i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 8 7 1e1 1 8 8 5

Avai lab le a t www.sc iencedi rec t .com

journa l homepage : www.e lsev ier . com/ loca te /he

A theoretical study of inlet relative humidity control in PEMfuel cell

K.H. Wong a,*, K.H. Loo b, Y.M. Lai a, Siew-Chong Tan a, Chi K. Tse a

aDepartment of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon,

Hong Kong SAR, Hong Kongb Faculty of Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, Hong Kong

a r t i c l e i n f o

Article history:

Received 25 February 2011

Received in revised form

26 May 2011

Accepted 4 June 2011

Available online 18 July 2011

Keywords:

Proton exchange membrane fuel cell

Water management

Inlet relative humidity control

Optimization

* Corresponding author.E-mail addresses: 08902493r@polyu.edu.h

0360-3199/$ e see front matter Copyright ªdoi:10.1016/j.ijhydene.2011.06.017

a b s t r a c t

In this paper, the individual roles of inlet anode and cathode humidification, and their

influences on PEM fuel cell’s electrical performance are discussed systematically by using

a pseudo two-dimensional, two-phase PEM fuel cell model. It follows that the maximum

power density point of a PEM fuel cell is strongly dependent on the combination of the inlet

anode and cathode humidification conditions. Their influences, however, are predicted to

be highly asymmetrical, with the anode and cathode humidification mainly affecting

ohmic and concentration overpotential, respectively. The physical explanation to this

asymmetry is given with the aid of a detailed set of simulation results. Finally, the

developed understanding of their influences are employed to formulate two examples on

the use of inlet relative humidity control as a simple and effective method for maximizing

the volumetric power density and operating range of PEM fuel cell, respectively.

Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights

reserved.

1. Introduction and to avoid irreversible physical degradation to the

Proton exchange membrane (PEM) fuel cell is considered an

alternative energy source that has demonstrated promising

potentials in various applications such as vehicular pro-

pulsion systems, portable power supplies and stationary

power generations by converting the chemical energy stored

in hydrogen into electric energy [1e8]. However, at the present

stage of development, there are various technical barriers,

including cost, power density, durability, and reliability, that

need to be surmounted before it becomes a commercially

viable and widely adopted alternative energy source [9].

Water management is a critical issue since the perfor-

mance of PEM fuel cell is strongly influenced by its internal

water distribution. A sufficient hydration is essential to facil-

itate protonic transport for an efficient fuel cell’s operation

k, richard.wkh@gmail.co2011, Hydrogen Energy P

membrane due to dehydration [10e13]. A summary of

membrane degradation models is given in the review article

published by Shah et al. [14]. In this respect, external humid-

ification, where moisture is carried by inlet reactant gases to

the internal of fuel cell, is often adopted to ensure that the

membrane remains well hydrated, however, when excess

water accumulates in the fuel cell, water flooding might be

resulted at the cathode region and degrades the PEM fuel cell’s

performance [15]. Both dehydration andwater flooding should

be avoided to maintain a satisfactory fuel cell’s performance

and to protect the fuel cell from physical damages. A balanced

water distribution, which is vital to optimizing PEM fuel cell’s

performance, should therefore be pursued.

External humidification has been used to enable a flexible

watermanagement for PEM fuel cell by directly controlling the

m (K.H. Wong).ublications, LLC. Published by Elsevier Ltd. All rights reserved.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 8 7 1e1 1 8 8 511872

relative humidity of inlet reactant gases. However, in early

systems, where the objective of water management has been

simply reduced to the essential idea of improving the protonic

conductivity of the membrane [16], fully humidified reactant

gases are normally fed to PEM fuel cell indiscriminately, hence

full humidification had become the typical operating condi-

tion. In any case, external humidificationmust be provided by

humidifier units that occupy space and consume energy [1].

Having considered the trade-off between the need to improve

membrane’s conductivity and the requirement of externally

installed humidifiers, some researchers prefer to seek for

alternative water management schemes.

Dry-gas operation was proposed in order to eliminate the

space and energy consumed in the operation of external

humidifiers. Some prior works were done by Buchi et al. [17]

who conducted modeling studies and experiments to vali-

date the feasibility of dry-gas operation. Some recent experi-

ments reported in [18,19] explored the influences of operating

conditions on the performance of PEM fuel cell under dry-gas

operation and demonstrated that dry-gas operation is prac-

tical under certain well-controlled operating conditions.

Further, there are experimental works that examined the

reactant species and current distributions [20], and the tran-

sient behavior [21] of PEM fuel cell under dry-gas operation.

The idea of dry-gas operation is inherently attractive as there

is no external humidification subsystem, but the previously

reported experimental works [17e19] indicate that the

performance of PEM fuel cell under dry-gas operation is low

compared to the conventionally operated fuel cell with

external humidification.

Several approaches that employ the principle of internal

humidification were introduced in the literature to address the

issue of sub-optimum performance resulted under dry-gas

operation of a conventionally designed PEM fuel cell. These

approaches aim to utilize the by-productwatermore efficiently

for an improved fuel cell’s performance without external

humidification. The use of self-humidified membrane with

enhanced water-retaining ability was proposed by Watanabe

et al. [22,23]. The membrane demonstrated a satisfactory

performance under dry-gas operation for low to medium

output current density, but gave rise to a smaller limiting

current density unless a slight external humidification was

applied [23]. Similar observations are still reported despite

numerous efforts have been made to improve self-humidified

membrane [24e26]. There are several studies on the design of

innovative gas delivery subsystems [27,28] or the integration of

wicking components [29e31] to recirculate by-product water

for humidifying membrane without external humidification.

These designs have strengthened the feasibility and aided the

practical implementation of dry-gas operation, but they

involve more advanced designs and increase the complexity of

a fuel cell system and raise concerns about the system’s

durability and reliability.

The main drawback associated with internal humidifica-

tion is that only a passive control of water distribution is

possible since the amount of by-product water available is

restricted by the fuel cell’s operating conditions. Therefore,

there is no guarantee that the water distribution is optimized

under all operating conditions. On the contrary, external

humidification is more flexible and provides an active control

of water distribution by directly monitoring and adjusting the

relative humidity of inlet reactant gases. As discussed above,

full humidification and dry-gas operation represent two

extreme operating conditions, and both give rise to sub-

optimum PEM fuel cell’s performance. In view of these

drawbacks, an intermediate relative humidity control is

required tomatch the relative humidity of inlet reactant gases

to the specific fuel cell’s operating conditions such that an

optimized water distribution within the fuel cell is constantly

achieved over a wide range of operating conditions. Although

humidifiers are required for inlet relative humidity control,

the recently developedmembrane humidifier and its dynamic

model that employ proton exchange membrane as the water

exchange material [32e34] has enabled a low-cost imple-

mentation of external humidification with a greatly reduced

space and power consumption.

A comprehensive study of the influences of external

humidification on the water distribution is vitally important to

identify the pathway for achieving an optimized water distri-

bution in PEM fuel cell. Nguyen et al. [16] performed detailed

simulations and reported that external humidification is

required for attaining a high protonic conductivity at high

current density. Besides, the polarization curves under various

inlet relative humidity of air were simulated and discussed by

several authors [35e37]. Natarajan et al. studied the influences

of the inlet relative humidity of air on the cathodic potential

distribution. Shah et al. [36] studied the combined effects of

temperature and inlet anode and cathode relative humidity.

Recently, Min et al. [37] summarized the researches on the

influences of the inlet relative humidity of air on the perfor-

mance of PEM fuel cell. Saleh et al. [38] conducted several

experiments for exploring the influences of symmetrical and

asymmetrical inlet relative humidity (with respect to anode

and cathode) on PEM fuel cell’s performance. Urbani et al. [39]

discussed the role of inlet relative humidity and reported that

PEM fuel cell performs better under an intermediatemagnitude

of inlet relative humidity. Hussaini et al. [40] recently intro-

duced a dynamic water management scheme for PEM fuel cell

operating under constant current density. These studies have

provided valuable information on the application of external

humidification on PEM fuel cell, and hence provided insights to

the work presented in this paper.

In this work, a comprehensive study based on this objective

is performed through the use of a two-phase PEM fuel cell

model. Themodel has been formulated to include a two-phase

gas-channel model to ensure that the fuel cell’s operation is

realistically coupled to the inlet conditions [41]. The different

roles of the inlet relative humidity at anode and cathode on the

overall water distribution in PEM fuel cell, and their interac-

tions with other fuel cell’s operating conditions are discussed

in depth. It is the aim of this paper to provide a unified view of

the mechanism of inlet relative humidity control and to theo-

retically quantify its effectiveness as a practical method for

optimizing the performance of PEM fuel cell.

2. Model description and assumptions

In this work, a steady-state, one-dimensional, two-phase,

isothermal unit PEM fuel cell model that was developed

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 8 7 1e1 1 8 8 5 11873

previously [41] is used to study the influences of the relative

humidity of inlet reactant gases on the performance of PEM

fuel cell. The model describes a typical unit PEM fuel cell that

consists of anode, cathode, and membrane forming a multi-

layer structure known as the membrane-electrode assembly

(MEA), as shown in Fig. 1. Each layer is assumed to be

homogenous and the fuel cell’s physical processes are

described in the through-plane direction only. The anode and

cathode, each consists of a GDL and a CL, are assumed to be

symmetrical about the proton exchange membrane, and are

constructed from materials having the same physical prop-

erties. The MEA is held between the anode and cathode GCs

that deliver reactant gases to the assembly for electro-

chemical reactions. An effective cooling system is assumed to

be in place such that the temperature of PEM fuel cell is

maintained constant throughout the stack [42]. To more

realistically couple inlet operating conditions to the assembly,

the GCs are described by a two-phase, along-the-channel

model so that the channel flooding phenomenon and the

drying effect of inlet gas flow can be modeled. The collection

of the MEA and gas-channel models therefore forms a pseudo

two-dimensional model.

3. Model formulation

3.1. Governing equations

In this model, six quantities are computed from a set of

conservation equations listed in Table 1. These quantities

represent the hydrogen concentration at anode cH2 , oxygen

concentration at cathode cO2 , water vapor concentration at

both anode and cathode cv, liquid water saturation at cathode

s, and dissolved water concentration cd and protonic potential

fp in membrane.

Diffusion is the primary transport mechanism for gas

species at the electrodes of PEM fuel cell. In general, the flux

termof gas species i, represented by the symbol Ji, is expressed

by the following equation:

Ji ¼ �Deffi Vci; (1)

Fig. 1 e Computational domain of the model. It includes

gas channels, gas diffusion layers and catalyst layers.

where Deffi is the effective diffusion coefficient of gas species i.

In GDL, the effective diffusion coefficient is described by

[43,44]:

Deffi ¼ 1:01ðe� 0:24Þ1:83ð1� sÞ2Di; (2)

whereas, in CL, it is described by [45]:

Deffi ¼ ½ð1� sÞe�1:5

1Di

þ 1

Dknui

!�1

: (3)

Here, e is the intrinsic porosity of GDL or CL. The presence of

liquid water decreases the porosity or increases the tortuosity

when the GDL or CL is flooded and part of the void space is

occupied by liquid water. Therefore, a correction term, (1-s)

[43,45] is introduced to describe the impeding effect of liquid

water on the transportation of gas species. Di and Dknui repre-

sent the binary and Knudsen diffusion coefficient for gas

species i, respectively.

For porous media, such as GDL and CL, Darcy’s law is

employed to describe the flowof liquidwater, where the liquid

water flux is proportional to the gradient of liquid water

pressure pl [43,46e48]. Since pl is equal to the sum of capillary

pressure, pc, and gas pressure, pg, and the gas pressure is

assumed uniform in the through-plane direction [49], i.e.,

Vpg ¼ 0, the liquid water flux is described by:

Jl ¼ �clkkrl

ml

Vpc; (4)

where cl and ml are, respectively, the concentration and

viscosity of liquid water. k is the permeability of liquid water

at GDL or CL, which measures the ability of the media to pass

liquid water when they are completely flooded. In the case of

partial flooding, a correction term known as the relative

permeability krl is introduced for obtaining the effective

permeability.

The proton flux across the membrane is described by the

Ohm’s law as follows:

Jp ¼ �seffp

FVfp; (5)

where F is Faraday’s constant and sp is the effective conduc-

tivity of membrane that is given by:

seffp ¼ emsp: (6)

Here, em represents the fraction of the media occupied by

membrane phase, and sp is the intrinsic protonic conductivity

of membrane.

In membrane, dissolved water is transported by three

mechanisms, i.e., diffusion, electro-osmotic drag and

pressure-driven permeation. They are represented by the first,

second and third term on the right hand side of the following

equation, respectively.

Jd ¼ �DdVcd þ ndJp � clKl

ml

dpl

dx; (7)

where Dd is the diffusion coefficient of dissolved water. The

dissolved water concentration, cd, is given as the product of

dry membrane concentration, cm, and water content, l. In the

second term, nd represents the electro-osmotic drag

Table 1 e Governing equations.

Variables AGDL ACL Membrane CCL CGDL

cO2 e e e V,JO2 ¼ �SO2 V,JO2 ¼ 0

cH2 V,JH2 ¼ 0 V,JH2 ¼ �SH2 e e e

cv V,Jv ¼ 0 V,Jv ¼ �Sd e V,Jv ¼ �Svl � ð1� sÞSd V,Jv ¼ �Svlfp e V,Jp ¼ 2SH2 V,Jp ¼ 0 V,Jp ¼ �4SO2 e

s e e e V,Jl ¼ 2SO2 þ Svl � sSd V,Jl ¼ Svlcd e V,Jd ¼ Sd V,Jd ¼ 0 V,Jd ¼ Sd e

pl pl ¼ pc þ pg pl ¼ pc þ pgd2pldx2

¼ 0 pl ¼ pc þ pg pl ¼ pc þ pg

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 8 7 1e1 1 8 8 511874

coefficient that is linearly dependent on the water content.

The last term represents the pressure-driven permeation [50],

and in this term, Kl is the relative permeability of dissolved

water within the membrane.

At both anode and cathode, reactant gases must diffuse

through CL and undergo electrochemical reactions simulta-

neously. The slow kinetic of oxygen reduction reaction is

described by using the Thiele modulus approach [51], and the

reaction rate SO2 is given by [49,50,52]:

SO2¼�

1aagg

�dlHl;O2

Dl;O2

þ dmHm;O2

Dm;O2

�þ Hm;O2

xkr;O2

��1

cO2RT: (8)

The electrochemical reaction rate kr;O2is described by the

ButlereVolmer equation. The parameter aagg represents the

outer surface area of the agglomerates per unit volume of CL.

The physical constants, Da;O2and Ha;O2

, are the diffusion

coefficient and Henry constant of oxygen in phase a, respec-

tively. The parameter da represents the thickness of ionomer

membrane or water covering the catalyst agglomerates. x is

the effectiveness factor for CL that correlates the oxygen

reduction reaction to the diffusion of oxygen through the

agglomerates.

Hydrogen is oxidized at the anode CL and protons are

produced. Since the oxidization of hydrogen has a fast kinetic,

the ButlereVolmer equation is used to compute the reaction

rate of hydrogen directly, i.e.,

SH2¼ �aeff ;Ptiref ;H2

2F

�cH2

cH2 ;ref

�1=2�2FRT

fp

�; (9)

where aeff ;Pt and iref ;H2are the effective specific area of the

platinum catalyst and exchange current density of hydrogen

oxidization, respectively, and cH2 ;ref is the reference hydrogen

concentration.

The interfacialmass transfer rate betweenwater vapor and

liquid water, Svl, due to condensation or evaporation is

assumed to be proportional to the difference between water

vapor pressure cvpg and saturation water vapor pressure psat

[49].

Svl ¼�cvpg � psat

�� kcondeð1� sÞcv=RT; cvpg > psat

kevapescl; otherwise: (10)

The transport parameters, kcond and kevap, represent the

condensation and evaporation rate, respectively.

Themass transfer between dissolved water (in membrane)

and water vapor and liquid water (in CL) is described by the

rate-limitedmodel where thewater content inmembrane and

the water activity at CL are assumed to be in a non-

equilibrium state [36,53]. Therefore,

Sd ¼ kdcmleq � l

: (11)

Here kd denotes the rate coefficient of water transfer between

membrane and CL, and leq is the water content in membrane

that exists in equilibrium with the water activity at the adja-

cent CL.

The magnitude of kd represents the rate of adsorption or

desorption of water from or to CL. A faster adsorption or

desorption is denoted by a larger magnitude of kd; this gives

rise to a smaller difference between the non-equilibrium and

equilibrium water content. If the magnitude of kd further

approaches to infinity, the rate-limited model reduces to an

equilibrium formulation and the water content in CL equals

the equilibrium value.

3.2. Boundary conditions

The boundary conditions used in the model are listed in

Table 2. The influences of inlet conditions are coupled to the

MEA through the one-dimensional (along the channel and

represented by z), two-phase gas-channel model. This is done

by computing the mean values of the fluid properties along

the GC, such as the concentrations of reactant gases and

capillary pressure, and use them as the boundary conditions

at the gas diffusion layer (GDL)-gas channel (GC) interface. A

detailed description of the derivation of the boundary condi-

tions are discussed elsewhere [41].

At the cathode GDL-GC interface, the boundary conditions

are given by:

cO2jCGDL�CGC ¼

�cg;0cO2 ;0 þ

SO2z

vg;0

�z

; (12)

cvjCGDL�CGC ¼�Gðzsat � zÞ

�cv;0cv;0 þ

Svzvg;0

�þ Gðz� zsatÞcsatv

�z

; (13)

pcjCGDL�CGC ¼�sGðz� zsatÞ

r

�z

: (14)

The subscript 0 denotes the value of a given quantity

measured at the inlet position, i.e., z ¼ 0. The symbol GðxÞrepresents a switching function that takes a value of 1 if x � 0.

z indicates a position along the GC measured from the inlet,

and zsat represents the phase transition position where liquid

water begins to form [54]. vg is the gas velocity in the GC. The

source term Si denotes themass transfer of species i across the

GDL-GC interface. Finally, the operator hiz represents an

averaging action similar to the operator ðR LGC

0 dzÞ=LGC.

Table 2 e Boundary conditions.

Variables AGC-AGDL GDL-ACL ACL-MEM MEM-CCL CCL-CGDL CGDL-CGC

cO2 e e e e Continuous Eq. (12)

JO2 e e e 0 Continuous e

cH2 Eq. (13) Continuous e e e e

JH2 e Continuous 0 e e e

c v Eq. (13) Continuous e e Continuous Eq. (12)

Jv e Continuous 0 0 Continuous e

fp e Continuous Continuous Continuous Continuous e

Jp 0 Continuous Continuous Continuous Continuous 0

s e e e e p�c ¼ pþc Eq. (12)

Jl e e e 0 Continuous e

cd e Continuous Continuous Continuous Continuous e

Jd 0 Continuous Continuous Continuous Continuous 0

pl pl ¼ pg Continuous Continuous Continuous Continuous pl ¼ pg

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 8 7 1e1 1 8 8 5 11875

At the anode GDL-GC interface, the boundary conditions

are given by:

cijAGDL�AGC ¼�cg;0ci;0 þ

Sizvg;0

�z

; (15)

where i denotes hydrogen or water vapor at the anode GC.

Other constitutive relations used in the model that are not

specifically discussed here are listed in Table 3, and the

physical parameters used are listed separately in Tables 4

and 5.

Table 3 e Constitutive relations of physical and transport prop

Properties

Binary diffusion coefficient of oxygen [55], DO2 6:4

Binary diffusion coefficient of water vapor [55], Dv 4:4

Binary diffusion coefficient of hydrogen [55], DH2 2:2

Knudsen diffusion coefficient, Dknui

2rc3

Relative permeability of liquid water in GDL/CL [43], krl s3

Capillary pressure, pc sco

Leverett function [56], L(s)

(

Protonic conductivity of the membrane [57], sp ð0:

Dissolved water diffusion coefficient [58], Dd ex

Drag coefficient of water [57], nd 2:5

Oxygen electrochemical reaction rate, kr;O2

aeff

4F

Cathode overpotential, hc Vce

Oxygen diffusion coefficient of electrolyte [59], Dm;O2 3:1

Oxygen diffusion coefficient of water [60], Dl;O21:9

Henry’s constant of oxygen at electrolyte [59], Hm;O2 1:3

Henry’s constant of oxygen at water [61], Hl;O25:1

Thickness of liquid water film, dl eCL

The effectiveness factor, x ð3F

Thiele modulus, Frag

3

Equilibrium water content, leq 22s

Phase transition position, zsat ðcsvSaturation water vapor pressure, psatðPaÞ �2

4. Experimental verification of model

In this section, the developed PEM fuel cell model is verified by

comparison with some published experimental data in the

literature in order to examine its ability to predict the

performance of PEM fuel cell under various inlet conditions.

The data produced by the two experiments conducted by

Williams et al. [18] and Saleh et al. [38] are used for verification.

These reported experiments include detailed polarization

erties.

Expressions

88� 10�5T1:823p�1

52� 10�6T2:334p�1

� 10�5T2:334p�1

rit

ffiffiffiffiffiffiffiffiffi8RTpMi

s

s q�ek

�0:5LðsÞ

1:417s� 2:12s2 þ 1:263s3; q >p

21:417ð1� sÞ � 2:12ð1� sÞ2 þ 1:263ð1� sÞ3; q <

p

2

514l� 0:326Þexp"1268

1

303� 1T

!#

p

e2436T

!(3:1� 10�7lðe0:28l � 1Þ; l˛ð0;3Þ4:17� 10�8lð161e�l þ 1Þ; l>�3

l=22

;Ptiref ;O2

cO2 ;refexp

� Fhc

RT

!

ll � fp � Voc

� 10�7expð�2768=TÞ8� 10�9ðm293K=mTÞðT=293Þ48� 105expð�666=TÞ47� 105expð�498=TÞs=aagg

coth3F� 1Þ=3F2

g ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikr½Dm;O2 ðeaggm Þ1:5ð1� eCLÞ1:5��1

qþ ð0:3þ 10:8Q� 16Q2 þ 14:1Q3Þð1� sÞ

at � cg;0cg;0Þvg;0=Sv846:4þ 411:24ðT� 273:15Þ � 10:554ðT� 273:15Þ2 þ 0:16636ðT� 273:15Þ3

Table 4 e Parameters of gas channel, gas diffusion layerand catalyst layer.

Parameter Value

Gas channel

Length, LGC (m) 0.5

Width, WGC (mm) 0.5

Depth, DGC (mm) 0.5

Gas diffusion layer

Absolute permeability, kGDL

(m2) [36, 53]

8.7 � 10�7

Porosity, eGDL 0.55

Contact angle, qGDLðoÞ 93.5

Thickness, lGDLðmmÞ 250

Catalyst layer

Absolute permeability,

kCLðm2Þ [36, 53]10�13

Porosity, eCL 0.2

Contact angle, qCLðoÞ 90.5

Thickness, lCLðmmÞ 15

Fraction of electrolyte, eCLm 0.3

Critical pore radius, rcritðnmÞ 50

Specific surface area of catalyst Pt,

aptðm2 kg�1Þ [62]105

Catalyst Pt loading, mptðkg m�2Þ [49] 0.004

Reference oxygen concentration,

cO2 ;ref ðmol m�3Þ101325H�1

m;O2

Reference hydrogen concentration,

cH2 ;ref ðmol m�3Þ34.52

Reference exchange current density

of oxygen reduction, iref ;O2ðAm�2Þ [63]

10�3

Reference exchange current density

of hydrogen oxidization, iref ;H2ðAm�2Þ

18.75

Table 5 e Parameters of proton exchange membrane,agglomerate and other physical parameters.

Parameter Value

Proton exchange membrane

Thickness, lmðmmÞ 30

Dry membrane concentration,

cmðmol m�3Þ [64]1800

Relative permeability,

klðm2Þ [50]1.8 � 10�18

Agglomerate

Outer surface area of the

agglomerates, aaggðm�1Þ5 � 106

Thickness of membrane

covering, dmðnmÞ20

Radius of the agglomerate,

raggðnmÞ [65]200

Fraction of PEM electrolyte

in agglomerate, eaggm

0.4

Physical parameters

Faraday constant, FðC mol�1Þ 96487

Gas constant, RðJ mol K�1Þ 8.314

Water viscosity, mlðPas�1Þ [66] 2:73� 10�3 � 6:69� 10�6T

Air viscosity, mgðPas�1Þ [67] 2:04�10�5

Water surface tension,

sðNm�1Þ [66]0:12398� 0:00017393T

Water concentration,

clðmol m�3Þ [66]64500 � 29:84T

Water molecular mass,

Mvðkg mol�1Þ1.8 � 10�2

Oxygen molecular mass,

MO2 ðkg mol�1Þ3.2 � 10�2

Mole fraction of nitrogen

of air, cN2 ;air

0.8

Mole fraction of oxygen

of air, cO2 ;air

0.2

Condensation rate,

kcondðs�1Þ [62]1

Evaporation rate,

kevapðPa�1 s�1Þ [62]5 � 105

Water transfer coefficient of

the electrolyte, kdðPa�1 s�1Þ1.5

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 8 7 1e1 1 8 8 511876

curves that weremeasured under various inlet humidification

conditions, hence are useful for verifying the model’s accu-

racy in respect of modeling the influences of inlet humidifi-

cation on the performance of PEM fuel cell.

The polarization curves obtained under the conditions

studied in the experiment of Williams et al. are simulated by

the model. The predicted polarization curves are plotted in

Fig. 2, and the results are compared with the experimental

data of Williams et al. [18] plotted in the same figure. The

experimental result shows that, when the inlet cathode

humidification is completely removed, the test cell can func-

tion properly and maintain an adequate output voltage when

the anode’s hydrogen gas remains fully humidified. The same

is predicted by the model, which theoretically demonstrates

the practical feasibility of dry-cathode operation. On the

contrary, when the inlet anode humidification is removed, the

performance of the test cell degrades significantly as can be

justified from the large difference between the measured

polarization curves under 100/0 and 0/0 conditions (Qa=Qc

denotes the inlet relative humidity at anode and cathode in %,

respectively). The simulated polarization curves show that

a similar case is predicted by the model. Although there are

some mismatches between the measured and predicted

polarization curves in numerical values, the model has

generally demonstrated the ability to produce close qualita-

tive predictions on the influences of inlet anode and cathode

humidification on the performance of PEM fuel cell.

By inspecting the measured polarization curves, when the

inlet relative humidity at anode is fixed at 100%, different

limiting current densities are produced under various inlet

cathode humidification conditions. As the inlet relative

humidity at cathode is reduced from 100%, to 75%, and to 0%,

it is observed that the test cell’s performance has improved by

producing a higher limiting current density, hence a wider

operating range is obtained. On the other hand, by examining

the intermediate current density region, an increase in ohmic

overpotential is observed as the inlet relative humidity at

cathode is reduced, leading to a higher ohmic power loss

when the test cell operates at this current density region. One

exception to these trends is the case when both anode and

cathode are fully humidified, i.e., 100/100, where themeasured

curve shows an early fall in output voltage, indicating that the

gain in performance due to the reduced ohmic overpotential

in a strongly hydrated membrane is largely offset by the

increased concentration overpotential resulting from a more

severe flooding. In general, these trends have been success-

fully captured by the model, where the simulation results are

plotted in Fig. 2 for comparison.

Fig. 2 e A comparison of polarization curves between the

data from experimental studies in Williams et al. [18] and

the results based on the simulation in this paper. The inlet

relative humidities shown includes 100/100, 100/75, 100/

0 and 0/0 ðQa=QcÞ.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 8 7 1e1 1 8 8 5 11877

In the experimental work conducted by Saleh et al. [38], the

polarization curves of a PEM fuel cell operating under various

symmetrical (with respect to anode and cathode) inlet

humidification conditions were measured and the results are

shown in Fig. 3. For comparison, these cases are simulated by

themodel and the predicted results are also plotted in Fig. 3. It

can be seen from the experimental studies that a higher inlet

relative humidity generally improves the performance of PEM

fuel cell at the intermediate current density region, as

expected, due to the reduced ohmic overpotential in the

presence of a well-hydrated membrane. A similar trend is

demonstrated by the predicted polarization curves shown in

Fig. 3. In respect of limiting current density, an opposite trend

is concluded from both the experimental and simulation

Fig. 3 e A comparison of polarization curves between the

data from experimental studies in Saleh et al. [38] and the

results based on the simulation in this paper. The inlet

relative humidities shown includes 100/100, 60/60, 35/35,

27/27 and 0/0 ðQa=QcÞ.

results. In general, a higher inlet relative humidity does not

favor the operation of PEM fuel cell at high current density

since it could lead to a more severe flooding condition and

degrade the fuel cell’s performance by enhancing concentra-

tion overpotential.

From these experimental and simulation studies, the dual-

role of water in the operation and performance of PEM fuel cell

is implied. On one hand, water is required for hydrating

membrane; on the other hand, the presence of excessive

water impedes the transportation of reactant gases, especially

for oxygen at cathode. Therefore, a balanced water manage-

ment is needed for optimizing the performance of PEM fuel

cell. While external humidification provides a direct control

over the rate of water supply to a fuel cell, the volume flow

rates of reactant gases can also be utilized to control the rate

of water removal from the fuel cell due to their drying effects.

The interplay between these control parameters in a single

PEM fuel cell system should be understood when designing an

appropriate water management scheme. In the next section,

the verified model is used to perform a detailed simulation

study on the influences of inlet humidification and volume

flow rate conditions on the performance of PEM fuel cell.

Compared to oxygen at cathode, the naturally fast hydrogen

oxidation kinetics at anode tends to have a weak impact on

the overall performance of PEM fuel cell and, in practice, its

flow rate is typically kept close to one stoichiometry for

minimization of wastage, therefore the volume flow rate of

hydrogen is excluded from the study in order to keep a clear

presentation of the essential ideas only.

5. Results and discussion

In this section, the model is used to perform a detailed

simulation study on the influences of various combinations of

inlet anode and cathode humidification and air flow rate

conditions (see Table 6) on the performance of PEM fuel cell.

The predicted polarization curves are plotted in Figs. 4 and 5,

and some general conclusions are drawn by a systematic

analysis of these curves.

The figure sets in Figs. 4 and 5 are conveniently arranged in

a matrix form, where eachmatrix’s element represents a case

of variation of one parameter while the other two parameters

are kept constant. For instance, in Fig. 4, each matrix’s

element represents the case where the inlet relative humidity

at cathode and air stoichiometry are kept constant while the

inlet relative humidity at anode is varied from 20%, to 60%,

and to 100%. Other elements in the same column are repeated

Table 6 e The range of simulated operating conditions.

Inlet condition Symbol Value

Inlet operating temperature T 80 C

Inlet anode and cathode pressure pa=c 1 atm

Anode stoichiometry za 1.2

Cathode stoichiometry zc 1, 2 & 4

Anode inlet relative humidity Qa 20, 60 & 100%

Cathode inlet relative humidity Qc 20, 60 & 100%

Fig. 4 e Predicted performances of PEM fuel cell under various inlet anode humidification conditions (zc=Qa=QC stand for the

cathode stoichiometry, inlet anode and cathode relative humidity, respectively).

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 8 7 1e1 1 8 8 511878

similarly for other inlet cathode humidification conditions,

whereas other elements in the same row are repeated simi-

larly for other air stoichiometry values. Fig. 5 follows the same

arrangement but with the inlet relative humidity at cathode

varied from 20%, to 60%, and to 100% while the inlet relative

humidity at anode and air stoichiometry are kept constant for

each matrix’s element. The reason for adopting such an

arrangement for Figs. 4 and 5 is to enable a clearer visualiza-

tion of the individual role or contribution of inlet anode and

cathode humidification on the overall fuel cell’s performance

in the presence of various air flow rates.

From Fig. 4, it can be seen that inlet anode humidification

mainly affects the polarization curves of the simulated PEM

fuel cell at the intermediate current density region where

ohmic overpotential dominates. As shown by each matrix’s

element in the figure set, the limiting current density remains

virtually unchanged under various inlet anode humidification

conditions when inlet cathode humidification is kept

constant. On the contrary, Fig. 5 shows that the variation of

inlet cathode humidification has an almost negligible effect on

the polarization curves at the intermediate current density

region, but produces a significant influence on the value of

limiting current density and hence the operating range of the

simulated fuel cell. From these simulated trends, it appears

that the role of inlet anode and cathode humidification are

asymmetrical in nature under the operating conditions being

studied. Thus, we propose to consider their roles individually

in the following discussion and attempt to optimize the

performance of fuel cell by controlling these parameters

separately.

The origin of this asymmetry lies in the formation of water

at the cathode of PEM fuel cell that constantly maintains the

cathode at an adequately hydrated state. Since water also

arrives from anode by electro-osmotic drag, and water

desorption frommembrane for removal through cathode GDL

is an inherently slow process, water tends to accumulate at

the cathode region near the interface betweenmembrane and

CL. By means of back-diffusion and even pressure-driven

permeation, the high water content at the cathode region

then acts as a concentration barrier to prevent further

incoming water from anode by electro-osmotic drag. In this

way, any incoming water due to inlet anode humidification

will tend to be circulated and confined within the membrane

by the counteracting actions of electro-osmotic drag and back-

Fig. 5 e Predicted performances of PEM fuel cell with various inlet cathode humidification conditions (zc=Qa=QC stand for the

cathode stoichiometry, inlet anode and cathode relative humidity, respectively).

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 8 7 1e1 1 8 8 5 11879

diffusion, aided by the blocking action of the high water

concentration at cathode, and pressure-driven permeation.

The back-diffusion process further helps to distribute water

more evenly across the membrane, a mechanism that is well

known from the literature, and lower the overall membrane’s

resistivity. Since the amount of water to be circulated within

the membrane is mainly determined by the incoming water

from inlet anode humidification, the membrane’s resistivity,

and hence ohmic overpotential, becomes highly susceptible to

the variation of inlet relative humidity at anode. Therefore, for

eachmatrix’s element in Fig. 4, fully humidified anode always

gives rise to the smallest ohmic overpotential and hence the

maximum deliverable power density. This is supported by the

plots of water content and ohmic overpotential in Fig. 6.

Due to the same mechanism as described above, in the

presence of electro-osmotic drag that transports water in the

opposite direction, the water accumulated at the cathode

region cannot be effectively transported through membrane

by back-diffusion and pressure-driven permeation towards

anode for subsequent removal. Therefore, this water should

be mainly removed by transportation through cathode GDL in

the form of water vapor or liquid water, and the effectiveness

of thismethod relies critically on the humidification condition

in cathode GDL and GC, hence the inlet cathode humidifica-

tion condition. By means of this reasoning, it can be argued

that the removal of the accumulated water will become more

impeded as the inlet relative humidity at cathode is increased.

The excessive accumulation of water then leads to the

formation of liquid water that occupies the GDL pores and

partially blocks the transportation of oxygen to CL; these

effects of increased inlet cathode humidification are reflected

by the plots of liquid water saturation and the corresponding

concentration overpotential in Fig. 7. It can be seen from Figs.

5 and 6 that although inlet cathode humidification does affect

membrane’s resistivity, the effect is less significant compared

to its effect on concentration overpotential and hence the

limiting current density. In summary, the influence of inlet

cathode humidification on the performance of PEM fuel cell is

more pronounced in respect of its contribution to the control

of liquid water saturation at the cathode region.

Therefore, the simulation study shows that, in accordance

to the asymmetrical roles of anode and cathode humidifica-

tion, as discussed, the inlet relative humidity at anode should

be ideally kept at 100% in order to maintain a well hydrated

Fig. 6 e Calculated membrane’s resistivity and ohmic overpotential under various inlet humidification conditions (zc=Qa=QC

stand for the cathode stoichiometry, inlet anode and cathode relative humidity, respectively).

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 8 7 1e1 1 8 8 511880

membrane for minimizing ohmic overpotential (at the inter-

mediate current density region), while the inlet relative

humidity at cathode should be kept very low to minimize

concentration overpotential by preventing the formation of

liquid water, i.e., flooding, in cathode GDL and GC. These

conditions typically give rise to an absolute maximum power

density under a given air flow rate. However, a closer look at

Fig. 5 reveals an exceptional case that deserves further

explanation. It can be seen that, when the air stoichiometry is

increased to 4, the maximum power density point is attained

when the inlet relative humidity at cathode is 60% instead of

20%. The high air stoichiometry is responsible for an

enhanced drying of cathode GDL and GC, as shown by the

reduced liquid water saturation and concentration over-

potential in Fig. 7, which also undesirably drains water from

membrane and decreases its conductivity. The combined

effect of increased oxygen supply and water removal under

a high air stoichiometry diminishes the role of concentration

overpotential, and the fuel cell’s performance becomes

dominated by ohmic overpotential. Hence, when such a high

air flow rate is needed, the dehydration of membrane should

be remedied (or the loss of water compensated) by increasing

the inlet relative humidity at cathode. However, it can be seen

that the performance gain by increasing the inlet cathode

humidification from20% to 60% is very limited considering the

apparently weak influence of inlet cathode humidification on

membrane’s resistivity due to the water transportation

mechanism discussed previously. From the simulated case, it

is clear that the performance gain is offset by the much more

significant reduction in the limiting current density.

The influences of inlet anode and cathode humidification

can be utilized in two ways to control the performance of PEM

fuel cell, and each is now illustrated by using a simulated

example. The first example relates to the casewhen a PEM fuel

cell is intended to operate at static condition and an absolute

maximum power density is always desired, such as in grid-

connected power generation. For analysis, a comparison

between the highest and lowest maximum power density

under each air stoichiometry value ismade, as shown in Fig. 8.

They correspond to the highest and lowest maximum power

density extracted from the nine output power curves plotted

in Fig. 4 or Fig. 5. It is interesting and important to note that the

maximum power density attained under a given air stoichi-

ometry can vary significantly depending on the inlet anode

and cathode humidification conditions under which a PEM

fuel cell operates. For example, under one air stoichiometry,

0.37 W cm�2 is obtained when both anode and cathode are

fully humidified, but it can be improved significantly to

0.54 W cm�2 by simply reducing the inlet relative humidity at

cathode from 100% to 20%. For other air stoichiometry values,

different absolute maximum power density values can be

obtained similarly.

The second example relates to the case when a PEM fuel

cell is intended to operate at moving-static condition in

Fig. 7 e Calculated liquid water saturation (at cathode GDL) and concentration overpotential under various inlet

humidification conditions (zc=Qa=QC stand for the cathode stoichiometry, inlet anode and cathode relative humidity,

respectively).

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 8 7 1e1 1 8 8 5 11881

response to a slowly changing load. In this case, the inlet

humidification should be adjusted according to the operating

point of the fuel cell. The polarization curves shown in Fig. 9

are used for the following discussion. It can be seen that at

low current density, both anode and cathode should be fully

humidified in order to minimize ohmic overpotential.

Fig. 8 e Predicted highest and lowest maximum power

density of PEM fuel cell under various air flow rates.

However, these conditions cannot sustain the fuel cell’s

operation at intermediate current density due to the excessive

concentration overpotential that occurs at about 1 A cm�2. To

avoid the collapse of voltage and power, the inlet relative

humidity at cathode should be reduced to 60%, with which the

fuel cell will continue to operate until the current density

reaches about 1.5 A cm�2. Similar as before, when the fuel cell

operates beyond 1.5 A cm�2, the inlet relative humidity at

Fig. 9 e Calculated polarization curves under 2

stoichiometries and 100% inlet anode relative humidity.

Fig. 10 e Calculated polarization curves under two inlet

relative humidity values, each simulated using three

different values of kd covering two orders of magnitude.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 8 7 1e1 1 8 8 511882

cathode should be further reduced to 20% for sustaining its

operation at high current density. It is evident from the

discussion that the primary objective of the dynamic

humidity control is to maximize the fuel cell’s power density

at each current density by dynamically tracing the outer

envelope of the polarization and power density curves. With

the same control, the practical operating range of the fuel cell

is maximized compared to the case where fixed humidifica-

tion is employed.

6. Conclusion

In this work, the engineering feasibility of optimizing the

performance of PEM fuel cell by means of inlet relative

humidity control has been theoretically studiedwith the aid of

a pseudo two-dimensional, two-phase, isothermal unit PEM

fuel cell model. The individual influences of the inlet relative

humidity at anode and cathode have been systematically

investigated by simulating the polarization curves under

various combinations of inlet anode and cathode humidifi-

cation and air stoichiometry conditions. It is found that, under

the operating conditions being studied, the influences of the

inlet relative humidity at anode and cathode are highly

asymmetrical with the former mainly affecting membrane’s

conductivity while the latter mainly influences the level of

liquid water saturation, hence the severity of flooding, at the

cathode region. The origin of these asymmetrical influences is

postulated as due to the pressure-driven permeation and the

formation of water at cathode, which establishes a concen-

tration barrier that, on one hand, helps circulate membrane’s

water and renders ohmic overpotential susceptible to inlet

anode humidification, and, on the other hand, drives water to

cathode GDL and GC with a removal rate that is governed by

inlet cathode humidification. From the simulation study, it is

concluded that a fully humidified anode and a dry cathode are

typically required to maximize the power density delivered by

a PEM fuel cell, unless a high air flow rate is employed, in

which case the cathode should be operated with an interme-

diate relative humidity. Based on the developed under-

standing of the individual influences of inlet anode and

cathode humidification, two examples on the use of inlet

relative humidity control formaximizing the volumeric power

density and operating range of PEM fuel cell have been dis-

cussed. Its usefulness as a simple and effectivemethod for the

performance optimization of PEM fuel cell has been theoreti-

cally demonstrated.

Acknowledgments

This research was funded by University Grants Committee of

the Hong Kong Special Administrative Region, Research

Grants Council Earmarked Research Grant (ERG) number

PolyU 5283/08E.

Appendix A. Discussion on the coefficient ofwater transfer

In themodeling of PEM fuel cell, the values of the coefficient of

water transfer, kd, reported in the literature can differ signif-

icantly, sometimes up to several orders of magnitude. This

raises concerns about the sensitivity of the simulation results

produced by these fuel cell models, and hence the accuracy of

the conclusions drawn from them, on the adopted values of

kd. In this respect, we have explicitly computed the polariza-

tion curves of PEM fuel cell under two inlet relative humidity

values, each simulated using three different values of kdcovering two orders of magnitude.

The simulated results are plotted in Fig. 10, from which it

can be clearly seen that the influences of the value of kd on the

computed polarization curves are significantly smaller

compared to the influences of the inlet humidification

conditions. Therefore, it can be concluded that, in the absence

of an accurate knowledge of kd, the simulation results, and

hence the conclusions drawn, from the carefully derived PEM

fuel cell models in the literature can be generally interpreted

with good confidence.

Nomenclature

aagg outer surface area of agglomerates

apt specific area of platinum catalyst

av local water vapor activity

c concentration

D depth

d film thickness on agglomerate

Dknui knusden diffusivity of species i

Dd water diffusivity in membrane

Di binary diffusivity of species i

F Faraday constant

H Henry’s constant

iref exchange current density

J molar flux

k absolute permeability

kcond/evap condensation/evaportation rate of water

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 8 7 1e1 1 8 8 5 11883

kd water transfer coefficient of the electrolyte

kr electrochemical reaction rate

kra relative permeability of phase a

L length

L(s) Leverett function

M molecular mass

mPt platinum catalyst loading

nd electro-osmotic drag coefficient

p pressure

psat saturation water vapor pressure

pc capillary pressure

R gas constant

ragg radius of an agglomerate

S source term

s liquid water saturation

T temperature

v velocity

Vcel cell voltage

Voc open-circuit voltage

W width

zsat phase transition position

Greek letters

c mole fraction

h overpotential

G Heaviside step function

l membrane’s hydration

m viscosity

F Thiele modulus

fp protonic potential

sp membrane conductivity

s water surface tension

Q inlet gas channel relative humidity

q contact angle

e porosity

X resistance to oxygen diffusion in agglomerate

x effectiveness factor for catalyst layer

z stoichiometry

Subscripts

0 inlet position

a/c anode or cathode

air air

d dissolved water

eq equilibrium-state

g gas phase

H2O water

H2 hydrogen

l liquid phase

m electrolyte (membrane phase)

O2 oxygen

p proton

v water vapor

Superscripts

agg agglomerate

CL catalyst layer

eff effective value

GC gas channel

GDL gas diffusion layer

Pt platinum catalyst

r e f e r e n c e s

[1] Larminie J, Dicks A. Fuel cell systems explained. John Wiley& Sons; 2003.

[2] Li X. Principles of fuel cells. Taylor & Francis; 2006.[3] Mench MM. Fuel cell engines. Wiley; 2008.[4] Stewart EM, Lutz AE, Schoenung S, Chiesa M, Keller JO,

Fletcher J, et al. Modeling, analysis and control systemdevelopment for the Italian hydrogen house. InternationalJournal of Hydrogen Energy 2009;34(4):1638e46.

[5] Ulleberg Østein, Nakken Torgeir, Ete Arnaud. The wind/hydrogen demonstration system at Utsira in Norway:evaluation of system performance using operational dataand updated hydrogen energy system modeling tools.International Journal of Hydrogen Energy 2010;35(5):1841e52.

[6] Suha Yazici M. Hydrogen and fuel cell activities at UNIDO-ICHET. International Journal of Hydrogen Energy 2010;35(7):2754e61.

[7] Wang Yun, Chen Ken S, Mishler Jeffrey, Chan Cho Sung,Adroher Xavier Cordobes. A review of polymer electrolytemembrane fuel cells: Technology, applications, and needs onfundamental research. Applied Energy 2011;88(4):981e1007.

[8] Suha Yazici M. UNIDO-ICHET support to hydrogen and fuelcell technologies in Turkey. International Journal ofHydrogen Energy, in press.

[9] Marcinkoski Jason, Kopasz John P, Benjamin Thomas G.Progress in the US DOE fuel cell subprogram efforts inpolymer electrolyte fuel cells. International Journal ofHydrogen Energy 2008;33(14):3894e902.

[10] Knights Shanna D, Colbow Kevin M, St-Pierre Jean,Wilkinson David P. Aging mechanisms and lifetime of PEFCand DMFC. Journal of Power Sources 2004;127(1e2):127e34.

[11] Endoh Eiji, Terazono Shinji, Widjaja Hardiyanto,Takimoto Yasuyuki. Degradation study of MEA for PEMFCsunder low humidity conditions. Electrochemical and Solid-State Letters 2004;7(7):A209e11.

[12] Yu Jingrong, Matsuura Toyoaki, Yoshikawa Yusuke, NazrulIslam Md, Hori Michio. In situ analysis of performancedegradation of a PEMFC under nonsaturated humidification.Electrochemical and Solid-State Letters 2005;8(3):A156e8.

[13] Huang Xinyu, Solasi Roham, Zou Yue, Feshler Matthew,Reifsnider Kenneth, Condit David, et al. Mechanicalendurance of polymer electrolyte membrane and PEM fuelcell durability. Journal of Polymer Science Part B: PolymerPhysics 2006;44(16):2346e57.

[14] Shah AA, Luo KH, Ralph TR, Walsh FC. Recent trends anddevelopments in polymer electrolyte membrane fuel cellmodelling. Electrochimica Acta 2011;56(11):3731e57.

[15] Weng Fang-Bor, Hsu Chun-Ying, Li Chun-Wei. Experimentalinvestigation of PEM fuel cell aging under current cyclingusing segmented fuel cell. International Journal of HydrogenEnergy 2010;35(8):3664e75.

[16] Nguyen Trung V, White Ralph E. A water and heatmanagement model for proton-exchange-membrane fuelcells. Journal of the Electrochemical Society 1993;140(8):2178e86.

[17] Buchi Felix N, Srinivasan Supramaniam. Operating protonexchange membrane fuel cells without externalhumidification of the reactant gases. Journal of theElectrochemical Society 1997;144(8):2767e72.

[18] Williams Minkmas V, Russell Kunz H, Fenton James M.Operation of Nafion based PEM fuel cells with no externalhumidification: influence of operating conditions and gasdiffusion layers. Journal of Power Sources 2004;135(1e2):122e34.

[19] Zhang Jianlu, Tang Yanghua, Song Chaojie, Cheng Xuan,Zhang Jiujun, Wang Haijiang. Pem fuel cells operated at 0%

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 8 7 1e1 1 8 8 511884

relative humidity in the temperature range of 23-120 �C.Electrochimica Acta 2007;52(15):5095e101.

[20] Yang Xiao Guang, Burke Nick, Yang Wang Chao,Tajiri Kazuya, Shinohara Kazuhiko. Simultaneousmeasurements of species and current distributions in a PEFCunder low-humidity operation. Journal of theElectrochemical Society 2005;152(4):A759e66.

[21] Yu Hongmei, Ziegler Christoph. Transient behavior ofa proton exchange membrane fuel cell under dry operation.Journal of the Electrochemical Society 2006;153(3):A570e5.

[22] Watanabe Masahiro, Uchida Hiroyuki, Seki Yasuhiro,Emori Masaomi, Stonehart Paul. Self-humidifying polymerelectrolyte membranes for fuel cells. Journal of theElectrochemical Society 1996;143(12):3847e52.

[23] Watanabe Masahiro, Uchida Hiroyuki, Emori Masaomi.Analyses of self-humidification and suppression of gascrossover in Pt-dispersed polymer electrolyte membranes forfuel cells. Journal of the Electrochemical Society 1998;145(4):1137e41.

[24] Yang Tae-Hyun, Yoon Young-Gi, Kim Chang-Soo,Kwak Sang-Hee, Yoon Ki-Hyun. A novel preparation methodfor a self-humidifying polymer electrolyte membrane.Journal of Power Sources 2002;106(1e2):328e32.

[25] Hagihara Hiroki, Uchida Hiroyuki, Watanabe Masahiro.Preparation of highly dispersed SiO2 and Pt particles inNafion� 112 for self-humidifying electrolyte membranes infuel cells. Electrochimica Acta 2006;51(19):3979e85.

[26] Han M, Chan SH, Jiang SP. Investigation of self-humidifyinganode in polymer electrolyte fuel cells. International Journalof Hydrogen Energy 2007;32(3):385e91.

[27] Qi Zhigang, Kaufman Arthur. Pem fuel cell stacks operatedunder dry-reactant conditions. Journal of Power Sources2002;109(2):469e76.

[28] Hogarth Warren HJ, Benziger Jay B. Operation of polymerelectrolyte membrane fuel cells with dry feeds: design andoperating strategies. Journal of Power Sources 2006;159(2):968e78.

[29] Hai Ge Shan, Guang Li Xu, Ming Hsing I. Water managementin PEMFCs using absorbent wicks. Journal of theElectrochemical Society 2004;151(9):B523e8.

[30] Ge Shanhai, Li Xuguang, Ming Hsing I. Internally humidifiedpolymer electrolyte fuel cells using water absorbing sponge.Electrochimica Acta 2005;50(9):1909e16.

[31] Litster Shawn, Santiago Juan G. Dry gas operation of protonexchange membrane fuel cells with parallel channels: non-porous versus porous plates. Journal of Power Sources 2009;188(1):82e8.

[32] Park Sang-Kyun, Choe Song-Yul, Choi Seo ho. Dynamicmodeling and analysis of a shell-and-tube type gas-to-gasmembrane humidifier for pem fuel cell applications.International Journal of Hydrogen Energy 2008;33(9):2273e82.

[33] Huizing Ryan, Fowler Michael, Merida Walter, Dean James.Design methodology for membrane-based plate-and-framefuel cell humidifiers. Journal of Power Sources 2008;180(1):265e75.

[34] Kadylak David, Merida Walter. Experimental verification ofa membrane humidifier model based on the effectivenessmethod. Journal of Power Sources 2010;195(10):3166e75.

[35] Natarajan Dilip, Nguyen Trung Van. A two-dimensional,two-phase, multicomponent, transient model for thecathode of a proton exchange membrane fuel cell usingconventional gas distributors. Journal of the ElectrochemicalSociety 2001;148(12):A1324e35.

[36] Shah AA, Kim GS, Gervais W, Young A, Promislow K, Li J,Ye S. The effects of water and microstructure on theperformance of polymer electrolyte fuel cells. Journal ofPower Sources 2006;160(2):1251e68.

[37] MinChun-Hua.Anovel three-dimensional, two-phaseandnon-isothermal numerical model for proton exchange membranefuel cell. Journal of Power Sources 2010;195(7):1880e7.

[38] Saleh Mahmoud M, Okajima Takeoshi, Hayase Masahiko,Kitamura Fusao, Ohsaka Takeo. Exploring the effects ofsymmetrical and asymmetrical relative humidity on theperformance of H2/air pem fuel cell at differenttemperatures. Journal of Power Sources 2007;164(2):503e9.

[39] Urbani Francesco, Barbera Orazio, Giacoppo Giosue,Squadrito Gaetano, Passalacqua Enza. Effect of operativeconditions on a pefc stack performance. InternationalJournal of Hydrogen Energy 2008;33(12):3137e41.

[40] Hussaini IS, Wang CY. Dynamic water management ofpolymer electrolyte membrane fuel cells using intermittentRH control. Journal of Power Sources 2010;195(12):3822e9.

[41] Wong KH, Loo KH, Lai YM, Tan Siew-Chong, Tse Chi K.Treatment of two-phase flow in cathode gas channel for animproved one-dimensional proton exchange membrane fuelcell model. International Journal of Hydrogen Energy 2011;36(6):3941e55.

[42] Matian Mardit, Marquis Andrew, Brandon Nigel. Model baseddesign and test of cooling plates for an air-cooled polymerelectrolyte fuel cell stack. International Journal of HydrogenEnergy 2011;36(10):6051e66.

[43] Nam JH, Kaviany M. Effective diffusivity and water-saturation distribution in single- and two-layer PEMFCdiffusion medium. International Journal of Heat and MassTransfer 2003;46(24):4595e611.

[44] Zamel Nada, Li Xianguo, Shen Jun. Correlation for theeffective gas diffusion coefficient in carbon paper diffusionmedia. Energy and Fuels 2009;23(12):6070e8.

[45] Bruggeman DAG. Berechnung verschiedener physikalischerkonstanten von heterogenen substanzen. Annals of Physics1935;416(24):636e64.

[46] HeWensheng, Yi Jung S, Nguyen Trung Van. Two-phase flowmodel of the cathode of pem fuel cells using interdigitatedflow fields. AIChE Journal 2000;46:2053e64.

[47] Meng Hua. Multi-dimensional liquid water transport in thecathode of a pem fuel cell with consideration of the micro-porous layer (mpl). International Journal of Hydrogen Energy2009;34(13):5488e97.

[48] Das Prodip K, Li Xianguo, Liu Zhong-Sheng. Analysis of liquidwater transport in cathode catalyst layer of pem fuel cells.International Journal of Hydrogen Energy 2010;35(6):2403e16.

[49] LinG,HeW,NguyenTV.Modeling liquidwater effects in the gasdiffusion and catalyst layers of the cathode of a PEM fuel cell.Journalof theElectrochemicalSociety2004;151(12):A1999e2006.

[50] Wang Xuhai, Nguyen Trung Van. Modeling the effects of themicroporous layer on the net water transport rate across themembrane in a PEM fuel cell. Journal of the ElectrochemicalSociety 2010;157(4):B496e505.

[51] Thiele EW. Relation between catalytic activity and size ofparticle. Industrial& EngineeringChemistry 1939;31(7):916e20.

[52] Wang X, Nguyen TV. Modeling the effects of capillaryproperty of porous media on the performance of the cathodeof a PEMFC. Journal of the Electrochemical Society 2008;155(11):B1085e92.

[53] Shah AA, Kim GS, Sui PC, Harvey D. Transient non-isothermal model of a polymer electrolyte fuel cell. Journal ofPower Sources 2007;163(2):793e806.

[54] WangY,BasuS,WangCY.Modeling two-phaseflowinPEMfuelcell channels. Journal of Power Sources 2008;179(2):603e17.

[55] Bird RB, Stewart WE, Lightfoot EN. Transport Phenomena.John Wiley & Sons; 1960.

[56] Pasaogullari U, Wang CY, Chen KS. Two-phase transport inpolymer electrolyte fuel cells with bilayer cathode gasdiffusion media. Journal of the Electrochemical Society 2005;152(8):A1574e82.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 1 8 7 1e1 1 8 8 5 11885

[57] Springer TE, Zawodzinski TA, Gottesfeld S. Polymerelectrolyte fuel cell model. Journal of the ElectrochemicalSociety 1991;138(8):2334e42.

[58] Motupally S, Becker AJ, Weidner JW. Diffusion of water inNafion 115 membranes. Journal of the ElectrochemicalSociety 2000;147(9):3171e7.

[59] Bernardi DM, Verbrugge MW. Mathematical model of a gasdiffusion electrode bonded to a polymer electrolyte. AIChEJournal 1991;37(8):1151e63.

[60] Ye Q, Nguyen TV. Three-dimensional simulation of liquidwater distribution in a PEMFC with experimentally measuredcapillary functions. Journal of the Electrochemical Society2007;154(12):B1242e51.

[61] Amphlett JC, Baumert RM, Mann RF, Peppley BA, Roberge PR,Harris TJ. Performance modeling of the Ballard Mark IV solidpolymer electrolyte fuel cell. Journal of the ElectrochemicalSociety 1995;142(1):1e8.

[62] Nguyen TV, He W. Ch.8. In: Handbook of fuel cell-Fundamentals, Technology and applications, vol. 3. JohnWiley & Sons; 2003.

[63] Ziegler C, Yu HM, Schumacher JO. Two-phase dynamicmodeling of PEMFCs and simulation of cyclo-voltammograms. Journal of the Electrochemical Society2005;152(8):A1555e67.

[64] Meng H, Wang CY. Model of two-phase flow andflooding dynamics in polymer electrolyte fuel cells.Journal of the Electrochemical Society 2005;152(9):A1733e41.

[65] Litster S, McLean G. Pem fuel cell electrodes. Journal of PowerSources 2004;130(1e2):61e76.

[66] Incropera FP, Dewitt DP. Fundamentals of heat and masstransfer. John Wiley & Sons; 1990.

[67] Lide DR, Haynes WM. CRC handbook of chemistry andphysics. The CRC Press; 2010.