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Liquid water distribution in hydrophobic gas-diffusion layers with interconnect rib geometry:An invasion-percolation pore network analysis

Kyu-Jin Lee a, Jung Ho Kang b, Jin Hyun Nam c,*aDepartment of Mechanical Engineering, Myongji University, Yongin 449-728, Republic of Koreab School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Republic of KoreacSchool of Mechanical and Automotive Engineering, Daegu University, Gyungsan 712-714, Republic of Korea

a r t i c l e i n f o

Article history:

Received 29 October 2013

Received in revised form

13 January 2014

Accepted 31 January 2014

Available online 24 February 2014

Keywords:

Polymer electrolyte membrane fuel

cell

Gas diffusion layer

Liquid water transport

Pore network

Invasion-percolation

Interconnect ribs

* Corresponding author. School of Mechanica714, Republic of Korea. Tel.: þ82 53 850 6675

E-mail address: jinhnam@gmail.com (J.H0360-3199/$ e see front matter Copyright ªhttp://dx.doi.org/10.1016/j.ijhydene.2014.01.2

a b s t r a c t

Water distribution in gas diffusion layers (GDLs) of polymer electrolyte membrane fuel cells

(PEMFCs) is determined by the pore morphology of the GDL as well as the flow conditions

between the GDL and the gas flow field, where interconnect ribs and gas channels are

placed side-by-side. The present study employs a steady state pore network model based

on the invasion-percolation (IP) process to investigate the water transport in the under-rib

region, in the under-channel region, and in between those regions inside the GDL. The

interconnect rib partially blocks the outlet surface of the GDL, which forces water transport

paths from the under-rib region to grow towards the gas channel through an extra IP

process. The pore network model predicts spatially non-uniform water distributions inside

the GDL due to the interconnect ribs, especially with an increased saturation level in the

under-rib region. Parametric studies are also conducted to investigate the effects of several

geometrical factors, such as width of the rib and the channel, thickness of the GDL, and

water intruding condition at the inlet surface of the GDL.

Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights

reserved.

1. Introduction

Polymer electrolytemembrane fuel cell (PEMFC) is a promising

replacement for internal combustion engines in vehicles due

to high efficiency and zero-CO2 emission [1]. Successful

application of PEMFCs to automobile systems has been chal-

lenged by high cost of platinum catalyst, performance loss at

low temperature, low durability, etc. Water management is

l and Automotive Engine; fax: þ82 53 850 6689.. Nam).2014, Hydrogen Energy P06

among the most significant issues concerning the commer-

cialization of PEMFCs because it is related with high power

performance, essential for automobile powertrains. While a

PEMFC system requires an adequate amount of water in the

polymermembrane for fast proton exchange, excessive liquid

water flooding in the porous components hinders reactant gas

flow passages, resulting in limited current generation [2].

In order to address the water management problem,

polymer membrane is humidified by supplying reactant gases

ering, Daegu University, 15 Naeri-ri, Jinryang-eup, Gyungsan 712-

ublications, LLC. Published by Elsevier Ltd. All rights reserved.

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 9 ( 2 0 1 4 ) 6 6 4 6e6 6 5 6 6647

with saturated water vapor in gas channels whereas the gas

diffusion layers (GDLs) are coated with hydrophobic polymer

(PTFE) for repelling liquid water [3]. When a PEMFC operates at

high power conditions, the water generation rate often ex-

ceeds to the water removal rate resulting in the flooding of the

GDL and the catalyst layer (CL). Thus, various efforts have

beenmade to mitigate the flooding in porous media by proper

management methods on the basis of the knowledge of water

transport mechanisms [4e6]. Many experimental and nu-

merical studies have been conducted to reveal the water

transport mechanisms in the GDL and in the CL and thus to

predict liquid water distributions in PEMFC systems [7e14].

For numerical model studies, the continuum two-phase flow

models have been widely used, which incorporate the Darcy’s

law for flow in porous media and the experimentally deter-

mined correlations for capillary pressure and relative

permeability [8,10e12]. However, recent numerical studies

[15e20] suggested that the continuum transport theory may

not be applicable or should be significantly modified since

liquid water transport through hydrophobic GDLs is driven by

the capillary fingering flow (capillary fingering regime) [21].

Previous pore network results of Lee et al. [15] proposed that

the capillarity is themain driving force for the water transport

in GDLs. The consecutive study [22] showed that pore

morphological factors of GDLs, such as pore connectivity, pore

size distribution, etc. play a major role on water distribution

because the capillary fingering flow is governed by the

invasion-percolation process which makes the liquid water to

preferentially occupy a pore with the largest size in hydro-

phobic porous media.

Experimental studies adopted in-situ visualization tech-

niques such as X-ray tomography [23e25] and neutron radi-

ography [26,27] tomeasure liquid water distribution inside the

GDL, in the in-plane or through-plane directions. Using the

high resolution neutron radiography, Turhan et al. [27] pre-

sented that water distribution in a cathode GDL is rather in-

dependent of the water production rates under the operating

currents of 0.2 Am�2 and 1.0 Am�2. Their observation, i.e., the

weak influences of the water flow rate on the invasion-

percolation process, supports the proposition of Lee et al.

[15] that the capillary fingering flow is the dominant mecha-

nism for the water transport in the cathode GDL. The obser-

vation by Hartnig et al. [23] using the synchrotron X-ray

tomography seems to be opposite to the results of Turhan

et al. [27], indicating strong dependence of the water distri-

bution in a GDL on the water production rate. However, in

their experiments, gas in flow channels was relatively dry so

that water could be removed as vapor; this results in low

water accumulation in the cathode GDL at low current

conditions.

It has been observed in many experiments that water

accumulation in the GDL is more severe under an intercon-

nect rib than under a gas channel [28e32]. Kowal et al. [28]

quantified the water volume in a carbon paper GDL and ob-

tained a volume ratio of 6:4 for liquid water stored under ribs

to that under channels (the rib width was the same as the

channel width). Boillat et al. [29] obtained high resolution

images for water distribution across the MEA structure using

neutron radiography and showed strong variation of water

content under the ribs and channels. Deevanhxay et al. [30]

discovered in their soft X-ray radiography images that, at

low current density, liquid water accumulated under the rib

but not under the channel. They attributed the localizedwater

generation to the enhanced oxygen reduction reaction in the

under-rib region due to faster electron transfer. Deevanhxay

et al. [31,32] also investigated the transient liquid water

transport in a microporous layer (MPL) and a GDL under

interconnect ribs and reported that pore morphology signifi-

cantly impacts on water accumulation behaviors. Despite of

technological advances for visualizing water distributions in

the GDL, water transport mechanism with interconnect rib

geometries has not been well understood. Improving the

configuration of gas flow field plates of PEMFCs cannot be

achieved without understanding how the rib design in-

fluences liquid water distribution inside GDLs. Thus, experi-

mental studies have been conducted for the practical

purposes related with gas flow field designs. Yoon et al. [33]

performed several experimental tests to investigate the ef-

fects of channel and ribwidths on the performance of a PEMFC

and concluded that the narrower ribs lead to a better cell

performance. Numerical models [34,35] also have been

developed for exploring the channel and rib designs of

PEMFCs; however, thesemodels generally failed to capture the

microscopic liquid water transport in GDLs which can signif-

icantly influence the performance of PEMFC at high current

conditions.

This study investigates the water transport and saturation

distribution in the GDL under the interconnect rib and under

the channel. A pore network model based on an invasion-

percolation path-finding process, developed in the previous

studies [22,36], is used for the calculation. Parametric studies

are also conducted to clarify the effects of pore geometrical

factors, such as width of the rib and the channel, thickness of

the GDL, and water intruding condition at the inlet surface of

the GDL (at the CL/GDL interface).

2. Theory and calculation

2.1. Pore network generation

The pore network geometries developed in the previous

studies [22,36] are used to simulate the pore morphology of

GDLs. The calculation domain is presented in Fig. 1(a) as the

network of regularly stacked cubic cells where pores and

throats are enclosed. The boundary conditions (BCs) are also

shown in Fig. 1(a), where the bottomplane of the domain is the

inlet boundary through which liquid water enters the pore

network. The outlet boundary is corresponding to the central

part of the top plane, which is open to the gas channel under a

constant air pressure. The top plane underneath the inter-

connect rib is regardedas theclosedwall boundarybecause the

interconnect rib does not allow liquid water exhaust out of the

GDL. Cyclic connectivity is assumed for side planes to extend

the calculation domain infinitely in planar x and y directions.

At the inlet boundary, a spatially uniform flux of liquid

water is assumed to enter the GDL from the CL. That is, liquid

water is assumed to randomly invade into the pores adjacent

to the inlet boundary while the number of those water-

invaded pores is prescribed according to the inlet invaded

Fig. 1 e Pore network generation: (a) regularly arranged cubic cells and boundary conditions, and (b) box-shaped pores (gray)

and throats (white).

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pore-fraction fin. Note that the inlet invaded pore-fraction, fin,

is defined as the ratio of the number of the water-invaded

pores to the number of all pores adjacent to the inlet bound-

ary. Previous studies [22,36,37] showed that fin is one of the

most crucial parameters which governs the water saturation

distribution inside the GDL. The parameter fin is believed to be

closely related with the area-specific number density of liquid

water breakthrough sites from the CL (which is moderately

dependent on the water production rate) as well as the pore

size in the GDL [37]. To investigate the effects of the inlet

condition of the GDL in the parametric study, fin is treated as a

variable parameter.

The domain size of the simulated pore network is

20 � 80 � 10 in cell numbers, which corresponds to the

physical dimension of 500 mm� 2000 mm� 250 mm in the x-, y-,

and z-directions (the length of the cubic cell, Lcell, is 25 mm).

Thewidth of interconnect ribs and that of gas channels are set

equal to 1000 mm. Thus, the closed-wall BCs are imposed at

two separate parts of the top plane (0e500 mm and

1500e2000 mm in the y-direction) while the outlet BC is

imposed at the central part of the top plane (500e1500 mm). As

shown in Fig. 1(b), each cubic cell consists of a box-shaped

pore at the center and six throats attached to the pore. A

box-shaped throat connects two neighboring pores for flow

passage. To account for random nature of the GDL, three edge

lengths of box-shaped pores are randomly chosen between

0.7Lcell and 0.9Lcell (17.5e22.5 mm). Similarly, two edge lengths

of box-shaped throats are also randomly chosen between

0.2Lcell and 0.7Lcell (5e17.5 mm).

The geometric parameters of the pore network are chosen

by referring to the porosity and gas permeability data for

carbon papers which are commonly used for GDL materials

[38]. The mean porosity of the pore network is 0.633 (with

standard deviation of 0.001) and the mean gas permeability is

3.39 � 10�12 m2 (with standard deviation of 0.08 � 10�12 m2).

The generated pore network geometries are isotropic in na-

ture, although the actual pore structure of GDL materials is

generally anisotropic due to their fibrous structure. The use of

isotropic pore-networks may be justified by the fact that the

degree of anisotropy of GDLmaterialsmeasured by directional

(in-plane and through-plane) permeabilities or diffusivities is

relatively small [38,39]. All surfaces of pores and throats are

assumed to be hydrophobic with a contact angle of 120�. More

detailed information for the pore networkmodel can be found

in Lee et al. [22,36].

2.2. Invasion-percolation calculation

Two-phase flow in partially saturated porous media with a

small capillary number (Cah minvq/scos q less than about 10�7)

is characterized as the capillary fingering flow regime, which

is primarily driven by the invasion-percolation (IP) process

[21]. In the operating range of PEMFCs (less than 2 A cm�2), the

water flow rate is so small that the capillary fingering flow is

induced even if the whole produced vapor is condensed in the

CL and then gets into the GDL as liquid. For example, a current

density of 1 A cm�2 roughly corresponds to q of about

10�6 m s�1 and Ca of about 10�8. Our previous steady pore

networkmodels [22,36] are based on the IP path-finding for the

capillary fingering flow in the GDL. Condensation which is

another major source of water transport and accumulation in

the GDL is not considered in this study.

The model in Ref. [22] consists of two calculation steps: IP

path-finding and subsequent viscous flow calculation. An IP

procedure determines the essential transport paths by

searching for the largest flow passages with the smallest

capillary entry pressure in the hydrophobic pore network. The

capillary entry pressure can be calculated as Pc,e¼ 2sjcos qj/r, afunction of the surface tension s, the contact angle q, and the

mean radius of curvature for thewater/air interface r (which is

strongly dependent on the size of flow passages). The liquid

pressure determined by this capillary entry pressure of each

throat is the lower-limit for maintaining percolated pore

clusters for liquid water transport. If the viscous pressure

drops are not negligibly small, viscous flow calculation should

be performed for the percolated pore clusters after the IP

procedure. However, the viscous drop through a throat (con-

necting two neighbored pores) is much smaller, about 5 Pa at a

current density of 1 A cm�2, compared to the mean capillary

entry pressure of about 12 kPa. Therefore, in this study, only

the IP path-finding calculation is performed (flow rate condi-

tion is not required) to obtain the steady distribution of liquid

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 9 ( 2 0 1 4 ) 6 6 4 6e6 6 5 6 6649

water and the corresponding capillary pressure in hydropho-

bic GDLs. Ceballos and Prat [40] also used a similar IP pore

network model to study the liquid water transport in hydro-

phobic GDLs.

The algorithm of the present IP path-finding procedure is

summarized in Fig. 2. The throat searching pool (TSP) denotes

a list of uninvaded throats adjacent to the pores that have

been already invaded by liquid water. At each step, a throat

with a minimum capillary entry pressure is searched in the

current TSP, followed by the updating of capillary pressure for

currently flooded pores as shown in Fig. 2. Then, the throat

with the minimum entry pressure and a pore connected to it

are marked as flooded to advance the liquid water front and

TSP is updated accordingly. This procedure is repeated until

the liquid water front extends to the outlet boundary at the

GDL/Channel interface (breakthrough) or merges with other

percolated clusters previously determined. The spatially uni-

form flux condition considered in this study assumesmultiple

liquid water injection sites at the inlet boundary of the GDL.

Thus, the above IP procedure should be performed sequen-

tially for all inlet pores (randomly chosen according to a given

fin). At the end of the IP path-finding calculation, liquid water

volume is determined using the capillary pressure, based on

the water/air interfacial shape in the pores and throats [22].

3. Results and discussion

The liquid water distribution in the GDL was obtained by

statistically averaging the data from 500 pore network re-

alizations for each simulated condition. In the previous pore

network studies [22,36], the converged saturation distribution

in the through-plane direction (z-direction, across the GDL)

was obtained by averaging the data from about 20 pore

network realizations. However, much more pore-network re-

alizations were required to obtain converged water saturation

distributions in the in-plane direction (preferentially y-direc-

tion) due to the effects of interconnect rib geometries.

3.1. Water distribution with interconnect rib geometry

Increased liquidwater accumulation in the GDL under the ribs

is considered as a common phenomenon [28]. Many obser-

vations based on in-situ visualization techniques showed that

Fig. 2 e Invasion-percolation (IP) path-finding algorithm

used for steady pore network model.

the water distribution in the GDL is significantly influenced by

geometries of the interconnect rib and the gas channel

[29e33]. However, the detailed mechanism of water transport

inside the GDL with the rib/channel geometries is not fully

understood yet. The present study based on the IP pore

network model is believed to provide meaningful data

revealing the formation of transport paths under the partially

closed outlet boundary condition. A reference case with a

domain size of 500 mm� 2000 mm� 250 mm is simulated for the

inlet invaded pore-fraction, fin, of 100%while the interconnect

ribs are assumed to be placed (and thus block the water

exhaust) at 0e500 mm and 1500e2000 mm in the outlet

boundary. The condition of fin ¼ 100% denotes that every pore

just adjacent to the inlet boundary of the GDL is assumed to be

invaded by liquid water from below (from the CL or the MPL).

The mean saturation of liquid water is obtained by aver-

aging the pore network simulation data from the 500 re-

alizations. The distribution of mean water saturation will be

presented in the z-direction (through-plane direction) by Szand in the y-direction (in-plane direction) as Sy. In addition,

mean water saturation in the under-rib region, Sz,rib, and that

in the under-channel region, Sz,ch, are also determined.

Fig. 3(a) and (b) shows the mean saturation distribution inside

the GDL. In Fig. 3(a), the saturation level near the inlet

boundary is relatively high as 0.81 for both regions under the

rib and the channel, indicating a weak influence of the outlet

boundary condition on water transport in the upstream re-

gion. In addition, the prescribed inlet condition, fin ¼ 100%, is

thought to make the saturation level in the upstream region

less sensitive to the outlet boundary conditions. The satura-

tion level is observed to decrease along the z-direction by

merging of water transport paths according to the invasion-

percolation (IP) process. On the under-channel region of the

GDL, the saturation level rather linearly decreases along the z-

direction and finally reaches about 0.05 near the outlet

boundary (open to the channel allowing water exhaust).

However, in the under-rib region, the saturation distribution

shows a smaller decrease in the z-direction, ending up with a

saturation level of about 0.2 near the outlet boundary.

The observed difference in the saturation distributions can

be explained as follows. Since the interconnect rib geometry

does not allow liquidwater passage, liquid water in the under-

rib region is forced to find additional transport paths towards

the channel. Thus, more IP process occurs after liquid water

front arrives at the interconnect rib geometry, invading more

pores with higher capillary pressures and expanding flooded

pore clusters in the under-rib regions of the GDL. The

increased saturation levels under the interconnect rib are also

well observed by the mean saturation distribution in the y-

direction, Sy, shown in Fig. 3(b). In this study, the extended IP

process occurring in the under-rib region rib after liquid water

front contacts the interconnect rib is called “the extra IP pro-

cess”. This process is believed to explain many phenomena

regarding water transport in the GDLs with interconnect rib

geometries.

The mean capillary pressure calculated for water-invaded

pores is presented in Fig. 3(c). As mentioned previously,

capillary pressure in this study corresponds to the lower-limit

value determined by the invasion-percolation path-finding

process ignoring small viscous pressure drop. Fig. 3(c) shows

Fig. 4 e Approximate regions of liquid water distribution in

a GDL with interconnect rib/gas channel geometries.

Fig. 3 e Effects of interconnect rib/gas channel geometries

on the distribution of (a) mean liquid water saturation in

the through-plane direction, Sz, (b) mean liquid water

saturation in the in-plane direction, Sy, and (c) mean

capillary pressure in the through-plane direction, Pz.

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 9 ( 2 0 1 4 ) 6 6 4 6e6 6 5 66650

that the capillary pressure under the channel, Pz,ch, decreases

from10.9 kPa near the inlet boundary to 9.5 kPa near the outlet

boundary open to the channel. Liquid water invades many

pores and throats in search for preferential transport paths by

the capillary fingering process (IP process searching paths

with smaller capillary entry pressures). During this process,

many water transport paths merge together in the down-

stream region of the GDL and finally form several “backbone

transport paths” that lead to breakthrough sites. This results

in the observed low capillary pressure near the outlet

boundary shown in Fig. 3(c). However, liquid water in the

under-rib region of the GDL should experience an extra IP

process to arrive at the water breakthrough sites (the back-

bone transport paths), which results in higher capillary pres-

sure under the rib, Pz,rib, than Pz,ch. In Fig. 3(c), the capillary

pressure under the rib, Pz,rib, is relatively uniform around

10.3 kPa for 100 � z � 250 mm. The nearly uniform distribution

of Pz,rib in the downstream also indicates that many “dead-

end” pores blocked by the interconnect rib become invaded by

liquid water during the extra IP process.

Fig. 4 presents the three-dimensional (3D) iso-surface plot

for the liquid water saturation field, Sc(x,y,z) ¼ 0.5, obtained

from a pore network realization. The liquid water saturation

in a cell, Sc(x,y,z), is calculated by summing up all the water

volume inside the cell and then dividing it with the void vol-

ume. Then, the iso-surfaces shown in Fig. 4 represent

approximate water/air interfaces while the presence of solid

structures is ignored. The number of breakthrough sites from

the GDL to the gas channel was estimated about 10 for the

reference case, by averaging the data from 500 realizations. It

is well observed in Fig. 4 that liquid water saturation is low

near the breakthrough sites since the capillary fingering pro-

cess is ceased upon liquid water finds the exhaust paths. The

liquid water saturation is much higher under the rib than

under the channel due to the extra IP process, by which liquid

water invades pores in the GDL laterally (primarily, in the y-

direction) to find breakthrough sites. The results presented in

Figs. 3 and 4 are consistent with the experimental results (an

increased amount of water accumulation under the ribs) ob-

tained by Kowal et al. [28]. The partial blocking of water

exhaust by the interconnect rib geometries forces liquid water

to experience an extra IP process under the rib to form

transport paths to the outlet boundary open to the channel.

This results in the increased saturation level as well as the

increased capillary pressure in the under-rib region of the GDL

during the operation of PEMFCs.

3.2. Effects of interconnect rib width

The effects of the interconnect rib width on water distribution

are investigated by varying the rib width, Lrib, as 0.2 mm,

0.6 mm, 1.0 mm, 1.4 mm, and 1.8 mm, while the lateral

domain size, Ly (¼Lch þ Lrib) is fixed at 2 mm. The saturation

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distribution in the z-direction is presented in Fig. 5(a) for the

under-rib region and in Fig. 5(b) for the under-channel region.

In Fig. 5(a), the saturation distribution under the rib, Sz,rib, is

increased as the rib becomes wider, especially in the down-

stream region at z � 100 mm. On contrary, the saturation dis-

tribution under the channel, Sz,ch, shows smaller dependence

on the rib width in Fig. 5(b). In addition, the saturation level is

almost unchanged near the inlet plane (z � 75 mm) in Fig. 5(a)

and (b), indicating that the change of the outlet BC has less

impact on the water transport in the upstream region. Note

that the saturation level is fixed at 0.81 near the inlet boundary

since all the pores adjacent to the inlet are assumed to be

invaded by liquid water with the inlet BC of fin ¼ 100%.

The increased saturation level underneath the intercon-

nect rib can be explained by the extra IP process required for

liquid water to exhaust from under the rib towards the outlet

boundary open to the channel. As the rib width increases, the

distance from the under-rib region to the channel outlet in-

creases. Thus, the extra IP process is intensified for liquid

water to find long transport paths stretched laterally in the y-

direction, resulting in the increase of Sz,rib. The capillary

pressure distribution under the rib, Pz,rib, is also shown in

Fig. 5(c), where higher pressure level with a larger rib width

indicates that liquid water has invaded smaller pores during

the intensified extra-IP process.

In Fig. 5(b), the water transport under the channel seems to

be independent of the rib width with almost unchanged

saturation distribution, Sz,ch, except for an extremely wide rib

width, Lrib, of 1.8 mm (Lch ¼ 0.2 mm). In addition, Fig. 5(d)

Fig. 5 e Effects of interconnect rib width on the distribution

of mean liquid water saturation (a) under the rib, Sz,rib, and

(b) under the channel, Sz,ch, and mean capillary pressure (c)

under the ribs, Pz,rib, and (d) under the channel, Pz,ch.

presents nearly identical distribution of capillary pressures,

Pz,ch, irrespective of the rib width. Liquid water from the

under-channel region simply forms percolated transport

paths from the inlet boundary towards the outlet boundary

(the distance equivalent to the thickness of the GDL). Then,

the water transport paths from the under-rib region become

connected to those existing percolated pore clusters in the

under-channel region in order to be exhausted from the GDL.

Thus, no additional pores are needed to be invaded to trans-

port liquid water from the under-rib region, resulting in con-

stant Pz,ch and Sz,ch in the under-channel region. In summary,

increasing the rib width greatly increases the IP process in the

under-rib region of the GDL but does not affect the IP process

in the under-channel region. The higher capillary pressure

level in the under-rib region is the direct evidence of the

intensified IP process since smaller pores are invaded by liquid

water at higher capillary pressures.

The water distribution in the y-direction, Sy, is presented

for different rib widths in Fig. 6, where Sy is relatively uniform

at around 0.35 in the under-channel region. Under the rib,

liquid water saturations increase from the edge toward the rib

center but the curves become flattened at certain levels of

saturation, such as about 0.48 for Lrib ¼ 1.8 mm, about 0.47 for

Lrib ¼ 1.4 mm, about 0.46 for Lrib ¼ 1.0 mm, about 0.43 for

Lrib ¼ 0.6 mm, and about 0.35 for Lrib ¼ 0.2 mm. The smooth

saturation distribution near the center of the rib indicates that

the extra IP process occurs uniformly over the under-rib re-

gion of the GDL.

Fig. 7 presents the 3D iso-surface plot for the liquid water

saturation field corresponding to Sc(x,y,z) ¼ 0.5 for the narrow

rib case of Lrib ¼ 0.2 mm and for the wide rib case of

Lrib ¼ 1.8 mm (two extreme cases for explaining the effects of

the ribwidth). Themeannumber of breakthrough sites formed

at the outlet boundary is obtained to be about 18, 14, 10, 7, and 3

for the rib width of 0.2 mm, 0.4 mm, 1.0 mm, 1.4 mm, and

1.8mm, respectively, by averaging the simulation results from

500 different pore network realizations. Fig. 7 clearly shows

that the extra IP process is intensified with larger Lrib, with

more water volume residing under the interconnect rib. The

area-specific number density of breakthrough sites (the num-

ber of breakthrough sites divided by areas of the channel

outlet) is rather constant about 20 mm�1 for the rib width of

0.2mm, 0.4mm, and 1.0mm.This indicates that the formation

Fig. 6 e Effects of interconnect rib width on the distribution

of mean liquid water saturation in the in-plane direction,

Sy.

Fig. 7 e Approximate regions of liquid water distribution in

a GDL with the rib width of (a) 0.2 mm and (b) 1.8 mm. (For

interpretation of the references to color in this figure

legend, the reader is referred to the web version of this

article.)

Fig. 8 e Effects of GDL thickness on the distribution of

mean liquid water saturation (a) under the rib, Sz,rib, and (b)

under the channel, Sz,ch, and mean capillary pressure (c)

under the ribs, Pz,rib, and (d) under the channel, Pz,ch.

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 9 ( 2 0 1 4 ) 6 6 4 6e6 6 5 66652

of water transport paths in the under-channel region is not

much influenced by that in the under-rib region. However, for

narrow channel cases, the area-specific number density of

breakthrough sites increases to about 23 mm�1 for

Lrib ¼ 1.4 mm and about 30 mm�1 for Lrib ¼ 1.8 mm, which

implies that the IP process in the under-rib region starts to

influence that in the under-channel region. In Fig. 7(a) and (b),

one identical breakthrough site (marked by yellow circles) is

formed in both the narrow channel and the wide channel

cases. Note that this breakthrough site corresponds to the final

pore of thewater transport paths that exhaust liquidwater out

of the GDL and is created independently of the rib width. The

other breakthrough site shown in Fig. 7(b) is thought to be the

one that is newly formed because the IP process in the under-

rib region affects that in the under-channel region.

3.3. Effects of GDL thickness

The previous IP pore network study [22] investigated thewater

saturation distribution in the GDL for different GDL thick-

nesses. The results indicated that a smaller GDL thickness

suppresses the IP process inside the GDL and thus leads to a

lower local saturation level and a larger number of break-

through sites at the outlet surface. As an extension to the

previous study, water saturation distributions in the GDLwith

interconnect rib/gas channel geometries are investigated in

this study by varying the thickness of the GDL. Similar to Ref.

[22], the number of unit cells in the z-direction is varied as 4, 6,

10, 14, and 16, which corresponds to the GDL thickness, LGDL,

of 0.1 mm, 0.15 mm, 0.25 mm, 0.35 mm, and 0.4 mm, respec-

tively. The inlet invaded pore-fraction, fin, is fixed at 100% for

these simulations.

In Fig. 8(a) and (b), the saturation near the inlet boundary is

found to be less sensitive to the GDL thickness, LGDL, for both

the under-rib region and the under-channel region. This in-

dicates that the high inlet invaded pore-fraction, fin, of 100%

dominantly controls the saturation level near the inlet

boundary. The comparison of Fig. 8(a) and (b) points out that

the saturation distribution under the rib, Sz,rib, is always

higher than that under the channel, Sz,ch. In order to clarify the

effects of LGDL on the water transport in the GDL, the satura-

tion distribution in the under-channel region, Sz,ch, is exam-

ined first. Fig. 8(b) shows that local Sz,ch at a given location in

the z-axis increases as the GDL thickness increases. This in-

dicates that the IP process in the through-plane direction (z-

direction) is intensified for larger LGDL because the transport

length from the inlet to the outlet boundary increases. How-

ever, the saturation level just beneath the outlet boundary

becomes lower as LGDL increases, pointing out that the num-

ber of breakthrough sites decreases according to the merging

of many transport paths in a thicker GDL by the intensified IP

process. In Fig. 8(d), the capillary pressure under the channel,

Pz,ch, showsmilder declining trends along the z-direction with

a thicker GDL. Note that the water saturation and capillary

pressure distributions shown in Fig. 8(b) and (d) are quite

similar to the results of Ref. [22] where the interconnect rib

geometry was not considered. Thus, it can be inferred that the

interconnect rib geometry has minor effects on the water

transport in the under-channel region.

The liquid water saturation in the under-rib region, Sz,rib,

evolves in somewhat different ways, especially when the

thickness of the GDL is small. The merging of water transport

Fig. 10 e Approximate regions of liquid water distribution

in a GDL with the GDL thickness of (a) 0.1 mm and (b)

0.4 mm.

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 9 ( 2 0 1 4 ) 6 6 4 6e6 6 5 6 6653

paths by the IP process is suppressed in a thin GDL due to

insufficient spreading of capillary fingering fronts. This is

because the capillary fingering fronts from an injection site

are expected to reside in a spherical domain of a certain radius

in isotropic porous media. Thus, many water transport paths

come to reach the closed wall boundary just beneath the

interconnect rib. If the IP process terminates at this point,

the saturation distribution under the rib, Sz,rib, will be almost

the same as Sz,ch, as shown in Fig. 8(b). However, being blocked

by the rib, these water transport paths in the under-rib region

continue to move laterally towards the outlet boundary

through the extra IP process in the in-plane direction (y-di-

rection). Since more pores and throats are invaded during the

extra IP process, the resulting Sz,rib is always higher than Sz,ch.

In addition, local Sz,rib at a given location near the inlet slightly

increases for a thinner GDL as shown in Fig. 8(a) due to the

extra IP process. The mean capillary pressure in the under-rib

region, Pz,rib, is shown in Fig. 8(c), where Pz,rib is observed to be

higher for a thin GDL because the extra IP process under the

rib is intensified as the thickness of the GDL, LGDL, decreases.

The capillary pressure of liquid water should be higher in

order to invade into smaller pores and throats by the extra IP

process. Fig. 8(c) shows that, for LGDL larger than 350 mm, Pz,ribconverges to a line with a relatively flat part (around 10.2 kPa)

at the downstream region. This trend points out that the

enhancement of the extra IP process under the rib becomes

negligible with large thickness of the GDL.

The saturation distribution in the y-direction, Sy, with

different LGDL is shown in Fig. 9. It is interesting to find that the

saturation distribution, Sy, decreases as LGDL increases. It

should be noted that the mean saturation, Sy, is obtained by

averaging the water saturation in the z-directions. From

Fig. 8(a) and (b), it is clear that increasing LGDL will decrease the

mean saturation, Sy, when averaged over the GDL thickness.

In Fig. 9, the difference in Sy between the under-rib region and

the under-channel region seems to decrease as LGDL increases.

However, the ratio of Sy under the rib to that under the

channel is found to be almost unchanged by variation of the

GDL thickness.

Fig. 10 shows the 3D iso-surface plot for Sc(x,y,z) ¼ 0.5

which represents the approximate water/air interfaces in the

GDL with LGDL of 0.1 mm and 0.4 mm. For the thin GDL of

0.1 mm thickness, it is clearly shown that many water trans-

port paths arrive at the outlet boundary open to the channel

and also the closed wall boundary blocked by the rib, which

results in a large number of breakthrough sites as well as high

saturation level under the rib. But, for the thick GDL of 0.4 mm

Fig. 9 e Effects of GDL thickness on the distribution of

mean liquid water saturation in the in-plane direction, Sy.

thickness, water transport paths are reduced much in the

downstream region under the rib and the channel, with only 6

breakthrough sites at the outlet boundary and a few water

transport paths blocked by the rib. The averaged number of

breakthrough sites is estimated to be about 47, 25, 10, 6 and 5

for LGDL of 0.1 mm, 0.15 mm, 0.25 mm, 0.35 mm, and 0.4 mm,

from the simulation results of 500 pore network realizations.

3.4. Effects of inlet invaded pore-fraction

Nam et al. [37] suggested that, in the capillary fingering

regime, the amount of liquid water residing inside a GDL is

much more sensitive to the number of injection sites (liquid

water breakthrough sites fromaCL to the GDL) than the rate of

water injection (flow rate from the CL to the GDL). Gostick et al.

[41] experimentally obtained the reduced GDL saturation with

an impermeable mask with a small puncture instead of the

MPL to control the number of injection sites. Kang et al. [42]

conducted similarity model experiments to visualize the

non-wetting fluid transport in hydrophobic porous layers,

from which they demonstrated a water management role of

MPL that an MPL decreases saturation level in a GDL by

reducing the number of liquid injection sites at the inlet

boundary of the GDL. In this study, the inlet invaded pore-

fraction, fin, is defined as the number of water-invaded pores

to the number of all pores adjacent to the inlet boundary.

Then, the effects of the liquid injection site number on water

distribution in the GDL were investigated by varying fin as

100%, 25%, 5%, and 1% (corresponding to the number of water-

invaded pores of 1600, 400, 80, and 16, respectively). The

water-invaded pores were randomly selected among the 1600

pores adjacent to the inlet boundary.

Fig. 11(a) and (b) presents the saturation distribution under

the interconnect rib (under-rib region), Sz,rib, and under the

Fig. 11 e Effects of inlet invaded pore-fraction on the

distribution of mean liquid water saturation (a) under the

rib, Sz,rib, and (b) under the channel, Sz,ch, and mean

capillary pressure (c) under the ribs, Pz,rib, and (d) under the

channel, Pz,ch.

Fig. 12 e Effect of the inlet invaded pore-fraction on the

distribution of mean liquid water saturation in the in-

plane direction, Sy.

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 9 ( 2 0 1 4 ) 6 6 4 6e6 6 5 66654

gas channel (under-channel region), Sz,ch, for different inlet

invaded pore-fractions, fin. It is clearly noticed that fin signif-

icantly impacts the saturation levels for both the under-rib

and under-channel regions. Fig. 11(a) and (b) shows a

considerable reduction of the water saturation near the inlet

boundary (z ¼ 0 mm) for smaller fin but this saturation reduc-

tion becomes less conspicuous in the downstream region near

the outlet boundary (z ¼ 250 mm). The comparison of Fig. 11(a)

and (b) indicates that the saturation level is more noticeably

reduced with smaller fin in the under-channel region than in

the under-rib region. In Fig. 11(a), the saturation level in the

under-rib region decreases from 0.81 to 0.62, 0.40, and 0.24

near the inlet boundary during fin is reduced from 100% to

25%, 5%, and 1% (the saturation level is rather constant

around 0.17 near the outlet boundary). However, in Fig. 11(b),

the saturation level in the under-channel region decreases

from 0.81 to 0.61, 0.37, and 0.16 near the inlet boundary (the

saturation level is rather constant around 0.05 near the outlet

boundary). The extra IP process under the interconnect rib is

believed to increase the saturation level in the under-rib re-

gions, compensating the effects of lower fin.

For very small inlet invaded pore-fractions, such as fin ¼ 5%

and 1%, a local maximum is observed in the water saturation

distribution inside the GDL, which agrees with the experi-

mental results of Turhan et al. [27]. Such low fin means that

the number ofwater injection sites is small and thus thewater

injection sites are sparsely located at the inlet boundary of the

GDL. However, liquid water from those injection sites still

needs to explore many pores and throats according to the IP

process before finding possible transport paths and forming

percolated clusters. Thus, saturation level increases along the

z-direction near the inlet boundary as pores and throats are

invaded by active IP process searching for possible paths.

After pores and throats are sufficiently explored, then the

saturation level decreases along the z-direction due to the

merging of these transport paths.

The mean capillary pressures in the water-invaded pores

are presented in Fig. 11(c) for the under-rib region, Pz,rib, and in

Fig. 11(d) for the under-channel region, Pz,ch. As the inlet

invaded pore-fractions, fin, decreases, the capillary pressures

under the rib, Pz,rib, becomes rather flat around 10.3 kPa.

Similarly, the capillary pressure under the channel, Pz,ch, also

decreases especially near the inlet boundary. These observa-

tions clearly indicate that fin primarily affects the water

transport in the upstream region near the inlet. The mean

saturation distribution in the y-direction, Sy, is presented in

Fig. 12, where low fin significantly reduces the saturation level

in the GDL as observed in Fig. 11(a) and (b). The variation of

water saturation between the under-rib region and the under-

channel region becomes more noticeable for smaller fin. In

Fig. 12, the difference in the saturation level between the two

regions is about 0.1 for fin ¼ 100% but it increases to 0.2 for

fin ¼ 1%. Since an MPL is believed to reduce the number of

liquid water injection sites into a GDL, the results in Fig. 12

indicate that lower saturation level in the GDL can be ach-

ieved by employing an MPL. However, the water distribution

under the flow field of PEMFCs may be more non-uniform

(between the under-rib region and the under-channel re-

gion) when an MPL is used.

4. Conclusion

Water distributions in hydrophobic GDLs were evaluated

using a steady pore network model based on the IP procedure

for the cases when the outlet boundary was partially blocked

by interconnect rib geometries. The water saturation and

capillary pressure were observed to be higher in the under-rib

region of the GDL than in the under-channel region. These

results were attributed to the extra IP process in the under-

rib region that drives water transport paths to expand from

under the closed wall boundary (blocked by the interconnect

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 9 ( 2 0 1 4 ) 6 6 4 6e6 6 5 6 6655

rib) towards the outlet boundary (open to the gas channel)

through additional capillary fingering in the in-plane direc-

tion. Parametric studies were also conducted to investigate

the effects of several geometrical factors on the water

transport in GDLs, including the interconnect rib width, the

GDL thickness, and the inlet invaded pore-fraction. It was

observed in the simulation results that a larger rib width

increases the water saturation level in the under-rib region of

the GDL but has less impact on that in the under-channel

region. This indicates that water transport in the under-

channel region is almost independent of that in the under-

rib region.

It was also shown that a thin GDL decreases the local

saturation level at a given location (in the z-axis) under the

channel. However, the local saturation level under the rib is

found to remain rather constant near the inlet boundarywhen

the GDL thickness decreases. The merging of water transport

paths is suppressed during the IP process in the through-plane

direction (z-direction) in a thin GDL. Then, the extra IP process

under the rib should be intensified to redirect many water

transport paths in the in-plane direction (y-direction) from

under the rib towards the channel. The combined effects of

these phenomena result in a relatively constant water satu-

ration in the under-rib region near the inlet boundary. Finally,

we investigated the effects of the inlet invaded pore-fraction

at the inlet boundary of the GDL, which is closely related

with the number of liquid injection sites into the GDL (water

breakthrough sites from the CL or the MPL). Decreasing the

inlet invaded pore-fraction changed the saturation distribu-

tion curve along the through-plane direction (z-direction) of

the GDL from amonotonically decreasing one to an increasing

and then decreasing one. In addition, non-uniformitywas also

increased in the water saturation level between the under-rib

region and the under-channel region. In summary, the IP

processwas able to explain several important aspects of liquid

water transport in uniformly hydrophobic GDLs in contact

with flow field plates having interconnect ribs and gas

channels.

Acknowledgment

This work was supported by 2012 Research Fund of Myongji

University.

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