentialacross the membrane is higher when anode GDL is hydrophilic.However, this difference becomes less significant whencathode GDL is coated with MPL. Due to its smaller pore size,MPL has much smaller permeability; therefore, liquid waterflow requires higher pressure differential across the MPL,increasing liquid pressure on the cathode side of the membrane.Here, the permeability of MPL is calculated from the followingexpression given by Rumpf and Gutte (Kaviany, 1995) forpacked beds with narrow range of distribution in size:5.52K = ε d(31)5.6where d is the average pore diameter. For an MPL of mean poresize of 1 µm and porosity of 0.5, this expression gives apermeability of 3.95·10 -15 m 2 , which is comparable withexperimentally measured values.Figure 5 shows the liquid saturation profiles in anode andcathode GDM at the same current density. It is seen that theliquid saturation in cathode GDL is decreased by use of anMPL due to decreased cathode water flux. It is also seen incathode GDM, there is a discontinuity in the liquid saturationprofile at the GDL-MPL interface. This discontinuity isgoverned by the continuity of phase pressures at this interface.Since both gas and liquid pressures are continuous at thisinterface, the capillary pressure is also continuous. Followingthe definition of capillary pressure in Eq. (13), one has thefollowing relation for pressure continuity at the GDL-MPLinterface.GDL1 2MPL1 2GDL ⎛ ε ⎞GDLMPL ⎛ ε ⎞MPL( ) ⎜ ⎟ J ( s ) = cos( θ ) ⎜ J ( s )cos θcGDL intcMPL intK⎜ K ⎟ (32)⎜ ⎟⎝ ⎠⎝ ⎠It is clear that this discontinuity is a function of wettingand porous characteristics of MPL and GDL, as well as theliquid flux in the cathode. Due to this discontinuity, liquidsaturation in cathode catalyst layer-GDM interface may also besmaller than single-layer configurations depending on themicro-structure of MPL; therefore catalyst layer flooding canalso be reduced with MPL.It is also seen from Figure 5 that when hydrophilic GDL isused in anode, the liquid saturation in the anode GDL increases,which is particularly due to smaller capillarity effects inhydrophilic GDL. It has been shown that capillary watertransport is stronger in hydrophobic GDLs than hydrophilicGDLs, particularly at lower liquid saturations (Pasaogullari andWang, 2004).Similar water transport characteristics that are observedwith MPLs can also be achieved by adjusting the operatingconditions, such as using higher cathode and lower anodepressures. Particularly, operating with pressure differentials hasbeen shown to significantly improve the performance (Voss etal., 1995, Jannsen and Overvelde, 2001, Beattie et al. 1999). Inall these examples, an increased pressure differential across themembrane is formed to enhance the back-flux (i.e. towardsanode) of water, similar to what MPL causes.Effect of MPL ThicknessThe effect of the thickness of the MPL is analyzed usingthe model explained in the earlier sections. The parametersused for this case are the same as in Table 2, except that thethickness of the MPL is varied between 10 µm and 50 µm. Asseen in Figure 6, the net water transport coefficient is a strongfunction of MPL thickness. As the MPL thickness increases,the net water transport coefficient curve shifts downwardsindicating that the water flux towards the anode is increasing.With increasing MPL thickness, the resistance to liquid waterflow in the cathode GDM increases, and this increasedresistance causes the fraction of water transported through themembrane towards anode to increase, hence results in adecrease in cathode water flux. Inset of the Figure 6 shows thechange of net water transport coefficient with MPL thickness atseveral current densities. It is seen that the thickness of theMPL is particularly effective at lower current densities due tosmaller electro-osmotic drag flux.Effect of Mean Pore Size of MPLFigure 7 shows the net water transport coefficient acrossthe membrane for different mean pore sizes of MPL. Here, theproperties of the MPL are taken from the base case, which aregiven in Table 2 except for the mean pore size. The net watertransport curve shifts downwards with decreasing mean poresize, indicating increasing water flux towards anode. Thepermeability of MPL decreases with the pore size (see Eq.(31)), which increases the resistance to water flow towardscathode channel. Therefore, water tends to flow in the pathwhich has smaller resistance, which in turn increases the flowrate towards anode. This effect obviously is much more visiblein lower current densities, where back-flux of water isdominating over the electro-osmotic drag. As the currentdensity increases, the electro-osmotic drag of water across themembrane becomes larger, diminishing the effect of MPL. Asseen in the inset of Figure 7, the effect of the mean pore size ofMPL starts to disappear for larger pore sizes as the MPLpermeability becomes closer to GDL permeability. As theabsolute permeability is directly proportional to the square ofthe mean pore size (Eq. (31)), liquid pressure differential acrossthe MPL is magnified with decreasing pore size. This increasein the MPL pressure differential causes a higher pressuredifferential across the membrane, causing higher back-flux ofwater towards anode.It is evident that smaller pore size in MPL is increasing thetendency of liquid water flow towards anode. However,smallest pore size is probably not the optimal design, thus thegas phase transport will be hampered with the decreasing poresizes. The gas-phase transport is most likely to be in theKnudsen regime in MPL due to the much smaller pore sizes. InKnudsen regime, the wall-to-molecule interactions dominatesover the molecule-to-molecule interactions, and the pore sizebecomes the most important factor for gas diffusion. On the5 Copyright © 2004 by ASME

and water-saturation distribution in single- and two-layerPEMFC diffusion medium,” Int. J. Heat and Mass Tr., Vol. 46,4595-4611.Pasaogullari, U. and Wang, C.Y., 2004, Two-PhaseTransport and the Role of Micro-Porous Layer in PolymerElectrolyte Fuel Cells,” Electrochim. Acta, Vol. 49, 4359-4369.Pasaogullari, U. and Wang, C.Y., 2004, “Liquid WaterTransport in Gas Diffusion Layer of Polymer Electrolyte FuelCells,” J. Electrochem. Soc., Vol. 151, pp. A399-A406.Pasaogullari, U. and Wang, C.Y., 2004, “Two-PhaseModeling and Flooding Prediction of Polymer Electrolyte FuelCells,” J. Electrochem. Soc., in press.Qi, Z. and Kaufman, A., 2002, “Improvement of watermanagement by a microporous sublayer for PEM fuel cells,” J.Power Sources, Vol. 109, pp. 38-46.Springer, T.E., Wilson, M.S., and Gottesfeld, S., 1991,“Polymer Electrolyte Fuel Cell Model”, J. Electrochem. Soc.,Vol. 136, pp. 2334-2342.Voss, H.H., Wilkinson, D.P., Pickup, P.G., Johnson, M.C.and Basura, V. 1995, “Anode water removal: a watermanagement and diagnostic technique for solid polymer fuelcells,” Electrochim. Acta, Vol. 40, pp. 321-328.Wang, C.Y. and Cheng, P., 1997, “Multiphase Flow andHeat Transfer in Porous Media,” Advances in Heat Transfer,Vol. 30. pp. 93-196.Weber, A. and Newman, J., Abstract Nr: 1038 204 thElectrochemical Society Meeting, October 12-16, 2003,Orlando, Florida.Wilson, M.S., Valerio, J.A. and Gottesfeld, S., 1995, “Lowplatinum loading electrodes for polymer electrolyte fuel cellsfabricated using thermoplastic ionomers,” Electrochim. Acta,Vol. 40, pp. 355-363.Zawodzisnki, T.A., Springer, T.E., Uribe, F. andGottesfeld S., 1993, “Characterization of polymer electrolytesfor fuel cell applications,” Solid State Ionics, Vol. 60, pp. 199-211.Zawodzisnki, T.A., Davey, J., Valerio, J. and Gottesfeld S.,1995, “The water content dependence of electro-osmotic dragin proton-conduting polymer electrolytes,” Electrochim. Acta,Vol. 40, pp. 297-302.Table 2 Material properties, transport parameters and operatingconditionsParameterValueTransport parametersSurface tension, σ0.0625 N/mAnode gas kinematic viscosity, ν g,a4.45×10 -5 m 2 /sCathode gas kinematic viscosity, ν g,c1.78×10 -5 m 2 /sLiquid kinematic viscosity, ν l3.52×10 -7 m 2 /sLiquid density, ρ l974.85 kg/m 3Material propertiesGDL absolute permeability, K GDL 8.7×10 -12 m 2GDL porosity, ε GDL0.7Hydrophobic GDL contact angle, θ c110ºHydrophilic GDL contact angle, θ c70ºAnode GDL thickness, δ AGDL 300 µmCathode gas diffusion medium thickness, δ C 300 µmMembrane thickness (Nafion® 112), δ mem 50.8 µmMembrane hydraulic permeability, K mem 2×10 -20 m 2Base case MPL propertiesThickness, δ MPL 30 µmPorosity, ε MPL0.5Average pore size, d MPL1000 nmAbsolute permeability, K MPL 3.95×10 -15 m 2Contact angle, (θ c ) MPL120ºOperating ConditionsCell temperature, T353.15 KAnode channel pressure, p A1.5 atmCathode channel pressure, p C1.5 atmAnode GDL PEM MPL Cathode GDLElectroosmoticLiquid FlowLiquid FlowDragGas FlowGas FlowxTable 1 Mass and water flux for individual layers of PEFCMass Flux, j mWater Flux, j wH2I ⎛ MH O⎞I2Anode⎜ + α M⎟αGDLF ⎝ 2 ⎠FIMembrane N/A αFO2I ⎡ M⎤Cathode⎛ 1 ⎞ H O I ⎛ 1 ⎞2⎢−+ ⎜α+ ⎟M⎥ ⎜α + ⎟GDL/MPL F ⎣ 4 ⎝ 2 ⎠ ⎦ F ⎝ 2 ⎠Gas and Liquid PressureLiquid FlowGas PressureGas FlowLiquid FlowLiquidPressureGas FlowxFigure 1 Schematics of modeling domain, transport phenomenaand individual phase pressure profiles in PEFCs with microporouslayers7 Copyright © 2004 by ASME

175170Configuration 1Configuration 2Configuration 3Configuration 4Liquid pressure [kPa]1651601551501450 0.25 0.5 0.75 010.25 0.5 0.75 10 0.25 0.5 0.75 1Anode GDMPEMCathode GDMDimensionless distance along the cell thicknessFigure 2 Membrane water uptake. Symbols are experimentalmeasurements of Zawodzinski et al. for Nafion® membranes at80ºC.Figure 4 Liquid pressure profiles across the cell thickness fordifferent GDM configurations at 1.5 A/cm 2 . For configurationand material properties, refer to Figure 2. Inset shows thedetails of liquid pressure across the membrane.Net water transport coefficient, α0.20.150.10.050-0.05-0.1-0.15-0.2Configuration 1Configuration 2Configuration 3Configuration 4Configuration 1:Anode: Hydrophobic GDL/Cathode: Hydrophobic GDLConfiguration 2:Anode: Hydrophilic GDL/Cathode: Hydrophobic GDLConfiguration 3:Anode: Hydrophobic GDL/Cathode: Hydrophobic GDL+MPLConfiguration 4:Anode: Hydrophilic GDL/Cathode: Hydrophobic GDL+MPLα0.050-0.05-0.10.1 0.2 0.3I[A/cm 2 ]0.5 1 1.5 2Current density, I [A/cm 2 ]Liquid saturation, s0.050.040.030.020.01Configuration 1Configuration 2Configuration 3Configuration 400 0.25 0.5 0.75 010.25 0.5 0.75 10 0.25 0.5 0.75 1Anode GDMPEMCathode GDMDimensionless distance along the cell thicknessFigure 3 Net water transport coefficient, α for different GDMconfigurations. MPL properties are taken from base case givenin Table 2. Inset shows the enlarged view at lower currentdensities.Figure 5 Liquid saturation profiles across the GDM/MEAthickness for different MEA thickness at 1.5 A/cm 2 . Theconfiguration details are given in Figure 2.8 Copyright © 2004 by ASME