A mathematical multi-species modelling framework for polymer electrolyte fuel cells (PEFCs) is presented on the basis of fundamental molecular theory. Characteristically, the resulting general transport equation describes transport in concentrated solutions and also explicitly accommodates for multi-species electro-osmotic drag. The multi-species nature of the general transport equation allows for cross-interactions to be considered, rather than relying upon the superimposition of Fick's law to account for the transport of any secondary species in the membrane region such as hydrogen. The presented general transport equation is also used to derive the key transport equations used by the historically prominent PEFC models. Thus, this work bridges the gap that exists between the different modelling philosophies for membrane transport in the literature. The general transport equation is then used in the electrode and membrane regions of the PEFC with available membrane properties from the literature to compare simulated one-dimensional water content curves, which are compared with published data under isobaric and isothermal operating conditions. Previous work is used to determine the composition of the humidified air and fuel supply streams in the gas channels. Finally, the general transport equation is used to simulate the crossover of hydrogen across the membrane for different membrane thicknesses and current densities. The results show that at 353 K, 1 atm, and 1 A/cm2, the nominal membrane thickness for less than 5 mA/cm2equivalent crossover current density is 30 μm. At 3 atm and 353 K, the nominal membrane thickness for the same equivalent crossover current density is about 150 μm and increases further to 175 μm at 383 K with the same pressure. Thin membranes exhibit consistently higher crossover at all practical current densities compared with thicker membranes. At least a 50 per cent decrease in crossover is chieved at all practical current densities, when the membrane thickness is doubled from 50 to 100 μm.
CostamagnaP.SrinivasanS.Quantum jumps in the PEMFC science and technology from the 1960s to the year 2000; part I. Fundamental scientific aspects. J. Power Source., 2001, 102, 242–252.
2.
CostamagnaP.SrinivasanS.Quantum jumps in the PEMFC science and technology from the 1960s to the year 2000; part II. engineering, technology development and application aspects. J. Power Source., 2001, 102, 253–269.
3.
BaschukJ. J.LiX.Carbon monoxide poisoning of proton exchange membrane fuel cells. Int. J. Energy Res., 2001, 25, 695–713.
4.
WangJ. T.SavinellR. F.Simulation studies on the fuel electrode of a H2-O2 polymer electrolyte fuel cell. Electrochem. Acta, 1992, 37, 2737–2745.
5.
ChanS. H.GohS. K.JiangS. P.A mathematical model of polymer electrolyte fuel cell with anode CO. kinetics. Electrochem. Acta, 2003, 48, 1905–1919.
6.
BaschukJ. J.RoweA. M.LiX.Modelling and simulation of PEM fuel cells with CO Poisoning. Trans. ASME, 2003, 125, 94–100.
7.
AmphlettJ. C.BaumertR. M.MannR. F.PeppleyB. A.RobergeP. R.RodriguesA.The effect of carbon monoxide contamination on anode efficiency in PEM fuel cells. Am. Chem. Soc.: Div. Fuel Chem., 1993, 38, 1477–1482.
8.
OetjenH. F.SchmidtV. M.StimmingU.TrilaF.Performance data of a proton exchange membrane fuel cell using H2/CO as fuel gas. J. Electrochem. Soc., 1996, 143, 3838–3842.
9.
DharH. P.ChristnerL. G.KushA. K.MaruH. C.Performance study of a fuel cell Pt-on-C anode in presence of CO and CO2, and calculation of adorption parameters for CO poisoning. J. Electrochem. Soc., 1986, 133, 1547–1582.
10.
QiZ.HeC.KaufmanA.Effect of CO in the anode fuel on the performance of the PEM fuel cell cathode. J. Power Source., 2002, 111, 239–247.
11.
SpringerT. E.RockwardTZawodzinskiT. A.GottesfeldS.Model for Polymer electrolyte fuel cell operation on reformate feed. J. Electrochem. Soc., 2001, 148, A11–A23.
12.
MooreJ. M.AdcockP. L.LakemanJ. B.MepstedG. O.The effects of battlefield contaminants on PEMFC performance. J. Power Source., 2000, 85, 254–260.
13.
OkadaT.Theory for water management in membranes for polymer electrolyte fuel cells; part 1. The effect of impurity ions at the cathode side on the membrane performances. J. Electroanal. Chem., 1999, 465, 1–17.
14.
OkadaT.Theory for water management in membranes for polymer electrolyte fuel cells; part 1. The effect of impurity ions at the cathode side on the membrane performances. J. Electroanal. Chem., 1999, 465, 18–29.
15.
BernardiD. M.VerbruggeM. W.A mathematical model of the solid-polymer-electrolyte fuel cell. J. Electrochem. Soc., 1992, 139, 2477–2491.
16.
WeberA. Z.NewmanJ.Transport in polymer-electrolyte membranes; II. mathematical model. J. Electrochem. Soc., 2004, 151, A311–A325.
17.
LiQ.HeR.JensenJ. O.BjerrumN. J.PBI-based polymer membranes for high temperature fuel cells â preparation, characterisation and fuel cell demonstration. Fuel Cells, 2004, 4, 147–159.
18.
RamaP.ChenR.ThringR.A polymer electrolyte membrane fuel cell model with multi-species input. Proc. Institute Mech. Engrs. Part A: J. Power and energy, 2005, 219, 255–271.
19.
RidgeS. J.WhiteR. E.TsouY.BeaverR. N.EismanG. A.Oxygen reduction in a proton exchange membrane test cell. J. Electrochem. Soc., 1989, 136, 1902–1909.
20.
BernardiD. M.VerbruggeM. W.Mathematical model of a gas-diffusion electrode bonded to a polymer electrolyte. Am. Institute Chem. Engineers, 1991, 37, 1151.
21.
BerndardiD. M.Water-balance calculations for solid-polymer-electrolyte fuel cells. J. Electrochem. Soc., 1990, 137, 3344–3350.
22.
PisaniL.MurgiaG.ValentiniM.D'AguannoB.A working model of polymer electrolyte fuel cells. J. Electrochem. Soc., 2002; 149, A898–A904.
23.
PisaniL.MurgiaG.ValentiniM.D'AguannoB.Analytical pore scale modelling of the reactive regions of polymer electrolyte fuel cells. J. Electrochem. Soc., 2003, 150, A1549–A1559.
24.
MurgiaG.PisaniL.ValentiniM.D'AguannoB.Electrochemistry and mass transport in polymer electrolyte fuel cells; I. model. J. Electrochem. Soc., 2002, 149, A31–A38.
25.
DjilaliN.LuD.Infuence of heat transfer on gas and water transport in fuel cells. Int. J. Therm. Sci., 2002, 41, 29–40.
26.
BerningT.DjilaliN.Three-dimensional computational analysis of transport phenomena in a PEM fuel cell â a parametric study. J. Power Source., 2003, 124, 440–452.
NguyenT. V.WhiteR. E.A water and heat management model for proton-exchange-membrane fuel cells. J. Electrochem. Soc., 1993, 140, 2178–2186.
29.
OkadaT.XieG.MeegM.Simulation for water management in membranes for polymer electrolye fuel cells. Electrochem. Acta, 1998, 43, 2141–2155.
30.
YiJ. S.NguyenT. V.An along-the-channel model for proton exchange membrane fuel cells. J. Electrochem. Soc., 1998, 145, 1149–1159.
31.
NataranjanD.NguyenT. V.A two-dimensional, two-phase, multicomponent, transient model for the cathode of a proton exchange membrane fuel cell using conventional gas distributors. J. Electrochem. Soc., 2001, 148, A1324–A1335.
32.
NataranjaD.NguyenT. V.Three-dimensional effects of liquid water flooding in the cathode of a PEM fuel cell. J. Power Source., 2003, 115, 66–80.
33.
van BusselH. P. L. H.KoeneF. G. H.MallantR. K. A. M.Dynamic model of solid polymer fuel cell water management. J. Power Source., 1998, 71, 218–222.
34.
SiegelN. P.EllisM. W.NelsonD. J.von SparkovskyM. R.A two-dimensional computational model of a PEMFC with liquid water transport. J. Power Source., 2004, 128, 173–184.
35.
ChenFSuY.-G.SoongC.-Y.YanW.-M.ChuH.-S.Transient behaviour of water transport in the membrane of a PEM fuel cell. J. Electroanal. Chem., 2004, 566, 85–93.
36.
YanW.-M.ChenF.WuH.-Y.SoongC.-Y.ChuH.-S.Analysis of thermal and water management with temperature-dependant diffusion effects in membrane of proton exchange membrane fuel cells. J. Power Source., 2004, 566, 85–93.
37.
RoweA.LiX.Mathematical modelling of proton exchange membrane fuel cells. J. Power Source., 2001, 102, 82–96.
38.
KulikovskyA. A.Quasi-3D modeling of water transport in polymer electrolyte fuel cells. J. Electrochem. Soc., 2003, 150, A1432–A1439.
39.
GeS.-H.YiB.-L.A mathematical model for PEMFC in different flow modes. J. Power Source., 2003, 124, 1–11.
40.
SunH.LiuD.GuoL-J.PEM fuel cell performance and its two-phase mass transport. J. Power Source., 2005, 143, 125–135.
41.
YuX.XhouB.SobiesiakA.Water and thermal management for Ballard PEM fuel cell stack. J. Power Source., 2005, 147, 184–195.
42.
FullerT. F.NewmanJ.Water and thermal management in solid-polymer-electrolyte fuel cells. J. Electrochem. Soc., 1993, 140, 1218–1225.
43.
FullerT. F.NewmanJ.A Concentrated solution theory model of transport in solid-polymer-electrolyte fuel cells. Electrochem. Soc. Proc. Ser., 1989, PV 89-14, 25–38.
44.
JanssenG. J. M.A Phenomenological model of water transport in a proton exchange membrane fuel cell. J. Electrochem. Soc., 2001, 148, A1313–A1323.
45.
WeberA. Z.NewmanJ.Transport in polymer-electrolyte membranes; I. physical model. J. Electrochem. Soc., 2003, 150, A1008–A1015.
46.
WeberA. Z.NewmanJ.Transport in polymer-electrolyte membranes; III. model validation in a simple fuel-cell model. J. Electrochem. Soc., 2004, 151, A326–A339.
47.
MeyersJ. P.NewmanJ.Simulation of the direct methanol fuel cell; I. thermodynamic framework for a multicomponent membrane. J. Electrochem. Soc., 2002, 149, A710–A717.
48.
MeyersJ. P.NewmanJ.Simulation of the direct methanol fuel cell; II. modelling and data analysis of transport and kinetic phenomenon. J. Electrochem. Soc., 2002, 149, A718–A728.
49.
MeyersJ. P.NewmanJ.Simulation of the direct methanol fuel cell; III. design and optimisation. J. Electrochem. Soc., 2002, 149, A729–A735.
50.
WohrM.BolwinK.SchnurnbergerW.FischerM.NeubrandW.EigenbergerG.Dynamic modelling and simulation of a polymer membrane fuel cell including mass transport limitation. Int. J. Hydrogen Energ., 1998, 23, 213–218.
51.
FuterkoP.HsingI.-M.Two-dimensional finite-element method study of the resistance of membranes in polymer electrolyte fuel cells. Electrochem. Acta, 2000, 45, 1741–1751.
52.
HsingI.-M.FuterkoP.Two-dimensional simulation of water transport in polymer electrolyte fuel cells. Chem. Eng. Sci., 2000, 55, 4209–4218.
53.
ThampanT.MalhotraS.TangH.DattaR.Modelling of conductive transport in proton-exchange membranes for fuel cells. J. Electrochem. Soc., 2000, 149, 3242–3250.
54.
EikerlingM.KharkatsY. I.KornyshevA. A.VolfkovichY. M.Phenomenological theory of electro-osmotic effect and water management in polymer electrolyte proton-conducting membranes. J. Electrochem. Soc., 1998, 145, 2684–2699.
55.
MeierF.EignerbergerG.Transport properties for the modelling of water transport in ionomer membranes for PEM-fuel cells. Electrochem. Acta, 2004, 49, 1731–1742.
56.
BaschukJ. J.LiX.Modelling of polymer electrolyte membrane fuel cells with variable degrees of water flooding. J. Power Source., 2000, 86, 181–196.
57.
AmphlettJ. C.BaumertR. M.MannR. F.PeppleyB. A.RobergeP. R.Performance modelling of the ballard mark IV solid polymer electrolyte fuel cell. J. Electrochem. Soc., 1995, 142, 1–8.
58.
MannR. F.AmphlettJ. C.HooperM. A. I.JensenH. M.PeppleyB. A.RobergeP. R.Development and application of a generalised steady-state electrochemical model for a PEM fuel cell. J. Power Source., 2000, 86, 173–180.
HirschfelderJ. O.CurtissC. F.BirdR. B.Molecular theory of gases and liquids, 1964 (John Wiley & Sons, Inc., New York).
62.
NewmanJ.Electrochemical systems, 1973 (Prentice-Hall, Inc., Englewood Cliffs, New Jersey).
63.
WangZ. H.WangC. Y.ChenK. S.Two-phase flow and transport in the air cathode of proton exchange membrane fuel cells. J. Power Source., 2001, 94, 40–50.
64.
FreireT. J. P.GonzalezE. R.Effect of membrane characteristics and humidification conditions on the impedence response of polymer electrolyte fuel cells. J. Electroanal. Chem., 2001, 503, 57–68.
65.
SenaD. R.TicianelliE. A.PaganinV. A.GonzalezE. R.Effect of water transport in a PEFC at low temperatures operating with dry hydrogen. J. Electranal. Chem., 1999, 477, 164–170.
66.
MatsuyamaH.MatsuiK.KitamuraY.MakiT.TeramotoM.Effect of membrane thickness and membrane preparation condition on facilitated transport of CO2 through ionomer membrane. Sep. Purif. Technol., 1999, 17, 235–241.
67.
Hydrogen, Fuel Cells & Infrastructure Technologies Program. US Department of Energy, 2005; DOE/GO-102003-1741.
68.
SlatteryJ. C.BirdR. B.Calculation of the diffusion coefficient of dilute gases and of the selfdiffusion coefficient of dense gases. Am. Institute Chem. Eng., 1958, 4, 137–141.
