Impact of carbon paper structural parameters on the performance of a polymer electrolyte fuel cell cathode via lattice Boltzmann method

Abstract

Polymer electrolyte fuel cells (PEFCs) being employed in fuel cell electric vehicles (FCEVs) are promising power generators producing electric power from fuel stream via porous electrodes. Structure of carbon paper gas diffusion layers (GDLs) applying in the porous electrodes can greatly affect the PEFC performance, especially at the cathode side where electrochemical reaction is more sluggish. To discover the role of carbon paper GDL structure on the mass transfer properties, different cathode electrodes with dissimilar structural parameters are simulated via lattice Boltzmann method (LBM). 3D contours of oxygen and water vapor concentration through the GDL as well as the 2D contours of current density on the catalyst layer are illustrated and examined. The results indicate that the carbon fiber diameter has a negligible impact on the current density while the impact of carbon paper thickness and porosity is significant. In fact, increasing of carbon paper thickness or porosity leads to lack of cell performance.

Full text

Vol.:(0123456789)
1 3
Acta Mechanica Sinica
https://doi.org/10.1007/s10409-019-00919-1
RESEARCH PAPER
Impact ofcarbon paper structural parameters ontheperformance
ofapolymer electrolyte fuel cell cathode vialattice Boltzmann
method
M.Nazemian1· G.R.Molaeimanesh1
Received: 10 May 2019 / Revised: 26 July 2019 / Accepted: 11 November 2019
© The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract
Polymer electrolyte fuel cells (PEFCs) being employed in fuel cell electric vehicles (FCEVs) are promising power genera-
tors producing electric power from fuel stream via porous electrodes. Structure of carbon paper gas diffusion layers (GDLs)
applying in the porous electrodes can greatly affect the PEFC performance, especially at the cathode side where electrochemi-
cal reaction is more sluggish. To discover the role of carbon paper GDL structure on the mass transfer properties, different
cathode electrodes with dissimilar structural parameters are simulated via lattice Boltzmann method (LBM). 3D contours
of oxygen and water vapor concentration through the GDL as well as the 2D contours of current density on the catalyst
layer are illustrated and examined. The results indicate that the carbon fiber diameter has a negligible impact on the current
density while the impact of carbon paper thickness and porosity is significant. In fact, increasing of carbon paper thickness
or porosity leads to lack of cell performance.
Keywords Polymer electrolyte fuel cell (PEFC)· Lattice Boltzmann method (LBM)· Microstructure reconstruction·
Carbon paper· Mass transfer properties
List of symbols
Variables
a
Roughness factor
c
Velocity of particle in the lattice Boltzmann method
(LBM) (lu·ts−1, lu and ts denote the units of length
and time in LBM, respectively)
cs
Speed of sound in the LBM (lu·ts−1)
d
Carbon fiber diameter (μm)
F
Faraday constant (A·s·mol−1)
f
Density distribution function in the LBM
j
Current density (A·cm−2)
p
Directional density function (Eq.(1))
Ru
Universal gas constant (J·mol−1·K−1)
r
Space position
T
Temperature (K)
t
Time (ts); also gas diffusion layer (GDL) thickness
(μm)
u
Fluid velocity vector
w
Weighting factor in LBM
Greek symbols
𝛽
Anisotropy parameter
𝜂
Activation over-voltage
𝜀
GDL porosity
𝜆
Altitude
𝜌
Density of chemical species in LBM (lm·lu−3)
𝜎
GDL electrical conductivity (Ω−1·cm−1)
𝜏
Relaxation time (ts)
𝜑
Longitude
Subscripts and superscripts
eq Equilbrium
i ith direction in LBM
ref Reference
1 Introduction
Fuel cells systems convert chemical energy of a fuel stream
directly into electrical energy [1]. Among different kinds of
fuel cells polymer electrolyte fuel cells (PEFCs) are one of
the most beneficent ones facing a developing market for the
* G. R. Molaeimanesh
molaeimanesh@iust.ac.ir
1 Research Laboratory ofAutomotive Fluids andStructures
Analysis, Automotive Engineering School, Iran University
ofScience andTechnology, Tehran16846-13114, Iran

M.Nazemian, G.R.Molaeimanesh
1 3
traction system of fuel cell electric vehicles (FCEVs) [2–6].
However, the PEFC performance depends on many param-
eters such as the cell design and structure, material proper-
ties, operation conditions, heat and water management, etc.
[7]. The role of most of the above-mentioned parameters is
investigated widely and they are currently well-understood.
However, only a few efforts have been made to investigate
the impact of gas diffusion layer (GDL) structure—which is
a complicated fibrous and porous structure with anisotropic
and heterogeneous properties [8, 9]—on the cathode current
density distribution [10–22]. In such efforts, employing a
pore-scale simulation procedure that is capable of capturing
the GDL pore structure is inevitable.
In fact, the structure of a carbon paper GDL can be well
defined by four parameters: carbon paper thickness, diameter
of carbon fibers, the number of carbon fibers per volume
(which is dictated by the GDL porosity), and the alignment
of carbon fibers. The effect of the latest structural parameter
on the cathode current density distribution has been inves-
tigated by Molaeimanesh and Akbari [16]; however, to the
best of authors’ knowledge, no pore-scale investigation has
been performed to discover the effects of other three struc-
tural parameters on the cathode current density distribution.
Indeed, variation of the four mentioned structural param-
eters causes the change of GDL transfer properties such as
permeability and diffusivity which in turns may affect the
current density distribution. However, using a pore-scale
simulation procedure enables one to examine the current
density distribution changes due to the variation of struc-
tural parameters directly and without any need to evaluate
the changes of such transfer properties (i.e., a mid-step is
skipped) [23]. Therefore, using a pore-scale simulation tech-
nique such as lattice Boltzmann method (LBM) will be a
more accurate and more reliable approach for investigating
the current density distribution changes due to the variation
of structural parameters.
In the current study, the more reliable and more accurate
approach of pore-scale simulation via LBM is employed to
investigate the impact of three structural parameters of car-
bon paper GDL (carbon paper thickness, diameter of carbon
fibers, carbon paper porosity) on the cathode current density
distribution.
2 Reconstruction ofcarbon paper
microstructure
2.1 Reconstructed carbon papers
Carbon paper GDL microstructure reconstruction is usually
implemented via two methods of stochastic reconstruction
and imaging combination [8]. In imaging combination meth-
ods sequential X-ray images of carbon paper are provided
and integrated into a 3D image while in stochastic recon-
struction methods a geometric model is generated stochas-
tically and it is confirmed to the real carbon paper micro-
structure by adapting a few of its characteristic parameters.
Due to the lower cost and easier implementation most of
researchers prefer stochastic reconstruction methods than
imaging combination techniques [8]. Therefore, in order to
reconstruct the carbon paper microstructure the stochastic
method proposed by Schulz etal. [24] is applied in the cur-
rent investigation. In this regard, eight 100μm × 120μm
carbon paper GDLs with dissimilar thicknesses, fiber diam-
eters and porosities are reconstructed. More details of these
8 GDLs are presented in Table1. GDL 1 is the base GDL
and the other GDLs are produced by altering the GDL 1
thickness (GDLs 2–3), fiber diameter (GDLs 4–5), or poros-
ity (GDLs 6–8).
2.2 Stochastic reconstruction method
The stochastic reconstruction method proposed by Schulz
etal. [24] is applied in the current investigation. This method
is based on the reconstruction technique proposed by Schla-
ditz etal. designed for the microstructure reconstruction
of nonwoven fibrous porous microstructures [25]. In this
method, the following assumptions regarding the carbon
paper microstructure are made.
(1) Fibers are thin cylinders with infinite length and with-
out any axis curvature.
(2) No interface exists between the fibers.
(3) The distribution of fibers in the material plane, i.e., x–y
plane, is homogeneous and isotropic.
Based on these three assumptions, a stationary Poisson
line generating procedure with one-directional distribu-
tion factor is adopted in this method. The resulted lines are
defined as the axes of thin cylinders (i.e., fibers) and the
voxels that their closest distances from the line are not more
than the fiber radius are defined as solid voxels.
Table 1 Features of the reconstructed GDLs
GDL No. Thickness (μm) Fiber diameter
(μm)
Porosity
1 100 7 80
2 200 7 80
3 300 7 80
4 100 8 80
5 100 9 80
6 100 7 75
7 100 7 85
8 100 7 90

Impact ofcarbon paper structural parameters ontheperformance ofapolymer electrolyte fuel…
1 3
In stochastic reconstruction method proposed by Schulz
etal. [24], a directional density function which is a func-
tion of altitude
𝜆∈[0, π)
and longitude
𝜑∈[0, 2π)
is
adopted [26]. This directional density function (p)—which
does not depend on φ due to the aforementioned assump-
tion (3)—is defined as:
In the above equation, β is the anisotropy factor which
calibrates the anisotropy intensity of the reconstructed car-
bon paper. E.g., if β = 0 the generated fibers will be aligned
vertically, if β = 1 the generated fibers will have aniso-
tropic alignment, and if
𝛽
→
∞
the generated fibers will
be aligned horizontally. By calculating the ratio between
the number of fibers crossing a through-plane section of
carbon paper and the number of fibers crossing an in-plane
section of carbon paper one can derive the anisotropy fac-
tor for a specific carbon paper. Here, value of β is chosen
10,000 which is the value of Toray090 [24]. Fibers with a
predefined diameter are sequentially generated in the 3D
medium with a predefined thickness until the 3D medium
porosity reaches its prescribed value.
It is worth mentioning that in the stochastic meth-
ods using for the reconstruction of carbon paper GDLs,
the inputs are the porosity and the thickness of carbon
paper, as well as the diameter and alignment of carbon
fibers, where that later is tuned by the anisotropy factor.
Therefore, other parameters such as pore-size distribu-
tion (which can be obtained by the characterization of
the GDL) are not required as the inputs of the stochas-
tic reconstruction method. However, changing the fiber
diameter and the fiber alignment can affect the pore size
distribution through the GDL; this can be the subject of
an individual study.
3 Numerical method
3.1 Lattice Boltzmann method (LBM)
Lattice Boltzmann method is a powerful pore-scale numeri-
cal method for simulation and analysis of porous media with
complicated, anisotropic and heterogeneous microstructures
such as the carbon paper GDLs in PEFCs [27].
Advantages of LBM over the other conventional numeri-
cal methods include superior capability in handling com-
plicated boundaries in a sophisticated microstructure,
easy development of an efficient parallelizable algorithm,
and easy simulation of multi-phase flow through a porous
medium [28].
(1)
p
=
1
4π
𝛽sin 𝜆
[
1+
(
𝛽2−1
)
cos2𝜆
]
2
3
.
Lattice Boltzmann method is based on the solution of
lattice Boltzmann equation regarding a lattice [28] which
is as follows:
In the above equation,
r
is space position, t denotes
time, Δt indicates the time interval,
c
refers to the veloc-
ity vector in ith direction, τ refers to the relaxation time,
fi
is density distribution function in ith direction, and f
eq
i
denotes equilibrium density distribution function in ith
direction. f
eq
i
is calculated by:
(2)
fi(r+cΔt,t+Δt)=fi(r,t)+
Δt
𝜏[
feq
i(r,t)−fi(r,t)
].
Fig. 1 Computational domain and its boundaries (schematic view)
Table 2 Values of parameters related to the simulations
Parameter Value
Temperature of operation (°C) 80
Pressure of operation (atm.) 1.500
Inlet–outlet pressure difference (atm.) 0.001
Inlet molar fraction of nitrogen 0.79
Inlet molar fraction of oxygen 0.21
Inlet molar fraction of water vapor 0.0
Nitrogen’s dynamic viscosity (kg·m−1·s−1)2.01 × 10−5 [34]
Oxygen’s dynamic viscosity (kg·m−1·s−1)2.34 × 10−5 [34]
Water vapor’s dynamic viscosity (kg·m−1·s−1)1.20 × 10−5 [34]
Oxygen diffusivity within the mixture (m2·s−1)
1.891 ×10
−
5
[33]
Reference concentration of oxygen (mol·m−3) 10.875 [33]
Surface roughness factor of CL 2000 [35]
Reference current density (A·m−2)
1.3874 ×10
−
2
[36]
Forward oxygen transfer coefficient 0.5 [37]
Reverse oxygen transfer coefficient 1 [37]

M.Nazemian, G.R.Molaeimanesh
1 3
where
wi
denotes weighting factor of ith direction,
cs
indi-
cates the sound speed,
𝜌
=
∑
i
f
i
is density of fluid, and
u
=
∑
i
fic∕
∑
i
f
i
is velocity of fluid. In order to solve Eq.(2)
(3)
feq
i=wi𝜌
[
1+
ci⋅u
c2
s
+1
2
(
ci⋅u
)2
c4
s
−1
2
u⋅u
c2
s
],
collision and streaming procedures ought to be conducted.
However, to finalize solving Eq.(2) in a computational
domain, those
fi
s positioned on the boundaries of computa-
tional domain and directed to the interior of the domain
should be known. Here, if the boundary condition is no-slip
wall, LBM offers a powerful and simple treatment of no-slip
wall which is known as bounce-back boundary condition.
Fig. 2 3D contours of oxygen mole fraction in three carbon paper GDLs with dissimilar thicknesses: a t = 100 μm, b t = 200 μm, and
c t = 300μm. The legend and the coordinate system of all subfigures are the same as the first one

Impact ofcarbon paper structural parameters ontheperformance ofapolymer electrolyte fuel…
1 3
This boundary condition is conceptually based on the idea
that when a particle hits a wall, it will bounce off the wall in
the opposite direction. This kind of wall treatment empowers
LBM for simulating flow through geometries with intricate
morphologies and microstructures such as the pore geometry
of a carbon paper [28]. In order to find
fi
at the boundaries
where pressure or velocity is given, the famous method pro-
posed by Zou and He [29] can be conducted.
Single-phase and multi-component (i.e., multi-species)
fluid flows can be simulated either actively or passively.
When they are simulated actively the velocity fields are
calculated individually for all species. On the contrary,
when they are simulated passively, the velocity field is
calculated only for the solvent, the chemical species with
the greatest molar fraction. Furthermore, the concentra-
tion distributions of other species are calculated by solving
the concentration equation for them. Although when fluid
Fig. 3 3D contours of water vapor mole fraction in three carbon paper GDLs with dissimilar thicknesses: a t = 100 μm, b t = 200 μm and
c t = 300μm. The legend and the coordinate system of all subfigures are the same as the first one

M.Nazemian, G.R.Molaeimanesh
1 3
flows are simulated passively less computational cost is
required, high accuracy may not be achieved, especially
when concentrations of species are comparable [28]; in
such cases actively simulating of flow is inevitable. To
actively simulate a single-phase and multi-component flow
by LBM, a multi-phase and multi-component model must
be selected and some of its constraints must be omitted to
lower the quantity of phases to one.
Modeling of the electrochemical reaction over the
catalyst layer (CL) via LBM seems as a major challenge
in the modeling of the cathode electrode [30]. Neverthe-
less, in a few studies [11–20, 31] the electrochemical
reaction is also modeled via LBM. In the present study,
a well-validated 3D single-phase LB model previously
presented by our group [16] is employed to investigate
the impact of structural parameters of carbon paper GDL
on the cathode performance. In the mentioned model, CL
is treated as a surface that the oxygen reduction takes
place on it. The progress rate for the electrochemical
half-reaction is governed by famous Butler–Volmer
equation:
In the above equation a denotes the roughness factor of
CL surface,
𝜌0,ref
indicates the reference density of oxygen,
𝜌ref
is reference value of current density,
𝜌0
is the oxygen
density on the CL surface,
𝜂
refers to activation over-voltage,
𝛼f
and
𝛼r
denote transfer coefficients of forward and reverse
reactions, respectively.
The mentioned LB model is based on a collision operator
with single relaxation time (known as BGK operator [32])
and a lattice with D3Q19 scheme [28]. In D3Q19, 3 refers to
dimensions of lattice while 19 refers to number of directions
possible for particle movement in the lattice. The mentioned
LB model benefits from actively modeling of species distribu-
tion. More details about this model is presented in Ref. [16].
(4)
r
�� =
{
a
4f
(
j
ref
𝜌0,ref
)[
exp
(
𝛼fF𝜂
R
u
T
)
−exp
(
−𝛼rF𝜂
R
u
T
)]}
𝜌0
.
Fig. 4 2D contours of current density (A·cm−2) on the CL surface for three carbon paper GDLs with dissimilar thicknesses: a t = 100 μm,
b t = 200μm and c t = 300μm

Impact ofcarbon paper structural parameters ontheperformance ofapolymer electrolyte fuel…
1 3
3.2 Modeling changes ofelectrical resistivity
Changing the structural parameters of carbon paper GDL
such as thickness, fiber radius and porosity will lead to the
changes of GDL electrical conductivity as well as the gas
permeability and diffusivity. However, since pore-scale sim-
ulation of a large computational domain is computationally
expensive, only 100μm × 120μm carbon paper samples are
simulated. For such a samples, most of carbon fibers are in
contact with the horizontal land at out of the computational
domain and therefore, it is impossible to directly incorporate
the role of structural parameters on the electrical resistivity.
Thus, in order to incorporate the role of structural param-
eters on the electrical resistivity we adopted the following
correlations:
(1) Incorporating the effect of GDL thickness changes:
When only the thicknesses of two carbon paper GDLs
are dissimilar, the ratio between the electrical resist-
ances of the two GDLs will be inversely proportional
to the ratio between their thicknesses [33]. Therefore,
when the GDL thickness is increased from t to t′, the
electrical resistance will be increased from R to R′ and
consequently, by assuming constant over-voltage the
current density will be decreased from j to j′ as:
(2) Incorporating the effect of fiber diameter changes:
When the fiber diameter of a GDL is increased from 7
to 8μm or 9μm (which is a slight relative increment),
the electrical resistances of the GDL will experience
negligible changes [33]. Hence, when the fiber diam-
eter is changed from 7 to 8μm or 9μm (which are the
typical values of fiber diameter in practical GDLs), the
current density is considered unchanged.
(5)
j
�
j
=R
R
�
=t
t
�
.
Fig. 5 3D contours of oxygen mole fraction in three carbon paper GDLs with dissimilar carbon fiber diameter: a d = 7µm, b d = 8 µm, and
c d = 9µm. The legend and the coordinate system of all subfigures are the same as the first one

M.Nazemian, G.R.Molaeimanesh
1 3
(3) Incorporating the effect of GDL porosity changes:
When the porosity of a carbon paper GDL is increased
from ε to ε′, GDL conductivity is decreased from σ to
σ′ as [33]:
(6)
𝜎
�
𝜎
=
(
1−𝜀�
)0.5
(1−𝜀)
0.5
.
Consequently, by assuming constant over-voltage the cur-
rent density will be decreased from j to
j′
as:
3.3 Computational domain andits boundary
conditions
In this study, the computational domain comprises carbon
paper GDL, CL and land as depicted in Fig.1. CL is consid-
ered as an infinitely thin layer on which the oxygen reduction
takes place. The gas inlet and outlet of the computational
(7)
j�
j=𝜎�
𝜎
=
(
1−𝜀�
)0.5
(1−𝜀)
0.5
.
Table 3 Average current density on the CL surface for three carbon
paper GDLs with dissimilar thicknesses
Carbon paper thickness (μm) 100 200 300
Average current density (A·cm−2) 1.3307 0.6654 0.4436
Fig. 6 3D contours of water vapor mole fraction in three carbon paper GDLs with dissimilar carbon fiber diameter: a d = 7µm, b d = 8µm, and
c d = 9µm. The legend and the coordinate system of all subfigures are the same as the first one

Impact ofcarbon paper structural parameters ontheperformance ofapolymer electrolyte fuel…
1 3
domain are the two vertical lateral sides opposing each other
at x = 0μm and x = 100μm, respectively. The other two ver-
tical lateral sides at y = 0μm and y = 100μm are treated as
symmetry faces.
The inlet air has 1.500atm. (1atm. = 0.101MPa) total
pressure, 0.21mol fraction of oxygen, and 0.79mol frac-
tion of nitrogen. The oxygen of the inlet air reduces over
the CL surface and water vapor is generated. In order to
sustain the air flow 0.001atm. pressure decrease is con-
sidered from the inlet to the outlet. In this regard, the inlet
total pressure is set 1.501atm. while the outlet total pres-
sure is set 1.500atm. In order to execute these two bound-
ary conditions at the inlet and the outlet, the Zou and He
method [29] is applied. One must note that at the outlet,
only the air total pressure is given and the partial pres-
sures of oxygen, nitrogen and water vapor are not given.
Hence, to determine the partial pressures of these spe-
cies at an outlet node it is assumed that for each of these
species the mole fraction at that node is equal the mole
fraction at the preceding node. The no-slip bounce-back
boundary condition [29] is applied for treating the surfaces
of all non-reactive solid walls. All species are considered
as ideal gases having dissimilar kinematic viscosities. A
parallel code is written by FORTRAN language based on
the presented method in Sects.3.1 and 3.2 and it is utilized
for conducting simulations. Values of parameters used in
the simulations are presented in Table2.
4 Results anddiscussion
As mentioned previously, in the applied stochastic recon-
struction technique for producing pore geometry of GDL,
the carbon paper structure can be completely defined by
carbon paper thickness, diameter of carbon fibers, the
number of carbon fibers per volume (i.e., GDL porosity)
and the alignment of carbon fibers. Since the impact of
the latest parameter on the distributions of current den-
sity and species has been previously investigated [16], the
impact of the three former parameters is investigated in
the present study and the results will be presented in the
following three subsections.
Fig. 7 2D contours of current density (A·cm−2) on the CL surface for three carbon paper GDLs with dissimilar carbon fiber diameters:
a d = 7µm, b d = 8µm, and c d = 9µm

M.Nazemian, G.R.Molaeimanesh
1 3
4.1 Impact ofcarbon paper thickness
The reactive air flow through three different carbon paper
GDLs with dissimilar thicknesses is simulated by pore-
scale LBM. The thicknesses of GDLs are 100μm, 200μm
and 300μm (GDL 1, GDL 2 and GDL 3 in Table1,
respectively) while the fiber diameter and the porosity of
all three GDLs is similar. In Fig.2 the 3D contours of
oxygen mole fraction in the three mentioned GDLs are
shown. The black spots in this figure denote the sections
of carbon fibers placed in the computational domain. The
concentration boundary layer created on the CL surface
due to the passing of air flow through the GDL in the
positive direction of x-axis can be observed in this figure.
Besides, the oxygen mole fraction decreasing due to its
diffusion down toward the CL surface is evident in this
figure. Comparison of Fig.2a–c show that the thickness of
concentration boundary layer is not considerably affected
by the carbon paper thickness. Therefore, the mass transfer
capability of carbon paper is only slightly affected by the
carbon paper thickness. However, the electrical conduc-
tivity of the carbon paper is significantly affected by the
carbon paper thickness (as declared in Eq.(5)) which may
result in dissimilar current density distribution.
Figure3 illustrates the 3D contours of water vapor mole
fraction in the three GDLs with dissimilar thicknesses.
Due to the electrochemical water vapor production over
the CL surface the mole fraction of water vapor increases
in both normal direction away from the CL surface
(through-plane direction) and the direction of bulk flow
(in-plane direction); this fact indicates the created con-
centration boundary layer on the CL surface. Inspecting
Fig. 8 3D contours of oxygen mole fraction in three carbon paper GDLs with dissimilar porosity: a
𝜙
= 75%, b
𝜙
= 80%, c
𝜙
= 85%, and d
𝜙
= 90%. The legend and the coordinate system of all subfigures are the same as the first one

Impact ofcarbon paper structural parameters ontheperformance ofapolymer electrolyte fuel…
1 3
Fig.3 reveals that the thickness of water vapor concentra-
tion boundary layer is not significantly influenced by the
carbon paper thickness.
Shown in Fig.4 are the distributions of current den-
sity over the CL for three simulated cases with dissimi-
lar thicknesses of carbon paper GDLs. Since the oxygen
is consuming along the bulk flow (positive x axis), the
current density on the CL surface has a decreasing manner
along the bulk flow in this figure. Comparison of Fig.4a–c
establishes that increasing the carbon paper thickness
two or three times leads to a great decreasing of current
density.
Presented in Table3 are the average values of current
density over the CL surface of the three simulated cases
having dissimilar thicknesses. This table demonstrates that
increasing the GDL thickness leads to a great decreasing
of the average current density over the CL surface. This
fact is mainly due to the GDL electrical resistivity increas-
ing resulted from carbon paper thickness increasing and
the changes of mass transfer capability has a negligible
role.
Table 4 Average current density on the CL surface for three carbon
paper GDLs with dissimilar carbon fiber diameters
Fiber diameter (μm) 7 8 9
Average current density (A·cm−2) 1.3307 1.3298 1.3305
Fig. 9 3D contours of water vapor mole fraction in four carbon paper GDLs with dissimilar porosity: a
𝜙
= 75%, b
𝜙
= 80%, c
𝜙
= 85%, and d
𝜙
= 90%. The legend and the coordinate system of all subfigures are the same as the first one

M.Nazemian, G.R.Molaeimanesh
1 3
4.2 Impact ofber diameter
The reactive air flow through three different carbon paper
GDLs with three dissimilar carbon fiber diameters is simu-
lated by LBM. The fiber diameters have the three common
values of 7μm, 8μm and 9μm (GDL 1, GDL 4 and GDL
5 in Table1, respectively) while the carbon paper thick-
ness and porosity is the same in all three GDLs. Figure5
illustrates the 3D contours of oxygen mole fraction in the
reconstructed GDLs. Similar to the previous section, oxy-
gen mole fraction concentration near the CL is decreas-
ing during its diffusing downward the CL. A comparison
among Fig.5a–c reveals that the carbon fiber diameter has
a slight effect on the oxygen mole fraction distribution.
In fact, since the carbon papers have a similar porosity
increasing of fiber diameter leads to fewer numbers of car-
bon fibers in the domain. Therefore, fewer black spots can be
seen in Fig.5c relative to Fig.5a; however, the black spots
in Fig.5c are larger relative to Fig.5a. This means that in
Fig.5a the obstacles in the way of bulk flow are smaller
but more numerous relative to Fig.5c. These two opposing
effects compensate each other in a way that not significant
differences can be observed between the mole fraction dis-
tributions in these three GDLs.
Shown in Fig.6 are the distributions of water vapor mole
fractions through the mentioned GDLs with dissimilar fiber
diameters. The created water vapor concentration boundary
layer due to the water production by the oxygen reduction
reaction on the CL surface can be seen in this figure. An
examination of Fig.6a–c demonstrates that increasing of
carbon fiber diameter causes a slight changes in water vapor
distribution through GDL.
Shows in Fig.7 are the current density distributions
over the CL surface for three simulated cases. Comparison
of Figs.7a–c represents the fact that although the current
Fig. 10 2D contours of current density (A·cm−2) on the CL surface for three carbon paper GDLs with dissimilar porosities: a
𝜙
= 75%, b
𝜙
= 80%, c
𝜙
= 85%, and d
𝜙
= 90%
Table 5 Average current density on the CL surface for four carbon
paper GDLs with dissimilar porosities
Porosity (%) 75 80 85 90
Average current density (A·cm−2) 1.4888 1.3307 1.1556 0.9462

Impact ofcarbon paper structural parameters ontheperformance ofapolymer electrolyte fuel…
1 3
density distribution is affected by fiber diameter, this affect-
ing is not considerable. This fact is more evident in Table4.
4.3 Impact ofcarbon paper porosity
The reactive air flow through four different carbon paper
GDLs with four dissimilar porosities is simulated by LBM.
The four porosities are 75%, 80%, 85% and 90% (GDL 6,
GDL 1, GDL 7 and GDL 8 in Table1, respectively) while
the carbon paper thickness and carbon fiber diameter is
the same in all these four GDLs. The contours of oxygen
mole fraction in the four mentioned carbon paper GDLs
are depicted in Fig.8. Increasing of carbon paper poros-
ity causes fewer fibers in the computational domain; this
is clearly visible by the fewer spots in Fig.8d relative to
Fig.8a. Comparison of Fig.8a–d demonstrates the great
role of porosity on the oxygen distribution. It shows that
by increasing of porosity the oxygen concentration bound-
ary layer becomes thinner which indicates the better mass
transfer capability of cases with higher porosities. This is
also the case for the distribution of water vapor species as
depicted in Fig.9. In fact, higher porosity means less fibrous
obstacle in the way of air flow. However, one must note that
increasing porosity has an undesirable effect on the GDL
electrical conductivity.
Shown in Fig.10 are the 2D contours of current density
over the CL for four carbon papers with dissimilar porosi-
ties. Comparison of Fig.10a–d expresses that by increasing
the porosity the current density distribution on the CL is
decreased. This demonstrates the fact that by increasing of
GDL porosity the decreasing of GDL electrical conductivity
is more effective than the increasing of GDL mass transfer
capability. This is rigorously presented in Table5. Interest-
ingly, a blue malformed area can be observed in Fig.10a
which is due to the carbon paper microstructure near the
CL, in this case.
5 Conclusions
In order to discover the role of carbon paper GDL structure,
eight different cathode electrodes with dissimilar structural
parameters are simulated via pore-scale LBM. The 3D con-
tours of oxygen and water vapor molar fractions through the
GDLs as well as the 2D contours of current density on the
CL surfaces are illustrated and examined. The results indi-
cate that the carbon fiber diameter has a negligible impact on
the current density while the impact of carbon paper thick-
ness and porosity is significant.
In fact, the impact of these structural parameters on the
current density can be analyzed from two aspects: changing
the mass transfer capability of GDL and changing the elec-
trical resistivity of GDL. More specifically:
(1) Increasing of carbon paper thickness from 100 to
300μm leads to an increase of its electric resistiv-
ity while its mass transfer capability does not change
significantly. Hence, the current density decreases by
increasing of carbon paper thickness.
(2) Increasing of carbon fiber diameter from 7 to 9μm
results in slight changes of GDL mass transfer capa-
bility and GDL electrical resistivity. Hence, impact of
fiber diameter is negligible.
(3) Increasing of carbon paper porosity from 75 to 90%
leads to an increase of GDL mass transfer capability
and at the same time, an increase of GDL electrical
resistivity. However, increase of GDL resistivity is
more effective and consequently, increasing of GDL
porosity leads to a decrease of current density.
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