pore network modeling and synchrotron imaging of liquid ... · 3 unstructured pore network modeling...
TRANSCRIPT
Pore Network Modeling and Synchrotron Imaging of Liquid Water in the Gas Diffusion Layer of Polymer Electrolyte
Membrane Fuel Cells
by
James Thomas Hinebaugh
A thesis submitted in conformity with the requirements
for the degree of Doctor of Philosophy
Department of Mechanical and Industrial Engineering
University of Toronto
© Copyright by James Hinebaugh (2015)
ii
Pore Network Modeling and Synchrotron Imaging of Liquid Water in
the Gas Diffusion Layer of Polymer Electrolyte Membrane Fuel Cells
James Thomas Hinebaugh
Doctor of Philosophy
Department of Mechanical and Industrial Engineering
University of Toronto
2015
Abstract
Polymer electrolyte membrane (PEM) fuel cells operate at levels of high humidity, leading to
condensation throughout the cell components. The porous gas diffusion layer (GDL) must not
become over-saturated with liquid water, due to its responsibility in providing diffusion
pathways to and from the embedded catalyst sites. Due to the opaque and microscale nature of
the GDL, a current challenge of the fuel cell industry is to identify the characteristics that make
the GDL more or less robust against flooding. Modeling the system as a pore network is an
attractive investigative strategy; however, for flooding simulations to provide meaningful
material comparisons, accurate GDL topology and condensation distributions must be provided.
The focus of this research is to provide the foundational tools with which to capture both of these
requirements. The method of pore network modeling on topologically representative pore
networks is demonstrated to describe flooding phenomena within GDL materials. A stochastic
modeling algorithm is then developed to create pore spaces with the relevant features of GDL
materials. Then, synchrotron based X-ray visualization experiments are developed and conducted
to provide insight into condensation conditions.
iii
It was found that through-plane porosity distributions have significant effects on the GDL
saturation levels. Some GDL manufacturing processes result in high porosity regions which are
predicted to become heavily saturated with water if they are positioned between the condensation
sites and the exhaust channels. Additionally, it was found that fiber diameter and the volume
fraction of binding material applied to the GDL have significant impacts on the GDL
heterogeneity and pore size distribution. Representative stochastic models must accurately
describe these three material characteristics. In situ, dynamic liquid water behavior was
visualized at the Canadian Light source, Inc. synchrotron using imaging and image processing
techniques developed for this work. Liquid water primarily originated beneath the flow field
landings, sometimes spreading laterally into the less compressed regions of the GDL beneath the
flow field channels. Independent water clusters were tightly packed within the GDL, rarely
occupying more than 1 mm2 of planar area. These tools and observations provide the capability
to predictively design high performance GDL materials.
iv
Acknowledgments
I would like to sincerely thank those who have contributed to this project. Firstly, Dr. Aimy
Bazylak, my supervisor, has provided me with superb resources and guidance to do this work.
She has given me the freedom to work on a great range of projects, the experiences of which
have given me great depth as a research scientist. I would like to thank her for the trust she has
always had in me to do quality work. I would also like to thank the team at the Biomedical
Imaging and Therapy line at the Canadian Light Source. Beam scientist George Belev spent
dozens of hours at our side during our group’s first visit in 2010 to transfer his expertise onto our
team. Thanks also to Adam, Denise, Tomasz, and Dean for taking us into your facility to do great
science. Next, I would like to thank my lab mates for sharing their research with me, and for
allowing me to share my work with them. The collaborative atmosphere in our lab has been
remarkable, and has made the days go by enjoyably. I have never worked with a group of people
so concerned for each other’s sanity. While all of my lab mates have supported me in this
endeavor, I’d like to particularly thank Zachary Fishman, Jon Ellis, Ronnie Yip, Pradyumna
Challa, Jongmin Lee, Steven Bothello, and Nan Ge for the long discussions we’ve had about this
work over the years. There is likely not a paragraph of this thesis that was not somehow
influenced by your bright minds. I am sincerely grateful to the many sources of funding that have
made this research possible. Canada is blessed to have local businesses such as Hatch, the
Automotive Fuel Cell Cooperation, and Hydrogenics that actively encourage alternative energy
research. I am particularly grateful to Dr. Bert Wasmund of Hatch, who has made it a personal
mission to facilitate graduate research of renewables. Of course, I wouldn’t be writing these
words had it not been for my large, loving family that ensured that I was provided with every
tool required to achieve. They have been there for me my entire life, and their unwavering
support has given me the confidence to tackle this PhD. Finally, and most importantly, I would
like to thank my beautiful wife, whose love and sacrifice have kept me afloat these six years.
You are my guardian angel, Zeynep. I will be forever grateful of the wife you have been.
v
Table of Contents
Acknowledgments................................................................................................................... iv Table of Contents ..................................................................................................................... v List of Tables .......................................................................................................................... ix
List of Figures.......................................................................................................................... x List of Appendices .................................................................................................................xix 1 Introduction......................................................................................................................... 1
1.1 Background and Motivation .......................................................................................... 1
1.2 PEM Fuel Cell Background........................................................................................... 2 1.3 Modeling Two Phase Phenomena within the GDL ......................................................... 4 1.4 Stochastic Modeling of the GDL ................................................................................... 5 1.5 In Situ Visualizations of Liquid Water in the GDL ......................................................... 6
1.6 Primary Assumptions .................................................................................................... 9 1.6.1 Invasion algorithms ........................................................................................... 9 1.6.2 Visualized liquid water .................................................................................... 10
1.7 Contributions.............................................................................................................. 10
1.8 Organization of the Thesis .......................................................................................... 12 1.9 Co-Authorship ............................................................................................................ 13
2 Pore Network Modeling of Two-Phase Transport in PEM Fuel Cells ................................... 14 2.1 Abstract...................................................................................................................... 14
2.2 Introduction ................................................................................................................ 14 2.3 Invasion Algorithm ..................................................................................................... 18 2.4 Modeling Assumptions ............................................................................................... 21
2.4.1 Inlet Assumptions............................................................................................ 21
2.4.2 Pore and throat shape ....................................................................................... 22 2.4.3 Wettability ...................................................................................................... 22 2.4.4 Steady state ..................................................................................................... 23 2.4.5 Network size ................................................................................................... 24
2.4.6 Trapping ......................................................................................................... 24 2.5 Representative Highlights ........................................................................................... 24
2.5.1 Inlet assumptions ............................................................................................. 24 2.5.2 Pore-space assumptions ................................................................................... 26
2.5.3 Capillary fingering .......................................................................................... 27 2.5.4 Diffusion ......................................................................................................... 28
2.6 Conclusion ................................................................................................................. 29 3 Unstructured Pore Network Modeling with Heterogeneous PEM Fuel Cell GDL Porosity
Distributions...................................................................................................................... 30 3.1 Abstract...................................................................................................................... 30 3.2 Introduction ................................................................................................................ 30 3.3 Pore Network Model................................................................................................... 33
3.4 Results and Discussion................................................................................................ 36 3.4.1 Network size sensitivity ................................................................................... 36 3.4.2 Measured heterogeneous porosity distributions ................................................. 37
vi
3.4.3 Uniform, sine-, and square-wave porosity distributions ..................................... 41 3.4.4 Theoretical surface treatments.......................................................................... 43
3.5 Conclusions ................................................................................................................ 46
4 Stochastic Modeling of PEM Fuel Cell GDLs II. Physical Characterization ......................... 48 4.1 Abstract...................................................................................................................... 48 4.2 Introduction ................................................................................................................ 48
4.2.1 Fiber count in stochastic models ....................................................................... 50
4.2.2 MPL modeling ................................................................................................ 52 4.3 Methods ..................................................................................................................... 53
4.3.1 Fiber diameter ................................................................................................. 53 4.3.2 Fiber pitch ....................................................................................................... 55
4.3.3 Fiber co-alignment .......................................................................................... 57 4.3.4 Additive materials ........................................................................................... 57 4.3.5 MPL cracks ..................................................................................................... 58
4.4 Results and Discussion................................................................................................ 59
4.4.1 Fiber diameter ................................................................................................. 59 4.4.2 Fiber pitch ....................................................................................................... 60 4.4.3 Fiber co-alignment .......................................................................................... 61 4.4.4 Additive materials ........................................................................................... 61
4.4.5 MPL cracks ..................................................................................................... 62 4.5 Conclusions ................................................................................................................ 63
5 Stochastic Modeling of PEM Fuel Cell GDLs II. A Comprehensive Substrate Model with Pore Size Distribution and Heterogeneity Effects ................................................................ 64
5.1 Abstract...................................................................................................................... 64 5.2 Introduction ................................................................................................................ 64 5.3 Model Development ................................................................................................... 66
5.3.1 Model overview .............................................................................................. 67
5.3.2 Individual fiber placement ............................................................................... 67 5.3.3 Fiber count ...................................................................................................... 68 5.3.4 Generated fiber volume.................................................................................... 69 5.3.5 Through-plane material distribution ................................................................. 72
5.3.6 Fiber co-alignment .......................................................................................... 72 5.3.7 Fiber overlap ................................................................................................... 72 5.3.8 Binder placement............................................................................................. 72
5.4 Pore-space Characterization ........................................................................................ 73
5.4.1 Porosity heterogeneity ..................................................................................... 73 5.4.2 Mercury intrusion porosimetry simulations ....................................................... 74
5.5 Results and Discussion................................................................................................ 76 5.5.1 Stochastic model of Toray TGP-H 090 ............................................................. 76
5.5.2 Porosity heterogeneity ..................................................................................... 79 5.5.3 Mercury intrusion porosimetry simulations ....................................................... 81
5.6 Conclusions ................................................................................................................ 85 6 Visualizing Liquid Water Evolution in a PEM Fuel Cell Using Synchrotron X-ray
Radiography ...................................................................................................................... 87 6.1 Abstract...................................................................................................................... 87 6.2 Introduction ................................................................................................................ 87 6.3 Experimental Setup..................................................................................................... 89
6.3.1 Fuel cell assembly ........................................................................................... 89
vii
6.3.2 Imaging setup .................................................................................................. 90 6.3.3 Fuel cell operating conditions .......................................................................... 91 6.3.4 Liquid water quantification .............................................................................. 91
6.4 Results: Behavior of Visualized Water ........................................................................ 93 6.5 Future Design Considerations...................................................................................... 95
6.5.1 Membrane thickness ........................................................................................ 95 6.6 Uneven Attenuation .................................................................................................... 96
6.6.1 Channel alignment........................................................................................... 97 6.7 Pre-Monochromator Filters ......................................................................................... 98 6.8 Conclusions ................................................................................................................ 98
7 Accounting for Low Frequency Synchrotron X-ray Beam Position Fluctuations for
Dynamic Visualizations ....................................................................................................100 7.1 Abstract.....................................................................................................................100 7.2 Introduction ...............................................................................................................100 7.3 Imaging Setup ...........................................................................................................101
7.4 Experiments ..............................................................................................................102 7.5 Beer-Lambert Image Analysis ....................................................................................104 7.6 Ring Current Decay ...................................................................................................105 7.7 Beam Position Movement ..........................................................................................105
7.8 Image Analysis with Beam Position Pairing................................................................109 7.9 Image Processing Routine ..........................................................................................111 7.10 Conclusions ...............................................................................................................114
8 Quantifying Percolation Events in PEM Fuel Cell Using Synchrotron Radiography ............115
8.1 Abstract.....................................................................................................................115 8.2 Introduction ...............................................................................................................115 8.3 Method......................................................................................................................118
8.3.1 Fuel cell materials and assembly .....................................................................118
8.3.2 GDL materials................................................................................................119 8.3.3 Fuel cell control sequence ...............................................................................120 8.3.4 Beamline controls...........................................................................................121 8.3.5 Data collection ...............................................................................................122
8.3.6 Image normalization .......................................................................................123 8.3.7 Surface and edge breakthrough quantification..................................................124
8.4 Results ......................................................................................................................125 8.4.1 Visualized liquid water ...................................................................................125
8.4.2 Breakthrough density......................................................................................126 8.5 Discussion .................................................................................................................127
8.5.1 Water cluster size limits ..................................................................................127 8.5.2 Temperature effects ........................................................................................129
8.5.3 Anode flow rate ..............................................................................................129 8.6 Conclusions ...............................................................................................................130
9 Conclusions and Recommendations ..................................................................................131 9.1 Conclusions and Contributions ...................................................................................131
9.2 Future Work ..............................................................................................................134 References ............................................................................................................................135 Appendix A ..........................................................................................................................143 Appendix B ..........................................................................................................................144
B.1 Dark Current Correction .............................................................................................144
viii
B.2 Linear Intensity Correction .........................................................................................144 B.3 Beam Position Correction ...........................................................................................145 B.4 Flat Field Normalization .............................................................................................145
ix
List of Tables
Table 3.1 Summary of the GDL material properties obtained by tomography and breakthrough
saturation levels obtained through pore network simulations. ................................................... 41
Table 4.1 Material characteristics measured or calculated in this study. .................................... 61
Table 5.1 Parameters employed to create materials for this study. Underlined parameters are
assumed to best represent Toray TGP-H 090. .......................................................................... 77
Table 5.2 Mean pore diameter values for each studied combination of fiber diameter and binder
fraction .................................................................................................................................. 85
Table 5.3 Pore diameter ranges for each studied combination of fiber diameter and binder
fraction. ................................................................................................................................. 85
Table 8.1 GDLs chosen for water visualization study. Each letter represents a single cell build,
where the subscript denotes the number of data sets collected with that cell, at the specified
temperature. ..........................................................................................................................120
Table 8.2 Breakthrough (BT) density data for each data set. Cells are shaded according to their
relative breakthrough densities. .............................................................................................127
x
List of Figures
Figure 1.1 A 3D model of a GDL. PTFE (grey) coated fibers (black) with an MPL (green) coated
on one side. While this model was created to scale of actual GDL features and represents a
realistic GDL thickness, it only represents a 250 µm × 250 µm sample of a GDL, which typically
are on the order of 100 cm2 in area............................................................................................ 1
Figure 1.2. An illustration of standard configuration of PEM fuel cell. The CCM has a catalyst
layer (black) coated on both anode and cathode sides of the membrane (pink). The cathode flow
field has flow channels that cannot be seen in this orientation. Not to scale. ............................... 3
Figure 1.3 Node and bond (a) pore network representation of pore space (white) with
corresponding sphere and tube geometries (b) for pores and throats, respectively. ...................... 5
Figure 1.4 Exploded view of the PEM fuel cell components with through-plane and in-plane X-
ray beam orientations illustrated. .............................................................................................. 7
Figure 1.5 In-plane X-ray orientation, providing through-plane view of water distribution. Raw
absorption image (a) and imaged properly normalized for liquid water visualization (b). See
Chapter 6 for more details. ....................................................................................................... 8
Figure 1.6 Through-plane X-ray orientation, providing in-plane view of water distribution. A
circular viewing hole was drilled through the metallic components of the fuel cell to provide
“viewing” windows. The positions of 3 cathode channels are marked. For scale, each channel is
1 mm wide. See Chapter 8 for more details. .............................................................................. 8
Figure 2.1 Illustration of node/bond network representative of a pore space. Nodes are
considered to be locations of large void spaces (pores) in a porous material. Bonds illustrate the
connections (throats) present between pores. ........................................................................... 15
Figure 2.2 Illustration of pore network depicting pore space and key features of network ......... 15
Figure 2.3 Structured network (cubic). .................................................................................... 17
Figure 2.4 Unstructured pore network created around 2D material locations............................. 18
xi
Figure 2.5 Illustration of a non-wetting phase invading a pore space of variable diameter from
left to right. Seven interface locations are drawn in grey. ......................................................... 23
Figure 2.6 Predicted saturation levels at positions across the depth of the network, demonstrating
the effect of saturation in a 2D pore network model when a nucleation site is introduced at
various fractional distances (xns) from the inlet, within the domain [37]. ................................... 25
Figure 2.7 Steady state water saturation patterns predicted for networks generated with
prescribed porosity distributions by Hinebaugh et al. [38]. Water (blue) invades the pore space
(white) from the bottom face of this 2D pore network. (These figures are presented and described
in detail in Chapter 3)............................................................................................................. 26
Figure 2.8 Predicted saturation levels (blue) for networks generated with prescribed porosity
distributions (red) demonstrating the effect of porosity distribution on saturation profile in 2D
pore networks by Hinebaugh et al. [38]. (These figures are presented and described in detail in
Chapter 3).............................................................................................................................. 27
Figure 3.1 A through-plane cross section of Toray TGP-H-060 obtained through micro-computed
tomography (SkyScan 1172, 2.44 μm/pixel) illustrating through-plane pore structure. .............. 31
Figure 3.2 A 2D (600 μm x 200 μm) unstructured pore space generated by the random placement
of 7μm wide fibers (solid black disks) until the desired porosity of 0.80 is reached. As seen in the
magnified image (b), circular pores (hollow circles) are centered at the nodes of the overlaid
Voronoi diagram, connected to adjacent pores by throats which are represented by the bonds of
the Voronoi diagram. Each polygon of the Voronoi diagram is created by lines equidistant from
disks. ..................................................................................................................................... 34
Figure 3.3 Porosity and material fraction data, f, for a Toray TGP-H-060 GDL. Blue diamonds
represent the measured porosity distribution obtained from micro-computed tomography
visualizations [54] . The black line represents the calculated material fraction from interpolated
porosity data. The red line represents the resultant average porosity of 100 networks generated
with the calculated material fraction........................................................................................ 36
Figure 3.4 Aspect ratio and network size sensitivity study with invasion percolation simulations
run on stochastic networks created with Toray TGP-H-060 porosity data. a) Mean saturation
xii
levels generated using a constant network thickness of 200 μm. b) Comparison of three network
thicknesses. One standard deviation is displayed with each data point. ..................................... 37
Figure 3.5 Example saturation patterns (distinct realizations) using tomography derived porosity
distributions. The following materials are represented: a) Toray TGP-H-030, b) Toray TGP-H-
060, c) Toray TGP-H-090, d) Toray TGP-H-120, e) SGL Sigracet 10AA, and f) Freudenberg
H2315. .................................................................................................................................. 39
Figure 3.6 The heterogeneous porosity and breakthrough saturation profiles associated with six
commercially available GDL materials. Interpolated porosity values are shown in red. The
average saturation level for each pixel column is shown in blue. The following materials are
represented: a) Toray TGP-H-030, b) Toray TGP-H-060, c) Toray TGP-H-090, d) Toray TGP-H-
120, e) SGL Sigracet 10AA, and f) Freudenberg H2315. ......................................................... 40
Figure 3.7 The porosity and breakthrough saturation curves associated with three theoretical
GDL materials. Theoretical porosity values are shown in red. The average saturation level for
each pixel column (vertical slice) is shown in blue. Network thicknesses are set to 200 μm, and
an aspect ratio of 5 is maintained. ........................................................................................... 43
Figure 3.8 The porosity and breakthrough saturation curves associated with six commercially
available GDL materials with an inlet-side surface treatment. Interpolated porosity values are
shown in red. The average saturation level for each pixel column is shown in blue. Thin red and
blue lines represent the original porosity and saturation profiles respectively. The following
materials are represented: a) Toray TGP-H-030, b) Toray TGP-H-060, c) Toray TGP-H-090, d)
Toray TGP-H-120, e) SGL Sigracet 10AA, and f) Freudenberg H2315. ................................... 45
Figure 4.1 2D stochastic models demonstrating the similar pore-space effects caused by the
modeling assumptions: I fiber diameter, II fiber bundling, III and binder fraction. Pore space is
represented as white. Fibers, either 7 µm or 10 µm, are represented as black. Binder is
represented as grey. Each 100 µm × 100 µm model is created to be 65% porous, with randomly
distributed, non-overlapping fibers.......................................................................................... 51
Figure 4.2 3D stochastic model of the PEM fuel cell GDL. There is no scale for reference as this
model could have been made with any fiber diameter. ............................................................. 52
xiii
Figure 4.3 Edge of hand-torn GDL (a) with region of interest highlighted. Intensity profile (b) of
region of interest in direction perpendicular to fiber. The dotted line displays the value at 50% of
the average background intensity, defining the edge of the fiber............................................... 54
Figure 4.4 Visualized nano-CT dataset of Toray TGP-H 090 0 wt % PTFE. (a) Through-plane
cross sectional slice. (b) Planar cross-sectional slice. (c) 3D view with slice positions highlighted.
The blue reference cube has an edge length of 50 µm. ............................................................. 55
Figure 4.5 Through-plane cross sectional nano-CT slices of Toray TGP-H 090 0 wt % PTFE
with arrows indicating highlighted fiber positions. Slice (a) is separated from (b) by 50 µm in the
direction normal to the slices. ................................................................................................. 56
Figure 4.6 Imaged 35 µm thick sheets of nano-CT dataset of Toray TGP-H 090 0 wt % PTFE
with clearly bundled fibers painted in red, and clearly individual fibers highlighted in light blue.
.............................................................................................................................................. 57
Figure 4.7 Scanning electron micrographs of the MPL surfaces of (a) SGL Sigracet 25BC, and
(b) Freudenberg H2315 I3 C1, with annotated cracks. ............................................................. 59
Figure 4.8 Fiber diameter distributions for (a) Toray TGP-H 090 0 wt % PTFE, (b) SGL Sigracet
25AA, (c) Freudenberg H2315. .............................................................................................. 60
Figure 4.9 Fiber pitch distribution of 30 fibers measured from nano-CT image of Toray TGP-H
090 0 wt % PTFE. .................................................................................................................. 60
Figure 4.10 MPL cracks of GDL types. (a,b) SGL Sigracet 25BC, (c) Freudenberg H2315 I3 C1,
and (d) Freudenberg H2315 with custom PTFE and MPL treatments. ...................................... 62
Figure 5.1 Size comparison between a relatively small GDL sample area (5 cm × 5 cm) and a
relatively large stochastic model (1 mm × 1 mm). ................................................................... 66
Figure 5.2 Stochastic model of Toray TGP-H 090 GDL substrate and enlargement for detailed
view. Fibers (black) have diameter of 8 µm, binder (yellow) has binder fraction of 0.4. Sample
has dimensions 990 µm × 990 µm × 260 µm ........................................................................... 67
xiv
Figure 5.3 Fiber placed into a stochastic modeling domain. x, y, and z offsets, as well as angles φ,
and θ (pitch) were assigned based on an assumed probability distribution of possible values.
Portions of fibers extending beyond the domain were made to reappear at the opposite face of
domain. ................................................................................................................................. 68
Figure 5.4 Comparison of mean fiber volume, Vf,gen, and input diameter, dinput, for cylinder
generation algorithm. The ideal case of V = π l (dinput/2)2 is displayed as a dashed line. The
calculated equivalent diameter, deq, based on cylinders with volume = Vf,gen, is also displayed. . 71
Figure 5.5 Permitted resolution values, R, over the dinput values tested, for five hypothetical fiber
diameters, dexp. ....................................................................................................................... 71
Figure 5.6 Demonstration of a porosity heterogeneity analysis of a 2D example (a) with white
material on black void. The blue and red dashed regions each represent a randomly placed 502
pixel2 sample. After a sufficient number of similar random samples were examined, a
representative histogram of measured porosities (b) was obtained. Note: in the 3D models
characterized in this study, the random samples were 503 µm3 cubes........................................ 74
Figure 5.7 MIO demonstration on pore space shown in Figure 5.6a. The pore space coloring (a)
corresponds to the diameter of the largest circular structuring element (SE) that was accessible
from the top or bottom of the domain. The pore size distribution and saturation curves (b) were
calculated from the volume of each color shown in (a). Note: in the 3D models characterized
later in this study, the probing structuring element was spherical. ............................................ 75
Figure 5.8 Comparison between cross sectional slices of a µCT data set of Toray TGP-H 090 (a)
and a stochastically generated material generated with representative input parameters and a
binder fraction of 0.4 (b). Material (white) represents both fibers and binder material. .............. 77
Figure 5.9 Comparison between the µCT derived through-plane porosity distribution used as a
weighting function to stochastic fiber placement, and the porosity distribution of a single,
stochastically generated material............................................................................................. 78
Figure 5.10 Comparison between SEM micrographs (a) of top-down (xy plane) and edge (xz
plane) views of Toray TGP-H 090 material and similar views of stochastically generated, digital
materials (b). The scale bar in (a) applies to all images. ........................................................... 79
xv
Figure 5.11 Porosity heterogeneity comparison showing the relationship between binder fraction
and heterogeneity for fiber diameters: (a) 7 µm, (b) 8 µm, (c) 9 µm, (d) 10 µm, (e) 11 µm. Each
colored field is bound by two standard deviations above and below the mean value from 10
samples. The reference line in each figure corresponds to the mean value of materials generated
with 8 µm-diameter fibers and a binder fraction of 0.4. ............................................................ 80
Figure 5.12 MIO saturation curve comparison showing the relationship between binder fraction
and saturation curves for fiber diameters: (a) 7 µm, (b) 8 µm, (c) 9 µm, (d) 10 µm, (e) 11 µm.
Each colored region is bound by two standard deviations above and below the mean value
obtained from 10 samples. The reference line in each figure corresponds to the mean value of
materials generated with 8 µm-diameter fibers and a binder fraction of 0.4. ............................. 82
Figure 5.13 MIO pore size distribution comparison showing the relationship between binder
fraction and pore size distribution for fiber diameters: (a) 7 µm, (b) 8 µm, (c) 9 µm, (d) 10 µm,
(e) 11 µm. Each colored region is bound by two standard deviations above and below the mean
value obtained from 10 samples. The reference line in each figure corresponds to the mean value
of materials generated with 8 µm-diameter fibers and a binder fraction of 0.4. ......................... 83
Figure 5.14 An example distribution of mercury from a simulation of mercury intrusion
porosimetry with a spherical SE of diameter of 30 µm in a 1 mm × 1 mm × 263 µm modeled
material with a fiber diameter of 9 µm and a binder fraction of 0.2. Fibers were intentionally
hidden in this representation for clarity. .................................................................................. 84
Figure 6.1 Schematic illustrating the components of the PEM fuel cell assembly. After assembly,
GDL and gasket reside in the same plane. ............................................................................... 90
Figure 6.2 Synchrotron X-ray radiographs showing the cross-sectional view of an operating PEM
fuel cell: (a) raw (b) processed images. The white dashed selection represents the selection
shown in Figures 6.4 and 6.5. The grayscale calibration bar is in units of cm of liquid water.
Scale bars represent 1 mm. ..................................................................................................... 92
Figure 6.3 Current density and potential response of fuel cell when current density is increased
from 0.30 A/cm2 at a rate of 2 mA/cm2/s. Regions (a - d) represent the 17 seconds of combined
exposure for each of the four frames displayed in Figure 6.4. ................................................... 93
xvi
Figure 6.4 Liquid water evolution over 4 minutes. Liquid water forms near the catalyst layer
under the cathodic flow field landings (b,c) and appears to spread laterally through the bulk of
the GDL to the region under the channel (d). Black lines outline the location of the flow field
landings. Negative values represent artifacts caused by material relocation during membrane
hydration. The grayscale calibration bar is in units of cm of liquid water. Scale bars represent 0.5
mm. ....................................................................................................................................... 94
Figure 6.5 Radiograph taken at OCV normalized to the dry-state image used in this study (0.30
A/cm2) (inverted for consistency with Figures 6.4 and 6.5). Bright regions represent a net gain of
material between OCV and 0.30 A/cm2, while dark regions represent a net loss. Black lines
outline the location of the flow field landings. The scale bar represents 0.5 mm. ...................... 96
Figure 6.6 Single cross sectional slice of 3D computed tomograph taken of PTFE-coated
fiberglass gasket material. Brightness values represent X-ray attenuation. The fiberglass bundles
in the composite significantly attenuate the signal when compared to the PTFE influence. The
scale bar represents 0.25 mm. ................................................................................................. 97
Figure 7.1 Exploded view of fuel cell components and relative beam direction for in situ
experiment (a). Example radiograph of in situ experiment (b). ................................................102
Figure 7.2 Exploded view of injection apparatus components and relative beam direction for ex
situ experiment (a). Example radiograph of ex situ experiment (b). .........................................103
Figure 7.3 Radiographs normalized to the first dry-state image in the sequence demonstrating the
presence of high levels of artifacts appearing at some points in time (a), and little to no artifacts
are present at others (b). ........................................................................................................107
Figure 7.4 Raw radiograph (a) with two regions (highlighted) selected on either side of the
vertical hotspot position where the mean intensity value is to be calculated. Mean intensity
values for regions 1 and 2 over time (b). ................................................................................107
Figure 7.5 Raw radiograph (a) with two regions (highlighted) selected on either side of the
horizontal hotspot position where the mean intensity value is to be calculated. Mean intensity
values for regions 1 and 2 over time (b). ................................................................................108
xvii
Figure 7.6 Raw radiograph (a) with solid graphite block region (highlighted) used to find the
vertical beam intensity profile. Vertical beam intensity profile (black) with eighth-order
polynomial fit overlaid in red (b). Calculated vertical position of the beam hotspot over 3 min
(c). Vertical hotspot position versus time (d) for an extended period (gray), with the linear trend
overlaid in black. ..................................................................................................................109
Figure 7.7 Three regions of a normalized radiograph (a) displaying significant false water
artifacts. Region 1 is entirely within the solid graphite block. Region 2 samples a heterogeneous
region of the radiograph, including rib, channel and GDL. Region 3 samples a region of the
radiograph well below the vertical position of the hotspot. The mean water thickness values for
each of the three regions (solid lines), with a linear fit (dashed lines) at a single point in time (b).
Normalized values of the three regions’ gradients over 3 min compared with the calculated
vertical hotspot position for the same image sequence (c). ......................................................111
Figure 7.8 A comparison between radiographs normalized to the dry-state radiograph at t=0 and
the same radiographs normalized to the dry-state radiographs with matching false water
thickness gradient values. The pairs of radiographs at the top and bottom provide two examples
of this comparison. ................................................................................................................113
Figure 8.1 Images of modified 25 cm2 Fuel Cell Technologies PEM fuel cell. Note: Although
three viewing holes are present, only the lowermost hole was employed in this study. .............118
Figure 8.2 Calculated pressures under flow-field landings with respect to bolt torque for Toray
TGP-H 090 10 wt% PTFE. ....................................................................................................119
Figure 8.3 Voltage response to current and flow rate set-points for an example cell build (SGL
Sigracet 25BC, 60 ºC). Δ’s denote points used for time-synchronization with the image
collection process..................................................................................................................122
Figure 8.4 Illustration of possible configurations of imaging setup. Sequences of images were
taken in Configurations I, III, and IV for the processing steps highlighted in Section 2.6. ........123
Figure 8.5 An illustration of a fuel cell cross section (a) with droplets of water forming on the
surface of the GDL and at the edge of the gas channels, and a corresponding illustration of
xviii
visualized water (b) with “edge” and “surface” breakthrough locations annotated. Note that the
anode flow field channels are offset from the cathode. ............................................................125
Figure 8.6 Six frames from the final stage (λA=2.8, λC=1.4) of an example experiment (GDL:
Toray TGP-H 090 with 10 wt % PTFE1 and proprietary MPL. Cell temperature: 75 ºC).
Greyscale values correspond to thickness levels of liquid water, scaled between -0.2 mm and 0.6
mm. The positions of three cathode channels are highlighted on the left. For scale, each channel
width is 1 mm. ......................................................................................................................126
xix
List of Appendices
Appendix A ......................................................................................................................... 143
Appendix B ......................................................................................................................... 144
1
1 Introduction
1.1 Background and Motivation
The polymer electrolyte membrane (PEM) fuel cell is an energy conversion device that
facilitates the use of hydrogen gas as an energy carrier, an important step towards a future with
renewable energy. The key challenges currently impeding widespread PEM fuel cell
commercialization are their high costs and limited hydrogen availability [1,2]. Since fuel cell
material costs scale with active area, Srinivasan et al. [3] explained that a key to driving down
costs is to enable greater power densities from PEM fuel cells, so that smaller fuel cell
configurations can handle greater power ranges. However, as power densities increase, heat
transfer and gas diffusion rates become limiting factors to performance, and both of these factors
are heavily influenced by the porous transport layer often referred to as the gas diffusion layer
(GDL) [4,5].
Figure 1.1 A 3D model of a GDL. PTFE (grey) coated fibers (black) with an MPL (green) coated on one side. While this model was created to scale of actual GDL features and represents a realistic GDL thickness, it only
represents a 250 µm × 250 µm sample of a GDL, which typically are on the order of 100 cm2 in area.
The GDL is a highly porous, paper-like material, sandwiched between the catalyst layer and the
flow field and is typically built upon a carbon fiber substrate. A scale model of a section of GDL
is shown in Figure 1.1. Often, these fibers are immobilized with the use of a carbonized binder
2
material [6]. To mitigate the wet environment often found within the PEMFC, this substrate is
coated with a wet-proofing agent (usually polytetrafluoroethylene (PTFE)) to create hydrophobic
surfaces. Additionally, a fine-grained, hydrophobic, microporous layer (MPL) is often applied to
one face of the substrate for durability and water management purposes [6]. The primary
function of the GDL is to maintain abundant, distributed, low resistance transport pathways for
electrons, heat, water molecules, and reactant gases.
The GDL is a thin hydrophobic porous material with a mix of homogeneous and heterogeneous
pore spaces. The pore sizes in the heterogeneous regions are on a similar order of magnitude
with the GDL thickness. Due to the dominating capillary forces of the domain, liquid water can
be expected to become trapped in the largest of these pores, creating major discontinuous
obstacles to oxygen transport. Because different GDL types have been observed to have
drastically different effects on water transport and fuel cell performance [7], the question that
needs to be answered from a design point of view is, "How do the many decisions of GDL
manufacturing affect the tendency for these water clusters to cause dramatic changes in GDL
diffusivity?" To answer this question, we need a model of the GDL capable of capturing the
subtle differences in pore morphology caused by different GDL "recipes", and we need reliable
information with which to calibrate this model. I propose that pore network models extracted
from stochastically generated digital GDL materials are uniquely suited to handle the first
criteria, while synchrotron based in situ liquid water visualization provides a viable means of
validation for such a model.
1.2 PEM Fuel Cell Background
Hydrogen fuel cells electrochemically react hydrogen gas and oxygen. The hydrogen fuel cell
configuration most widely applied in consumer applications is the polymer electrolyte membrane
(PEM) fuel cell. This fuel cell utilizes an ionically conductive polymer to create a thin membrane
separating hydrogen and oxygen, across which hydrogen ions can travel. Two attractive
characteristics of this configuration are the low operating temperatures (< 100 °C) and zero-local
greenhouse gas emissions. With proper hydrogen and electrical safety measures, PEM fuel cell
systems can be extremely safe for both industrial and consumer applications.
3
Electrochemical reactions take place on each side of the PEM fuel cell membrane. The hydrogen
molecule is ionized on the anode side:
𝐻2 → 2 𝐻+ + 2 𝑒−, 1.1
and its product species are recombined with an oxygen atom to produce a water molecule on the
cathode side:
2 𝐻+ + 2 𝑒− +1
2 𝑂2 → 𝐻2𝑂. 1.2
The hydrogen ions reach the cathode half-cell reaction by traveling through the ionomer
membrane; however, the electrons are routed around an external circuit, providing useful
electricity. A precious metal catalyst coating on each side of the membrane allows these half-cell
reactions to occur at low temperatures.
Figure 1.2. An illustration of standard configuration of PEM fuel cell. The CCM has a catalyst layer (black) coated on both anode and cathode sides of the membrane (pink). The cathode flow field has flow channels
that cannot be seen in this orientation. Not to scale.
4
Individual cathode catalyst sites are only active if there are pathways connecting them to the
sources of each of the three reactant species: hydrogen ions, electrons, and oxygen gas. Because
the applied catalyst layer is a poor conductor of electrons, an electrically conductive, yet highly
porous material called the GDL is positioned adjacent to the catalyst coated membrane (CCM) to
supply catalyst sites with electrons while allowing oxygen to diffuse freely. Similarly, a GDL is
also placed adjacent to the anodic face of the CCM. This assembly is compressed between a pair
of conductive end-plates containing flow channels for reactant distribution. What results is the
standard configuration of a PEM fuel cell shown in Figure 1.
One of the challenges of the PEM fuel cell is that the ionomer is only ionically conductive when
humidified. In addition to electrical energy, water and heat are produced by the combined half-
cell reactions, producing complicated, three dimensional temperature and humidity gradients
throughout the cell that give rise to regions of condensation. This condensed water poses a
problem when it accumulates in the pore space of the catalyst layer and GDL, blocking gaseous
reactant pathways. This problem is often most severe in the cathode, primarily because O2 is less
mobile than H2, but also because the anode-cathode water balance almost always yields more
water in the cathode [6].
Water flooding in both the catalyst layer and in the GDL can negatively affect the fuel cell
performance. This thesis focuses specifically on the GDL.
1.3 Modeling Two Phase Phenomena within the GDL
Liquid water in the GDL has been observed to form discrete patches of saturation throughout the
GDL [8]. Because of the large pore length scales involved, it is not feasible to explicitly capture
this discontinuous behavior and their effects on oxygen diffusion with a continuum model of the
GDL. Pore network models have been proposed to offer a solution to this problem, providing
rich simulation environments in which basic assumptions can be explored, such as the
distribution and footprint of condensation sites [9]. An illustration of a pore network
representation of a porous material is provided in Figure 1.3.
A detailed analysis of the applicability of pore network modeling for GDL research is provided
in Chapter 2. To summarize: the insights gained from pore network modeling studies with
5
respect to the key factors that influence liquid water distributions within the GDL have been
profound. We have seen that geometrical inlet assumptions (the footprint and distribution of
condensation induced water clusters) can have dramatic effects on overall saturation [9,10].
Also, the pore topology factors (coordination number and pore size distribution) are
demonstrated to impact predicted saturations [9].
Figure 1.3 Node and bond (a) pore network representation of pore space (white) with corresponding sphere and tube geometries (b) for pores and throats, respectively.
Until recently, pore network models of GDL have primarily assigned pore locations to a rigid,
cubic lattice structure [9-18]. While experimentally derived pore size distributions can be applied
onto such a structured network [12], other topological features, such as pore connectivity and
pore size correlations can be harder to experimentally measure. However, with the development
of pore network extraction algorithms, it is now possible to generate topologically representative
pore networks based on a 3D image of the porous material, resulting in an unstructured network,
intrinsically capturing the topology with an accuracy only limited to the resolution of the image.
Luo et al. [19] demonstrated how this approach can be used to generate a two phase phenomena-
based comparison of two imagined materials, from their images alone.
1.4 Stochastic Modeling of the GDL
Microscale computed tomography (µCT) provides the capability to generate 3D images of the
GDL with sufficient resolution from which to extract accurate pore networks [20,21]; however,
very few facilities in the world are equipped to provide such high resolution tomograms. Instead,
researchers have set out to develop 3D stochastic models of the fibrous GDL (e.g. Figure 1.1),
with pore network modeling being just one of a variety of modeling applications [22-27]. The
6
relative ease of stochastic model generation makes it an attractive option for GDL research.
While most stochastic models of the GDL are generated with an existing material in mind, the
technique can also be used to search for idealized material configurations.
With the abundance of stochastic modeling of GDLs in the PEM fuel cell literature, it is
surprising that many of the fundamental modeling parameters have not been thoroughly
investigated. Fiber diameter, for example, is often only casually listed with little justification as
if it has little bearing on the final product, even though its impact has yet to be demonstrated.
Before truly representative pore spaces can be generated with stochastic models of the GDL,
comprehensive parametric studies must be performed, and relevant material properties must be
experimentally obtained.
1.5 In Situ Visualizations of Liquid Water in the GDL
Due to the strong capillary forces within the GDL, percolating water clusters will follow
predictable pathways [28]. This means that within a representative pore network, reliable water
distributions can be simulated, as long as appropriate inlet conditions can be determined.
Unfortunately, the condensation of liquid water in and around the GDL is a highly complex
phenomenon, which is difficult to predict, and equally difficult to directly observe due to the
opacity and microscale nature of the GDL. However, the resultant water clusters, can be directly
observed with the use of synchrotron radiography, as has been demonstrated by [8,29]. With the
deterministic nature of the water growth, it should be possible to work backwards from a known
water distribution to gain a more fundamental understanding of the condensation phenomena
expected in PEM fuel cells.
Dynamic liquid water behavior can be visualized in situ with synchrotron X-ray radiography due
to the high spatial and temporal resolutions associated with the technique [30]. Depending on
how the fuel cell is oriented with respect to the X-ray beam (Figure 1.4), one of two types of
images can be realized. With in-plane X-rays, the through-plane distributions of liquid water can
be obtained (Figure 1.5). In this orientation, however, the attenuation of water clusters along the
beam direction is combined, and only an average distribution can be obtained. This is still a
powerful tool with which to validate inlet assumptions, as averaged simulation results can
duplicate this effect. With a through-plane beam orientation, individual clusters of water can be
7
differentiated (Figure 1.6), while their through-plane positions must be inferred. A combination
of in-plane and through-plane imagining is proposed to provide a sufficient amount of data from
which to determine realistic inlet assumptions for pore network models.
Figure 1.4 Exploded view of the PEM fuel cell components with through-plane and in-plane X-ray beam orientations illustrated.
8
Figure 1.5 In-plane X-ray orientation, providing through-plane view of water distribution. Raw absorption image (a) and imaged properly normalized for liquid water visualization (b). See Chapter 6 for more details.
Figure 1.6 Through-plane X-ray orientation, providing in-plane view of water distribution. A circular viewing hole was drilled through the metallic components of the fuel cell to provide “viewing” windows. The
positions of 3 cathode channels are marked. For scale, each channel is 1 mm wide. See Chapter 8 for more details.
9
These imaging techniques have been demonstrated by a number of research groups [8,29,31];
however, there are a limited number of synchrotron facilities globally, each with highly
competitive beam time. Canada is fortunate to have the Canadian Light Source, Inc. in
Saskatoon, SK with a beamline capable of such experiments; however, before the work
associated with this thesis, no PEM fuel cell studies had been performed at that specific facility.
1.6 Primary Assumptions
The models of the PEM fuel cell employed in this work relied on a number of assumptions.
When simulating liquid water percolating through the GDL, the assumption that capillary forces
dominated the pore filling sequence allowed for a computationally inexpensive simulation
technique to be used, named invasion percolation (see Chapter 2). Also, during the image
processing steps involved with quantifying liquid water from X-ray radiographs, several
assumptions of imaging stability are made, and small artifacts are caused when the subject or the
illumination source are unstable (see Chapters 6-7).
1.6.1 Invasion algorithms
Capillary forces are assumed to dominate over gravitational, inertial, and viscous forces when
liquid water clusters are growing within the pore space of the GDL. This is a reasonable
assumption in the GDL substrate when the length and time scales of the percolation process are
taken into account. Water clusters can be assumed to occupy a 1 mm2 or less footprint (Chapter
8), while pore and throat diameters can be expected to fall between 18 µm and 48 µm (Chapter
5). Additionally, fuel cells produce water at a rate of 0.0934 mg s-1 for each ampere of current
produced. Should 100% of that water condense before reaching the flow field, a cell running at
an extremely high current density, 5 A cm-2, can be expected to generate only 4.7 nL s-1 per water
cluster. In Chapter 2, a list of non-dimensional numbers characterizing the ratios of the relevant
forces is presented. With the scales presented above, those non-dimensional numbers point to a
strongly capillary force dominated system.
This assumption may not hold if water clusters are connected under large delaminated regions
between the GDL and the catalyst layer. In this case, both the gravitational and the viscous forces
could generate substantial pressure gradients influencing the percolation process. Additionally, if
10
liquid water was assumed to percolate through the nanoscale pores of the MPL, the viscous
forces should be reconsidered.
1.6.2 Visualized liquid water
In Appendix B, a step by step procedure is provided for normalizing an X-ray radiograph of a
PEM fuel cell with a similar radiograph taken during a dry condition. A primary assumption
associated with this is that the solid fuel cell components remain fixed in position, relative to
both the X-ray beam and the imaging apparatus. Should any one of these three entities change in
position, the normalization process will produce inaccurate water thickness calculations. In
Chapter 7, artifacts due to beam position instabilities were demonstrated, and a modification to
the normalization algorithm was presented to account for this. In Chapter 6, major water
thickness artifacts were seen to be generated by fuel cell material movement. This is a problem
that can be partially corrected for with a more rigid fuel cell design. However, the thermal
expansion of the fuel cell apparatus and the sample stage may cause the entire cell to translate
relative to the beam and detector. Even 1 µm of movement can generate substantial artifacts
along the planes where fuel cell materials meet. Therefore, it is recommended that additional
image processing techniques should be developed to account for such movement.
It is assumed that the high capillary pressure water clusters within the GDL do not damage or
reorient the carbon fibers of the GDL. This assumption appears to be valid in that the
radiographs of a dried fuel cell acquired before and after water generation are indistinguishable
from each other.
In addition to position, the X-ray beam is assumed to maintain a steady, or predictable intensity
profile throughout the experiment. There has been no indication in the way of unexplained
imaging artifacts that would indicate that this assumption is unwarranted.
1.7 Contributions
My thesis is focused on the development of the tools with which to model two phase behavior in
PEM fuel cell GDLs. This includes developing a representative stochastic model of the GDL as
well as developing synchrotron based visualization tools with which to validate water inlet
assumptions employed in pore networks. As one of the two original graduate students of my
11
research group, I am pleased to see a large number of our new group members using the tools
that I helped develop.
My contributions are as follows:
Provided review of the state-of-the-art pore network modeling studies of liquid water in
the GDL.
Published as: Hinebaugh J, Bazylak A, Mukherjee PP. Multi-scale modeling of two-phase
transport in polymer electrolyte membrane fuel cells. In: Hartnig C, Roth C, editors. Polymer electrolyte membrane and direct methanol fuel cell technology. Cambridge, UK: Woodhead Publishing; 2012, p. 254.
Demonstrated the non-negligible impact that through-plane porosity distributions have on
liquid water originating from the catalyst layer.
Published as: Hinebaugh J, Fishman Z, Bazylak A. Unstructured pore network modeling with heterogeneous PEMFC GDL porosity distributions. Journal of the Electrochemical Society 2010; 157(11):B1651-7.
Provided in-depth characterization of GDL fiber properties (diameter, pitch, co-
alignment) as well as MPL properties (areal volume, crack size, crack distribution)
specifically relevant to stochastic modeling.
Submitted as: Hinebaugh J, Bazylak A. Stochastic Modeling of PEMFC GDLs I. Physical
Characterization. Journal of Power Sources (Submitted November 2014).
Developed stochastic model of GDL fibrous substrate incorporating measured fiber pitch,
co-alignment, and diameter. Demonstrated the impact of fiber diameter and binder
fraction on pore space.
Submitted as: Hinebaugh J, Bazylak A. Stochastic Modeling of PEMFC GDLs II. A Comprehensive Substrate Model with Pore Size Distribution and Heterogeneity Effects. Journal of Power Sources (Submitted November 2014).
Led the first investigations of PEM fuel cell water dynamics at the Canadian Light
Source, Inc. synchrotron (CLS). Co-developed methods for both in-plane and through-
plane imaging.
Published as: Hinebaugh J, Lee J, Bazylak A. Visualizing Liquid Water Evolution in a PEM Fuel
Cell Using Synchrotron X-ray Radiography. Journal of the Electrochemical Society 2012; 159(12):F826.
and: Lee J, Hinebaugh J, Bazylak A. Synchrotron X-ray radiographic investigations of liquid water transport behavior in a PEMFC with MPL-coated GDLs. Journal of Power Sources 2013; 227(0):123-30.
Identified and developed post-processing correction for vertical beam instabilities at the
CLS.
12
Published as: Hinebaugh J, Challa PR, Bazylak A. Accounting for low frequency synchrotron x-ray beam position fluctuations for dynamic visualizations. J. Synchrotron Rad. 2012; 19:994.
Quantified distribution of visualized individual water clusters in the GDL based on
synchrotron imaging.
Currently being prepared for submission to the Journal of Power Sources.
The link between the experimental and numerical contributions can be summarized as follows.
The primary motivation behind this work is the need to predict the distribution of liquid water in
various GDL morphologies. For that, both realistic domains and realistic boundary conditions
(i.e. condensation assumptions) are needed. Realistic domains can be obtained from a rigorous
study of GDL morphologies. The precise nature of condensing water in the GDL and catalyst
layer, however, is a non-trivial process and extremely difficult to model. That being said, in a
capillary force dominated system, the final water distribution has much less to do with
condensation rates, as it has with the physical distribution and density of active condensation
sites. Therefore, instead of explicitly modeling condensation, condensation information is
gathered from resultant water accumulations, visualized in situ with synchrotron based
radiography. In Chapter 8, the lower bounds of the number of condensation sites is determined.
In Chapter 6, through-plane distributions of liquid water are identified, which can be compared
with simulated results in order to calibrate the assumed distribution of condensation sites.
1.8 Organization of the Thesis
This thesis is organized into nine chapters. The background and motivations are presented in
Chapter 1, along with an overview of the contributions of the thesis. A review of pore network
modeling of two phase phenomena in PEM fuel cell GDLs is provided in Chapter 2. Chapter 3
provides a demonstration of the usefulness of pore network modeling as a tool for predicting the
discrete distributions of liquid water in the GDL, with a specific emphasis on the effects that a
non-uniform through-plane porosity can have on the predicted distributions. Chapter 4 provides a
detailed study of a variety of commercial GDLs such that stochastic modeling parameters of the
materials can be obtained. Chapter 5 describes an algorithm for stochastic model generation of
GDL. A demonstration of synchrotron based, in-plane oriented, in situ imaging of liquid water in
the GDL is provided in Chapter 6, with an overview of best practices for experimental setup.
Vertical beam position movement is addressed in Chapter 7, and a technique for post-processing
13
is developed and demonstrated that corrects for this movement. Chapter 8 employs through-
plane oriented synchrotron-based imaging to quantify the distribution and size of liquid water
clusters within the GDL. Conclusions and a road map for future work are provided in Chapter 9.
1.9 Co-Authorship
Chapter 2 was previously published as the first half of a book chapter. Dr. Partha Mukherjee was
a co-author on the Chapter, but his contribution was limited to the second half, concerning lattice
Boltzmann modeling, which was not included in this thesis.
Chapters 3, 6, and 7 were previously published in journals. Chapters 4 and 5 have been
submitted to the Journal of Power Sources. Chapter 8 is being prepared for submission to the
Journal of Power Sources. Prof. Aimy Bazylak, my supervisor, was a co-author on all journal
articles book chapters and manuscripts prepared for publication.
Zachary Fishman was a co-author to the publication resulting from Chapter 3. Zachary led the
porosity distribution analysis, and aided in the development of the 2D stochastic model of the
GDL.
Prof. Jeffery Gostick from McGill University was a co-author on the submitted manuscript
resulting from Chapter 5. Prof. Gostick provided the morphological image opening algorithm
employed to simulate mercury intrusion porosimetry.
Jongmin Lee was a co-author on publication and manuscript associated with Chapters 6 and 8,
respectively. Jongmin led the design of the fuel cell modifications and helped run the 24-hr/day
experimental schedule required of this facility.
Pradyumna Challa was a co-author on the publication resulting in Chapter 7. While I produced
the research, Pradyumna, a user of the correction algorithm, wrote a first draft of this chapter and
contributed to the final written product.
All image processing in Chapter 8 was performed by an undergraduate summer research
assistant, Craig Mascarenhas.
14
2 Pore Network Modeling of Two-Phase Transport in PEM Fuel Cells
2.1 Abstract
The accumulation and distribution of liquid water in the polymer electrolyte membrane fuel cell
(PEM) fuel cell is highly dependent on the porous gas diffusion layer (GDL). Oftentimes, the
accumulation of liquid water is simply reduced to a relationship between liquid water saturation
and capillary pressure; however, recent experimental studies have provided valuable insight that
the microstructure of the GDL as well as the dynamic behavior of liquid play important roles in
how water will be distributed in a PEM fuel cell. Due to the importance of the GDL
microstructure, there have been recent efforts to provide predictive modeling of two-phase
transport in PEM fuel cells including pore network modeling and lattice Boltzmann modeling.
2.2 Introduction
Pore network modeling is a method of reducing a complex pore space into a node/bond network.
Nodes, called pores, represent large void regions within the material. Bonds, called throats,
represent the constrictions which connect the pores. Transport calculations can then be
generalized for pore-to-pore interactions, governed by pore and throat characteristics. Figure 2.1
is an illustration of a pore space, with the pores (dark points) connected by throats (straight
lines). A planar pore space can be represented with a two-dimensional (2D) pore network, as
shown in Figure 2.2. In Figure 2.2, the pores, throats, pore radii, and throat radii are illustrated.
Intrinsically, a pore network contains the pore space’s connectivity data, where the term
“coordination number” represents the number of throat connections at each pore. In addition to
this topological information, the size and shape of each element can be incorporated. A pore
network model can be tuned to have the necessary level of detail required to achieve one’s
specific modeling goals. Additional information might be added to each element by specifying
values such as shape factor, temperature, and wettability.
15
Figure 2.1 Illustration of node/bond network representative of a pore space. Nodes are considered to be
locations of large void spaces (pores) in a porous material. Bonds illustrate the connections (throats) present between pores.
Figure 2.2 Illustration of pore network depicting pore space and key features of network
Recently, pore network modeling has been applied to simulate the accumulation of liquid water
saturation within the porous electrodes of PEM fuel cells. The impetus for this effort is the
understanding that liquid water must reside in what would otherwise be reactant diffusion
pathways. It therefore becomes important to be able to describe the effect that saturation levels
have on reactant diffusion. Equally important is the understanding of how the properties of
porous materials affect local saturation levels. This requirement is in contrast to most continuum
modeling of the PEM fuel cell, where porous materials are treated with volume averaged
16
properties. For example, the relationship between bulk liquid saturation and capillary pressures
found through packed sand and other soil studies are often employed in continuum models [32].
Experimental and numerical studies of diffusion properties of dry GDL materials are available,
as described in [33]. However, due to the presence of liquid water in the PEM fuel cell
electrodes, these relationships must be modified to accurately describe PEM fuel cell
performance. Measuring diffusion rates under saturated conditions is difficult; however, pore
network modeling can be used to provide this information conveniently through numerical
simulations. Similar modeling techniques that may also provide this information include Lattice
Boltzmann modeling and pore morphology modeling.
Pore network modeling has the advantage of requiring a minimized number of modeling
elements while maintaining an equivalent topology; therefore, it is generally regarded as a
computationally inexpensive technique. Often, pore network definitions representing GDL
materials are stochastically generated, and the model can provide valuable statistical transport
data [9-11,14,16-18,34-38]. Additionally, modeled phenomena in individual pore networks
(deterministic simulations) have also been studied to provide detailed insight into the
consequences of a particular set of assumptions [12,13,19,39].
The geometric and transport assumptions of pore network models built to study GDL invasion
often vary. A primary distinction is in how the pore space is defined. For visual purposes, it is
useful to illustrate two-phase flow behavior using a planar, 2D network [34,35,37-40]; however,
a three-dimensional (3D) network is required to achieve a realistic network topology.
Additionally, many pore network models created to study GDL invasion, such as [9-18,34-
37,40], can be classified as structured networks, where pores are positioned along a rigid lattice
(Figure 2.3). In such a model, pore and throat sizes can be randomly generated from distributions
of pore and throat sizes. The majority of structured networks are based on a cubic lattice [9-
18,36], where the coordination number can be adjusted by either adding to or deleting bonds
from the original lattice. For better or for worse, each of these models except for [9,18] have
maintained a coordination number of 6. Along with the coordination number, a structured
network allows the direct assignment of pore and throat size distributions, spatial correlation, and
anisotropy. Demonstrated in Gostick et al. [12], this flexibility can be employed to calibrate a
model to experimental mercury intrusion porosimetry data.
17
Figure 2.3 Structured network (cubic).
Unstructured networks, where nodal positions are not predetermined, can either be made by
randomly placing nodes and applying a Voronoi/Delaunay tessellation to determine connectivity
as in [41], or by analyzing an available pore space. The former method has been proposed
specifically for fibrous materials [41]; however only the latter method has been applied to study
two-phase flow in GDLs [19,38,39]. To characterize a GDL pore space, micro- or nano-scale
computed tomography (CT) images of GDL materials can be acquired and reconstructed into 3D
binary images. While this technique could be applied to generate pore networks, many
researchers alternately use stochastic modeling to characterize the GDL pore space [19,38,39].
The use of stochastic models avoids any resolution or sample size limitations associated with CT
images. Chapuis et al. [39] and Hinebaugh et al. [38] applied 2D stochastic models of randomly
placed material disks to create pore spaces (Figure 2.4), while Luo et al. [19] developed
algorithms for the random placement of cylinders to create a 3D pore space. Pore networks that
are found through an available pore space have the advantage of having pore and throat size
distributions and coordination numbers that are intrinsically appropriate to the physical pore
space of the actual GDL. This reduces the number of tunable parameters in a model, with the
expectation of improved predictability.
18
Figure 2.4 Unstructured pore network created around 2D material locations.
Once a pore space is known, a pore network can be created through a variety of methods.
Methods that reduce the pore space into a topologically equivalent skeleton involve either a
thinning algorithm [42] or, in the case of the 2D models [38,39], a Voronoi diagram around the
material locations. An alternative method to determine the representative pore network for a pore
space is the maximal ball method [21], which is a computationally inexpensive technique that
has been demonstrated for GDL-like structures in [19].
2.3 Invasion Algorithm
Pore network models have been frequently employed to simulate the invasion of a dry GDL by a
liquid water phase [9-19,34-40]. A convenient attribute of the modeling subject is that capillary
and viscous forces are expected to dominate forces from gravity and inertia due to the
corresponding Bond and Reynolds numbers of this system. The Bond number is defined as
𝐵𝑜 =𝑔∆𝜌𝐿2
𝜎 , 2.1
where 𝑔 is the acceleration of gravity, 𝜌 is the density difference between the fluids, 𝐿 is the
characteristic length, and 𝜎 is the interfacial surface tension. The Reynolds number is defined as
𝑅𝑒 = 𝜌𝑉𝐿
𝜇, 2.2
where V is the mean velocity of the fluid, and µ is the dynamic viscosity of the fluid.
19
Having both Bond and Reynolds numbers much less than 1 suggests that capillary and viscous
forces dominate gravity and inertial forces, respectively. With pore sizes less than 100 μm, Bond
numbers of droplets within the GDL can be assumed to be below 5×10-3 and Reynolds numbers
can be assumed to be less than 1×10-3. Similarly, many researchers [9,10,12,14,16,17,19,36,39]
state that the system’s associated capillary number suggests that viscous forces are also
negligible during an invasion process of GDL, where the capillary number can be defined as:
𝐶𝑎 =𝜇𝑉
𝜎, 2.3
where μ is the viscosity of liquid water, v is the mean velocity of liquid water, and σ is the
surface tension of the fluid/fluid interface. The mean velocity considered in the equation for
capillary number is often an average velocity across the inlet face of the modeled domain
[15,39]. While the average velocity in this situation is very small, this representation does not
capture the velocities experienced in individual throats, especially at the invading front, where
the associated flow is divided between a handful of throats. Therefore, a macroscopically
determined capillary number may not be well suited to solely determine the ratio of forces
present in microscopic throats and pores.
With the above said about the use of capillary number, the assumption that viscous forces can be
neglected allows for a highly simplified simulation of GDL invasion. For each throat of a pore
network, an associated entry pressure can be calculated, where entry pressure is typically
proportional to cos(θcontact)/rthroat, where θcontact is the contact angle that the interface makes
against the material, and rthroat is the radius of the throat. Then, a brief algorithm, as outlined
below, can be conducted to simulate the growth of a water cluster:
1. Assign a list of pores that are initially filled with liquid water.
2. Identify interfacial throats (between fully unsaturated pores and fully saturated pores).
3. Identify the interfacial throat, thmin, with lowest entry pressure.
4. Invade thmin and any air-filled pore adjacent to thmin with liquid water.
5. Repeat steps 2-4 until percolation or predefined stopping point.
The above algorithm is commonly referred to as “invasion percolation” as defined by Wilkinson
and Willemsen [43] and has been employed by Bazylak and coworkers [34,35,38], Prat and
coworkers [14,36,39], and Zhu and coworkers [9,17,18] to simulate the quasi-static growth of
20
liquid water clusters in PEFMC GDLs. In invasion percolation, the rate of accumulation of liquid
water in the system is assumed constant or limited, and the liquid pressure can freely fluctuate,
but will maintain the lowest value possible. The physical mechanism at work is that, if the entire
liquid water cluster can be assumed to be at a uniform pressure, as liquid water accumulates in
the system, its fluid pressure will increase until the smallest entry pressure is reached, and the
associated throat will no longer contain a “stable” (static) interface.
When the assumption of negligible viscous forces is not made, researchers have modified the
invasion percolation algorithm to incorporate a flow-induced pressure drop within the invading
cluster in a variety of ways [10,11,15,37] typically following a “dynamic invasion” algorithm,
such as the following:
1. Assign a list of pores that are initially filled with liquid water.
2. Identify interfacial throats.
3. Identify any interfacial throats at which the pressure difference across the interface
exceeds the entry pressure of the throat, label as thunstable.
4. Invade thunstable, and begin filling any air-filled pore adjacent to thunstable with liquid water.
5. Calculate the flow induced pressure distribution within the water cluster.
6. Advance the simulation clock by Δt.
7. Repeat steps 2-6 until percolation or predefined stopping point.
As was described by Lenormand and Touboul [44], this algorithm requires a convergence step
due to the fact that the list of unstable throats can only be determined after a pressure distribution
is calculated, while the pressure distribution is determined based on a flow pattern, including
flow through any unstable throats. A convergent pressure distribution is typically found by
iterating steps 2-5. Due to the non-linear nature of this problem, some researchers have employed
a relaxation process to solve the pressure distribution [10,44]. Hinebaugh and Bazylak [37]
achieved relatively fast convergence when a combination of invasion percolation and dynamic
invasion was used, where, during each time step, the throat with the lowest entry pressure was
assumed to be unstable regardless of the network pressure distribution; however, other throats
could also be simultaneously invaded according to the pressure distribution. An alternative
approach involves simulation time steps that are small compared to the filling time of a pore,
while assuming that the saturation level of pores containing liquid water is a function of pressure.
21
This strategy has been employed for GDL invasion in [11,40] and allows the calculation of flow
patterns even when pressures do not predict throat instability.
2.4 Modeling Assumptions
Once the structure and invasion algorithm are defined, current pore network models of GDL
invasion differ due to the following assumptions.
2.4.1 Inlet Assumptions
A pore network model of GDL invasion must include assumptions of the mechanisms which
produce liquid water within the GDL. Two mechanisms have been employed thus far in
literature: liquid water enters at the GDL/catalyst layer interface due to pressure buildup of
condensed liquid water in the catalyst layer [9-19,34-40], or liquid water enters within the bulk
of the GDL due to a condensation mechanism [13,37]. These mechanisms can be explained
respectively by the high humidity levels near the catalyst layer driving the diffusive flux of
water-vapor to the gas channel and by the relatively low temperatures near the ribs of the flow
field. A third mechanism has yet to be applied: liquid water entering the GDL at the GDL/gas
channel interface due to upstream accumulation.
When the inlet assumptions state that water is entering the GDL at its interface with the catalyst
layer, further clarification must be made between what has been called the uniform flux
assumption or the uniform pressure assumption [10]. The uniform flux assumption includes an
individual source of liquid water for every inlet throat along the GDL/catalyst layer interface,
where the uniform pressure assumption includes only a single source of liquid water that is
connected to each inlet throat along the GDL/catalyst layer interface. Physically, the uniform
pressure assumption assumes that there is a water cluster outside the GDL with negligible
hydraulic resistance from one side to another. Due to the microstructure of the catalyst layer, this
scenario would approximate reality only if a pocket of liquid water could form between the
catalyst layer and the GDL. Conversely, the uniform flux assumption assumes no hydraulic
connectivity outside of the GDL between inlet locations. A compromise between these two
assumptions was made by Hinebaugh and Bazylak [37] in a 2D structured pore network model
of GDL invasion, where the first row of pores and throats within the GDL is initialized as fully
22
saturated. Similar to the uniform flux assumption, a liquid water source was added to each such
pore, but similar to the uniform pressure assumption, these sources were hydraulically connected
by their adjoining throats.
Further specification of catalyst layer inlet assumptions can be made through the fraction of
GDL/catalyst layer interfacial throats that are assumed to be in contact with an inlet. While most
pore network models of GDL invasion assume that 100% of such throats are potential inlets,
several models have been created to study the effects of this assumption [10,14,36].
2.4.2 Pore and throat shape
Typically, pore network models of GDLs assume cubic or spherical pores and square or
cylindrical throats. Conveniently, these pore geometries require standard calculations of volume,
and these throat geometries are assumed to facilitate Poiseuille-like flow. Furthermore, the
hydraulic conductance is a simple function of throat size, length, and fluid viscosity. An
alternative to this method, when creating a pore network from a predefined pore space, is to
incorporate a shape factor for each pore and throat, which is then incorporated into the
conservation and flow equations. Luo et al. [19] demonstrate this method by choosing a shape
factor based on the surface to volume ratio of the physical elements that were converted into pore
network elements.
2.4.3 Wettability
For simplicity, many pore network models of GDL invasion assume that the GDL surfaces are
uniformly hydrophobic, where a single value of contact angle is assumed, often within the range
of 100-120º [10,11,14-16,37,40]. However, manufactured GDLs are typically treated with a
hydrophobic coating; therefore, uniform wettability assumes a uniform application of this
coating. There is little evidence to support this assumption due to the fact that it is extremely
difficult to visualize the coating on individual fibers as well as the liquid water/air contact angle
at the fiber-scale. Sinha and Wang [16] model a non-uniform GDL by allowing a fraction of
pores and throats to be hydrophilic (θcontact < 90) with a specified spatial distribution.
23
Figure 2.5 Illustration of a non-wetting phase invading a pore space of variable diameter from left to right.
Seven interface locations are drawn in grey.
2.4.4 Steady state
Often, a pore network simulation of GDL invasion ends once a steady state condition is reached.
This condition requires assumptions to be made of the mechanism of water transport from the
GDL into the gas channel. Because the associated capillary pressure within the ~1 mm gas
channel is dramatically less than the capillary pressures associated with the ~0.02 mm pores and
throats within the GDL, the “breakthrough” event, where liquid water enters the gas channel, is
given special significance. Often researchers assume that a simulation reaches steady state at
breakthrough, as it is assumed to be impossible for the pressure of the cluster to reach the entry
pressures associated with throats within the GDL [13,14,36,40]. Justification for this assumption
is shown in Figure 2.5, where a non-wetting phase invades a pore space, reaching a relatively
low pressure at breakthrough. However, several researchers allow the simulation to continue
after breakthrough, either by assigning a relatively high associated capillary pressure within the
channel [15,16], or by simply not considering flow into the channel until all GDL/channel
interfacial throats are invaded [34].
24
2.4.5 Network size
The assumption of a representative sample size becomes especially consequential when only a
single water cluster is considered and the initial breakthrough is assumed to be at steady state. In
this case, breakthrough density, the number of breakthrough locations per unit area, will become
solely dependent on the sample size and no other parameter.
2.4.6 Trapping
The invasion algorithm can be further modified with trapping assumptions. Trapping is a
phenomenon described as a portion of one phase becoming hydraulically disconnected from its
source [43]. In the case of GDL invasion, where the invading phase, liquid water, might trap the
defending phase, air, there must be absolutely no thin film of air connecting the trapped cluster to
the primary cluster of air in the system. Researchers [16] often cite the geometrical finding of
Concus and Finn [45] that states that thin films of a wetting fluid can only persist in cracks
crevices that have an angle smaller than θcontact - 90.
2.5 Representative Highlights
The following is an account of some influential conclusions reached about GDL invasion after
pore network investigations.
2.5.1 Inlet assumptions
The mechanism with which liquid water enters the pore network has been demonstrated to
heavily influence the resulting steady state saturation levels within the material
[9,10,13,14,36,37]. From work conducted by Lee et al. [10], a striking difference can be seen
between the uniform pressure and uniform flux inlet conditions described above. The uniform
flux inlet generated a breakthrough saturation roughly twice as large as that produced with a
uniform pressure boundary condition. Rebai and Prat [14] demonstrated a dramatic result when a
uniform pressure boundary condition was compared with a single throat inlet. The relatively low
saturation levels generated from the single throat inlet condition was shown to be a strong
function of the network dimensions, and in all cases has a very different concavity from the other
boundary conditions.
25
Wu et al. [9] investigated a new inlet condition where liquid water was assumed to agglomerate
in finite sized droplets between the catalyst layer and gas diffusion media. In this study, a bi-
layer gas diffusion media was assumed, where liquid water must first percolate the MPL before
reaching the fibrous substrate. Similar to the distinction between uniform pressure and uniform
flux, when many small droplets are assumed to coat the inlet, a high overall saturation is
observed, and when only a few large droplets are considered, saturation levels are minimized in
both materials.
Figure 2.6 Predicted saturation levels at positions across the depth of the network, demonstrating the effect of saturation in a 2D pore network model when a nucleation site is introduced at various fractional distances
(xns) from the inlet, within the domain [37].
Finally, when researchers assume liquid water enters the network due to bulk GDL condensation,
saturation profiles are even further distinct [13,37]. As seen in Figure 2.6, Hinebaugh and
Bazylak [37] demonstrated that a peak in the saturation profile tends to line up with the through-
plane position of water cluster nucleation.
26
2.5.2 Pore-space assumptions
Several researchers have shown that the assumed geometry of the GDL pore space can have an
impact on modeled transport [12,35,38]. Gostick et al. [12] found that the anisotropic
permeability observed in GDLs could be recreated in a pore network by correlating pore and
throat sizes in directions of higher permeability. Bazylak et al. [35] demonstrated that saturation
can be directed by imposing spatial biasing to the throat sizes of a network. A similar study was
conducted by Hinebaugh et al. [38], where experimentally derived through-plane porosity
gradients are imposed onto an unstructured pore network. As can be seen in Figures 2.7 and 2.8,
Hinebaugh et al. [38] found that liquid water tends to accumulate in pockets of high porosity
when they exist between the inlet and outlet of the GDL.
Figure 2.7 Steady state water saturation patterns predicted for networks generated with prescribed porosity
distributions by Hinebaugh et al. [38]. Water (blue) invades the pore space (white) from the bottom face of this 2D pore network. (These figures are presented and described in detail in Chapter 3)
(a)
(b)
(c)
(d)
(e)
(f)
27
Figure 2.8 Predicted saturation levels (blue) for networks generated with prescribed porosity distributions (red) demonstrating the effect of porosity distribution on saturation profile in 2D pore networks by
Hinebaugh et al. [38]. (These figures are presented and described in detail in Chapter 3)
2.5.3 Capillary fingering
The characteristic breakthrough saturation pattern in capillary dominated systems is capillary
fingering, where the invading phase follows the path of least resistance, with no notion of
directionality. Such invasion has been characterized by Wilkinson and Willemsen [43], where
breakthrough saturation levels are strong functions of network size, connectivity and
dimensionality. In pore network models that include viscous forces, researchers [11,15,37] have
found that capillary fingering has breakthrough saturations that are low to moderate compared to
those observed when the liquid water’s viscous forces dominate. Employing these models, the
(a) (b)
(c) (d)
(e) (f)
28
researchers found that, simulating the possible operating conditions of a PEM fuel cell, viscous
forces had no effect on the breakthrough saturation patterns. However, two unrelated pore
network studies provided evidence that high saturations can occur in intermediately wet, or
mixed wet GDLs without viscous forces playing a role [16,39]. Chapuis et al. [39] demonstrated
that due to an increased likelihood of coalescence of neighboring invading fronts at lower contact
angles, a nearly fully saturated breakthrough condition could be reached even without
consideration of viscous forces. By assuming that there is a minimum capillary pressure required
for the invading cluster to break through the outlet, Sinha and Wang [16] also neglected viscous
forces but were able to obtain high saturated conditions in mixed wet pore networks.
2.5.4 Diffusion
Few pore network models of GDL materials have been applied to calculate the material’s relative
diffusivity after an invasion process. This could be due to the fact that most models apply inlet
conditions such as uniform pressure or uniform flux, where it is assumed that liquid water is
present at each throat at the catalyst layer GDL interface. However, with a uniform pressure
boundary condition, Gostick et al. [12] modeled diffusion at various stages of saturation and
calculated the limiting current density due to reactant transport across the GDL. They were able
to do this for two reasons. First, they did not consider the effect of the inlet reservoir on reactant
transport. Therefore, reactants could diffuse through inlet throats as long as they had not yet been
invaded by water. Secondly, they investigated a scenario where there was thin film of air in
liquid saturated pores and throats through which reactants could diffuse.
In subsequent work, Gostick et al. [13] again modeled diffusion through gas diffusion media, this
time incorporating an MPL and water generated through condensation near the flow field ribs.
With the calculated limiting current densities, the group concluded that gas diffusion media alone
could not account for the mass transport losses experienced in PEM fuel cells.
Wu et al. [18] also modeled effective diffusivities of oxygen in a saturated GDL after an invasion
process. A uniform pressure boundary condition was assumed; however, the group avoided
having the flooded catalyst layer by only sampling the central 50% of the network thickness. The
group calculated the effective diffusivities with respect to a large number of modeling
parameters, finding that diffusion rates after saturation are most affected by the network’s
29
through plane coordination number and through plane throat sizes. They determined that
diffusion through an unsaturated network is also highly influenced by these two modeling
parameters.
2.6 Conclusion
Within less than a decade, pore network modeling has gained momentum as a promising method
of studying the liquid water saturation in the PEM fuel cell GDL as a function of key parameters,
such as capillary pressure, diffusion, and permeability. Several key challenges for this technique
still remain, such as how to accurately represent the GDL pore space in order to produce
predictive results on a stochastic scale, and how to accurately represent the dominating forces
that govern the multiphase transport at the microscale for the fibrous substrate and nanoscale for
the MPL.
30
3 Unstructured Pore Network Modeling with
Heterogeneous PEM Fuel Cell GDL Porosity Distributions
3.1 Abstract
This is the first investigation of liquid water saturation profile dependence on empirically
determined heterogeneous polymer electrolyte membrane cell (PEM) fuel cell gas diffusion layer
(GDL) porosity distributions. An unstructured, two-dimensional pore network model using
invasion percolation is presented. Random fiber placements are based on the heterogeneous
porosity distributions of six commercially available GDL materials recently obtained through X-
ray computed tomography visualizations. The pore space is characterized with a Voronoi
diagram, and simulations are performed with a single inlet liquid water cluster. Saturation
profiles are also computed for GDLs with uniform, sinusoidal, and square-wave porosity
distributions. It is shown that liquid water tends to accumulate in regions of high porosity due to
the associated lower capillary pressures. The results of this work suggest that GDLs tailored to
have smooth porosity distributions will have fewer pockets of high saturation levels within the
bulk of the material. Finally, a study on theoretical surface modifications demonstrates that low
porosity surface treatments at the catalyst layer | GDL interface result in greatly reduced overall
saturation levels of the material.
3.2 Introduction
Water is introduced into the cathode of the PEM fuel cell at the catalyst layer (CL) as both a
product of the electrochemical reaction and via electroosmotic drag through the polymer
electrolyte membrane. Water is also introduced at the flow field (FF) inlet from humidified
oxidant streams. In studies [46,47], saturated relative humidity levels have been predicted at the
GDL|CL boundary, indicating that liquid water streams within the cathode may originate near
the GDL|CL boundary under specific operating conditions.
Pore network models have been employed to describe the liquid water saturation patterns
generated from the invasion of hydrophobic, porous materials [10,11,13-16,34-36,39,48], where
31
heterogeneity is often provided by randomizing pore and throat radii on pore networks structured
upon a square or cubic lattice. Two phase flow for GDL materials has recently been modeled
within three-dimensional pore spaces found from either micro-computed tomography [49] or
stochastic geometry generation [50-52]. The modeling techniques employed were the Lattice-
Boltzmann method [25,53] and pore morphology modeling [25,49]. While pore space
heterogeneity is obtained intrinsically with these methods, the detailed, three dimensional images
are required for all simulations and transport calculations, which can result in high computational
costs. More recently, a topologically equivalent pore network model by Luo et al. [19] has been
developed for three-dimensional stochastic models of GDL materials, which applies the maximal
ball method [21] to reduce the pore space into an unstructured pore network. The work published
by Luo et al. [19] demonstrates the utility of a pore network for efficient invasion simulations in
GDL-like microstructures and for modeling single- and multi-phase flows.
Figure 3.1 A through-plane cross section of Toray TGP-H-060 obtained through micro-computed
tomography (SkyScan 1172, 2.44 μm/pixel) illustrating through-plane pore structure.
Recently, our group has characterized the through-plane dependence of porosity for various
commercial GDL materials [54]. Using micro-computed tomography, Fishman et al. [54]
measured heterogeneous through-plane porosity distributions for seven commercially available
GDL materials. Our measured distribution of Toray TGP-H-060 was similar to the single
porosity distribution published by Büchi et al [20]. A single through-plane slice of commercial
220 μm
32
GDL material (Toray TGP-H-060) obtained through micro-computed tomography is displayed in
Figure 3.1.
The concept of non-uniform GDL porosity has appeared in only a few PEM fuel cell models in
recent years [55-57]. However, these models exhibit non-uniform porosities due to the
obstruction of GDL pores with liquid water, rather than due to the heterogeneity of the GDL
itself. Gurau et al. [55] and Chu et al. [56] model the PEM fuel cell cathode with a porosity
gradient that increases from the catalyst layer to the flow channel, in order to simulate the effects
of water saturation. Roshandel et al. [57] build on this work with the addition of rib compression
effects on the porosity gradient. However, Roashandel et al. [57] assume that there is a uniform
GDL porosity distribution prior to compression and water saturation. Zhan et al. [58] employ a
one dimensional model to further investigate the difference between a GDL with a uniform
porosity and a gradient porosity, recommending a linear porosity gradient of 0.4x +0.4, where x
is the fractional GDL thickness. While the work presented by Zhan et al. [58] provides
interesting insight into new GDL designs, it is necessary to understand the effects of
heterogeneous porosity distributions that are already present in the GDL. Previous studies [55-
58] have all concluded that GDLs with high porosities achieve larger current densities by
facilitating improved reactant transport and product water removal; however, further
investigation is vital for understanding the effect that GDL heterogeneity has on liquid water
transport, which will in turn, affect PEM fuel cell performance.
In this work, an unstructured, two-dimensional pore network model is described and employed to
characterize the liquid water invasion of six GDL materials that exhibit heterogeneous porosity
distributions. Details of the micro-computed tomography visualizations employed to evaluate the
heterogeneity of these GDL materials are presented in [54]. A network size sensitivity analysis is
performed, and a comparison between porosity distributions and breakthrough saturation profiles
will provide insight into the passive water management qualities of several GDL morphologies.
Finally, a theoretical surface treatment is proposed as a strategy to reduce the breakthrough
saturation levels in GDL materials
33
3.3 Pore Network Model
Unstructured two-dimensional pore networks were generated for this work by randomly placing
circular disks, representing carbon fibers, into the network domain until a desired porosity was
achieved, where porosity was defined as the ratio of non-material area to total area. To place the
disk centers according to a specific distribution, each pixel (0.5µm/pixel) of the network domain
was given a probability of being randomly selected. Matching the approximate diameter of the
carbon fibers in typical gas diffusion layers [6], the randomly placed disks were each 7 μm in
diameter. During placement, disk overlap was not permitted by repeatedly shifting an
overlapping disk a random distance in the in-plane direction away from the original location until
overlap is avoided. Similar to the pore network model created by Chapuis et al. [39], pore space
was described with a Voronoi diagram, as shown in Figure 3.2, where circular pores are outlined.
Pores were centered at the nodes of the Voronoi diagram and connected to adjacent pores at the
bonds of the diagram. Pore radii were calculated as the distance from the pore center to any of
the three bordering disks. Throat radii were calculated as the distance between the adjacent disks.
For this and all similar diagrams in this paper, the GDL|CL interface is oriented along the left
hand side, and the GDL|FF interface is oriented along the right hand side of the figure.
The application of Voronoi diagrams in this paper was different than that of Thompson [59],
who established a method of generating three-dimensional pore network models for
stochastically generated fibrous models. In Thompson’s work, fibrous materials were represented
as the bonds of Voronoi diagrams formed around pre-defined pore locations, whereas in this
work, it was the material location that was pre-defined, and the Voronoi diagram described the
pore and throat locations as stated above.
To simulate the slow evolution of liquid water clusters within the PEM fuel cell GDL, an
invasion percolation algorithm was employed. The liquid water inlet boundary condition was
defined by a single water cluster, which was in contact with each throat at the GDL|CL interface.
Invasion percolation, as described by Wilkinson and Willemsen [43], assumes that an advancing
fluid interface follows the path of least resistance, such that the invading phase maintains the
lowest possible pressure at each simulation step. When the invading phase is non-wetting, such
as water in a hydrophobically-treated GDL, and the viscous forces within the fluid clusters can
be assumed to be negligible, the path of least resistance during invasion is determined by the
34
throat size with the lowest barrier capillary pressure [43][60]. Throat capillary pressure, 𝑃𝑐 ,
defined as the pressure difference between the invading and defending fluids, can be
approximated with a form of the Young-Laplace equation:
𝑃𝑐 = −2 𝜎 cos(𝜃)
𝑟, (3.1)
where 𝜎 is the interfacial surface tension, 𝜃 is the contact angle of the interface, and is the radius
of the throat. Surface tension and contact angle were assumed to be uniform throughout the
network. Water was therefore assumed to invade the largest available throat at each simulation
step, and no pressure calculations were required.
Figure 3.2 A 2D (600 μm x 200 μm) unstructured pore space generated by the random placement of 7μm wide fibers (solid black disks) until the desired porosity of 0.80 is reached. As seen in the magnified image (b),
circular pores (hollow circles) are centered at the nodes of the overlaid Voronoi diagram, connected to adjacent pores by throats which are represented by the bonds of the Voronoi diagram. Each polygon of the
Voronoi diagram is created by lines equidistant from disks.
With respect to breakthrough saturation levels, pore network models of GDL invasion
considering viscous forces have thus far demonstrated no noticeable effects of such consideration
at water generation rates associated with PEM fuel cell operation [11,15,37]. Viscous forces
within the fluid clusters are therefore not considered in this study.
200μm
600μ
m
(b)(a)
35
The invasion percolation algorithm employed in this investigation includes the following
assumptions:
1. The system was isothermal.
2. The gas phase could not become completely trapped by the liquid and solid phases.
3. Viscous forces within the liquid water clusters at the GDL|CL interface and within the
GDL were negligible.
4. The GDL was uniformly hydrophobic; therefore the capillary pressures associated with
pore entry were only inversely proportional to throat width.
5. A steady state condition was reached once the cluster invades a throat at the GDL|FF
interface, an event labelled breakthrough. At breakthrough, the water cluster ceased to
grow within the GDL due to the low capillary pressures associated with a water droplet
either in the channel or in contact with a relatively hydrophilic rib.
6. The GDL was initially dry. Liquid water at the gas channel was not considered.
While uneven distributions of PTFE within GDL materials have been reported [6], it is unclear if
the hydrophobicity of the GDL is heterogeneous as a result. A thin film of PTFE on fiber
surfaces combined with large PTFE agglomerates throughout the material could produce this
effect while maintaining a uniform contact angle.
The pore network model was developed in MATLAB. Simulations were run on a single
workstation with 8 GB of RAM and dual 2.33 GHz CPUs. Individual simulations required
between 5 and 30 s to reach breakthrough, depending on the network size. A total of 1500 such
simulations were run for this study.
As was described by Fishman et al. [54], three dimensional X-ray tomographic reconstructions
were used to characterize the porosity distributions of various commercially available GDL
materials. The bulk porosities and thicknesses of these materials are summarized in Table 1. A
porosity distribution was defined as the porosity of each thin, in-plane slice of the material with
respect to its through-plane position. As described in [54], each slice represented a 5000 μm ×
5000 μm × 2.44 μm slice of the material oriented parallel to the plane of the material. It is
important to note that the porosities of various materials are strong functions of the through-
plane position. Also, the six materials chosen for use in this study were untreated and
uncompressed.
36
To apply the experimentally found porosity distributions to the disk distributions of two-
dimensional pore networks, porosity levels were first linearly interpolated between data points to
attain a resolution of 0.5 μm. Then, to provide the proper weight to the probability distribution
for disk placement, the interpolated porosity distribution, 𝜀(𝑥), was converted into a material
fraction distribution, 𝑓(𝑥), as follows:
𝑓(𝑥) = 1 − 𝜀(𝑥), 3.1
where x is the through-plane distance through the material. Using Toray TGP-H-060 as an
example, Figure 3.3 presents the porosity distribution, material fraction distribution, and the
average resultant porosity distribution from 100 generated networks with a thickness of 220 μm
and length of 1100 μm.
Figure 3.3 Porosity and material fraction data, f, for a Toray TGP-H-060 GDL. Blue diamonds represent the
measured porosity distribution obtained from micro-computed tomography visualizations [54] . The black
line represents the calculated material fraction from interpolated porosity data. The red line represents the resultant average porosity of 100 networks generated with the calculated material fraction.
3.4 Results and Discussion
3.4.1 Network size sensitivity
To compare GDL materials of a range of thicknesses, we began by determining the pore network
model’s sensitivity to network aspect ratio. In this study, dimensions were chosen such that the
network length was greater than the network thickness. The aspect ratio was increased from 2 to
11 by varying network length, while a constant network thickness (200 μm) and f(x) for Toray
TGP-H-060 were employed. For each aspect ratio, 100 random network definitions were
generated for invasion percolation simulations. The breakthrough saturation of each simulation
37
was calculated as the ratio of water filled pore space to total pore space. The mean breakthrough
saturation value for each ratio was displayed in Figure 3.4a. Saturation levels were most sensitive
to low aspect ratios (below 5). To determine whether saturation levels were more affected by the
aspect ratio or overall network size, a similar sensitivity study was performed with aspect ratios
of 3, 5, and 7 with network thicknesses 120 μm, 220 μm, and 320 μm. As seen in Figure 3.4b,
the network size had little influence on breakthrough saturation levels as long as a single aspect
ratio was maintained. Therefore, an aspect ratio of 5 was chosen and employed for all subsequent
simulations discussed in this paper.
Figure 3.4 Aspect ratio and network size sensitivity study with invasion percolation simulations run on stochastic networks created with Toray TGP-H-060 porosity data. a) Mean saturation levels generated using a constant network thickness of 200 μm. b) Comparison of three network thicknesses. One standard deviation
is displayed with each data point.
3.4.2 Measured heterogeneous porosity distributions
Invasion percolation simulations were run until the breakthrough condition was reached for 100
random networks for each material. Pore networks associated with different GDL materials were
distinct in that they are generated with specific input thicknesses and porosity distributions, while
other properties such as fiber size and network aspect ratios were held constant for the entire
study. Thickness and bulk porosity data were obtained from X-ray tomography visualizations
[54] (Table 3.1). Example breakthrough saturation patterns are displayed in Figure 3.5. The
resulting average saturation profiles are displayed in Figure 3.6, and the mean saturation levels
are listed in Table 3.1. Saturation profiles were defined as the ratio of liquid filled pore space to
all pore space for each vertical slice (0.5 μm thick) across the network thickness. It should be
(a) (b)
38
noted that the pore space used in saturation calculations did not include the void space contained
uniquely in throats and around the perimeter of the domain.
Furthermore, because GDL samples were uncompressed when the X-ray tomography data was
attained, local porosity values and pore and throat sizes of the resultant pore networks near the
GDL|CL and GDL|FF interfaces were expected to be larger than would otherwise be expected in
the compressed environment of a PEM fuel cell. Due to the increased throat sizes at the GDL|CL
interface, these throats were nearly always invaded by the end of the simulation. As can be seen
from Figure 3.5, this fact led to a prediction of fully saturated conditions at the GDL|CL
interface.
To account for the lack of symmetry of porosity distributions, a second set of 100 random
simulations were run for each distribution, beginning the invasion from the opposite face. As
seen in Table 1, the mean saturation levels of a specific material varied by as much as 0.09,
depending on the orientation. Saturation profiles presented in Figure 3.6 were the results of
orientations with the lowest corresponding saturation level.
The saturation profiles displayed in Figure 3.6 were highly correlated with the applied porosity
distributions. This was most apparent with the simulation results of Toray TGP-H materials 060,
090, and 120, where the porosity distributions contained multiple local minimums. The local
porosity distribution minimums correlated well with the local saturation profile minimums.
Similarly, it can be seen in Figures 3.5 and 3.6 that pairs of dense regions of disks (local
minimums in porosity) could create “water traps” causing spikes in the saturation profile. As
shown in Table 3.1, breakthrough saturation levels varied only from 0.29 to 0.37 for one
orientation of each commercial GDL material; however, the breakthrough saturation levels of the
Toray TGP-H-060 simulations exhibited the widest range of saturation, with a standard deviation
of 0.09.
Toray TGP-H GDL materials are classified as “papers”, and the thicknesses of these papers were
generated by bonding thin layers together [6]. The results displayed in Figures 3.5 and 3.6
indicate that this manufacturing process had a large impact on the breakthrough saturation
profiles, as the layering process used to create thicker Toray papers led to highly heterogeneous
porosity distributions, with well-defined peaks and valleys [54]. The SGL Sigracet 10AA, and
Freudenberg H2315 materials are both classified as “felts” where carbon fibers were hydro-
39
entangled during the manufacturing process [6]. In contrast to Toray paper GDLs, felt porosity
distributions did not result in saturation profiles with the same degree of heterogeneity as seen
for paper.
Figure 3.5 Example saturation patterns (distinct realizations) using tomography derived porosity distributions. The following materials are represented: a) Toray TGP-H-030, b) Toray TGP-H-060, c) Toray
TGP-H-090, d) Toray TGP-H-120, e) SGL Sigracet 10AA, and f) Freudenberg H2315.
(a) (b) (c) (d) (e) (f)
40
Figure 3.6 The heterogeneous porosity and breakthrough saturation profiles associated with six commercially
available GDL materials. Interpolated porosity values are shown in red. The average saturation level for each pixel column is shown in blue. The following materials are represented: a) Toray TGP-H-030, b) Toray TGP-
H-060, c) Toray TGP-H-090, d) Toray TGP-H-120, e) SGL Sigracet 10AA, and f) Freudenberg H2315.
(a) (b)
(c) (d)
(e) (f)
41
Table 3.1 Summary of the GDL material properties obtained by tomography and breakthrough saturation levels obtained through pore network simulations.
GDL Type Thickness a
(μm) Bulk
Porositya
Orientation 1 Breakthrough
Saturation Levelb
Orientation 2 Breakthrough
Saturation Levelb
Surface Treatment on Orientation 1 Saturation Levelb
Toray TGP-H-030 117 0.829 0.37 ± 0.04 0.45 ± 0.06 0.15 ± 0.04
Toray TGP-H-060 220 0.821 0.31 ± 0.08 0.35± 0.09 0.13 ± 0.05
Toray TGP-H-090 298 0.826 0.29 ± 0.05 0.31 ± 0.07 0.11 ± 0.04
Toray TGP-H-120 359 0.787 0.36 ± 0.07 0.38 ± 0.06 0.15 ± 0.06
SGL Sigracet 10AA 344 0.847 0.33 ± 0.04 0.39 ± 0.05 0.08 ± 0.02
Freudenberg H2315 290 0.802 0.34 ± 0.04 0.41 ± 0.05 0.10 ± 0.03
Uniform 200 0.800 0.27 ± 0.08 - -
Sine Wave 200 0.800 0.27 ± 0.11 - -
Square Wave 200 0.800 0.30 ± 0.11 - -
a Calculated from micro-computed tomography visualizations [54]. b The average result and standard deviation of 100 simulations performed on random networks.
Pore network models of PEM fuel cell GDL invasion generally produced saturation profiles
containing one local maximum (at the CL) and one local minimum (at the FF) [11,12,15,34].
When the inlet condition was modified to allow fewer entry throats at the CL, the single local
maximum was seen to shift slightly into the bulk [10,14,36]. Peaks in saturation within the GDL
bulk were predicted by a pore network model that included bulk generation of liquid water due to
condensation [13,37]. Bulk saturation extrema were also witnessed when a wettability gradient is
imposed on a mixed-wettability pore network model [16]. The model presented in our paper
provided an additional explanation to the peaks in saturation within the bulk of the GDL to those
which have been reported in [29,61,62], where water tends to accumulate between areas of low
porosity.
3.4.3 Uniform, sine-, and square-wave porosity distributions
To verify the impact that heterogeneous porosity distributions have on saturation profiles,
invasion simulations with networks generated from theoretical porosity distributions were also
performed. Three distributions were generated to have an average porosity value of 0.80:
uniform porosity, sine-wave porosity, and square-wave porosity. Both the sine- and square-wave
porosity distributions were comprised of 3 periods, which oscillate between porosity values of
0.75 to 0.85, as shown in Figure 3.7 (red). Each porosity distribution was applied to 100
stochastic networks of thickness 200 μm and aspect ratio 5. The resultant average breakthrough
saturation profiles are displayed in Figure 3.7 (blue), and mean saturation levels are summarized
42
in Table 1. As shown in Figure 3.7, and in agreement with Figure 3.6, there was a strong
correlation between the heterogeneous porosity distributions and resultant average saturation
profiles. In fact, the correlation is even more apparent in Figure 3.7 than in Figure 3.6. Peaks in
saturation profiles generated from sine- and square-wave porosity inputs were directly beneath
peaks in the original porosity distributions. Also, the flat top of the square-wave porosity input is
carried over to the resultant saturation profile.
In contrast to the results generated from measured material porosities, where the first 10-20% of
the network adjacent to the CL was fully saturated with liquid water, the breakthrough saturation
profiles for uniform, sine-wave, and square-wave porosity each had sharp, negative initial slopes
of saturation near the CL. This difference can be explained by the relatively high porosities at the
CL|GDL interfaces from measured materials (Figure 3.6), which led to large throats being
flooded at the inlet. This effect was diminished by the average or below average porosity levels
near the inlet in networks generated from the three theoretical porosity distributions discussed
here (uniform, sine-wave, and square-wave). The results of these simulations provide insight into
the influence of near-surface porosities on near-surface and overall material saturation levels.
43
Figure 3.7 The porosity and breakthrough saturation curves associated with three theoretical GDL materials. Theoretical porosity values are shown in red. The average saturation level for each pixel column (vertical
slice) is shown in blue. Network thicknesses are set to 200 μm, and an aspect ratio of 5 is maintained.
3.4.4 Theoretical surface treatments
To further investigate the influence of near-surface porosities on breakthrough saturation,
theoretical surface treatments were explored. Here, simulations were performed on 100
additional random networks for each commercial GDL material studied, where the originally
obtained porosity distributions were adjusted to create a linear transition from a porosity of 0.60
(a)
(b)
(c)
44
at the GDL|CL interface to the first local minima of the original porosity distribution. The choice
of this surface modification was intended to represent the application of a lower porosity material
to the GDL, where the resultant composite would transition from the low porosity material into
purely GDL material. This modification was inspired by current micro-porous layer (MPL)
treatments. Ostadi et al. [63] reported a local MPL porosity of 0.40 in a region without cracks or
large defects using focused ion beam/scanning electron microscopy. To account for the presence
of cracks and defects, a porosity value of 0.60 was chosen for this study. The modified porosity
distributions and resultant breakthrough saturation profiles are shown in Figure 3.8. The mean
saturation levels are summarized in Table 1.
Figure 3.8 provides a direct comparison between the saturation profiles generated from porosity
distributions with and without the surface treatment. This figure indicates the highly beneficial
impact that such a treatment would have to GDL materials in terms of liquid water management.
The saturation levels at the CL|GDL interface were significantly reduced with the addition of the
surface treatment. This was attributed to the presence of much smaller throats near the inlet
region, which are associated with significantly higher capillary pressures than the bulk of the
material. The positive slope at the inlet side of the porosity distribution created a situation where
associated average capillary pressures decreased as the liquid|gas interface advances into the
bulk of the network. Although this treatment has lowered the average saturation levels by 58-
76% (Table 3.1), saturation profiles remained correlated to the porosity distributions used to
generate their pore networks, where visible local maxima in porosity distributions of Toray TGP-
H 060, 090, and 120 were still reflected in the resultant saturation profiles.
45
Figure 3.8 The porosity and breakthrough saturation curves associated with six commercially available GDL
materials with an inlet-side surface treatment. Interpolated porosity values are shown in red. The average saturation level for each pixel column is shown in blue. Thin red and blue lines represent the original porosity
and saturation profiles respectively. The following materials are represented: a) Toray TGP-H-030, b) Toray TGP-H-060, c) Toray TGP-H-090, d) Toray TGP-H-120, e) SGL Sigracet 10AA, and f) Freudenberg H2315.
(a) (b)
(c) (d)
(e) (f)
46
3.5 Conclusions
This was the first investigation of liquid water saturation profile dependence on empirically
determined heterogeneous GDL porosity distributions. A two-dimensional unstructured pore
network model for simulating the liquid water invasion percolation in a PEM fuel cell GDL was
presented. With this model, we demonstrated a powerful method of applying porosity
distributions to the definition of pore networks. By randomly placing circular fibers (disks) in a
defined two-dimensional area, with disk placement probabilities weighted by a given porosity
distribution, X-ray computed tomography data become an input to the definition of each
generated pore network.
Aspect ratio and network size sensitivity studies were performed, and an aspect ratio of 5 was
employed for all investigations. Based on simulation results, it was found that local saturation
levels have a high correlation to the local porosity levels in the through-plane direction. The
peaks and valleys present in the porosity distributions of thick carbon fiber papers created highly
saturated regions in the bulk of the GDL, with peaks in porosity distributions corresponding to
highly saturated regions. It is recommended that GDLs are created to have porosity distributions
with few local minimums.
A comparison between the shape of saturation profiles generated from uniform, sine-wave, and
square-wave porosity distributions revealed that, not only did the amplitude and frequency of
through-plane porosity fluctuations impact saturation levels, but also the shape of the
fluctuations was reflected in the shape of the saturation profile.
Finally, an inlet-side surface treatment was theoretically applied to the experimentally derived
porosity distributions of GDL materials, where a lower porosity was applied to the inlet and was
linearly transitioned to the first local minimum in porosity. Simulation results suggested that this
treatment can reduce saturation due to percolation by 58-76%, and drastically decrease saturation
levels near the catalyst layer.
It should be noted that based on the boundary condition of a single liquid water cluster at the
CL|GDL interface, the assumption that viscous forces were negligible, and the assumption that
liquid water transport would reach steady state once breakthrough is achieved, only one
breakthrough point would ever be expected in an operational fuel cell cathode. However, in-situ
47
experiments have shown this not to be the case [8]; therefore, further investigations are required
to determine the influence of viscous forces and water cluster connectivity within the CL and
GDL on liquid water transport in the PEM fuel cell.
48
4 Stochastic Modeling of PEM Fuel Cell GDLs II. Physical Characterization
4.1 Abstract
Stochastic modeling of GDL structures requires a detailed characterization of the constituent
elements of the material. In this work, a variety of imaging methods, including optical
microscopy, microscale computed tomography, and scanning electron microscopy, were used to
characterize seven commercially available gas diffusion layers (GDLs). The result is a catalogue
of the following geometrical characteristics: fiber diameter, fiber pitch and co-alignment, areal
weight and volume, and microporous layer (MPL) crack size and frequency. This catalogue,
when combined with previous GDL characterizations is expected to provide enough information
to create representative, predictive, stochastic models of the GDL.
4.2 Introduction
GDL materials have been extensively characterized using standard porous material analysis
techniques to determine bulk average properties such as permeability [64-66], effective
diffusivity [67,68], and the relationship between capillary pressure and saturation by a non-
wetting fluid [69-71]; however, there are many decisions that go into GDL manufacturing, some
of which have already been shown to impact these bulk properties [23,24,67,70,72]. These
decisions include GDL thickness, carbon fiber diameter, binder quantity, PTFE quantity, PTFE
distribution, MPL quantity, and MPL composition [6]. With so many variables involved, there is
a need for sophisticated, predictive models of transport within the GDL, able to capture the
effects of each of these decisions. With such a tool, GDL types can be compared theoretically,
and idealized materials can be envisioned.
One modeling method available involves the generation of digital, stochastic representations of
the microscopic GDL geometry, on which transport phenomena can be directly modeled with
various computational fluid dynamic modeling techniques [23,27,28,53,73] or indirectly
modeled with pore network modeling techniques [19]. Such stochastic representations of the
GDL microstructure are labelled “stochastic models”. Stochastic models require, as input
49
parameters, characteristics of the common repeating elements (fibers) and additive materials
(binder, PTFE, and MPL) used in GDL manufacturing. Representative models of currently
available materials must make reasonable approximations of these values. Mathais et al. [6] gave
a thorough description of GDL manufacturing techniques that provides useful insight into how
the GDL constituents are arranged. Additionally, Fishman and coworkers provided a catalog of
characteristic through-plane distributions of material porosity [54,74,75], while other researchers
[6,73,76] studied the through-plane distribution of PTFE. This body of work is extremely
important for building pore-scale models that aim to resolve the microscale features of the GDL;
however, key characteristics that are necessary to accurately resolve the GDL are missing,
namely: characteristic distributions of fiber diameter and orientation, volume fraction estimates
of the constituent elements, and the water transport related characteristics of the microporous
layer (MPL), namely its crack distributions.
Fiber pitch is defined as the angle the fiber makes with the plane of the material. Carbon fibers
have been observed to be in orientations largely coplanar to the GDL [54]. Therefore, many
stochastic models apply zero pitch to individual fibers [24,26,77,78]. Other models, in order to
fine-tune material anisotropy, have applied distributions of small pitch values [22,25]. However,
due to recent advances in computed tomography resolutions, the 3D orientation of fibers can
now be measured directly and used as an input to stochastic models.
While manufactures typically only state the PTFE weight (wt) % of their GDLs, estimates of the
quantities of the other additive materials can be made through a comparison of similar GDLs
with respect to their areal weight, defined as the area-specific mass of the GDL. While this
specification is often available from the GDL manufacturer, conducting the measurement of a
batch-specific value is a relatively simple procedure. These measurements can also provide an
understanding of the batch-to-batch variability of the manufacturing process.
A material property analogous to areal weight is areal volume, defined as the solid volume per
unit area. A known areal volume of a material regulates the proportion of a stochastic modeling
domain that must be solid. Furthermore, a comparison of the areal volumes of similar materials
can indicate the volume fractions of constituent elements of the GDL, which allows stochastic
models to more properly represent these elements.
50
Using lattice Boltzmann modeling, Nabovati and coworkers have demonstrated that both fiber
diameter and the assumed solid fractions of binder and PTFE, have strong positive correlations
with calculated permeability when porosity was held constant [23,24]. Interestingly, they found
that additive material fraction also has a positive correlation with tortuosity [24]. GDL fiber
diameters have been reported to fall within the range of 7 to 10 µm [6,79,80]; however, a
statistical analysis of fiber diameters has not been presented in the literature. As will be described
next, fiber diameter, binder and PTFE fractions, and fiber orientation can all be expected to have
similar effects on the pore space of the GDL and therefore should all be characterized.
4.2.1 Fiber count in stochastic models
Stochastic models, as defined above, are generated by the repeated random placement of solid
objects into an originally empty domain. In the case of GDLs, these repeating objects are most
often cylindrical fibers. Each additional fiber that is placed can cut through the existing pore
space, further dividing it into smaller pores. Dividing the pore space by a number of independent
fibers is useful for understanding the commonality between fiber diameter, fiber co-alignment,
and additive materials (binder and PTFE). After the final material porosity and fiber length are
chosen, the number of independent fibers which divide the pore space is fully defined.
Figure 4.1 contains four simplified representations of GDL materials made from 2D stochastic
modeling. Each material is of equal porosity, where three comparisons can be made. In
comparison I, we see that the smaller 7 µm-diameter fibers divide the pore space into smaller
“pores” than are created from the larger 10 µm-diameter fibers. In comparison II, we see that if
fibers are bundled together, each bundle acts as a single larger fiber and creates fewer, larger
pores than are created if the fibers are independent of each other. In comparison III, 50% of the
fibers are replaced with modeled binder, which can be safely assumed to reside in the tight
spaces between fibers [22,24,77]. This binder leaves the large pore spaces untouched, and again
results in fewer, larger pores than seen in the original material. The common theme is that the
fewer independent fibers there are in the substrate, the fewer pores can be expected, and the more
open the material should be.
51
Figure 4.1 2D stochastic models demonstrating the similar pore-space effects caused by the modeling assumptions: I fiber diameter, II fiber bundling, III and binder fraction. Pore space is represented as white.
Fibers, either 7 µm or 10 µm, are represented as black. Binder is represented as grey. Each 100 µm × 100 µm model is created to be 65% porous, with randomly distributed, non-overlapping fibers.
The effect of independent fibers on the pore size distribution is most clearly demonstrated with
further consideration of comparison I. In Figure 4.2, we see a section of a 3D stochastically
modeled GDL with a porosity of 75%. However, without a scale bar, there is no indication that
the structure displayed in Figure 4.2 is made with smaller or larger fibers. If this material was
made up of 7 µm-diameter fibers, the domain would represent a (100 µm)3 cube. On the other
hand, if the fiber diameters were set to 10 µm, the domain would represent a (142 µm)3 cube,
which is nearly 3 times the volume of a (100 µm)3 cube. While the domain volumes depend on
fiber size, the number of resulting pores would be unaffected. In fact, a material made with larger
fibers would be, by nature, more heterogeneous than a similar porosity material made with
smaller fibers, since a larger volume of the larger fiber material is necessary to obtain a
geometrically similar pore size distribution to the smaller fiber material. It is the authors’
hypothesis that pore size distribution and heterogeneity are affected similarly by fiber bundling
and presence of additives (binder and PTFE).
52
Figure 4.2 3D stochastic model of the PEM fuel cell GDL. There is no scale for reference as this model could
have been made with any fiber diameter.
In this discussion, manufacturing parameters such as fiber length, ply thickness in paper-made
materials, or water-jet separation in hydro-entangled felts are not accounted for. However, a
simplified geometrical representation of the GDL structure is a necessary tool for investigating
the fundamental effects of fiber diameter, fiber orientation, and additive materials.
4.2.2 MPL modeling
The MPL provides two theoretical services to the GDL [6,81]. First, it is hydrophobically
treated, making the micropores particularly difficult to become flooded by local accumulations
of liquid water. Second, when compared to the fibrous substrate, the relatively smooth surface of
the MPL can more evenly distribute the applied assembly forces to the catalyst coated
membrane, reducing local contact resistances while protecting the membrane from punctures.
However, researchers have proposed that the transport characteristics of the MPL differ
significantly from that of the fibrous substrate [82]. Therefore, a stochastic model of the GDL
would be incomplete without including the salient features of the MPL.
The MPL is composed of sub-micron carbon black particles held together by PTFE, yielding
reported porosities between 0.35 and 0.62 [83-85]. While nanoscale stochastic models of the
MPL have been created [84], the difference in length-scales between the MPL and the substrate
make it difficult to explicitly model both materials concurrently, while including a representative
volume of the substrate. However, stochastic modeling could follow the example of Gostick et
al. [13], who employed a pore network representation of the GDL. In that work, the pores of the
53
substrate were explicitly modeled, while bulk-averaged transport properties were applied to
regions designated as the MPL. An analogous stochastic model would explicitly describe
substrate geometrical features, but only describe the larger geometrical features of the MPL.
Each voxel designated as MPL would then represent a porous material with effective transport
properties.
The pore sizes of the MPL are typically described with a bimodal distribution [75] with micron
to sub-micron pores homogeneously distributed throughout the bulk of the material, while cracks
or pockets of gas trapped in the manufacturing process can also be present [75]. The cracks in the
MPL have been postulated as relatively low capillary pressure conduits for excess liquid water to
pass through the MPL from the catalyst layer to the porous substrate [86], and evidence for this
has been shown with in-situ X-ray imaging [87,88]. It is therefore of interest to characterize
MPL treatments with respect to the size and frequency of these cracks for more accurate
stochastic models of the MPL.
In this paper, we address a set of gaps in our understanding of the GDL which each impact
critical input parameters of 3D stochastic models [19,23,24,26,27,53,73]. An assortment of
commercially available GDL materials is studied, and detailed characterizations are provided of
the following properties: fiber diameter, fiber pitch, fiber co-alignment, areal weight, areal
volume, MPL crack frequency, and MPL crack diameter. This information, when combined with
previously reported properties, can sufficiently define the GDL for the purposes of stochastic
modeling.
4.3 Methods
4.3.1 Fiber diameter
A technique employed to perform fiber diameter measurements was developed for this study.
Measurements were obtained from the intensity profiles across isolated silhouettes of individual
fibers. To accomplish this, GDLs were torn to create frayed edges. Digital images of silhouetted
fibers were obtained from a back-lit, compound microscope with a 2 megapixel monochrome
charge coupled device (CCD) camera (PCO 1600). The back lighting was adjusted so that the
background intensity reached 10x the intensity measured at the center of a fiber silhouette in
54
focus. An example field of view is shown in Figure 4.3a, and the mean greyscale profile of a
single fiber is shown in Figure 4.3b. The fiber edge location was defined as the point where the
greyscale profile reached 50% of the background intensity.
The above technique was developed using a 559 µm-diameter graphite cylinder as a reference.
The cylinder was measured at multiple positions with a micrometer and then imaged at a
magnification scaled to match the pixel-to-cylinder diameter size ratio available for carbon fiber
imaging. The technique produced precise diameter measurements, with a confidence interval of
3%. On the length scale of a carbon fiber, this represents a maximum error of 0.3 µm per
measurement.
Figure 4.3 Edge of hand-torn GDL (a) with region of interest highlighted. Intensity profile (b) of region of
interest in direction perpendicular to fiber. The dotted line displays the value at 50% of the average background intensity, defining the edge of the fiber.
55
Figure 4.4 Visualized nano-CT dataset of Toray TGP-H 090 0 wt % PTFE. (a) Through-plane cross sectional
slice. (b) Planar cross-sectional slice. (c) 3D view with slice positions highlighted. The blue reference cube has an edge length of 50 µm.
4.3.2 Fiber pitch
A nanoscale computed tomography (nano-CT) dataset (courtesy of Skyscan 2011, Belgium) of
Toray TGP-H 090 with a voxel-resolution of 390 nm was analyzed to provide a first look at fiber
orientation statistics. Figure 4.4 displays this nano-CT data-set, with through-plane and in-plane
cross-sections and a 3D representation.
56
Figure 4.5 Through-plane cross sectional nano-CT slices of Toray TGP-H 090 0 wt % PTFE with arrows indicating highlighted fiber positions. Slice (a) is separated from (b) by 50 µm in the direction normal to the
slices.
To measure fiber pitch, the nano-CT domain shown in Figure 4 was first segmented into solid
(white) and void (black). Then, 30 easily identifiable fibers were traced for 50-100 µm of their
lengths. Their pitch, θ, was calculated as:
𝜃 = sin−1(|∆𝑧| 𝐿)⁄ , 4.1
where |∆𝑧| is the absolute difference in the fiber center position, with respect to the direction
normal to the plane of the material, and 𝐿 is the traced distance.
In Figure 4.5, this tracing is demonstrated on four fibers. Figure 4.5a shows the segmented, cross
sectional view of the GDL. Four identified fibers are highlighted in four unique colors. Figure
4.5b shows a cross sectional slice at a position of 50 µm from the first slice. Colored arrows
highlight original and final fiber positions. The three dimensional vector was recorded, and the
fiber pitch was calculated.
57
4.3.3 Fiber co-alignment
The nano-CT data set can also provide insight on the frequency of fiber co-alignment. To obtain
an estimate of this bundling phenomenon, the nano-CT data set was visualized through the
observation of 35 µm-thick, planar sheets. Then, as shown in Figure 4.6, the aligned fibers were
highlighted in red, while the individual fibers were highlighted in light blue.
Figure 4.6 Imaged 35 µm thick sheets of nano-CT dataset of Toray TGP-H 090 0 wt % PTFE with clearly
bundled fibers painted in red, and clearly individual fibers highlighted in light blue.
4.3.4 Additive materials
Measuring the mass of a GDL sample with a known planar area produces an areal weight
measurement. For the measurements provided in this paper, material images were compared to a
calibration standard to attain a precise area measurement, and mass was measured with an
analytical balance. The image resolution combined with the precision of the balance yielded
areal weight measurements with a maximum error of 1 g m-2.
To calculate areal volume from areal weight, knowledge of the material makeup of the GDL is
required, including its constituent elements, relative proportions, and densities. This relationship
is as follows:
𝐴𝑉 = 𝐴𝑊 ∑𝑊𝛼
𝜌𝛼𝛼 , 4.2
where 𝐴𝑉 is the areal volume, 𝐴𝑊 is the measured areal weight, and 𝑊𝛼 and 𝜌𝛼 are the
approximated weight fraction and density of component 𝛼, respectively. Graphitized carbon
fibers are expected to have densities ranging from 1.9-2.0 g cm-3 [6]. Binder material can be
expected to consist of amorphous carbon with a density of approximately 1.65 g cm-3 [6].
Unfortunately, the volume fractions of fibers and binder were not supplied by manufacturers, but
58
from qualitative image analysis this fraction appeared to be consistently less than 0.5. For the
purposes of this study, this volume fraction was assumed to be 0.5, yielding an average density
of 1.8 g/cm3 for the solid matrix of the untreated carbon fiber substrates. The carbon black in the
MPL was assumed to have a density of 1.8 g cm-3 [89,90], and the PTFE within the MPL and
coating the substrate, was assumed to have a density of 2.25 g cm-3 [91]. Because manufactures
have not published the detailed composition of the MPL, the weight fraction of the MPL was
found as:
𝑊𝑀𝑃𝐿 =𝐴𝑊,𝐺𝐷𝐿1−𝐴𝑊,𝐺𝐷𝐿2
𝐴𝑊,𝐺𝐷𝐿1+𝐴𝑊,𝐺𝐷𝐿2 , 4.3
where 𝐴𝑊,𝐺𝐷𝐿1 is the areal weight of a GDL with an MPL present, and 𝐴𝑊,𝐺𝐷𝐿2 is the areal
weight of the same GDL type without an MPL. Additionally, the MPL was assumed to be 20 wt.
% PTFE [92], leading to a combined solid density of 1.88 g cm-3.
4.3.5 MPL cracks
For each GDL type containing an MPL, SEM micrographs were acquired with a pixel resolution
of 2 µm and a field of view large enough to contain at least 4 mm2 of MPL surface area. Figure
4.7 displays two example micrographs with crack locations annotated. Crack density is defined
as the number of cracks observed, divided by the visualized area. Crack diameter is defined as
the diameter of the largest circle that could fit within the crack. Crack diameters were measured
with an open source imaging software (distance tool in FIJI1). Visible cracks were counted and
their diameters were measured. Two such micrographs were characterized for each material type,
yielding a total area of 8 mm2 per material type. It should be noted that the pixel resolution
yielded an error of up to 4 µm per diameter measurement. This resolution was chosen to
facilitate a large field of view, as the accuracy of crack density measurements was deemed more
valuable for stochastic models than that of the crack diameters.
1 http://fiji.sc/
59
Figure 4.7 Scanning electron micrographs of the MPL surfaces of (a) SGL Sigracet 25BC, and (b) Freudenberg H2315 I3 C1, with annotated cracks.
4.4 Results and Discussion
4.4.1 Fiber diameter
The diameters of 30 fibers for each of three substrate types were measured. Histograms of the
individual measurements are displayed in Figure 4.8. The distributions of fiber diameter are seen
to be tight around the mean, with standard deviation values of 0.8 µm, 0.6 µm, and 0.9 µm for
the materials Toray TGP-H 090, SGL Sigracet 25AA, and Freudenberg H2315, respectively. The
mean fiber diameter values appear on Table 1.
60
Figure 4.8 Fiber diameter distributions for (a) Toray TGP-H 090 0 wt % PTFE, (b) SGL Sigracet 25AA, (c) Freudenberg H2315.
When creating stochastic models of GDL materials, voxel-sizes are often approximately (2 µm)3
[24-26] and rarely smaller than (1 µm)3 due to the computational challenges of manipulating
larger images. Therefore, it may be impossible to recreate the fine details of such tight
distributions of fiber diameters, as are shown in Figure 8. In these cases, uniform fibers of the
mean diameters reported in Table 1 may be employed.
4.4.2 Fiber pitch
Figure 9 shows the absolute pitch distribution of the 30 untreated Toray TGP-H 090 fibers
measured. The mean absolute pitch was 2.44° and individual values never exceeded 7°.
Figure 4.9 Fiber pitch distribution of 30 fibers measured from nano-CT image of Toray TGP-H 090 0 wt %
PTFE.
61
4.4.3 Fiber co-alignment
Also from the nano-CT dataset of untreated Toray TGP-H 090, a total of 54 fibers were clearly
aligned with others, while 95 fibers were clearly not aligned with others. As described in Section
4.2.1, fiber bundling is expected to have a non-negligible effect on the pore size distribution and
tortuosity of the pore space. Therefore, 36% of fibers should be co-aligned in stochastic models
of paper-made GDLs.
4.4.4 Additive materials
The areal weight was measured for seven materials, yielding values ranging from 35 g m-2 to 156
g m-2 (Table 4.1). Estimates of constituent component weight fractions can be made by
comparing like materials from the same manufacturer, as in the SGL Sigracet 25 series or the
Freudenberg H2315 series. SGL Sigracet 25 AA had no PTFE or MPL, whereas both the
substrates of the SGDL 25 BA and SGL 25 BC materials had a common PTFE coating, and the
SGL 25 BC material had an MPL coating. The SGL 25 BA material had a weight of 37 g m-2,
which was 2 g m-2 greater than the untreated SGL 25 AA material. This indicates that PTFE
represented roughly 5.4 wt % of the SGL 25 BA material. This compared well with the specified
5 wt % PTFE provided by the manufacturer. Similarly, approximately 59% of mass of SGL 25
BC was calculated to be the MPL.
Table 4.1 Material characteristics measured or calculated in this study.
Material
Areal Weighta (g m-2)
Areal Volume
(cm3 m-2)
Mean Fiber Diameter
(µm)
Mean Fiber Pitch
(degrees)
MPL Crack Density (mm-2)
MPL Crack Radius
(µm)
Toray TGP-H 090 131 (157) 72.8 7.7 2.44 - -
SGL Sigracet 25 AA 35 19.4 7.6 - - -
SGL Sigracet 25 BA 37 (40) 20.1 - - - -
SGL Sigracet 25 BC 90 (86) 48.3 - - 8.33 6.26
Freudenberg H2315 96 53.3 10.8 - - -
Freudenberg H2315 I6 119 (115) 63.6 - - - -
Freudenberg H2315 I3C1 156 (145) 83.2 - - 6.26 3.38
a Values in parentheses represent manufacturers specifications.
It is worth noting that many of the areal weight values measured varied from the GDL
specifications, indicating that some degree of variability in GDLs can be expected. The authors
62
recommend a focused study on areal weight variability due to batch-to-batch inconsistencies,
and/or macro-scale material heterogeneity.
The areal volume values reported in Table 4.1 can be directly applied to stochastic modeling.
Similar to the comparisons of areal weights, the areal volumes of similar materials can also be
compared to get an approximation of relative fractions of constituent elements. For example,
SGL Sigracet 25 BC had an areal volume of 48.3 cm3 m-2. A stochastic model of a 1 mm × 1 mm
planar section of this material with (1 µm)3 cubic voxels contained 19.4 cm3 m-2 × 10-6 m2 / 10-12
cm3 = 1.94 × 107 solid voxels representing the fibrous substrate, since the areal volume of the
untreated fibrous substrate (SGL Sigracet 25 AA) was 19.4 cm3 m-2. From the comparison of
SGL 25 BA and SGL 25 AA areal volumes, SGL 25 BC required 7 × 105 voxels (0.7 cm3 m-2) of
PTFE coating. Similarly, through a comparison of the areal volume values of SGL 25 BC and
SGL 25 BA materials, this SGL 25 BC required 2.82 × 107 (28.2 cm3 m-2) voxels of solid MPL.
It should be noted that stochastic models of MPL may not contain sufficient resolution to
properly describe the sub-micron pores, and therefore the MPL voxel count may need to be
adapted to account for the nano-scale porosity of the MPL voxels.
Figure 4.10 MPL cracks of GDL types. (a,b) SGL Sigracet 25BC, (c) Freudenberg H2315 I3 C1, and (d) Freudenberg H2315 with custom PTFE and MPL treatments.
4.4.5 MPL cracks
The MPL crack characteristics were determined for two materials: SGL Sigracet 25 BC and
Freudenberg H2315 I3 C1 (Table 4.1). Cracks were 100% more frequent and, on average, were
33% larger in the SGL material compared to the Freudenberg material. The MPL of the
63
Freudenberg material would therefore present a stronger capillary barrier than that of the SGL
material. Distributions of crack diameters of each material type are presented in Figure 4.10.
While few millimeter-scale stochastic models of MPL are already available in the literature, the
above characterizations of MPL cracks will be highly valuable for the eventual stochastic models
that are built for studies of two-phase phenomena.
4.5 Conclusions
In this chapter, a number of important, but previously uncharacterized GDL properties were
identified and measured. These properties were each shown to be specifically relevant to pore-
scale stochastic models of the GDL. A novel technique was developed to measure fiber
diameters with a backlit, optical microscope. Measurements of fiber diameters were seen to vary
based on GDL manufacturer, yet tight distributions around their individual means were observed.
To the authors’ knowledge, this paper provides the first reported measurements of GDL fiber
pitch, which was seen to be minimal (2.44°) in Toray TGP-H 090. While fiber pitch may not
have a strong impact on pore size distributions, it will impact solid phase transport processes,
such as electron and thermal transport, which must follow the paths defined by the fiber network
[27,93]. From the analysis of nano-CT images of Toray TGP-H 090, 36% of fibers were
observed to be bundled together. This co-alignment of fibers is expected to have a large impact
on models of both the pore space and the solid matrix. Areal weight values were measured and
found to be in agreement with manufacturers. Areal volumes were calculated based on material
densities. These values, or similarly derived areal volumes should be used when creating
stochastic models to ensure that the proper proportions of constituent elements. Finally, MPL
cracks were counted and measured from high-resolution SEM micrographs. These characteristics
are expected to prove essential in the creation of representative stochastic models of the GDL.
64
5 Stochastic Modeling of PEM Fuel Cell GDLs II.
A Comprehensive Substrate Model with Pore Size Distribution and Heterogeneity Effects
5.1 Abstract
A stochastic modeling algorithm was developed that accounts for porosity distribution, fiber
diameter, fiber co-alignment, fiber pitch, and binder and/or polytetrafluoroethylene fractions.
Materials representative of a commercially available gas diffusion layer (GDL) (Toray TGP-H
090) were digitally generated based on empirical measurements of these various properties.
Materials made with varying fiber diameters and binder/fiber volume ratios were compared with
a generated reference material through porosity heterogeneity calculations and mercury intrusion
porosimetry simulations. Fiber diameters and binder/fiber ratios were found to be key modeling
parameters that exhibited non-negligible impacts on the pore space. These key parameters were
found to positively correlate with heterogeneity and mean pore diameter and exhibit a
complementary relationship in their impact on the pore space. Because both parameters directly
impacted the number of fibers added to the domain, modeling techniques and parameters
pertaining to fiber count must be considered carefully.
5.2 Introduction
Performance models of polymer electrolyte membrane (PEM) fuel cells have typically relied on
assumptions about the bulk transport properties of the GDL [32]. The presence of liquid water in
the GDL can dramatically alter the pore-space available for reactant diffusion, and therefore,
dramatically alter the bulk-transport properties of the GDL. Current PEM fuel cell performance
models would benefit from accurately defined relationships between GDL structure, GDL
flooding, and resultant gas transport. In order to gain insight into microscale heat and mass
transport through these materials, researchers are now performing numerical simulations directly
on images of the microstructure obtained through X-ray tomography or stochastic fiber
placement algorithms [22,23,27,94,95]. Simulating the invasion of water into these images
enables the determination of valuable multiphase transport parameters that can otherwise be
challenging and expensive to measure experimentally [19,25,28,53,96]. However, in order to
65
rely on the results of invasion simulations into artificially generated images, the generation
algorithm must be accurate. Becker et al. [94] applied voxel-based solvers on X-ray tomography
images and was able to match experimentally measured diffusivity, permeability, and
conductivity. However, in the same study they employed state-of-the-art stochastic modeling
techniques to create a virtual material image, but could not reconcile many numerical results
between the stochastic model and the tomography-based model. Permeability values calculated
in the stochastic domain were higher than expected, and all three properties had
uncharacteristically low levels of anisotropy. They attributed these discrepancies to a lack of
sufficient heterogeneity in the generated material [94].
Most stochastic models of the GDL involve cylindrical representations of carbon fibers. The
groups at the Fraunhofer Institute (Kaiserslautern) and the Institute of Stochastics (Ulm) were
instrumental contributors to the development and use of such GDL models in the fuel cell
community [25,26,42,73,94,97,98]. In some studies, cylinder orientations were randomized, and
orientation distributions were controlled to prescribe material anisotropy [25,94]. As was first
demonstrated in our previous work [38,99], the random placement of cylinders (fibers) can be
spatially constrained to replicate porosity distributions that have been observed to exist in most
GDL materials [54,74,75]. Binder and PTFE are often assumed to attach to the fibers as highly
wetting fluids and thus recede into the smaller pores of the material upon drying, sintering or
carbonization. Therefore, in stochastic models it is common practice to approximate binder
and/or PTFE addition with the morphological opening of the fibrous pore space
[22,24,77,94,100].
Several groups have provided valuable characterizations of stochastic modeling parameters.
Nabovati et al. [23] discussed material permeability dependence on fiber diameter. When
modeling binder with the morphological opening of the pore space, Didari et al. [22] found that
anisotropic permeability values could be arrived by employing a 2D disc shaped, co-planar
structuring element. Nabovati et al. [24] found that enforcing experimentally obtained, through-
plane porosity distributions on the stochastic fiber placement also increased the anisotropic
permeability when compared to uniformly distributed fibers. They also found that the degree of
anisotropy in the permeability was dependent on the assumed volume fraction of binder [24].
Inoue et al. [78] studied the impacts of bulk porosity and fiber diameter on the generated pore
space of stochastically generated GDLs. By comparing in-plane porosity distributions, they
66
determined that heterogeneity was strongly related to fiber diameter, while heterogeneity did not
have a noticeable relationship with the bulk porosity. Their heterogeneity comparison involved
porosity calculations of through-plane columns of voxels; therefore, through-plane sources of
heterogeneity (such as a through-plane porosity distribution [54,74,75]) were not resolved.
In this work, a methodology for stochastically generating fibrous substrates is presented. These
stochastic models of fibrous substrates are created to match the reported properties of one of the
materials reported in Part 1 of this study [101], and the resultant materials are characterized in
terms of heterogeneity and pore size distributions. The impact of fiber diameter and binder
fraction (volumetric solid fraction of binder material) are each demonstrated to dramatically alter
the heterogeneity and pore size distribution of generated materials.
Figure 5.1 Size comparison between a relatively small GDL sample area (5 cm × 5 cm) and a relatively large stochastic model (1 mm × 1 mm).
5.3 Model Development
In this work, a detailed exploration of GDL generation parameters and techniques was performed
to create a valid and representative virtual structure. Figure 5.1 shows a typical realization of a 1
mm2 domain, and its size relative to a full scale GDL sample. The stochastic modeling algorithm
employed in this work was based on the algorithm developed previously [24], and was enhanced
to incorporate the fiber pitch and fiber co-alignment frequency observed in Part 1 of this study
[101]. The algorithm requires the following inputs: domain dimensions, fiber diameter, fiber
length, areal volume, fiber pitch distribution, through-plane porosity distribution, binder fraction,
67
and voxel resolution. Binder fraction, fb, was defined as the desired fraction of the solid volume
occupied by binder, as opposed to fiber. From these inputs, the algorithm returned a stochastic
model of the substrate, an example of which is displayed in Figure 5.2.
Figure 5.2 Stochastic model of Toray TGP-H 090 GDL substrate and enlargement for detailed view. Fibers (black) have diameter of 8 µm, binder (yellow) has binder fraction of 0.4. Sample has dimensions 990 µm ×
990 µm × 260 µm
5.3.1 Model overview
Fibers of uniform length and diameter were placed into the domain based on an experimentally
measured, through-plane porosity distribution. The fiber center was given random xy-
coordinates, as well as a random planar angle, φ. Fibers were also given random z-coordinates;
however, those coordinates were chosen from an experimentally measured through-plane
material distribution. Fibers were assigned a random pitch, θ, which was chosen from the
experimentally measured distribution described in [101]. All coordinates were converted from
standard units to units of voxels.
5.3.2 Individual fiber placement
A novel feature of this model is that any portion of a placed fiber extending beyond a side-wall
domain boundary reappears at the opposite boundary, as shown in Figure 5.3. This was done to
68
ensure isotropic in-plane porosity distributions, while creating materials that are intrinsically
well-suited for numerical transport simulations with periodic side-wall boundary conditions.
Figure 5.3 Fiber placed into a stochastic modeling domain. x, y, and z offsets, as well as angles φ, and θ (pitch)
were assigned based on an assumed probability distribution of possible values. Portions of fibers extending beyond the domain were made to reappear at the opposite face of domain.
5.3.3 Fiber count
The number of fibers traversing the domain are expected to have a critical impact on the pore
size distribution and heterogeneity of the pore space. It is therefore important to carefully
determine the appropriate number of fibers to add to the domain. Due to the voxelated nature of
the present reconstructions, this determination turns out to be surprisingly non-trivial. For
instance, even if the experimentally measured fiber diameter, dexp, is well known, one is forced to
round this quantity to the nearest voxel. The voxelized fiber volume is also prone to error due to
the voxelated fiber cross-section. To circumvent these issues, the fiber count, nf, was determined
by first calculating the idealized volume, Vf,ideal, of a cylinder with length, l, and experimentally
derived diameter, dexp:
𝑉𝑓,𝑖𝑑𝑒𝑎𝑙 = 𝜋 𝑙 (𝑑𝑒𝑥𝑝/2)2 . 5.1
Then, the total volume of all fibers required was calculated as:
69
𝑉𝑓,𝑡𝑜𝑡𝑎𝑙 = 𝑉𝑑𝑜𝑚𝑎𝑖𝑛 × (1 − 𝑓𝑏), 5.2
where Vdomain is the total volume of the domain. Finally fiber count was calculated as:
𝑛𝑓 = 𝑉𝑓,𝑡𝑜𝑡𝑎𝑙/ 𝑉𝑓,𝑖𝑑𝑒𝑎𝑙. 5.3
By forcing nf to be calculated by idealized cylindrical volumes instead of the voxelized volumes
of generated fibers, a more realistic pore space is ensured.
This volume-based approach is necessary for placing the correct number of fibers. Consider an
alternative approach, where, for example, two voxelated fibers of 1000 voxels each added to a
domain. If they overlap in 100 voxels, then the total voxel volume added would be 1900 voxels,
not 2000. This effect can become quite insidious if many fibers overlap each other in many
places, resulting in far too many fibers added to the domain. The volume-based approach
outlined above avoids this by counting the volume before it is added to the domain, thus
overlapping does not impact the final fiber count. Another subtle but vital benefit to using this
approach is that fiber intersections are properly accounted for. This is discussed in detail below
in section 5.3.7.
5.3.4 Generated fiber volume
Although nf is independent of the voxelized volume of generated fibers, it remains important to
closely match generated fiber volumes with ideal fiber volumes. In the final step of the material
generation, binder material is placed to reach the correct bulk porosity, and if an appropriate
number of fibers are placed, but with inappropriate volumes, the result would be an inappropriate
amount of binder placed in the domain.
Fibers were generated with the use of a cylinder generation sub-function obtained from the
MATLAB File Exchange2. The sub-function accepted the following parameters in units of
voxels: an input diameter, dinput, and input endpoint coordinates. Voxels were assigned to a
2 https://www.mathworks.com/matlabcentral/fileexchange/21758-cylinder-surface-connecting-2-points
70
nearby fiber if they were within a radial distance of dinput/2 of the line segment formed by the
fiber endpoints.
A voxel resolution, R, with units of µm/voxel, was required in order to dimensionalize voxel-
based lengths. The dimensional input diameter, dinput × R, was not matched to the experimentally
derived dexp. This is because, due to the voxelized nature of the system, generated fibers volumes,
Vf,gen, were limited to discrete numbers of voxels which rarely precisely coincided with Vf,ideal/R3.
Compounding this problem, was the fact that fibers of different orientations would have different
volumes, depending on their alignment with the voxel orientation. As a result, complementary
dinput and R values had to be found such that �̅�𝑓,𝑔𝑒𝑛 ≈ 𝑉𝑓,𝑖𝑑𝑒𝑎𝑙/𝑅3, where �̅�𝑓,𝑔𝑒𝑛 is the average
generated fiber volume.
To determine complementary dinput and R values for a given dexp and corresponding Vf,ideal, a short
study was conducted. First, 200 individual, randomly oriented fibers were generated for each of a
range of dinput values between 1 voxel to 20 voxels. For each fiber, a summation of the associated
voxels was determined, and the mean volume of each group of 200 cylinders was found (Vf,mean).
The relationship between dinput and �̅�𝑓,𝑔𝑒𝑛 is shown in Figure 5.4 along with the ideal case of V =
π l (dinput/2)2. It can be seen that �̅�𝑓,𝑔𝑒𝑛 contains only discrete values which are consistently
higher than the ideal case. Equivalent diameters of generated fibers were found as:
𝑑𝑒𝑞 = 2 (𝑉𝑓,𝑔𝑒𝑛 𝑅
𝜋 𝑙)
0.5
, 5.4
which represent the diameter of an idealized cylinder with volume, �̅�𝑓,𝑔𝑒𝑛 and dimensionless
length l/R. Finally, voxel resolutions for any dinput were found as:
𝑅 = 𝑑𝑒𝑥𝑝/𝑑𝑒𝑞, 5.5
where dexp is measured in µm and deq is measured in voxels. Figure 5.5 illustrates the possible
voxel resolutions that result from the dexp values discussed in this work.
To check that this results in reasonable generated fiber volumes, equations 5.1 and 5.5 were first
combined to yield:
𝑉𝑓,𝑖𝑑𝑒𝑎𝑙 = 𝜋 𝑙 (𝑑𝑒𝑞 𝑅 2⁄ )2, 5.6
71
which can then be combined with equation 5.4, resulting in the following desired relationship:
�̅�𝑓,𝑔𝑒𝑛 = 𝑉𝑓 ,𝑖𝑑𝑒𝑎𝑙 𝑅3⁄ . 5.7
Figure 5.4 Comparison of mean fiber volume, �̅�𝒇,𝒈𝒆𝒏, and input diameter, dinput, for cylinder generation
algorithm. The ideal case of V = π l (dinput/2)2 is displayed as a dashed line. The calculated equivalent diameter,
deq, based on cylinders with volume = �̅�𝒇,𝒈𝒆𝒏, is also displayed.
Figure 5.5 Permitted resolution values, R, over the dinput values tested, for five hypothetical fiber diameters, dexp.
72
5.3.5 Through-plane material distribution
Substrate models were prescribed porosity profiles by randomly choosing through-plane fiber
positions from a known through-plane material distribution. This distribution can be found as the
complement of a µCT derived through-plane porosity distribution [38].
5.3.6 Fiber co-alignment
Each placed fiber was assigned a probability of being co-aligned (paired) with the most recently
placed fiber in the system. If the fiber was selected for co-alignment, its xy-position was offset
from that of the previous fiber by a distance of one fiber diameter in the direction normal to that
fiber. Its z-position, φ, and θ values were identical to those of the previous fiber.
5.3.7 Fiber overlap
When placing fibers it is not reasonable to avoid fiber intersections. As outlined above, the
volume of fibers involved in an intersection was fully accounted for, resulting in the correct
number of fibers added to the domain. However, these intersections resulted in a slight inflation
of neighboring pore sizes. The addition of binder to the image offered one way to qualitatively
correct for this, as binder coalesces in the corners and crevices precisely at fiber intersection
points. In this work, binder was added to the sample until the known porosity of the material
was reached. By bulking up the regions near the intersections, this step had the effect of
mimicking the displacement and bending of fibers at these point locations.
5.3.8 Binder placement
After nf fibers were placed into the domain, the application of binder was simulated with the
morphological opening of the pore space with a structuring element (SE) [100]. The SE
employed in this case was spherical, with a diameter determined through a half-interval search
algorithm, which resulted in the SE diameter providing the best match to the desired final
material porosity. As the SE was also voxelized, the accuracy of this process was limited by the
resolution chosen. With a resolution of 0.99 µm/voxel, the bulk porosity value for each material
was observed to fall within 1.4 % of the desired value. To avoid edge effects associated with
morphological opening, the domain dimensions were temporarily increased before this step; each
73
sidewall was padded with the first 25 voxel planes from the opposite sidewall; first the
corresponding xz-planes, and then the corresponding yz-planes were added.
5.4 Pore-space Characterization
Two characterization methods are presented to explore the effects of input parameters on the
resultant pore space of stochastically modeled GDLs. The first method was used to characterize
the heterogeneity of the material based on local porosity calculations. The second method was
used to characterize the pore size distributions of the generated materials by simulating mercury
intrusion porosimetry curves.
5.4.1 Porosity heterogeneity
The goal of the porosity-based heterogeneity test was to evaluate material uniformity. Numerous
subdomains were selected from the main domain and the porosity in each was calculated. The
size of these sub-domains (50 µm × 50 µm × 50 µm) was chosen to be sufficiently large such
that single fibers did not dominate the porosity value and sufficiently small to capture localized
regions of high and low porosities (porosity heterogeneity) throughout the GDL. 100,000 such
measurements were made of cubic sub-domains randomly selected from throughout the material.
If a sub-domain position was chosen near the edge of the domain, such that a portion of the cube
would be outside the primary domain, that portion of the cube was extended into the opposite
face of the domain, taking advantage of the fact that fibers were placed using periodic rules at the
side walls. A 2D example of this process is shown in Figure 5.6a, where two random samples are
outlined in dashed lines. The region outlined in blue did not overlap with the primary boundary
and had a local porosity of 78%. The region outlined in red happened to be placed near a corner,
and therefore this sub-domain extended into the opposite faces of the domain. Figure 5.6b shows
the distribution of local porosity of 150 random samples in the example 2D domain. If the
domain had been more heterogeneous, the distribution would be more widely spread. If the
domain was perfectly homogeneous, the porosity distribution width would approach zero with a
peak at a single value.
74
Figure 5.6 Demonstration of a porosity heterogeneity analysis of a 2D example (a) with white material on
black void. The blue and red dashed regions each represent a randomly placed 502 pixel2 sample. After a sufficient number of similar random samples were examined, a representative histogram of measured
porosities (b) was obtained. Note: in the 3D models characterized in this study, the random samples were 503
µm3 cubes.
5.4.2 Mercury intrusion porosimetry simulations
Mercury intrusion porosimetry (MIP) is widely used experimental tool for characterizing the
pore size distributions of porous materials [102,103]. In MIP studies an evacuated porous
material is invaded with mercury in a controlled step-wise manner, yielding a so-called capillary
pressure curve relating mercury saturation to capillary pressure. As the capillary pressure is
incrementally increased, the mercury penetrates pores of decreasing size. With knowledge of the
surface tensions involved, capillary pressures can be used to approximate pore sizes, resulting in
a pore size distribution [102,103].
Gostick [104] described a simple morphology-based simulation of two-phase invasion, built on
the work of Hilpert and Miller [105], entitled a morphological image opening (MIO) algorithm.
The MIO algorithm was used to determine the saturation of the invading phase as a function of
the capillary pressure of the invading fluid. This algorithm was employed in the present work to
characterize the pore size distributions of the generated materials. In traditional MIP, the
invading mercury has access to pores along all surfaces of the sample, and due to the sample size
requirements of a GDL sample, the contribution of side-wall invasion is expected to be
negligible. For example, the side-walls compose only 5% of the total surface area of a 1 cm × 1
cm sample of Toray TGP-H-090. However, for a typical numerically generated GDL of
75
dimensions 1 mm × 1 mm, the side-walls compose 33% of the sample, and sidewall invasion
could be expected to contribute to the resultant pore size distribution. To mitigate unrealistic
sidewall effects while characterizing the 0.99 mm × 0.99 mm materials generated in this work,
the MIO algorithm was implemented such that the invading fluid had access to both planar faces
of the material, but not the sidewalls.
The progression of the MIO technique is explained with the 2D demonstration illustrated in
Figure 5.7. Figure 5.7a shows a visualization of the pore space, where decreasing pore diameters
were accessible by the invading fluid with incrementally increasing capillary pressure. Figure 7b
displays the calculated saturation levels for each simulation step and the corresponding pore size
distribution that was obtained from the saturation data. It should be noted that since the primary
output of the MIO algorithm is a saturation vs. pore size curve, corresponding capillary pressures
need not be calculated.
Figure 5.7 MIO demonstration on pore space shown in Figure 5.6a. The pore space coloring (a) corresponds
to the diameter of the largest circular structuring element (SE) that was accessible from the top or bottom of the domain. The pore size distribution and saturation curves (b) were calculated from the volume of each
color shown in (a). Note: in the 3D models characterized later in this study, the probing structuring element
was spherical.
The saturation curve (e.g. Figure 5.7b, blue) was used to provide the following statistical
information of the pore space. The mean (volumetric) pore size was defined as the diameter
representing a saturation of 0.50. Similarly, arbitrary limits to the pore size distribution were set
as those that contain 90% of the pore volume. Minimum and maximum pore sizes were set to
diameters corresponding to saturation values of 0.95 and 0.05, respectively. In the 2D example
76
shown in Figure 5.7, the mean pore size was 7.4 pixels, and the pore size range was [3.3, 30.5]
pixels.
In the 2D example (Figure 5.7) described above, a majority of the internal pore space was
inaccessible to the invading fluid until higher pressures were reached. This was due to an
effective barrier of smaller pores near each surface. Therefore all pores in the interior of the
domain were categorized as small pores. Such mislabeling of pore sizes is a known limitation of
the MIP technique [49]; however, it remains a conventionally utilized tool for porous media
characterization and, as such, was an important experiment to numerically simulate.
5.5 Results and Discussion
5.5.1 Stochastic model of Toray TGP-H 090
The modeling algorithm described in Section 5.3 was employed with input parameters specific to
Toray TGP-H 090 without MPL or PTFE treatments. According to [101], this material is best
described by 7.7 µm-diameter fibers, a mean fiber pitch of 2.44º, an areal volume of 72.8 cm3
m-2, and a fiber co-alignment probability of 36%. Aside from fiber diameter, these parameters
were perfectly matched, including the full fiber pitch distribution reported in [101]. Fiber
diameters were varied in increments of 1 µm, and a diameter of 8 µm was assumed to be the
most representative of Toray TGP-H 090.
Voxel resolutions were based on their discretized relationship with input diameter (Section
5.3.4). A single voxel resolution of 0.99 µm/voxel was found to accommodate the integer dexp
values of 7 µm, 8 µm, 9 µm, 10 µm, and 11 µm, where respective dinput values were chosen
according to Figure 5.5.
Stochastically generated materials were generated with a domain size of 0.99 mm × 0.99 mm ×
0.26 mm. Cylindrical fibers were prescribed a length 0.99 mm. Modeling parameters are listed in
Table 1. A total of 20 parametric combinations were possible with 5 diameter values and 4
binder fraction values shown.
GDLs were stochastically generated with a range of binder fractions so that the best (most
realistic) binder fraction could be identified. The cross-sectional images of these GDLs were
77
visually compared to microscale computed tomography (µCT) cross-sections of Toray TGP-H
090. At a constant porosity and fiber diameter, stochastic materials generated to have higher
binder fractions required fewer fibers. Materials made with a binder fraction of 0.4 appeared to
have an appropriate number of fibers present. An example comparison between the cross
sections of the µCT dataset and a stochastic model is provided in Figure 5.8.
Figure 5.8 Comparison between cross sectional slices of a µCT data set of Toray TGP-H 090 (a) and a
stochastically generated material generated with representative input parameters and a binder fraction of 0.4 (b). Material (white) represents both fibers and binder material.
Table 5.1 Parameters employed to create materials for this study. Underlined parameters are assumed to best represent Toray TGP-H 090.
Property Name Symbol Unit Value
Area µm2 990 × 990
Thickness µm 263
Fiber diameter dexp µm 7, 8, 9, 10, 11
Fiber length l µm 990
Bulk porosity 0.72
Mean fiber pitch θmean ° 2.44
Binder fraction fb 0.0, 0.2, 0.4, 0.6
78
The through-plane porosity distribution of generated materials was prescribed with that of a 1
mm × 1 mm region of a µCT image of untreated Toray TGP-H 090 under minimal compression.
A comparison between the µCT image-based porosity distribution (model input) and the porosity
distribution of a single stochastically generated model (output) is displayed in Figure 5.9. Using
a sufficiently large domain (experimental and numerical) enabled a close agreement between the
input and output distributions. This was an improvement to our previous work, where smaller
domains were employed [24,38].
Figure 5.9 Comparison between the µCT derived through-plane porosity distribution used as a weighting function to stochastic fiber placement, and the porosity distribution of a single, stochastically generated
material.
Using the image processing software FIJI3, stochastic models were rendered in a fashion similar
to scanning electron microscopy (SEM). As can be seen in Figure 5.10, the stochastically
modeled material bears a reasonable resemblance to the top-down view from SEM. The edge
views (xz-plane) exhibit fewer similarities, where large pores are shown in Figure 5.10a that do
not appear in Figure 5.10b. This can be attributed to the existence of carbon fibers near the
sample edges that were broken during sample preparation to distort the depth perception. Such
large pore sizes were not as prominent in the µCT through-plane cross sections (Figure 5.8a).
For each possible combination of parameters in Table 5.1, 10 materials were stochastically
generated. It was assumed that the materials generated with a fiber diameter of 8 µm and binder
3 http://fiji.sc/
79
fraction of 0.4 most closely resembled Toray TGP-H 090. All materials were created to match
the µCT-derived through-plane porosity distribution displayed in Figure 5.9.
Figure 5.10 Comparison between SEM micrographs (a) of top-down (xy plane) and edge (xz plane) views of
Toray TGP-H 090 material and similar views of stochastically generated, digital materials (b). The scale bar in (a) applies to all images.
5.5.2 Porosity heterogeneity
Figure 5.11 displays the local porosity distributions for evaluating porosity heterogeneity for all
20 combinations of fiber diameter and binder fraction. Each shaded region in Figure 5.11
represents two standard deviations (2σ) about the mean distribution values. The 2σ fields contain
approximately 95.5% of the individual distribution values. To provide a frame of reference, the
mean values for the 8 µm diameter materials with a binder fraction of 0.4 were shown in each
subfigure.
This characterization method produced a distinct trend in the profiles for the various parametric
combinations. Highly heterogeneous materials (e.g. Figure 5.11e, blue) produced wide
distributions of porosity, and narrower distributions were realized with less heterogeneous
materials (e.g. Figure 5.11a, grey). The 2σ fields were seen to be situated tightly around the mean
curves. Also, upon examination of the curves in general, a change in binder fraction of 0.2
80
consistently resulted in a more dramatic change in heterogeneity than a 1 µm change in fiber
diameter. However, both parameters exhibited strong positive correlations to heterogeneity.
To determine the effects of fiber count, two materials with a similar number of fibers were
compared. Though not shown, it was found that the materials with 7 µm-diameter fibers and a
Figure 5.11 Porosity heterogeneity comparison showing the relationship
between binder fraction and heterogeneity for fiber diameters: (a) 7 µm, (b) 8 µm, (c) 9 µm, (d) 10 µm, (e) 11
µm. Each colored field is bound by two standard deviations above and below the mean value from 10 samples. The
reference line in each figure corresponds to the mean value of materials generated
with 8 µm-diameter fibers and a binder fraction of 0.4.
81
binder fraction of 0.6 (Figure 5.11a, blue) were generated with almost exactly the same number
of fibers as those generated with 10 µm-diameter fibers and a binder fraction of 0.2 (Figure
5.11d, red). However, the 7 µm-diameter material was more heterogeneous (wider local porosity
distribution) than the 10 µm-diameter material. Therefore, it can be said that, while parameters
that decrease fiber count can be expected to have a positive correlation with heterogeneity, fiber
count alone cannot be used to predict material heterogeneity when a combination of parameters
have been altered.
Three parameter combinations produce materials with local porosity distributions that are nearly
matching to the reference case. Materials made with 9 µm-diameter fibers and a binder fraction
of 0.4 (Figure 5.11c, green), 10 µm-diameter fibers and a binder fraction of 0.2 (Figure 5.11d,
red), and 11 µm-diameter fibers and a binder fraction of 0.2 (Figure 5.11e, red) produced similar
local porosity distributions. This demonstrates the complementary effect that the two parameters
have on material heterogeneity.
From these results, the authors recommended paying close attention to both fiber diameter and
assumed binder fraction when attempting to generate realistic material heterogeneities. Due to its
similar impact on effective fiber count [101], the inclusion of fiber bundling was expected to
generate a non-negligible impact on heterogeneity.
5.5.3 Mercury intrusion porosimetry simulations
The simulations of mercury intrusion porosimetry provided a quantitative measure of the effects
of fiber diameter and binder fraction on the pore space of the material.
The saturation curves and pore size distributions corresponding to each of the 20 possible
combinations of fiber diameter and binder fraction are displayed in Figure 5.12 and Figure 5.13,
respectively. Additionally, a visualized mercury distribution is shown in Figure 5.14,
representative of a typical early stage in a simulation (saturation = 0.16). Similar to porosity
heterogeneity distributions, MIO-based saturation curves were distinct for each of the material
types, and 0.99 mm × 0.99 mm samples appeared to be sufficiently large to provide domain size
independence.
82
Figure 5.12 MIO saturation curve
comparison showing the relationship between binder fraction and saturation curves for fiber diameters: (a) 7 µm, (b) 8
µm, (c) 9 µm, (d) 10 µm, (e) 11 µm. Each colored region is bound by two standard
deviations above and below the mean value obtained from 10 samples. The reference line in each figure corresponds
to the mean value of materials generated with 8 µm-diameter fibers and a binder fraction of 0.4.
83
Figure 5.13 MIO pore size distribution comparison showing the relationship between binder fraction and pore size
distribution for fiber diameters: (a) 7 µm, (b) 8 µm, (c) 9 µm, (d) 10 µm, (e) 11 µm. Each colored region is bound by two
standard deviations above and below the mean value obtained from 10 samples.
The reference line in each figure corresponds to the mean value of materials generated with 8 µm-diameter
fibers and a binder fraction of 0.4.
84
Figure 5.14 An example distribution of mercury from a simulation of mercury intrusion porosimetry with a spherical SE of diameter of 30 µm in a 1 mm × 1 mm × 263 µm modeled material with a fiber diameter of 9
µm and a binder fraction of 0.2. Fibers were intentionally hidden in this representation for clarity.
Unlike in the porosity heterogeneity comparison, only one other parameter combination, i.e. 10
µm-diameter fibers and a binder fraction of 0.2 (Figure 5.12d, red), resembled the reference
combination of 8 µm-diameter fibers and a binder fraction of 0.4. This result indicated that
porosity heterogeneity could not fully describe each material type and emphasized the
importance of implementing multiple characterization methods when generating representative
materials.
The mean pore diameters, as well as the pore diameter ranges are displayed for all material types
in Table 5.2 and Table 5.3, respectively. As shown in Tables 5.2 and 5.3, fiber diameter and
binder fraction exhibit a strong positive correlation to the minimum, mean, and maximum pore
sizes of the materials. An increase in binder fraction from 0 to 0.6 leads to the doubling of the
mean pore size, while an increase in fiber diameter from 7 µm to 11 µm leads to an increase in
the mean pore size by over 50%. On the log scale provided in Figure 5.13, it can be seen that the
width of the pore size distribution remains relatively constant throughout the range of parameter
combinations.
From these results, the authors recommend matching pore size distributions of stochastically
modeled materials to experimentally derived values, as each parametric combination of fiber
diameter and binder fraction resulted in distinct pore size distributions.
85
Table 5.2 Mean pore diameter values for each studied combination of fiber diameter and binder fraction
Mean Pore Diameter (µm)
Binder Fraction
0.00 0.20 0.40 0.60
Fiber
Diameter
(µm)
7 16 18 23 30
8 18 21 26 34
9 20 24 29 39
10 22 26 33 43
11 24 29 36 48
Table 5.3 Pore diameter ranges for each studied combination of fiber diameter and binder fraction.
Pore Diameter Range,
90th percentile [min, max] (µm)
Binder Fraction
0.00 0.20 0.40 0.60
Fiber
Diameter
(µm)
7 [8, 27] [12, 33] [16, 41] [22, 53]
8 [10, 32] [13, 38] [18, 48] [25, 60
9 [11, 36] [15, 43] [20, 54] [28, 67]
10 [12, 40] [17, 48] [23, 59] [31, 72]
11 [13, 45] [18, 53] [25, 62] [35, 77]
5.6 Conclusions
A methodology was presented for the stochastic generation of the carbon fiber substrates of PEM
fuel cell GDLs. This methodology was unique in that it incorporated experimentally derived
values for fiber diameter, fiber pitch, through-plane porosity distribution, and fiber bundling.
Also, particular emphasis was given to generating the correct number and volume of fibers,
which involved careful treatment of these experimentally derived parameters. A parametric study
was conducted on assumed fiber diameter and fiber/binder ratio (binder fraction). For each
parametric combination, 10 stochastic materials were generated and compared with a reference
material. It was found that each parameter had strong effects on both the material heterogeneity
and the pore size distributions derived from mercury simulations. Material heterogeneity and
pore size distribution were shown to be useful methods when characterizing the pore space of the
material, in that each parametric combination generated distinct, consistent profiles
86
corresponding to each method. Similar effects on the pore space can be achieved by either
increasing the fiber diameter or by increasing the binder fraction, in that nearly indistinguishable
materials can be generated with complementary adjustments of these two parameters. The
authors recommend that future studies involving stochastic models of the GDL substrate employ
carefully chosen values for these parameters. Additionally, when experimental data is available,
materials should demonstrate realistic porosity heterogeneity and pore size distribution.
87
6 Visualizing Liquid Water Evolution in a PEM Fuel Cell Using Synchrotron X-ray Radiography
6.1 Abstract
Synchrotron X-ray radiography was utilized to study the time evolution of liquid water in an
operating polymer electrolyte membrane (PEM) fuel cell. A high aspect ratio fuel cell designed
with offset anode and cathode flow field channels was operated at conditions that produced
critical water management issues. The X-ray beam was directed along the plane of the fuel cell,
and was therefore employed to elucidate the through-plane distribution of liquid water in the
porous materials. Due to the offset between the anode and cathode gas channels, the membrane
electrode assembly exhibited sinusoidal warping, and liquid water accumulated in possible areas
of delamination. Liquid water first appeared near the cathode catalyst layer, and then traveled
laterally within the porous gas diffusion layer. The experiment provides a basis for future design
considerations, including membrane thickness and attenuation estimates.
6.2 Introduction
Due to the micrometer scale of the GDL and the coupled relationship between local temperature
and phase change, it can be challenging to create realistic ex situ experiments of liquid water
forming in and around the GDL. Several groups have conducted invasion experiments to mimic
fuel cell conditions, where liquid water is assumed to enter the system from the interface
between the GDL and the catalyst layer and percolate to the opposite face [69,80,106,107]. Other
groups have utilized environmental scanning electron microscopy (ESEM) to visualize
condensation on the surface fibers of the GDL [108,109]. Each of these techniques involves
assumptions about the impact of the concentration and temperature gradients present in the GDL
material during fuel cell operation. The assumptions for these ex situ experiments must be better
informed to increase their applicability to the operating PEM fuel cell.
In situ experiments that give insight into the behavior of liquid water in PEM fuel cell materials
almost always require some means of visualizing the liquid water [8,29,30,110-118]. Optically
transparent flow fields have been employed by [110,111] to visualize liquid emerging from the
88
surface of the GDL and condensing on the channel walls. The drawback of this technique is that
the difference between the thermal properties of the transparent flow field and those of a metallic
or graphite material may significantly alter the in situ temperature distributions within the GDL
and induce unrealistic condensation behavior.
The theory behind using neutron and synchrotron X-ray radiography to visualize in situ liquid
water in PEM fuel cells is described in detail in [30], and several researchers have demonstrated
the usefulness of these [8,29,114-116,119]. The two techniques are similar in that they both
involve detecting changes in beam attenuation of an irradiated sample, with those changes being
directly related to the accumulation of liquid water in the system. Neutron radiography has the
advantage of facilitating few fuel cell modifications, due to the near transparency of metals and
graphite to a neutron beam and the high attenuation from water molecules. Recently, synchrotron
based X-ray radiography has been demonstrated to reach resolutions of less than 1 μm, compared
to a limit of ~20 μm in neutron radiography [30]. A very recent neutron radiography study [112]
reported a resolution of 13 μm, however a total of 60 minutes of images were averaged for noise
reduction. Because thick metals can be opaque to X-ray light, some fuel cell modifications are
sometimes performed to create viewing windows [8] for the system. These modifications are
seen to be less invasive than the use of a transparent flow field for optical visualizations.
Therefore, synchrotron X-ray radiography has emerged as a promising technology for the study
of liquid water within the porous materials of the PEM fuel cell.
A growing number of synchrotron facilities are beginning to conduct studies of liquid water in
PEM fuel cell materials [8,29,116,117], which results in many individuals participating in the
same learning curve regarding experimental design. This method of employing synchrotron X-
ray radiography to PEM fuel cell investigations could be further advanced with the development
of a best practices approach. In this study, we collected a time-series of radiographs at the
Canadian Light Source (CLS) in Saskatoon, Canada with the goal of learning best practices for
designing synchrotron-based experiments for investigating liquid water transport in an operating
PEM fuel cell.
89
6.3 Experimental Setup
The fuel cell utilized in this study was designed for synchrotron X-ray based visualization of in
situ liquid water while the plane of the cell is oriented in the direction of the X-ray beam. Similar
to the study performed by Hartnig et al. [29], the fuel cell employed here was designed for in-
plane imaging to produce cross-sectional information about the evolution of liquid water
transport. Additionally the cell was constructed such that channel and landing regions of each
membrane electrode assembly (MEA) could be distinguished in radiographs.
6.3.1 Fuel cell assembly
A 5 cm2 active area cell (Figure 6.1) was constructed with a high aspect-ratio in order to reduce
the amount of material (including gaskets) that the beam traversed before reaching the detector.
Single-serpentine flow-fields were machined into a graphite composite, with 1 mm landings and
channels and 25 turns over the active area. While the fuel cell is in a co-flow configuration, the
anode flow-field pattern was offset by 1 mm compared to the cathode pattern, such that the
cathode channels aligned with the anode landings. While this may induce additional sheer forces
and misalignments of the MEA components, the offset was necessary to mimic the configuration
of a concurrent visualization study [7]. The catalyst coated membrane (CCM) employed was
custom ordered from IonPower, Inc. (Delaware, US). A Nafion 115 membrane (dry thickness of
127 μm) was coated with a catalyst layer (thickness of 12 μm) with a Pt loading of 0.3 mg/cm2.
Toray TGP-H 090 GDLs (thickness of 280 μm) were used, treated with 10% wt.
polytetrafluoroethylene (PTFE), with no microporous layer. Surrounding the active area was a 5
mm width of 254 μm-thick PTFE coated fiberglass gasket material.
90
Figure 6.1 Schematic illustrating the components of the PEM fuel cell assembly. After assembly, GDL and gasket reside in the same plane.
6.3.2 Imaging setup
The experiment was performed at the BioMedical Imaging and Therapy Bending Magnet (05B1-
1) beamline at the Canadian Light Source (CLS) synchrotron (Saskatoon, Canada).
Monochromatic X-ray light provided at 25 keV was used to obtain absorption radiographs with a
Hamamatsu C9300-124 (12bit, 10 Megapixel) charged coupled device (CCD) camera placed 30
cm from the sample. The pixel resolution was 4.27 μm, and the spatial resolution of the optical
setup was 10 μm. Radiographs were obtained every 0.9 s. To reduce the effects of noise from the
CCD camera and the thermal instability of the monochromator [113], 19 consecutive images
were averaged, reducing the temporal resolution of the each frame to 17 seconds. Due to the
orientation of the fuel cell in this study, where the 1 cm width of the active area was aligned to
the beam path, individual pore-scale water accumulation events were overlapped by many
similar and simultaneous events along the width of the cell. Therefore, high temporal resolutions
were not necessary, as these combined events had much larger time scales than the individual
events.
91
6.3.3 Fuel cell operating conditions
A Scribner 850e Fuel Cell Test Station (Scribner Associates Inc., Southern Pines NC) was
utilized to regulate load, cell temperature, reactant flow rates, and reactant relative humidity
(RH). Prior to the experiment, the fuel cell was conditioned with 4 hours of load cycling. At the
time of the experiment, the fuel cell was operated at 65C, with a constant flow rate of 0.5 lpm
air at the cathode and 0.3 lpm hydrogen at the anode. Both reactants were humidified to 80%
RH, and the outlet pressure was atmospheric.
The initially dry cell was held at open circuit voltage (OCV) for 5 minutes. The cell was then
brought up to a current density of 0.30 A cm-2 at a rate of 2 mA cm-2 s-1. The cell was held at this
current for 15 min. Finally, the cell current density was increased at a rate of 2 mA cm-2 s-1 until
the cell potential fell below 0.1 V, which occurred at a current density of ~0.7 A cm-2.
See Appendix A for a detailed schematic of the fuel cell testing equipment.
6.3.4 Liquid water quantification
To quantify liquid water in the cell, each averaged radiograph in the “wet-state” must be
normalized to a “dry-state” radiograph obtained before the accumulation of liquid water. The
normalization process involved the Beer-Lambert law of attenuation as described in detail in
[113] (also see Appendix B for an improved methodology). The dry-state radiographs used for
normalization were the average of one hundred “dry-state” radiographs, each exposed for 0.9 s.
Due to membrane swelling, dry-state radiographs were chosen from the period of time where the
cell was held at 0.30 A/cm2. Since some water is expected to be in the system at 0.30 A/cm2, the
normalization may lead to undetected water. However, this dry-state condition was chosen to
prevent the majority of swelling-related artifacts. As will be discussed in the section titled
“Future Design Considerations,” this problem may be mitigated with careful membrane
selection.
Figure 6.2a displays a radiograph before normalization, showing the location of the fuel cell
components. The flow field channels and landings are seen as light and dark rectangles,
respectively, on both sides of the MEA. The 127 μm-thick membrane is seen as a thin, lighter
grey region, oriented along the center of the image (top-down). Finally, the GDL materials are
92
seen within the darkest regions, situated between the flow fields and the catalyst coated
membrane (CCM). Figure 6.2b displays this same image as Figure 6.2a, after normalization to a
dry-state radiograph, where liquid water and any other material movement become pronounced.
Figure 6.2 Synchrotron X-ray radiographs showing the cross-sectional view of an operating PEM fuel cell: (a) raw (b) processed images. The white dashed selection represents the selection shown in Figures 6.4 and 6.5.
The grayscale calibration bar is in units of cm of liquid water. Scale bars represent 1 mm.
93
6.4 Results: Behavior of Visualized Water
The following results describe the fuel cell performance and liquid water generation from a
comparatively dry state to a critically wet state, caused by a steady increase of 2 mA/cm2/s.
Figure 6.3 shows the voltage response while the cell is taken from 0.30 A/cm2 to ~0.7 A/cm2.
Four regions of this timeline, marked (a-d), are highlighted in Figure 6.3, representing the four,
17 s frames displayed in Figure 6.4. Region (d) is located near the point where mass transport
becomes a dominating factor in the over-potential of this cell.
Figure 6.3 Current density and potential response of fuel cell when current density is increased from 0.30 A/cm2 at a rate of 2 mA/cm2/s. Regions (a - d) represent the 17 seconds of combined exposure for each of the
four frames displayed in Figure 6.4.
94
Figure 6.4 Liquid water evolution over 4 minutes. Liquid water forms near the catalyst layer under the cathodic flow field landings (b,c) and appears to spread laterally through the bulk of the GDL to the region
under the channel (d). Black lines outline the location of the flow field landings. Negative values represent artifacts caused by material relocation during membrane hydration. The grayscale calibration bar is in units
of cm of liquid water. Scale bars represent 0.5 mm.
Figure 6.4 shows the time-evolution of water in the cathode GDL region at 4 points of the steady
ramp up from a current density of 0.30 A/cm2 to ~0.7 A/cm2. Figure 6.4a represents the state of
the cell 30 s before the beginning of the ramp, while the current density was maintained at 0.30
A/cm2. Figure 6.4b represents the state of the cell at 35 s into the ramp where the current density
is 0.37 A/cm2. Each subsequent image in the sequence represents a step of 60 s and 0.12 A/cm2.
Liquid water first appeared (Figure 6.4b) at the interface of the GDL and the catalyst layer, in
locations centered under the landings. At 95 s into the ramp, at a current density of 0.49 A/cm2,
Figure 6.4c shows that water continued to accumulate at these locations, with no invasion into
other regions of the GDL. Finally, by a current density of 0.61 A/cm2, liquid water had spread
laterally within the bulk of the GDL, into the less compressed region under the flow field
channel (Figure 6.4d).
A reasonable explanation for this observed behavior is that liquid water condensed in or near the
catalyst layer, under the cathode landings. The liquid water maintained a low capillary pressure
by only invading the large pores formed at the interface of the GDL and the catalyst layer. Then,
95
when a current density of 0.61 A/cm2 was reached, the volume of liquid water had occupied all
available low-capillary pressure locations, and was forced to reach pressures associated with
entering the bulk of the hydrophobic GDL (Figure 6.4d).
It is important to reiterate that the visualized liquid water is the combined water along the entire
1 cm-width of the active area (integrated in the in-plane direction) and may not be representative
of each individual growing water cluster in the system. The maximum value of quantified liquid
water thickness in the region of interest is 0.125 cm. This can be interpreted that 12.5% of the
total width of the active area is occupied with liquid water at these locations. With an estimated
70% porosity within the GDL under compression, this can be translated into a peak saturation
value of 18%.
6.5 Future Design Considerations
Several aspects of the fuel cell design and experimental design were shown to have a high impact
on the clarity of the experimental results. In order of importance, these design elements were:
membrane thickness, uneven attenuation, channel alignment, and pre-monochromator filtering.
The impacts of each design were made evident through a careful study of both the raw and
normalized radiographs, and will be described in detail below.
6.5.1 Membrane thickness
Nafion membrane materials have been reported to swell by as much as 50% as a result of current
density induced humidification [119]. In a fuel cell assembly, this tendency to swell can affect
the position of the catalyst layer and the GDL. The membrane used in this study was 127 μm
thick in its dry-state, which would correspond to a thickness change of 63 μm, when fully
humidified. Such swelling could lead to displaced positions of the anodic and cathodic GDLs
towards the flow fields. A comparison of the two membrane states is displayed in Figure 6.5,
where an image captured during open circuit voltage (OCV) was normalized to an average of
100 frames taken while the cell was held at 0.30 A/cm2. The water generated at this low current
density was enough to humidify the visualized region of the membrane and cause severe artifacts
in the normalized image due to the resulting shift of material position. In this case, little evidence
of liquid water was present in the comparison between these two states, so the 0.30 A/cm2 image
96
can be assumed to be in a dry-state as well. In fact, all normalized images presented in the
previous section were normalized to the cell at the 0.3 A/cm2 state. However, it was decided that
all future studies would be performed with 25 μm-thick membranes, to mitigate such artifacts,
and ensure zero water in the dry-state images. It is primarily for the reason of material movement
that the grayscale range was mapped to both negative and positive water thickness
measurements.
Figure 6.5 Radiograph taken at OCV normalized to the dry-state image used in this study (0.30 A/cm2) (inverted for consistency with Figures 6.4 and 6.5). Bright regions represent a net gain of material between OCV and 0.30 A/cm2, while dark regions represent a net loss. Black lines outline the location of the flow field
landings. The scale bar represents 0.5 mm.
6.6 Uneven Attenuation
While imaging the fuel cell, the raw radiographs must have sufficient signal in the regions of
interest so that any slight attenuation due to the presence of liquid water can be distinguished
from the noise of the CCD camera. Increased beam intensity addresses this problem; however, if
the beam intensity is too high, the image may become over saturated, such that the CCD pixels in
other regions (such as at the flow field channels) reach their maximum value or higher.
97
Therefore, it is important to ensure that all regions of interest will attenuate the synchrotron light
to roughly the same degree.
As can be seen in Figure 6.2a, the region with the highest level of attenuation, and therefore the
darkest region of the radiograph, is that of the GDL. The Beer-Lambert law states that the
intensity, I, of the attenuated beam can be solved as:
𝐼 = 𝐼0 𝑒− ∑𝜇𝑖𝑋𝑖 ,
where I0 is the incident beam intensity, Xi is the thickness of material, i, in the beam path, and µi
is the attenuation coefficient of that material. With this cell configuration, the GDL and gasket
materials reside in the same plane, and due to the alignment of the cell with the beam, they both
contribute to the attenuation in this region. While attenuation due to the GDL itself is
unavoidable, careful gasket material selection can reduce the attenuation to facilitate a stronger
signal in this primary region of interest. A micro-computed tomography image (Figure 6.6) of
the gasket material employed in this study reveals that the fiberglass fibers strongly attenuate X-
ray light, compared to their PTFE coating, and therefore it is recommended that in future studies,
pure PTFE gaskets are used in lieu of PTFE-coated fiberglass. Once the gasket material is chosen
and the associated beam attenuation can be estimated, the flow field plates can be designed so
that attenuation in the channel regions of the radiograph is comparable.
Figure 6.6 Single cross sectional slice of 3D computed tomograph taken of PTFE-coated fiberglass gasket
material. Brightness values represent X-ray attenuation. The fiberglass bundles in the composite significantly attenuate the signal when compared to the PTFE influence. The scale bar represents 0.25 mm.
6.6.1 Channel alignment
As can be seen from Figure 6.2a, the entire membrane electrode assembly takes on a sinusoidal
shape. This can be explained by the offset between anode and cathode channels. The stress that
98
the landings of the flow fields apply to each GDL translates into a displacement of the membrane
from the vertical center plane of the cell. The authors expect that this would not be the case if the
anode and cathode landings were aligned. It is unknown whether this misalignment promotes or
discourages delamination of the GDL from the catalyst layer. Should delamination be caused by
this configuration, the accumulation of liquid water at the interface may be exaggerated due to
the increased volume of low-capillary pressure pore space in the region. In future studies, both
this configuration and the symmetric flow field configuration will be compared.
6.7 Pre-Monochromator Filters
The 05B1-1 beamline consists of a bending magnet source followed by masks, collimators,
shutters, slits, filters and a double crystal Bragg monochromator at 13 m from the source (see
[120,121] for beamline details). The filtering system consists of sheets of aluminum and copper
at various thicknesses that can be placed between the source and the monochromator. While the
filters reduce the intensity of the entire spectrum of the signal, they have a stronger effect on
low-energy light, as attenuation coefficients, in general, decrease with photon energy level. The
filters can improve image quality by decreasing the intensity of the beam that reaches the silicon
crystals of the monochromator. This, in turn, reduces the associated thermal artifacts from the
monochromator, such as the beam position movement reported in [113]. However, the intensity
of the desired photon energy will also diminish with increased levels of filtering. This may lead
to the need for longer exposure times, which can have a negative impact on the signal-to-noise-
ratio of the CCD camera. In future studies, a variety of filter settings will be employed for
finding the proper balance between monochromator related artifacts and CCD noise levels.
6.8 Conclusions
In this work, a study was conducted of dynamic liquid water accumulation and transport in an
operating PEM fuel cell. The primary purpose of this study was to provide insight into the
technique of visualizing liquid water within the individual fuel cell components using
synchrotron X-ray radiography. The normalized images obtained of the high-aspect ratio fuel
cell designed for the experiment provided valuable insight into the formation and transport of
liquid water in a PEM fuel cell. While the performance of the fuel cell was generally lower than
expected, its operation still provided a means to evaluate liquid water accumulation at distinct
99
through-plane locations. It was observed that liquid water can accumulate near the interface of
the GDL and catalyst layer. This water was observed to saturate some regions of that pore space
to an estimated 18%, before appearing to spread laterally through the bulk of the GDL.
Future designs of this experiment will be modified to utilize thin, 25 μm-thick membranes which
will reduce the effect of humidity driven thickness changes. In addition to this primary
modification, the flow field plates will be designed to attenuate X-ray light to a similar degree to
the combination of GDL and PTFE gasket materials.
100
7 Accounting for Low Frequency Synchrotron X-
ray Beam Position Fluctuations for Dynamic Visualizations
7.1 Abstract
Synchrotron X-ray radiography on beeline 05B1-1 at the Canadian Light Source Inc. was
employed to study dynamic liquid water transport in the porous electrode materials of polymer
electrolyte membrane fuel cells. Dynamic liquid water distributions were quantified for each
radiograph in a sequence, and nonphysical liquid water measurements were obtained. It was
determined that the position of the beam oscillated vertically with an amplitude of ~25 mm at the
sample and a frequency of ~50 mHz. In addition, the mean beam position moved linearly in the
vertical direction at a rate of 0.74 mm s-1. No evidence of horizontal oscillations was detected. In
this work a technique is presented to account for the temporal and spatial dependence of
synchrotron beam intensity, which resulted in a significant reduction in false water thickness.
This work provides valuable insight into the treatment of radiographic time-series for capturing
dynamic processes from synchrotron radiation.
7.2 Introduction
Synchrotron-based X-ray radiography is advantageous for providing nearly parallel
monochromatic beams with high intensities (1011-1015 photons/s/cm2) to obtain radiographs
with high temporal (up to 0.8 s/frame) and spatial (up to 1 μm/pixel) resolutions [30]. It has been
recently employed by a number of researchers to investigate the evolution and distribution of
liquid water in the porous components of polymer electrolyte membrane (PEM) fuel cells
[8,31,61,117,119,122-124]. Readers are referred to a review provided by [125] for a thorough
overview of the various techniques that have been recently employed to visualize PEM fuel cells.
Using synchrotron radiography, the visualization of dynamic liquid water behavior in PEM fuel
cell materials can be achieved with a time-series of radiographs, where the change of liquid
water content between two radiographs can be quantified, assuming that the beam characteristics
remain constant. However, Chattopadhyay [126] reported that synchrotron generated beam
instabilities exist on time-scales ranging from 10-9 to 109 s. For synchrotron based X-ray
101
radiography of liquid water in PEM fuel cell materials, where temporal resolutions are on the
order of 1 s/frame and experiments may last from several minutes to an hour, X-ray beam
instabilities with time scales between 10-1 to 104 s may cause artifacts. Such instabilities may be
the result of mechanical vibrations, ground motion, cooling water temperature fluctuations,
electric power cycles, or atmospheric temperature cycles [126]. Additionally, a diffraction-based
monochromator can be employed to select a narrow bandwidth of X-ray energies for imaging
purposes. The high intensity, polychromatic light bombarding the initial monochromator crystal
can create thermal distortions of the crystal, generating instabilities [127] and affecting the
vertical beam position [128,129]. In this paper, we report on the observed time dependent
fluctuations in the beam position that manifested in obtained radiographs of dynamic liquid
water in PEM fuel cell materials, and we present a technique that reduces the effect of these
fluctuations while enabling the quantification of water content.
7.3 Imaging Setup
The analysis presented in this paper is based on X-ray absorption radiograph sequences collected
from PEM fuel cell experiments at the BioMedical Imaging and Therapy Bending Magnet
(05B1-1) beamline at the Canadian Light Source (CLS) synchrotron. The 05B1-1beamline
consists of a bending magnet source followed by masks, collimators, shutters, slits, filters and a
double crystal Bragg monochromator at 13 m from the source [120,121]. The samples were
placed at a distance of ~ 25 m from the source. Absorption radiographs were obtained with a
Hamamatsu C9300-124 (12bit, 10 Megapixel) CCD camera at 10-50 cm from the sample. A
2010 CLS Research Report [130] listed storage ring beam stability to ~ 1 μm vertically and a few
micrometers horizontally.
The optical equipment and camera settings (exposure and gain) chosen provided an exposure
time of 0.9 s and pixel size of 4.5 μm. The photon energy was set to either 23 keV or 25 keV
depending on the experiment. The optical setup was rated to yield a spatial resolution of 10 μm;
however, positions of sharp features in the radiographs could only be determined with an
accuracy of 20 μm. Therefore, from the radiographs, it was not possible to confirm a spatial
resolution of 10 μm.
102
7.4 Experiments
The experiments enabled the visualization of liquid water in the gas diffusion layer (GDL) of a
PEM fuel cell. The GDL is a planar, porous component of the PEM fuel cell that often becomes
saturated with liquid water during operation, affecting performance.
Two experiments were closely examined in this work to isolate the behavior of the synchrotron
X-ray beam: a) An in situ study of through-plane water distribution in the GDL of a PEM fuel
cell, and b) an ex situ study of through-plane water distribution in a PEM fuel cell GDL. Figure
7.1a schematically shows the in situ experimental setup and Figure 7.1b shows a typical raw
radiograph. In the ex situ study, liquid water was injected into GDLs compressed in a sample
holder. Figure 7.2a schematically shows the ex situ sample holder and Figure 7.2b a typical raw
radiograph. While both studies were oriented such that the plane of the GDL material was
parallel to the X-ray beam, the in situ study was vertically oriented while the ex situ study was
horizontal.
Figure 7.1 Exploded view of fuel cell components and relative beam direction for in situ experiment (a). Example radiograph of in situ experiment (b).
(a) (b)
103
Radiographs were collected at 0.9 s/frame over a period of time to enable the visualization of
dynamic water invasion processes. Imaging was initiated while materials were in a “dry” state,
containing no liquid water, for 2 to 15 minutes. Imaging continued through the “wet” state,
where liquid water entered the GDL. Water content in the GDL was calculated by normalizing
wet-state radiographs to dry-state radiographs using the techniques described in the following
section.
Although Schneider et al. [117] observed that the performance of a fuel cell decreased after
minutes of exposure to synchrotron radiation, it has to be noted that the performance drop was
only observed when the entire active area of a fuel cell was exposed to synchrotron radiation. In
the experiments described in this paper, the entire active area of the fuel cell was not exposed to
synchrotron radiation. However, local effects on the components of the GDL and the PEM fuel
cell that were exposed to synchrotron radiation are, as of yet, unknown.
Figure 7.2 Exploded view of injection apparatus components and relative beam direction for ex situ
experiment (a). Example radiograph of ex situ experiment (b).
(a)
(b)
104
7.5 Beer-Lambert Image Analysis
The Beer-Lambert law relates the attenuated intensity with the incident intensity and the
thickness of a single material in the path of an X-ray beam as [31]:
𝐼 = 𝐼0𝑒−𝜇𝑋, 7.1
where 𝐼 is the attenuated intensity, 𝐼0 is the incident intensity of the beam, 𝜇 is the attenuation
coefficient of the material with respect to the beam energy, and 𝑋 is the material thickness. The
intensity of the beam upon passing through the multi-component sample in the dry state is given
by:
𝐼𝑑𝑟𝑦 = 𝐼0 𝑒− ∑𝜇𝑖𝑋𝑖 , 7.2
where 𝜇𝑖 is the material attenuation coefficient, 𝑋𝑖 is the material thickness traversed by the
beam, and 𝑖 = 1...𝑛, where 𝑛 is the number of materials in the path of the beam. Similarly, the
intensity of the beam that passes through the sample in the wet state at time t is given by:
𝐼𝑤𝑒𝑡,𝑡 = 𝐼0 𝑒−(𝜇𝑤𝑎𝑡𝑒𝑟𝑋𝑤𝑎𝑡𝑒𝑟,𝑡+∑𝜇𝑖𝑋𝑖), 7.3
where 𝜇𝑤𝑎𝑡𝑒𝑟 is the attenuation coefficient of the water and 𝑋𝑤𝑎𝑡𝑒𝑟,𝑡 is the thickness of water
with respect to the beam direction at time 𝑡. From Equations 7.2 and 7.3, the following
expression is obtained for water thickness, 𝑋𝑤𝑎𝑡𝑒𝑟,𝑡 in the GDL with respect to dry-state and wet-
state intensity values:
𝑋𝑤𝑎𝑡𝑒𝑟,𝑡 = −[𝑙𝑜𝑔(𝐼𝑤𝑒𝑡,𝑡 /𝐼𝑑𝑟𝑦) /𝜇𝑤𝑎𝑡𝑒𝑟]. 7.4
In this manner, raw wet-state radiographs can be normalized to raw dry-state radiographs.
Equation 7.4 is employed with the assumption that 𝐼0 remains constant with respect to time,
allowing it to be removed when combining Equations 7.2 and 7.3. When the incident beam
changes intensity or position, this leads to the calculation of a non-physical addition or removal
of liquid water from the system. Likewise, false water signals can result from material movement
during an experiment, as 𝑋𝑖 is also assumed to remain constant for all materials other than water,
since the fuel cell apparatus does not contain moving parts. While material movement must be
105
minimized by experimental design, the following sections discuss the steps taken to account for
variations in the intensity and position of the incident beam.
It should be noted that the image processing steps presented in this chapter have been improved
upon in the work presented in Chapter 8. Detailed, up-to-date image processing steps can be
found in Appendix B.
7.6 Ring Current Decay
Synchrotron light is an emission resulting from the radial acceleration of electrons travelling at
near-light speeds. Synchrotron facilities maintain a high speed beam of electrons in a storage
ring, and the emitted light intensity is a function of several factors, including the number of
electrons contained in the ring. The electron beam within the storage ring at a synchrotron
facility naturally decreases in current over time and must be replenished regularly. At the CLS,
this decrease in ring current and subsequent light intensity degradation can be assumed to be
linear over short time periods, causing a linear decrease in image intensity. To account for this
linear intensity decrease, subsequent images from the first captured image are corrected via the
following equation:
𝐼𝑡,𝑐𝑜𝑟𝑟 = 𝐼𝑡 (𝐶0
𝐶𝑡), 7.5
where 𝐼𝑡,𝑐𝑜𝑟𝑟 represents the corrected intensity, It is the measured intensity, and Ct represents the
ring current at time 𝑡. 𝐶0 represents the ring current at a reference time, 𝑡 = 0.
7.7 Beam Position Movement
When the obtained radiographs from both the ex situ and in situ experiments were originally
analyzed prior to our observation of beam oscillations, we observed unrealistic water thickness
values (Figure 7.3a) when using a reference dry-state radiograph at time t=0. After
normalization, non-negligible water thickness values (±350 μm) were observed in regions that
were physically constrained and had no access to liquid water, such as the solid graphite or
polycarbonate components of the apparatuses. Therefore, it was determined that either the
illumination source or the imagining system was to causing the artifacts. Most originally
106
normalized radiographs in any given sequence were afflicted to some degree by these artifacts;
however, periodically, some normalized radiographs exhibited minimal artifacts (Figure 7.3b).
Such periodic artifacts could be explained with X-ray beam position oscillation.
The incident X-ray beam at the 05B1-1 line has dimensions of 240 mm (horizontal direction) by
7 mm (vertical direction) at the sample location, with the peak intensity, or “hotspot”, near the
center horizontal axis. If the beam position should rise in the vertical direction, for example, the
associated hotspot would also rise, leading to a brightening of the image above the hotspot and a
darkening of the image below the hotspot. From Figure 7.3a, it can be seen that the artifacts were
nearly uniform along the horizontal dimension but were a strong function of vertical position.
Additionally the artifact severity appeared to fluctuate over time.
To demonstrate these fluctuations, average intensity levels from the two positions outlined in
Figure 7.4a were calculated over a period of 3 min and displayed in Figure 7.4b. Regions 1 and 2
are within the graphite block (non-porous component), which was immobile and inaccessible to
liquid water. As can be seen from Figure 7.4a, these regions were located above and below the
vertical position of the hotspot. In the absence of beam position movement, the intensity should
have been constant over time. Instead, it can be seen that the intensity values fluctuated (Figure
7.4b). Region 2 exhibits an inverted intensity pattern compared to Region 1. Specifically, at time
t, when the intensity of Region 1 was increasing, the intensity of Region 2 was decreasing. This
result is consistent with the predicted behavior of vertical beam position movement described
above.
To identify the existence of significant horizontal beam position movement, the intensity data
collected during the horizontally oriented ex situ experiment was examined. As can be seen from
Figure 7.5a, Region 1 and Region 2 were located to the left and right of the horizontal position of
the hotspot. In the absence of beam position movement, the intensity should have been constant
over time. Instead, it can be seen that the intensity values fluctuate (Figure 7.5b). These regions
exhibited the same fluctuations. Specifically, at time t, when the intensity of Region 1 was
increasing, the intensity of Region 2 was also increasing. Analogous to the predicted behavior of
vertical beam position movement, horizontal beam position movement would have created
inverted intensity patterns. Since this is not the case in Figure 7.5, horizontal beam position
movement is considered negligible. It should be noted that for clarity, Region 1 was selected
107
with a shorter radial distance to the hotspot compared to Region 2 in order to create an offset in
the intensity values.
Figure 7.3 Radiographs normalized to the first dry-state image in the sequence demonstrating the presence of
high levels of artifacts appearing at some points in time (a), and little to no artifacts are present at others (b).
Figure 7.4 Raw radiograph (a) with two regions (highlighted) selected on either side of the vertical hotspot position where the mean intensity value is to be calculated. Mean intensity values for regions 1 and 2 over
time (b).
(a) (b)
(a) (b)
108
Figure 7.5 Raw radiograph (a) with two regions (highlighted) selected on either side of the horizontal hotspot position where the mean intensity value is to be calculated. Mean intensity values for regions 1 and 2 over
time (b).
A homogeneous section of the in situ experimental apparatus that was free of water during the
entirety of the visualization was chosen for examining the behavior of the beam hotspot position
(highlighted in Figure 7.6a). The vertical intensity profile was measured (black line in Figure
7.6b), and an 8th order polynomial was fit to the intensity profile of each frame (red line in Figure
7.6b), and the peak of the polynomial was assumed to represent the vertical position of the beam
hotspot. The peak was calculated for each frame over a period of 3 minutes and displayed in
Figure 7.6c. Oscillatory features of the peak position were present with a period of
approximately 20 s and a range of vertical positions spanning 50 μm. Over an extended period of
time (shown in Figure 7.6d) another trend was seen in the vertical hotspot position behavior,
where a linear fit of the data revealed that the average hotspot position moved vertically at a rate
of 0.74 μm/min.
No calculation has been made of the loss of spatial resolution due to beam position movement,
although such a study would indeed be of interest to the community. However, the effects of the
beam position movement can be mitigated using the techniques described in the following
sections, thereby decreasing such a loss in resolution.
(b)
(a)
109
Figure 7.6 Raw radiograph (a) with solid graphite block region (highlighted) used to find the vertical beam
intensity profile. Vertical beam intensity profile (black) with eighth-order polynomial fit overlaid in red (b). Calculated vertical position of the beam hotspot over 3 min (c). Vertical hotspot position versus time (d) for
an extended period (gray), with the linear trend overlaid in black.
7.8 Image Analysis with Beam Position Pairing
Under ideal circumstances (no beam position movement), a single dry-state radiograph could be
used to normalize all subsequent wet-state radiographs. When the beam position is not constant,
one way to address the problem of false water thickness calculations is to normalize wet-state
radiographs to dry-state radiographs obtained at similar beam positions (determined through
hotspot tracking, Figure 7.6). This beam position pairing approach is possible with a sufficiently
large set of dry-state images obtained over a range of beam positions. However, this beam
(a) (b)
(c)
(d)
110
position pairing approach was only possible with experiments that involved a vertically oriented
homogeneous region containing the vertical position of the hotspot, free of water during the
entirety of the visualization. When this region is not present in the radiograph, a more general
method is required to account for beam fluctuations.
A second approach to addressing the problem of false water thickness is to characterize the beam
position from the intensity of the false water thickness artifacts when all wet-state radiographs
were normalized by a single dry-state radiograph. A quantity entitled “false water gradient” was
employed to quantify the artifact intensity. To illustrate what is meant by the false water
gradient, consider again Figure 7.3a, where an overall vertical gradient is seen in the normalized
radiograph, displaying calculated water thickness.
For any subsection of a normalized radiograph, the value for the average vertical gradient of
false water thickness can be calculated. Three such subsections were chosen (outlined in Figure
7.7a), the average value of water thickness versus position was calculated (Figure 7.7b), and the
associated vertical water thickness gradient of each region as a function of time is displayed in
Figure 7.7c. The same 3 minute period analyzed in Figures 7.4b and 6c were analyzed for this
demonstration. The calculated vertical hotspot position data from Figure 7.6c was overlaid onto
Figure 7.7c to illustrate the relationship between the gradient values and the vertical hotspot
position. After all images were normalized to the first image, a net-positive change in beam
position produced as a negative vertical water thickness gradient. To illustrate the proportionality
of the vertical water thickness gradient and the beam position, the gradient values were overlaid
onto the position values in Figure 7.7c. Because there was a negative coefficient of
proportionality between these two properties, the gradient data was displayed on an inverted axis
in Figure 7.7c. Figure 7.7 also demonstrates that the region of interest (ROI) chosen for this
analysis can have been that of a highly heterogeneous portion of the radiograph, and was not
restricted to regions corresponding to homogeneous materials that was described before for the
first beam position pair approach. However, as the presence of water may distort the calculated
gradient in wet-state radiographs, it is necessary to choose a relatively dry portion of the
radiograph as the ROI for gradient calculation. Once each radiograph is characterized in terms of
gradient, dry-state radiograph and wet-state radiographs can be paired.
111
Figure 7.7 Three regions of a normalized radiograph (a) displaying significant false water artifacts. Region 1 is entirely within the solid graphite block. Region 2 samples a heterogeneous region of the radiograph,
including rib, channel and GDL. Region 3 samples a region of the radiograph well below the vertical position of the hotspot. The mean water thickness values for each of the three regions (solid lines), with a linear fit
(dashed lines) at a single point in time (b). Normalized values of the three regions’ gradients over 3 min
compared with the calculated vertical hotspot position for the same image sequence (c).
7.9 Image Processing Routine
The following automated processing routine was employed:
1. Account for the effects of ring current decay on radiograph intensity using Equation 7.5
2. Characterize the beam position of each radiograph by calculating false water thickness
gradients:
a. Select an ROI for gradient calculations, preferably in the absence of liquid water.
b. Normalize this ROI sequence with the same ROI of a single, arbitrary dry-state
radiograph using the Beer-Lambert law.
c. Label each radiograph with the average vertical water thickness gradient
calculated from the associated, normalized ROI.
(a) (c)
(b)
112
3. Pair each wet-state radiograph to the dry-state radiograph with the closest calculated ROI
gradient value from Step 2. Then, apply the Beer-Lambert law to each wet-state
radiograph with the paired dry-state image.
The pairing and normalizing process was automated with a routine written in MATLAB.
To reduce the noise associated with the charge coupled device (CCD) camera, the above
algorithm can be modified to pair the best n dry-state radiographs to a single wet-state
radiograph, where n is the number of dry-state radiographs with similar vertical water thickness
gradients.
Figure 7.8 displays two wet-state radiographs normalized with and without gradient pairing to
demonstrate the effectiveness of this technique. Due to the movement of the average hotspot
position, it is advisable to obtain dry images at various times throughout experiments, since the
range of dry hotspot positions should overlap the range of wet hotspot positions.
The primary difference between the processing routine used for this study and a more traditional
routine is the selection of an appropriate dry-state radiograph for each individual wet-state
radiograph for normalization. Therefore there was no expected loss of spatial or temporal
resolution due to these processing steps. In fact, the resultant spatial resolution was improved
when compared to that of a traditional processing routine, where a single dry-state radiograph
would be employed to normalize the entire sequence. In a traditional processing routine, the
beam positions associated with the majority of the wet-state radiographs would have been poorly
aligned to that of only one dry-state radiograph.
It should be noted that some experimental setups allow the capture of a “bright-field” radiograph,
where the sample is moved away from the field of view. This bright field data is then
incorporated into the normalization routine. However, for the experiments described in this
paper, the apparati were permanently fixed to the sample stage and bright-field data could not be
captured at a time near that of the experiment.
113
Figure 7.8 A comparison between radiographs normalized to the dry-state radiograph at t=0 and the same radiographs normalized to the dry-state radiographs with matching false water thickness gradient values.
The pairs of radiographs at the top and bottom provide two examples of this comparison.
114
7.10 Conclusions
Artifacts resulting from vertical beam position movement were observed upon processing
radiographs obtained through synchrotron X-ray radiography. Radiograph sequences, captured to
identify the dynamic behavior of liquid water in PEMFC materials were normalized, using the
Beer-Lambert law. Upon tracking the vertical beam position, it was determined that small
oscillations of beam position were present with an amplitude of ~ 25 μm and a frequency of ~ 50
mHz. In addition, the mean beam position was observed to move vertically at a speed of 0.74
μm/min. It was determined that small changes in beam position, measuring 25 μm, could result
in a “false water” signal representing up to ±350 μm of water thickness.
The vertical gradient of this false water artifact was employed to characterize the beam position
of each radiograph in the sequence. Then, instead of normalizing all wet-state radiographs
against a single dry-state radiograph, dry-state and wet-state radiographs were paired with
respect to this gradient. This technique was shown to mitigate artifacts associated with beam
position movement without causing any loss of temporal or spatial resolution, but required a
sequence of dry radiographs whose beam positions sufficiently overlap the beam positions of the
wet radiographs.
115
8 Quantifying Percolation Events in PEM Fuel Cell Using Synchrotron Radiography
8.1 Abstract
The distribution of independent water clusters within the gas diffusion layer (GDL) is an
important, yet poorly understood, characteristic of polymer electrolyte membrane fuel cells. A
better understanding of these water clusters would provide ex-situ invasion experiments and two-
phase models with a set of validation criteria that is currently absent from the literature.
Synchrotron based X-ray radiography was employed visualize liquid water emerging from the
polymer electrolyte membrane fuel cell GDL. Droplet formations, entitled “breakthrough” events
originated from either the channel or landing regions of the GDL. The number of breakthrough
events in a given area (breakthrough density) provides insight into the size and number of
independent water clusters evolving within the GDL. Water clusters were found under the flow
field landings more frequently than under the gas channels. Each 1 mm2 of projected GDL area
was found to have 1-2 individual water clusters during most conditions studied, regardless of the
GDL substrate or MPL type. The existence of percolating water clusters under flow field
channels depended on the combination of GDL type and operating conditions employed.
8.2 Introduction
PEM fuel cells employ an electronically conductive porous material, commonly referred to as the
gas diffusion layer (GDL) to allow electrons, heat, and gases to travel to and from
electrochemical reaction sites. These porous materials can become partially flooded due to
condensation creating clusters of liquid water, which can continue to grow as long as the local
environment favors condensation. Using a pore network model of the GDL, Wu et al. [9]
predicted that GDL saturation distributions were highly sensitive to the number of individual
water clusters simultaneously percolating through the GDL from the catalyst layer. While the
footprint of the combined clusters fully covered the sample area, the study showed that lower
overall saturation levels could be predicted when fewer, larger individual water clusters were
assumed.
116
Capillary theory suggests that once a growing water cluster reaches the large pore space within a
flow-field channel (point of breakthrough), there can be no further growth by that water cluster
throughout the hydrophobic pore-space of the GDL [9,15,37,38,48]. Additional condensed water
volume will be capillarily pumped to the channel through the breakthrough pathway. The
implication is that individual water clusters within the GDL cannot have multiple,
simultaneously active points of breakthrough into the gas channels. Simultaneously active
breakthrough locations observed by [7,8,131] must arise from multiple, disconnected water
clusters within the material.
Therefore, a concept entitled “breakthrough density” should be explored. Breakthrough density
describes the number of breakthrough locations per unit of projected surface area of the GDL in
an operating PEM fuel cell. This information is relevant when developing experiments and
models that study the expected distribution of liquid water in the GDL. Examples of such
experiments are [69,72,80,106,107,116,132-134], where syringe pumps or water columns were
employed to provide the controlled injection of liquid water into a dry GDL material. While
these ex-situ experiments provided highly valuable and novel insight into the behavior of liquid
water behavior in the GDL, ex-situ studies are prone to limitations from inlet source and sample
size.
In ex-situ liquid water invasion experiments, GDL materials are invaded from a single liquid
water source. With a single liquid water source, only a single percolating water cluster should
arise under capillary dominated flow. Also, in such ex-situ experiments, GDL sample size can
easily become constrained as a result of experimental requirements. In cases such as microscopy
[80,106,132,133] or X-ray micro-computed tomography (μCT) [116], the optical field of view
associated with the desired magnification restricted the sample size. Whereas, in other studies
[69,72,107,134], larger sample sizes were convenient for material preparation and apparatus
design. As a result of various experimental constraints, studied GDL samples have ranged from
4.9 mm2 [116] to 20 cm2 [134]. Despite this large range of sample sizes, only one breakthrough
location would be expected in these ex-situ experiments over the entire sample when a single
inlet liquid water reservoir was used. In contrast to these ex-situ experiments, high breakthrough
densities have been observed during in-situ studies. Breakthrough densities close to 1 mm-2 were
observed in visualizations provided by Ous and Arcoumanis [131] who employed an air-
breathing fuel cell with 5 mm-wide channels to allow for optical observation of gas channels.
117
Manke et al. [8] demonstrated the ability to visualize in-situ breakthrough events using
synchrotron X-ray absorption imaging. They determined that liquid water clusters underneath
flow field landings periodically gave rise to breakthrough events at the corners of
channel/landing/GDL interfaces. By applying a similar methodology, Lee et al. [7] provided a
comparison between GDL materials with and without microporous layer (MPL) coatings. Higher
breakthrough densities were observed in the cell built with MPL-coated GDLs; however, this
high breakthrough density did not appear to have a negative effect on cell performance. The
MPL was theorized as preventing water clusters near the catalyst layer from lateral spreading and
coalescing, thus allowing for more independent water clusters to percolate, while keeping the
catalyst layer accessible to oxygen diffusion.
During PEM fuel cell operation breakthrough densities are typically greater than 1 mm-2;
therefore, single inlet, ex-situ liquid water invasion experiments with GDL samples larger than 1
mm2 most likely possess unrealistic saturation levels and spatial distributions. Predictive
numerical simulations of GDL invasion that can account for arbitrary numbers and distributions
of independent water clusters are vital for understanding the nature of liquid water accumulation
at the interfaces and within the bulk of the GDL.
In this work the spatial densities of breakthrough events in 11 operational PEM fuel cells were
studied in order to gain insight into the nature of disconnected liquid water clusters within the
GDL. Synchrotron X-ray absorption was used to image liquid water droplets dynamically
emerging from the GDL. Six GDL types were studied, and their breakthrough densities are
presented. The number and sizes of water clusters under the gas channels and under the flow
field landings were estimated.
118
8.3 Method
8.3.1 Fuel cell materials and assembly
The fuel cell architecture was based on standard 25 cm2 assembly produced by Fuel Cell
Technologies4. It had an active area of 5 cm × 5 cm, a triple serpentine flow field, and 1 mm-
wide channels and landings. This setup was modified by machining the anode flow field pattern
possess a 1 mm offset from the cathode flow field pattern, so that liquid water residing in the
cathode could be deciphered between liquid water residing in the anode. Additionally, 11 mm-
diameter through-holes were added to the metallic end plates and current collectors to limit
unnecessary X-ray attenuation at viewing regions (see Figure 8.1). A detailed description of the
cell architecture can be found in [7].
Figure 8.1 Images of modified 25 cm2 Fuel Cell Technologies PEM fuel cell. Note: Although three viewing holes are present, only the lowermost hole was employed in this study.
All fuel cells assembled for this study were built with catalyst coated Nafion 115 membranes
with platinum loadings of 0.3 mg cm−2 for each electrode (Ion Power, New Castle, USA5).
Silicon gaskets for sealing the MEA were 254 µm-thick and 203 µm-thick, selected to match the
thickness of the GDL used in each cell-build.
4 http://www.fuelcelltechnologies.com/
5 http://www.ion-power.com/
119
The assembly pressure was calibrated for each GDL with Fujifilm Prescale pressure film placed
between the flow fields and the GDL/gasketing. During calibration, the bolt torque was
incrementally increased, and the cell was disassembled to facilitate the removal and analysis of
the film in the FPD-8010E Fujifilm Pressure Distribution Mapping System (Tekscan, USA). A
spatial distribution of applied assembly pressure was measured at each torque level. The mean
landing pressure was assumed to be twice the mean pressure for the active area, as landing
regions composed 50% of the total area. Based on repeated trials, this technique provided a
maximum error of 0.2 MPa. An example dataset is displayed in Figure 8.2. For all experiments,
1 MPa ± 0.2 MPa was applied to the GDL/landing interface.
Figure 8.2 Calculated pressures under flow-field landings with respect to bolt torque for Toray TGP-H 090 10 wt% PTFE.
8.3.2 GDL materials
Six GDL types were employed for this investigation. Two GDL types were commercially
available: SGL Sigracet 25BC and Freudenberg H2315 I3 C1. Four GDL types were supplied by
an industrial collaborator, who applied proprietary PTFE and MPL treatments to two
commercially available substrates: Toray TGP-H 090 and Freudenberg H2315. The PTFE
treatment procedure of the Toray materials was slightly altered to allow the collaborator to
compare two application methods, these are labelled as PTFE1 and PTFE2. It should be noted
120
that the proprietary MPLs placed on the Toray and the Freudenberg were distinct from each
other.
From the six GDL types, eleven fuel cells (a-k) were built, and some were imaged multiple times
and at multiple temperatures, as shown on Table 8.1.
Table 8.1 GDLs chosen for water visualization study. Each letter represents a single cell
build, where the subscript denotes the number of data sets collected with that cell, at the specified temperature. Cell Temp
Property Name Code 60 ºC 75 ºC
Toray TGP-H 090 10 wt % PTFE1 with no MPL TP1 a1 b1
Toray TGP-H 090 10 wt % PTFE1 with proprietary MPL TP1M c1 d1
Toray TGP-H 090 10 wt % PTFE2 with proprietary MPL TP2M e1 f1
SGL Sigracet 25 BC SPM g1 h1 i2 g1 h1 i2
Freudenberg H2315 I3 C1 FPM1 j1 j1
Freudenberg H2315 with proprietary MPL FPM2 k1 k1
8.3.3 Fuel cell control sequence
Fuel cell operation was controlled with a Scribner 850e fuel cell test station (Scribner Associates
Inc., Southern Pines NC6).
The cell temperature was held constant by resistive heating rods embedded within the aluminum
end plates. Depending on the experiment, the cell temperature was maintained at either 60 °C or
75 °C (measured within the cathode end plate).
A single scripted routine of current density set points and reactant flow rates was developed to
initiate saturation conditions while maintaining potentials above 0.1 V. All studies were
performed after the reactants (hydrogen and air) were brought to 65% relative humidity at the
operating temperature and after the cell had been drying at open circuit voltage for 20 minutes
under high hydrogen and air flow rates (~1 lpm).
6 http://www.scribner.com/
121
For the first 15 minutes of the recorded experiment, the current density was increased from 0.0 A
cm-2 to 0.6 A cm-2 in 5 minutes steps of 0.2 A cm-2. During these steps, flow rates of hydrogen
and air were maintained at 0.7 lpm and 1.2 lpm, respectively. These high flow rates were used in
order to retain dry conditions during the current steps. After 5 minutes at 0.6 A cm-2 the air flow
rate was decreased to maintain a stoichiometric ratio (λC) of 1.4 for 20 minutes, and then dropped
even further to maintain a stoichiometric ratio of 1.1 for 15 minutes. Following this step, the
hydrogen flow rate was decreased to reach an anode stoichiometry (λA) of 2.8, while the cathode
stoichiometry increased to 1.4. These conditions were chosen based on previously successful
observations of dynamic liquid water accumulation and transport [7].
A detailed schematic of the experiment is provided in Appendix A.
8.3.4 Beamline controls
All experiments described in this work were performed at the Biomedical Imaging and Therapy
Beamline (05B1-1) of the Canadian Light Source Inc. (CLS) (Saskatoon, Canada). The CLS is a
third generation 2.9 GeV synchrotron facility. The 05B1-1beamline consists of a bending magnet
source followed by masks, collimators, shutters, slits, filters and a double crystal Bragg
monochromator located 13 m from the source [120,121]. The samples were placed an additional
distance of ~ 12 m from the monochromator. Absorption radiographs were obtained with a
Hamamatsu C9300-124 (12 bit, 10 Megapixel) CCD camera combined with an AA40 imaging
unit. A10 μm-thick Gd2O2S:Tb scintillator was used. The scintillator of the imaging unit was
positioned 10 cm from the sample. This distance was minimized to reduce phase contrast related
artifacts and to improve image sharpness. This setup provided a spatial resolution of 10 µm.
Beam filter settings in this experiment were set to maximize the flux of monochromatic X-rays.
From the tested energy range of 16 keV to 35 keV, it was found that the most vivid normalized
image of water in the fuel cell was achieved with an energy level of 18 keV. Pre-monochromator
filtering was minimized (0.2 mm aluminum) to reach the most desirable image of liquid water in
the fuel cell.
122
8.3.5 Data collection
8.3.5.1 Voltage data
The primary performance output of the fuel cell test station was the cell voltage, measured
continuously throughout the experiment and recorded every second. An example voltage
response to the current and flow rate set points is provided in Figure 8.3.
Figure 8.3 Voltage response to current and flow rate set-points for an example cell build (SGL Sigracet 25BC,
60 ºC). Δ’s denote points used for time-synchronization with the image collection process.
8.3.5.2 Image data
The camera and beam settings allowed for images to be acquired at a maximum rate of 1 fps;
however, this temporal resolution was not necessary for observing breakthrough events. To
decrease file size an acquisition rate of 0.3 fps was achieved by applying frame integration.
The imaging sequence was initiated, followed by the test station script. To synchronize the image
data with the test station data, frame numbers were recorded at distinct points during the
experiment. These points are denoted with a Δ on the horizontal axis of Figure 8.3.
Image normalization was performed to identify and quantify the liquid water distribution. Figure
8.4 illustrates the possible configurations of the imaging setup. With the X-ray shutters, closed
(Configuration I), a dark field image can be taken. Configuration II is often used in radiography
for flat field corrections; however in this experiment, Configuration III was employed to
123
additionally account for the attenuation due to static fuel cell components. Configuration IV
represents an operational fuel cell, generating water.
Figure 8.4 Illustration of possible configurations of imaging setup. Sequences of images were taken in Configurations I, III, and IV for the processing steps highlighted in Section 2.6.
8.3.6 Image normalization
X-ray light is attenuated by any material in its path, including air. Due to the chemical
composition and density of a material, the degree to which the material attenuates can vary. A
relationship has been developed to predict the intensity of attenuated light, based on the work of
mathematicians August Beer and Johann Heinrich Lambert through the Beer-Lambert law [31].
The Beer-Lambert law relates the attenuated intensity of any light source with the thickness of a
single material in the path of the light beam as [31]:
𝐼 = 𝐼0𝑒−𝜇𝜒, 8.1
Incident light
No light
Incident light
Incident light
Attenuated light
Detector
I. For dark field correction
III. Alternative to II
II. For typical flat field
IV. Dynamic
124
where 𝐼 is the attenuated intensity, 𝐼0 is the incident intensity of the beam, 𝜇 is the mass
attenuation coefficient of the material with respect to the wavelength of the light, and 𝜒 is the
material thickness. Because attenuation coefficients vary with light wavelength, it is convenient
for quantification purposes to employ monochromatic light.
Several factors had to be accounted for before the quantitative liquid water distribution was
obtained with the Beer-Lambert law. First, all CCD cameras suffer from some amount of “dark
current,” which results in a small, relatively steady signal measured in each pixel, which
becomes added to the signal produced by X-ray intensities. Second, synchrotron illumination
sources decrease with intensity over time due to the continuous escape of electrons from their
storage rings. Third, the illumination source (the X-ray beam) was observed to slowly fluctuate
in vertical position by up to 20 µm [113]. And finally, there is a distribution of signal intensity
across the raw image which masks the attenuation signal of the water. This is due to a
combination of the beam intensity distribution, local attenuation from static fuel cell
components, and the distribution of scintillator/detector sensitivity levels across the image.
A detailed description of these normalization steps can be found in Appendix B.
8.3.7 Surface and edge breakthrough quantification
Breakthrough events were classified into two types: “surface breakthrough” and “edge
breakthrough.” Surface breakthrough events are described as water emerging in the middle of the
channel forming circular droplets that are most likely the result of liquid water condensing in the
channel region of the GDL or CL. Edge breakthrough events are described as semi-circular water
droplets emerging into the channel from the triple line formed by the channel, landing, and GDL.
Edge breakthrough events could be either the result of water condensing onto the base of the
landing, within the GDL, or percolating from the GDL/CL interface. An illustration describing
the breakthrough types is provided in Figure 8.5.
The local conditions and current densities within a PEM fuel cell can vary greatly from inlet to
outlet [135]. In the following study, only 4% of the total active area was visualized, and although
the average current density was constant, the local current density was expected to fluctuate with
humidity levels and local flooding.
125
Figure 8.5 An illustration of a fuel cell cross section (a) with droplets of water forming on the surface of the GDL and at the edge of the gas channels, and a corresponding illustration of visualized water (b) with “edge” and “surface” breakthrough locations annotated. Note that the anode flow field channels are offset from the
cathode.
8.4 Results
8.4.1 Visualized liquid water
Each of the 18 data sets listed in Table 8.1 corresponded to a ~1000 frame sequence of
normalized images that displayed the liquid water distributions throughout the testing procedure.
Figure 8.6 displays six water distributions of an example data set, where both surface and edge
breakthrough events were present. The greyscale values represent a range of measured water
thicknesses from -0.2 mm (black) to 0.6 mm (white). Negative values are shown to demonstrate
artifacts from the monochromator, scintillator, or cell movement.
In the data set associated with Figure 8.6, liquid water was barely visible until the final stage
(λA=2.8, λC=1.4) of the experiment, where the anode flow rate decreased. Within 90 seconds of
this operating condition (by t = 2790), new breakthrough events were visible in the centers of the
2nd and 3rd cathode channels. As can be seen in Figure 8.6, a typical observation was that
126
breakthrough events were not observed in the anode gas channels (offset from the cathode gas
channels).
Figure 8.6 Six frames from the final stage (λA=2.8, λC=1.4) of an example experiment (GDL: Toray TGP-H 090 with 10 wt % PTFE1 and proprietary MPL. Cell temperature: 75 ºC). Greyscale values correspond to
thickness levels of liquid water, scaled between -0.2 mm and 0.6 mm. The positions of three cathode channels
are highlighted on the left. For scale, each channel width is 1 mm.
8.4.2 Breakthrough density
The breakthrough densities were calculated over a 40 mm2 active area, representing 20 mm2
channel and 20 mm2 landing. The 1000+ image sequence of each experiment was carefully
inspected, and individual breakthrough locations were marked and categorized as either
“surface” or “edge”. These results are shown in Table 8.2.
1
2
3
1
2
3
t = 2700 s t = 2790 s t = 2880 s
t = 3150 st = 3060 st = 2970 s
127
Table 8.2 Breakthrough (BT) density data for each data set. Cells are shaded according to their relative breakthrough densities.
Cell Build
GDL Code
Temp (C)
Surface BT
Density (mm-2)
Edge BT
Density (mm-2)
Mean BT
Density (mm-2)
BT Type Fast Anode
Flow (λa = 6.6)
BT Type Slow Anode
Flow (λa = 2.8)
a TP 75 0.8 1.4 1.1 Edge Edge + Surface
b a TP 75 0.4 2.8 1.6 Edge Edge + Surface
c TP1M 75 7.2 2.6 4.9 Edge + Surface Edge + Surface
d a TP1M 75 3.2 3.6 3.4 Edge Edge + Surface
e TP2M 75 2.4 2.2 2.3 Edge Edge + Surface
f a TP2M 75 0.2 2.0 1.1 Edge Edge + Surface
g SPM 60 1.8 3.4 2.6 Edge Edge + Surface
g SPM 75 0.0 4.0 2.0 Edge Edge
h a SPM* 60 3.2 2.8 3.0 Edge + Surface Edge + Surface
h a SPM* 75 2.4 3.2 2.8 Edge Edge + Surface
i SPM 60 2.6 3.6 3.1 Edge + Surface Surface
i SPM 75 0.0 2.6 1.3 Edge Edge
i SPM 60 2.6 2.4 2.5 Edge + Surface Edge + Surface
i SPM 75 0.0 3.4 1.7 Edge Edge
j FPM1 60 1.6 1.8 1.7 Edge + Surface Surface
j FPM1 75 0.0 2.2 1.1 Edge Edge
k FPM2 60 0.0 3.4 1.7 Edge ---
k FPM2 75 0.0 3.0 1.5 Edge ---
a cell was built in a secondary, nearly equivalent, cell assembly
8.5 Discussion
8.5.1 Water cluster size limits
The number and sizes of individual water clusters within the GDL is valuable information for
researchers attempting to recreate realistic GDL saturations, either in simulations or with ex-situ
experiments. Although the image resolution was not sufficient to confidently identify the
outlines of individual water clusters within the cathode GDL, the breakthrough density values
reported in Table 8.2 can be combined with basic principles of capillary behavior to provide
limits to the minimum number of water clusters and the maximum size of the average water
cluster. Following from the description of capillary behavior in the Introduction, the following
assumptions can be made:
128
1) Any n simultaneously active breakthrough locations correspond to n isolated water
clusters.
2) Any n simultaneously active water clusters in a given area, A, should not, on average,
have individual projected areas larger than A/n, otherwise these clusters would have
likely coalesced during the percolation process.
3) A single water cluster with an active breakthrough location must be supplied by at least
one condensation source of liquid water.
4) There are at least as many active condensation “sources” in the system as there are
simultaneously active breakthrough locations.
5) Low breakthrough density could either indicate few active condensation sites, or large,
connected water clusters.
From the sequence of assumptions above, the following conclusions have been made, based on
the results shown in Table 8.2.
On average, there should be at least one isolated water cluster per square millimeter of
GDL.
In one extreme case, an average of 7.2 water clusters per millimeter were observed to
simultaneously percolate from underneath the flow field gas channels.
Clusters should not have an average footprint greater than 1mm2 and are sometimes at
least as small as 0.14 mm2.
Most observed breakthroughs appeared on the edge of the channel, indicating that most
individual water clusters resided under the landings. This can either indicate higher
condensation rates under the landings, or that there was less tendency for clusters to
coalesce under the compressed regions of the GDL.
When studying effects of GDL saturation on its effective transport properties, simple ex-situ
saturation methods are prone to misrepresent the distribution of water in the GDL due to the
challenges of producing multiple, isolated water clusters in relatively large GDL samples.
In single inlet ex-situ liquid water invasion experiments, breakthrough positions have been
observed to, on occasion, migrate over time [106,107]. Therefore, the values reported in Table
8.2 may include some double counting of single water clusters, and may not perfectly capture the
129
number of “simultaneously active” breakthrough locations per unit area. However, there may
have been breakthrough locations not captured in this analysis, if the droplets did not grow large
enough to be observed over the noise and resolution limits of the imaging setup.
8.5.2 Temperature effects
Fuel cells made with the SGL and Freudenberg materials were imaged at both 60 ºC and 75 ºC.
With one exception, surface breakthrough was not visualized during any experiments at 75 ºC.
This indicates that condensation under the channels was influenced by operating conditions. It is
interesting to note, that all fuel cells made with Toray materials were imaged at 75 ºC, and
surface breakthrough events were consistently observed in these fuel cells. In fact the highest
breakthrough density observed, 7.2 mm-2, was during a 75 ºC experiment (cell c).
Temperature did not seem to have a noticeable effect on edge breakthrough densities, and
therefore no conclusions can be made in this work about water cluster size in relation to
operating temperature.
8.5.3 Anode flow rate
As the reactant streams were only 65% humidified, faster anode flow rates allowed the anode to
more aggressively contribute to product water-removal through the back-diffusion across the
membrane.
With only one exception, surface breakthrough in cells made with Toray materials only appeared
during slow anode flow rates, while edge breakthrough events continued even with high anode
flow rates. This indicates that water clusters under landings were less affected by back diffusion
than those under gas channels. This might indicate that condensation in Toray GDLs under flow
field channels occurred in proximity to the membrane where back diffusion could play a role in
water removal. This trend was not observed in the other material types. This indicates that the
GDL type had a strong influence in the role of back diffusion in the water balance of the fuel
cell.
130
8.6 Conclusions
In this study, synchrotron based X-ray radiography was employed to visualize and quantify
liquid water percolation events, entitled “breakthrough events”, within a 40 mm2 viewing area of
a 25 cm2 PEM fuel cell. This data allows approximations to be made of water cluster sizes and
distributions within the GDL.
Breakthroughs were classified as either “surface” or “edge” depending on whether they emerged
from the GDL surface region or the edge of the cathode flow field channels, respectively.
Surface breakthroughs were assumed to result from water clusters located under the flow field
gas channels. Edge breakthroughs were assumed to result from water clusters located under the
flow field landings. With this assumption, it was determined that condensation under the
landings can be expected in practically all of the tested operating conditions and GDL types.
Condensation under the channels was also common, but seemed to be less frequent with the
Freudenberg GDLs studied and less frequent at high anode flow rates.
Because high breakthrough densities required tightly packed, independent water clusters within
the GDL, the observation of high breakthrough densities fundamentally limited water cluster
sizes. Water clusters within the GDL rarely consist of footprints larger than a square millimeter,
with a minimum size corresponding to 7 or more water clusters present in a single square
millimeter. These results should be taken into account when developing ex-situ GDL saturation
studies, as well as in two-phase, pore-scale models.
131
9 Conclusions and Recommendations
In this thesis, pore network modeling was proposed as an ideal modeling technique with which to
investigate the relationship between morphology and liquid water saturation in PEM fuel cell
GDLs. It was proposed that topologically representative pore networks extracted from
stochastically modeled GDLs would provide the best network architecture for such modeling.
Finally, it was proposed that synchrotron based in situ visualizations of dynamic liquid water
behavior would produce the best means of validating the inlet assumptions of pore network
modeling invasion algorithms. As a founding member of the research group, my research
contributions consist of developing the sophisticated tools that will be used in such a modeling
endeavor. These tools include a comprehensive 3D stochastic model of the GDL, as well as the
development of the fuel cell architectures, experimental routines, and post processing routines
necessary to visualize dynamic liquid water behavior at the Canadian Light Source, Inc.
synchrotron.
9.1 Conclusions and Contributions
Pore network modeling was identified in Chapter 2 as an ideal modeling tool for capturing the
capillary force dominated behavior of liquid water cluster percolations in the GDL. Chapter 3
provided a 2D pore network modeling study of the effects of the characteristic non-uniform
through-plane porosity distributions identified in our earlier work [54]. It was found that:
Through-plane porosity distributions can be recreated in stochastic models of the GDL.
The characteristic peaks and valleys present in the porosity distributions of thick carbon
fiber papers promote highly saturated regions at the local maxima of the porosity
distribution. This was due to the lateral invasion encouraged by the capillary barriers of
neighboring local minima.
Porosity distribution effects can be differentiated from GDL thickness effects by using a
consistent computational domain aspect ratio for all material types.
The inlet surface porosity has a drastic effect on GDL saturation, where a 58-76%
reduction in saturation results from a positive porosity gradient (in contrast to a
conventional negative gradient).
132
In Chapter 4, a number of GDL geometrical fiber and MPL properties were identified and
characterized for informing representative 3D stochastic models. It was found that:
Carbon fiber diameters of the GDL substrate vary with manufacturer, yet tight property
distributions around their mean values are observed.
Fiber pitch in Toray TGP-H 090 GDL is minimal (2.44°).
36% of fibers in Toray TGP-H 090 belong to bundles of co-aligned fibers.
Volume fractions of constituent GDL elements of known density were estimated from a
comparison of areal weight values with and without associated treatments.
The cracks formed in the MPLs of two GDL types were characterized in terms of
frequency and diameter.
The 3D stochastic modeling algorithm presented in Chapter 5 was the first of its kind to
incorporate experimentally observed through-plane porosity distributions, fiber diameters, fiber
pitch distributions, and fiber co-alignment. A necessary emphasis was given to generating the
correct number and volume of fibers. Methods for characterizing the heterogeneity and pore size
distributions of the modeled materials were presented. A parametric study of fiber diameter and
volumetric binder fraction was conducted. It was found that:
3D stochastic models of the GDL could be made to match experimentally observed
through-plane porosity distributions.
Material heterogeneity and pore size distributions were shown to be useful methods when
characterizing the pore space of the material, since each parametric combination
generated distinct, consistent profiles corresponding to each method.
Both fiber diameter and binder fraction were demonstrated to have strong effects on both
material heterogeneity and pore size distributions.
Similar effects on the pore space can be achieved by either increasing the fiber diameter
or by increasing the binder fraction, since nearly indistinguishable materials can be
generated with complementary adjustments of these two parameters.
In Chapter 6 and 7, the methodology for capturing and processing synchrotron radiography
images of dynamic, in situ liquid water behavior was presented. Some of these techniques were
133
specific to the Canadian Light Source, Inc. synchrotron, in Saskatoon SK, at which our group
conducted the first such PEM fuel cell experiments. It was found that:
The primary sources of data artifacts are: membrane swelling, un-even X-ray attenuation
by the various fuel cell components, and vertical beam position movement.
To minimize membrane swelling, thin, 25 µm-thick membranes should be used.
For in-plane oriented X-ray studies, PTFE gaskets without fiberglass reinforcement were
proposed to minimize unnecessary attenuation, while flow-field plate dimensions can be
adjusted to create similar attenuation levels in the GDL and the gas channels.
The vertical position of the X-ray beam was tracked and determined to oscillate
irregularly with amplitudes of ~ 25 µm and frequencies of ~ 50 mHz.
Vertical beam position movement was identified as creating gradient artifacts on
normalized images. The intensity of these gradient artifacts was found to directly
correlate with the vertical beam position and could therefore be used to pair appropriate
wet and dry images taken at similar beam positions.
Preliminary observations of liquid water from in-plane imaging demonstrated liquid
water accumulating near the interface of the GDL and catalyst layer. This water was
determined to represent an average local saturation value of 18%.
In Chapter 8, the size and distribution of liquid water clusters in the GDL was investigated for
the first time. Using through-plane oriented synchrotron X-ray radiography, regions of 40 mm2
of active area were imaged. Percolation events, labeled “breakthroughs” were categorized and
counted for a range of GDL types and operating conditions. It was found that:
Water clusters percolated from under the landings in nearly all of the tested operating
conditions and GDL types.
Water clusters only percolated from under the channels in certain combinations of GDL
types and operating conditions. The studied Freudenberg GDLs were less prone to
exhibiting percolation from under the channels.
It was observed that applying a high anode flow rate could frequently prevent percolation
from under the channels, indicating that back diffusion was playing a major role in the
removal of water condensing under the channels.
134
Independent water clusters were determined to be tightly distributed in regions promoting
condensation, as breakthrough densities were observed to be consistently greater than one
breakthrough per mm2 and sometimes as high as 7 per mm2.
It was concluded that ex situ invasion experiments as well as pore network models should
attempt to mimic the observations of tightly packed, independent water clusters in order
to generate realistic saturation distributions.
In summary, this thesis presents a new state-of-the-art in terms of 3D stochastic modeling of
paper GDLs, from which topologically representative pore network models can be generated.
Additionally, the Canadian Light Source, Inc. synchrotron was demonstrated to be capable of
generating high-resolution imaging of dynamic liquid water transport in the GDL. The data
collected from the visualization studies can be used to validate the inlet assumptions of future
pore network modeling simulations.
9.2 Future Work
To continue on this stream of research, it is recommended that:
Additional materials are analyzed in terms of fiber pitch and co-alignment, as high
resolution tomographs of those materials become available.
Mercury intrusion porosimetry data is collected for comparison to the simulations in
Chapter 5.
A model of the MPL that incorporates appropriate volumes and crack distributions is
developed and added to the current stochastic model developed in Chapter 5.
A pore network extraction algorithm similar to the one demonstrated in [21] is applied
and validated. This algorithm must capture pore and throat size information for capillary
simulations, pore connectivity, and the conduit (pore + throat + pore) geometrical
information relevant to single-phase transport modeling.
A pore network based investigation is conducted that isolates the possible inlet conditions
producing breakthrough densities similar to those observed in Chapter 8, while producing
through-plane liquid water distributions similar to those observed in Chapter 6. These
inlet conditions will act as the new standard for pore network based two phase
simulations.
135
References
[1] Barbir F. PEM fuel cells: theory and practice. PEM Fuel Cells: Theory and Practice. Boston: Elsevier
Academic Press; 2005, p. 399-426.
[2] Barbir F. PEM fuel cells: theory and practice. PEM Fuel Cells: Theory and Practice. Boston: Elsevier
Academic Press; 2005, p. 337-397.
[3] Srinivasan S, Velev OA, Parthasarathy A, Manko DJ, Appleby AJ. High-Energy Efficiency and High-
Power Density Proton-Exchange Membrane Fuel-Cells - Electrode-Kinetics and Mass-Transport. J.Power
Sources 1991; 36(3):299-320.
[4] Burheim OS, Su H, Pasupathi S, Pharoah JG, Pollet B. Thermal conductivity and temperature profiles
of the micro porous layers used for the polymer electrolyte membrane fuel cell. Int.J.Hydrogen Energy
2013; 38:8437-47.
[5] Pasaogullari U, Wang C. Two-phase transport and the role of micro-porous layer in polymer
electrolyte fuel cells. Electrochim.Acta 2004; 49(25):4359-69.
[6] Mathias M, Roth J, Fleming J, Lehnert WL. Diffusion media materials and characterisation. In:
Vielstich W, Lamm A, Gasteiger HA, editors. Handbook of fuel cells: fundamentals, technology, and
applications. Chichester, England; Hoboken, N.J.: Wiley; 2003, p. 1-21.
[7] Lee J, Hinebaugh J, Bazylak A. Synchrotron X-ray radiographic investigations of liquid water
transport behavior in a PEMFC with MPL-coated GDLs. J.Power Sources 2013;227(0):123-30.
[8] Manke I, Hartnig C, Gruenerbel M, Lehnert W, Kardjilov N, Haibel A, et al. Investigation of water
evolution and transport in fuel cells with high resolution synchrotron x-ray radiography. Appl.Phys.Lett.
2007; 90(17):174105.
[9] Wu R, Zhu X, Liao QA, Wang H, Ding YD, Li J, et al. A pore network study on water distribution in
bi-layer gas diffusion media: Effects of inlet boundary condition and micro-porous layer properties. Int.J
Hydrogen Energy 2010; 35(17):9134-43.
[10] Lee K, Nam JH, Kim C. Steady saturation distribution in hydrophobic gas-diffusion layers of
polymer electrolyte membrane fuel cells: A pore-network study. J.Power Sources 2010; 195(1):130-41.
[11] Lee KJ, Nam JH, Kim CJ. Pore-network analysis of two-phase water transport in gas diffusion layers
of polymer electrolyte membrane fuel cells. Electrochim.Acta 2009; 54(4):1166-76.
[12] Gostick JT, Ioannidis MA, Fowler MW, Pritzker MD. Pore network modeling of fibrous gas
diffusion layers for polymer electrolyte membrane fuel cells. J.Power Sources 2007; 173(1):277-90.
[13] Gostick JT, Ioannidis MA, Pritzker MD, Fowler MW. Impact of Liquid Water on Reactant Mass
Transfer in PEM Fuel Cell Electrodes. J.Electrochem.Soc. 2010; 157(4):B563-71.
[14] Rebai M, Prat M. Scale effect and two-phase flow in a thin hydrophobic porous layer. Application to
water transport in gas diffusion layers of proton exchange membrane fuel cells. J.Power Sources 2009;
192(2):534-43.
[15] Sinha PK, Wang C. Pore-network modeling of liquid water transport in gas diffusion layer of a
polymer electrolyte fuel cell. Electrochim.Acta 2007; 52:7936-45.
[16] Sinha PK, Wang C. Liquid water transport in a mixed-wet gas diffusion layer of a polymer
electrolyte fuel cell. Chemical Engineering Science 2008; 63(4):1081-91.
[17] Wu R, Zhu X, Liao Q, Wang H, Ding YD, Li J, et al. A pore network study on the role of micro-porous layer in control of liquid water distribution in gas diffusion layer. Int J Hydrogen Energy 2010;
35(14):7588-93.
136
[18] Wu R, Zhu X, Liao QA, Wang H, Ding YD, Li J, et al. Determination of oxygen effective diffusivity
in porous gas diffusion layer using a three-dimensional pore network model. Electrochim.Acta 2010;
55(24):7394-403.
[19] Luo G, Ji Y, Wang C, Sinha PK. Modeling liquid water transport in gas diffusion layers by
topologically equivalent pore network. Electrochim.Acta 2010; 55(19):5332-41.
[20] Büchi FN, Flückiger R, Tehlar D, Marone F, Stampanoni M. Determination of liquid water
distribution in porous transport layers. ECS Trans. 2008; 16(2):587-92.
[21] Dong H, Blunt MJ. Pore-network extraction from micro-computerized-tomography images. Physical
Review E 2009; 80(3).
[22] Didari S, Asadi A, Wang Y, Harris TAL. Modeling of composite fibrous porous diffusion media.
Int.J.Hydrogen Energy 2014; 39(17):9375-86.
[23] Nabovati A, Llewellin EW, Sousa ACM. A general model for the permeability of fibrous porous
media based on fluid flow simulations using the lattice Boltzmann method. Composites Part A: Applied
Science and Manufacturing 2009; 40(6-7):860.
[24] Nabovati A, Hinebaugh J, Bazylak A, Amon CH. Effect of porosity heterogeneity on the
permeability and tortuosity of gas diffusion layers in polymer electrolyte membrane fuel cells. J.Power
Sources 2014; 248:83-90.
[25] Schulz VP, Becker J, Wiegmann A, Mukherjee PP, Wang CY. Modeling of two-phase behavior in
the gas diffusion medium of PEFCs via full morphology approach. J Electrochem Soc 2007;
154(4):B419-26.
[26] Thiedmann R, Fleischer F, Hartnig C, Lehnert W, Schmidt V. Stochastic 3D modeling of the GDL
structure in PEMFCs based on thin section detection. J Electrochem Soc 2008; 155(4):B391-9.
[27] Yablecki J, Nabovati A, Bazylak A. Modeling the Effective Thermal Conductivity of an Anisotropic
Gas Diffusion Layer in a Polymer Electrolyte Membrane Fuel Cell. J.Electrochem.Soc. 2012;
159(6):B647-53.
[28] Hinebaugh J, Bazylak A, Mukherjee PP. Multi-scale modeling of two-phase transport in polymer
electrolyte membrane fuel cells. In: Hartnig C, Roth C, editors. Polymer electrolyte membrane and direct
methanol fuel cell technology. Cambridge, UK: Woodhead Publishing; 2012, p. 254.
[29] Hartnig C, Manke I, Kuhn R, Kardjilov N, Banhart J, Lehnert W. Cross-sectional insight in the water
evolution and transport in polymer electrolyte fuel cells. Appl.Phys.Lett. 2008; 92(13):134106.
[30] Hartnig C, Manke I. Structural Properties: Neutron and Synchrotron imaging for in-situ water
visualization. In: Garche J, editor. Encyclopedia of Electrochemical Power Sources. Amsterdam:
Elsevier; 2009, p. 738-757.
[31] Lee S, Kim S, Park G, Kim C. Quantitative visualization of temporal water evolution in an operating
polymer electrolyte fuel cell. Int J Hydrogen Energy 2010; 35(19):10457-63.
[32] Litster S, Djilali N. Two-phase transport in porous gas diffusion electrodes. In: Suden B, Faghri M,
editors. Transport Phenomena in Fuel Cells. Southampton: WIT Press; 2005, p. 175-213.
[33] Fishman Z, Bazylak A. Heterogeneous Through-Plane Distributions of Tortuosity, Effective Diffusivity, and Permeability for PEMFC GDLs. J.Electrochem.Soc. 2011; 158(2):B247-52.
[34] Markicevic B, Bazylak A, Djilali N. Determination of transport parameters for multiphase flow in porous gas diffusion electrodes using a capillary network model. J.Power Sources 2007; 171:706-17.
[35] Bazylak A, Berejnov V, Markicevic B, Sinton D, Djilali N. Numerical and microfluidic pore
networks: Towards designs for directed water transport in GDLs. Electrochim.Acta 2008; 53(26):7630-7.
137
[36] Ceballos L, Prat M. Invasion percolation with inlet multiple injections and the water management
problem in proton exchange membrane fuel cells. J.Power Sources 2010; 195(3):825-8.
[37] Hinebaugh J, Bazylak A. Condensation in PEM Fuel Cell Gas Diffusion Layers: A Pore Network
Modeling Approach. J.Electrochem.Soc. 2010; 157(10):B1382-90.
[38] Hinebaugh J, Fishman Z, Bazylak A. Unstructured pore network modeling with heterogeneous
PEMFC GDL porosity distributions. J.Electrochem.Soc. 2010; 157(11):B1651-7.
[39] Chapuis O, Prat M, Quintard M, Chane-Kane E, Guillot O, Mayer N. Two-phase flow and
evaporation in model fibrous media - Application to the gas diffusion layer of PEM fuel cells. J.Power
Sources 2008; 178(1):258-68.
[40] Medici EF, Allen JS. The Effects of Morphological and Wetting Properties of Porous Transport
Layers on Water Movement in PEM Fuel Cells. J.Electrochem.Soc. 2010; 157(10):B1505-14.
[41] Thompson KE. Pore-scale modeling of fluid transport in disordered fibrous materials. AICHE J.
2002; 48(7):1369-89.
[42] Thiedmann R, Hartnig C, Manke I, Schmidt V, Lehnert W. Local Structural Characteristics of Pore Space in GDLs of PEM Fuel Cells Based on Geometric 3D Graphs. J.Electrochem.Soc. 2009;
156(11):B1339-47.
[43] Wilkinson D, Willemsen JF. Invasion percolation - a new form of percolation theory. Journal of
Physics A-Mathematical and General 1983; 16(14):3365-76.
[44] Lenormand R, Touboul E, Zarcone C. Numerical-models and experiments on immiscible displacements in porous-media. J. Fluid Mech. 1988; 189:165-87.
[45] Concus P, Finn R. On Behavior of a Capillary Surface in a Wedge. Proc.Natl.Acad.Sci.U.S.A. 1969;
63(2):292.
[46] Basu S, Wang CY, Chen KS. Phase change in a polymer electrolyte fuel cell. J.Electrochem.Soc.
2009; 156(6):B748-56.
[47] Yamada H, Hatanaka T, Murata H, Morimoto Y. Measurement of flooding in gas diffusion layers of
polymer electrolyte fuel cells with conventional flow field. J.Electrochem.Soc. 2006; 153(9):A1748-54.
[48] Medici EF, Allen JS. Two dimensional network model simulations of water percolation through a
GDL. The Twentieth International Symposium on Transport Phenomena; 2009.
[49] Becker J, Schulz V, Wiegmann A. Numerical determination of two-phase material parameters of a
gas diffusion layer using tomography images. J.Fuel Cell Sci. and Tech.2008; 5(2).
[50] Kyan CP, Wasan D, Kintner R. Flow of single-phase fluids through fibrous beds.
Ind.Eng.Chem.Fundam. 1970; 9(4):596-603.
[51] Latt J, Chopard B, Malaspinas O, Deville M, Michler A. Straight velocity boundaries in the lattice
Boltzmann method. Phys. Rev. E 2008; 77(5):056703.
[52] Succi S. The lattice Boltzmann equation. For Fluid Dynamics and Beyond 2001.
[53] Mukherjee PP, Wang C, Kang Q. Mesoscopic modeling of two-phase behavior and flooding
phenomena in polymer electrolyte fuel cells. Electrochim.Acta 2009; 54(27):6861-75.
[54] Fishman Z, Hinebaugh J, Bazylak A. Microscale Tomography Investigations of Heterogeneous
Porosity Distributions of PEMFC GDLs. J.Electrochem.Soc. 2010; 157(11):B1643-50.
[55] Gurau V, Barbir F, Liu H. An Analytical Solution of a Half-Cell Model for PEM Fuel Cells.
J.Electrochem.Soc. 2000; 147(7):2468-77.
138
[56] Chu H, Yeh C, Chen F. Effects of porosity change of gas diffuser on performance of proton
exchange membrane fuel cell. J.Power Sources 2003; 123(1):1-9.
[57] Roshandel R, Farhanieh B, Saievar-Iranizad E. The effects of porosity distribution variation on PEM
fuel cell performance. Renewable Energy 2005; 30(10):1557-72.
[58] Zhan ZG, Xiao JS, Li DY, Pan M, Yuan RZ. Effects of porosity distribution variation on the liquid
water flux through gas diffusion layers of PEM fuel cells. J.Power Sources 2006; 160(2):1041-8.
[59] Davies L, Dollimore D. Theoretical and experimental values for the parameter k of the Kozeny-
Carman equation, as applied to sedimenting suspensions. J.Phys.D 2000; 13(11):2013.
[60] Fishman JZ, Hinebaugh J and Bazylak A. Anisotropic Porosity Profiles of PEMFC GDLs. Brooklyn,
New York, USA: ASME 2010 Eighth International Fuel Cell Science, Engineering and Technology
Conference; 2010.
[61] Hartnig C, Manke I, Kuhn R, Kleinau S, Goebbels J, Banhart J. High-resolution in-plane
investigation of the water evolution and transport in PEM fuel cells. J.Power Sources 2009; 188(2):468-
74.
[62] Hickner MA, Siegel NP, Chen KS, Hussey DS, Jacobson DL, Arif M. In situ high-resolution neutron
radiography of cross-sectional liquid water profiles in proton exchange membrane fuel cells.
J.Electrochem.Soc. 2008; 155(4):B427-34.
[63] Ostadi H, Rama P, Liu Y, Chen R, Zhang XX, Jiang K. 3D reconstruction of a gas diffusion layer
and a microporous layer. J.Membr.Sci. 2010; 351(1-2):69-74.
[64] Hussaini IS, Wang CY. Measurement of relative permeability of fuel cell diffusion media. J.Power
Sources 2010; 195(12):3830-40.
[65] Gostick JT, Fowler MW, Pritzker MD, Ioannidis MA, Behra LM. In-plane and through-plane gas permeability of carbon fiber electrode backing layers. J.Power Sources 2006; 162(1):228-38.
[66] Ismail MS, Damjanovic T, Hughes K, Ingham DB, Ma L, Pourkashanian M, et al. Through-Plane Permeability for Untreated and PTFE-Treated Gas Diffusion Layers in Proton Exchange Membrane Fuel
Cells. J.Fuel Cell Sci.and Tech.2010; 7(5):051016.
[67] Flückiger R, Freunberger SA, Kramer D, Wokaun A, Scherer GG, Büchi FN. Anisotropic, effective diffusivity of porous gas diffusion layer materials for PEFC. Electrochim.Acta 2008; 54(2):551-9.
[68] Hwang GS, Weber AZ. Effective-Diffusivity Measurement of Partially-Saturated Fuel-Cell Gas-
Diffusion Layers. J.Electrochem.Soc. 2012; 159(11):F683-92.
[69] Gostick JT, Ioannidis MA, Fowler MW, Pritzker MD. Direct measurement of the capillary pressure
characteristics of water–air–gas diffusion layer systems for PEM fuel cells. Electrochem.Commun. 2008; 10(10):1520-3.
[70] Gostick JT, Ioannidis MA, Fowler MW, Pritzker MD. Wettability and capillary behavior of fibrous
gas diffusion media for polymer electrolyte membrane fuel cells. J.Power Sources 2009; 194(1):433-44.
[71] Kumbur EC, Sharp KV, Mench MM. Validated leverett approach for multiphase flow in PEFC
diffusion media. J.Electrochem.Soc. 2007; 154(12):B1295-304.
[72] Gostick JT, Ioannidis MA, Fowler MW, Pritzker MD. On the role of the microporous layer in
PEMFC operation. Electrochem.Commun. 2009; 11(3):576-9.
[73] Gaiselmann G, Froning D, Toetzke C, Quick C, Manke I, Lehnert W, et al. Stochastic 3D modeling
of non-woven materials with wet-proofing agent. Int.J.Hydrogen Energy 2013; 38(20):8448-60.
[74] Fishman Z, Bazylak A. Heterogeneous through-plane porosity distributions for treated PEMFC
GDLs I. PTFE effect. J.Electrochem.Soc. 2011; 158(8):B841-5.
139
[75] Fishman Z, Bazylak A. Heterogeneous through-plane porosity distributions for treated PEMFC
GDLs. II. Effect of MPL cracks. J.Electrochem.Soc. 2011; 158(8):B846-51.
[76] Rofaiel A, Ellis JS, Challa PR, Bazylak A. Heterogeneous through-plane distributions of
polytetrafluoroethylene in polymer electrolyte membrane fuel cell gas diffusion layers. J.Power Sources
2012; 201(0):219-25.
[77] Daino MM, Kandlikar SG. 3D phase-differentiated GDL microstructure generation with binder and
PTFE distributions. Int.J.Hydrogen Energy 2012; 37(0):5180-9.
[78] Inoue G, Yoshimoto T, Matsukuma Y, Minemoto M. Development of simulated gas diffusion layer
of polymer electrolyte fuel cells and evaluation of its structure. J.Power Sources 2008; 175(1):145-58.
[79] Toetzke C, Gaiselmann G, Osenberg M, Bohner J, Arlt T, Markoetter H, et al. Three-dimensional
study of compressed gas diffusion layers using synchrotron X-ray imaging. J.Power Sources 2014;
253:123-31.
[80] Litster S, Sinton D, Djilali N. Ex situ visualization of liquid water transport in PEM fuel cell gas
diffusion layers. J.Power Sources 2006; 154(1):95-105.
[81] Barbir F. PEM fuel cells: theory and practice. PEM Fuel Cells: Theory and Practice Boston: Elsevier
Academic Press; 2005, p. 73-113.
[82] Wargo EA, Schulz VP, Çeçen A, Kalidindi SR, Kumbur EC. Resolving macro- and micro-porous
layer interaction in polymer electrolyte fuel cells using focused ion beam and X-ray computed
tomography. Electrochim.Acta 2013; 87(0):201-12.
[83] Nanjundappaa A, Alavijeha A, Hannacha M, Kjeanga E. A customized framework for 3-D
morphological characterization of microporous layers. Electrochim Acta 2013; 110:349-57.
[84] Becker J, Wieser C, Fell S, Steiner K. A multi-scale approach to material modeling of fuel cell diffusion media. Int.J. Heat and Mass Trans. 2011; 54:1360-8.
[85] Bajpaj H, Khandelwal M, Kumbur EC, Mench MM. A computational model for assessing impact of interfacial morphology on polymer electrolyte fuel cell performance. J.Power Sources 2010; 195:4196.
[86] Wu R, Zhu X, Liao Q, Chen R, Cui G. Liquid and oxygen transport in defective bilayer gas diffusion
material of proton exchange membrane fuel cell. Int.J.Hydrogen Energy 2013; 38(10):4067-78.
[87] Markoetter H, Haussmann J, Alink R, Toetzke C, Arlt T, Klages M, et al. Influence of cracks in the
microporous layer on the water distribution in a PEM fuel cell investigated by synchrotron radiography.
Electrochem.Commun.2013; 34:22-4.
[88] Sasabe T, Deevanhxay P, Tsushima S, Hirai S. Soft X-ray visualization of the liquid water transport
within the cracks of micro porous layer in PEMFC. Electrochem.Commun.2011; 13(6):638-41.
[89] Wang XL, Zhang HM, Zhang JL, Xu HF, Tian ZQ, Chen J, et al. Micro-porous layer with composite
carbon black for PEM fuel cells. Electrochim.Acta 2006; 51(23):4909-15.
[90] Cabot Corporation. Conductive Specialty Carbon Blacks. Available at:
http://www.cabotcorp.com/solutions/products-plus/specialty-carbon-blacks/conductive. Accessed 11/14,
2014.
[91] NIST. X-ray Mass Attenuation Coefficients. Available at:
http://physics.nist.gov/PhysRefData/XrayMassCoef/tab2.html. Accessed 11/14, 2014.
[92] Park S, Lee J, Popov BN. Effect of PTFE content in microporous layer on water management in
PEM fuel cells. J.Power Sources 2008; 177(2):457-63.
[93] Morris DRP, Gostick JT. Determination of the in-plane components of the electrical conductivity
tensor in PEM fuel cell gas diffusion layers. Electrochim.Acta 2012; 85:665-73.
140
[94] Becker J, Flückiger R, Reum M, Büchi FN, Marone F, Stampanoni M. Determination of material
properties of gas diffusion layers: Experiments and simulations using phase contrast tomographic
microscopy. J.Electrochem.Soc. 2009; 156(10):B1175-81.
[95] Wang Y, Cho S, Thiedmann R, Schmidt V, Lehnert W, Feng X. Stochastic modeling and direct
simulation of the diffusion media for polymer electrolyte fuel cells. Int.J.Heat Mass Transfer 2010; 53(5–
6):1128.
[96] Yablecki J, Hinebaugh J, Bazylak A. Effect of Liquid Water Presence on PEMFC GDL Effective
Thermal Conductivity. J.Electrochem.Soc. 2012; 159(12):F805-9.
[97] Schladitz K, Peters S, Reinel-Bitzer D, Wiegmann A, Ohser J. Design of acoustic trim based on
geometric modeling and flow simulation for non-woven. Comp.Mat.Sci. 2006; 38(1):56-66.
[98] Gaiselmann G, Thiedmann R, Manke I, Lehnert W, Schmidt V. Stochastic 3D modeling of fiber-
based materials. Comp.Mat.Sci. 2012; 59:75-86.
[99] Hinebaugh J, Bazylak A. PEM fuel cell gas diffusion layer modelling of pore structure and predicted
liquid water saturation. Proceedings of ASME 2011 5th International Conference on Energy
Sustainability & 9th Fuel Cell Science, Engineering and Technology Conference; Washington, DC.
August 2011.
[100] Soille P. Morphological Image Analysis: Principles and Applications. 2nd ed. Berlin: Springer;
2004.
[101] Hinebaugh J, Bazylak A. Stochastic Modeling of PEMFC GDLs I. Physical Characterization. J.
Power Sources (Submitted November 2014) .
[102] Han M, Xu JH, Chan SH, Jiang SP. Characterization of gas diffusion layers for PEMFC.
Electrochim.Acta 2008; 53(16):5361-7.
[103] Martínez-Rodríguez MJ, Cui T, Shimpalee S, Seraphin S, Duong B, Van Zee JW. Effect of
microporous layer on MacMullin number of carbon paper gas diffusion layer. J.Power Sources 2012;
207(0):91-100.
[104] Gostick JT. Random Pore Network Modeling of Fibrous PEMFC Gas Diffusion Media Using
Voronoi and Delaunay Tessellations. J.Electrochem.Soc. 2013; 160(8):F731-43.
[105] Hilpert M, Miller CT. Pore-morphology-based simulation of drainage in totally wetting porous
media. Adv.Water Resour. 2001; 24(3-4):243-55.
[106] Bazylak A, Sinton D, Djilali N. Dynamic water transport and droplet emergence in PEMFC gas diffusion layers. J.Power Sources 2008; 176(1):240-6.
[107] Lu Z, Daino MM, Rath C, Kandlikar SG. Water management studies in PEM fuel cells, part III: Dynamic breakthrough and intermittent drainage characteristics from GDLs with and without MPLs.
Int.J.Hydrogen Energy 2010; 35(9):4222-33.
[108] Nam JH, Kaviany M. Effective diffusivity and water-saturation distribution in single- and two-layer PEMFC diffusion medium. Int.J.Heat Mass Transfer 2003; 46(24):4595-611.
[109] Alink R, Gerteisen D, Merida W. Investigating the Water Transport in Porous Media for PEMFCs
by Liquid Water Visualization in ESEM. Fuel Cells 2011; 11(4):481-8.
[110] Nishida K, Murakami T, Tsushima S, Hirai S. Measurement of liquid water content in cathode gas
diffusion electrode of polymer electrolyte fuel cell. J.Power Sources 2010; 195(11):3365-73.
[111] Rosli MI, Borman DJ, Ingham DB, Ismail MS, Ma L, Pourkashanian M. Transparent PEM Fuel
Cells for Direct Visualization Experiments. J.Fuel Cell Science and Tech. 2010; 7(6):061015.
141
[112] Preston J, Pasaogullari U, Hussey DS, Jacobson DL. High Resolution Neutron Radiography
Imaging of Microporous Layers in PEFCs. ECS Trans. 2011; 41(1):319.
[113] Hinebaugh J, Challa PR, Bazylak A. Accounting for low frequency synchrotron x-ray beam
position fluctuations for dynamic visualizations. J.Synch.Rad. 2012; 19:994.
[114] Quan P, Lai M-, Hussey DS, Jacobson DL, Kumar A, Hirano S. Time-Resolved Water
Measurement in a PEM Fuel Cell Using High-Resolution Neutron Imaging Technique. Journal.Fuel Cell
Science and Technology 2010; 7(5):051009.
[115] Turhan A, Kim S, Hatzell M, Mench MM. Impact of channel wall hydrophobicity on through-plane
water distribution and flooding behavior in a polymer electrolyte fuel cell. Electrochim.Acta 2010;
55(8):2734-45.
[116] Flückiger R, Marone F, Stampanoni M, Wokaun A, Büchi FN. Investigation of liquid water in gas
diffusion layers of polymer electrolyte fuel cells using X-ray tomographic microscopy. Electrochim.Acta
2011; 56(5):2254-62.
[117] Schneider A, Wieser C, Roth J, Helfen L. Impact of synchrotron radiation on fuel cell operation in
imaging experiments. J.Power Sources 2010; 195(19):6349-55.
[118] Deevanhxay P, Sasabe T, Tsushima S, Hirai S. In situ diagnostic of liquid water distribution in
cathode catalyst layer in an operating PEMFC by high-resolution soft X-ray radiography.
Electrochem.Commun. 2012; 22(0):33-6.
[119] Krüger P, Markötter H, Haußmann J, Klages M, Arlt T, Banhart J, et al. Synchrotron X-ray
tomography for investigations of water distribution in polymer electrolyte membrane fuel cells. J.Power
Sources 2011; 196(12):5250-5.
[120] Belev G, Wysokinski TW, Chapman D, Mullin C, McKibben M. Set of measurements for
alignment of beamline components. Nuclear Instruments & Methods in Physics Research Section A-
Accelerators Spectrometers Detectors and Associated Equipment 2011; 649(1):225-7.
[121] Wysokinski TW, Chapman D, Adams G, Renier M, Suortti P, Thomlinson W. Beamlines of the
biomedical imaging and therapy facility at the Canadian light source - Part I. Nuclear Instruments &
Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 2007; 582(1):73-6.
[122] Maier W, Arlt T, Wannek C, Manke I, Riesemeier H, Krüger P, et al. In-situ synchrotron X-ray
radiography on high temperature polymer electrolyte fuel cells. Electrochem.Commun. 2010; 12(10):1436-8.
[123] Kuhn R, Scholta J, Krüger P, Hartnig C, Lehnert W, Arlt T, et al. Measuring device for synchrotron X-ray imaging and first results of high temperature polymer electrolyte membrane fuel cells. J.Power
Sources 2011; 196(12):5231-9.
[124] Markötter H, Manke I, Krüger P, Arlt T, Haußmann J, Klages M, et al. Investigation of 3D water transport paths in gas diffusion layers by combined in-situ synchrotron X-ray radiography and
tomography. Electrochem.Commun. 2011; 13(9):1001-4.
[125] Bazylak A. Liquid water visualization in PEM fuel cells: A review. Int.J.Hydrogen Energy 2009; 34(9):3845-57.
[126] Chattopadhyay S. Stability of High-Brilliance Synchrotron Radiation Sources. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated
Equipment 1990; 291(1-2):455-60.
[127] Leonard G, Nurizzo D, Mueller-Dieckmann C, Mitchell E, McCarthy J, Flot D, et al. Crystallographic Research Developments. In: Hardwell TG, editor. Astrophysics and Condensed Matter
(Horizons in World Physics, Volume 262) New York: Nova Science Publishers; 2008, p. 269.
142
[128] Chumakov A, Ruffer R, Leupold O, Celse JP, Martel K, Rossat M, et al. Performance of a
cryogenic silicon monochromator under extreme heat load. J.Synch.Rad. 2004; 11:132-41.
[129] Proux O, Nassif V, Prat A, Ulrich O, Lahera E, Biquard X, et al. Feedback system of a liquid-
nitrogen-cooled double-crystal monochromator: design and performances. J.Synch.Radiation 2006;
13:59-68.
[130] Dalzel M. Canadian Light Source Research Report. 2010.
[131] Ous T, Arcoumanis C. The formation of water droplets in an air-breathing PEMFC. Int J Hydrogen
Energy 2009; 34(8):3476-87.
[132] Bazylak A, Sinton D, Liu Z, Djilali N. Effect of compression on liquid water transport and
microstructure of PEMFC gas diffusion layers. J.Power Sources 2007; 163(2):784-92.
[133] Gao B, Steenhuis TS, Zevi Y, Parlange JY, Carter RN, Trabold TA. Visualization of unstable water flow in a fuel cell gas diffusion layer. J.Power Sources 2009; 190(2):493-8.
[134] Benziger J, Nehlsen J, Blackwell D, Brennan T, Itescu J. Water flow in the gas diffusion layer of
PEM fuel cells. J.Membr.Sci. 2005; 261(1-2):98-106.
[135] Heuer M, Bernstein PA, Wenske M, Styczynski ZA. Results of Current Density Distribution
Mapping in PEM Fuel Cells Dependent on Operation Parameters. Energies 2013; 6(8):3841-58.
143
Appendix A
Fig
ure A
.1. S
chem
atic o
f the fu
el cell testin
g eq
uip
men
t used
for th
is experim
ent.
(Chap
ters 6-8
)
144
Appendix B
The image acquisition from chapters 6-8 resulted in a sequence of 16-bit images, exportable to
TIFF format, where the brightness values of each pixel in the image provide an intensity map,
denoted as 𝐼𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑[𝑥, 𝑦, 𝑡]. The following steps were taken to transform the intensity map to a
water thickness map.
B.1 Dark Current Correction
A measure of the dark current present in the CCD camera used in this study was made by
collecting a sequence of dark frame images before each set of experiments. A dark frame image
is obtained by imaging while the safety shutter is closed (Figure 8.4, configuration I), preventing
X-rays from entering the experimental room. A minimum of 20 such images are taken, and
averaged, resulting in 𝐼𝑑𝑎𝑟𝑘[𝑥,𝑦]. The values of this averaged dark field image were subtracted
from every image in the experiment to result in:
𝐼𝑛𝑒𝑡[𝑥,𝑦, 𝑡] = 𝐼𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑[𝑥, 𝑦, 𝑡] − 𝐼𝑑𝑎𝑟𝑘[𝑥,𝑦]. B.1
B.2 Linear Intensity Correction
Due to the relatively short length of each experiment, the storage ring could be assumed to lose
current linearly and the X-ray beam intensity can be expected to also decrease linearly with time.
A proportional measure of the loss in beam intensity over the course of the experiment can be
made with the average value of 𝐼𝑛𝑒𝑡[𝑥,𝑦, 𝑡] at the first and last frame (Figure 8.4, configuration
III) of the experiment. These are denoted as �̅�𝑛𝑒𝑡[𝑡0] and �̅�𝑛𝑒𝑡[𝑡𝑒𝑛𝑑], respectively.
The ratio, 𝑓𝑒𝑛𝑑 = �̅�𝑛𝑒𝑡[𝑡0]/�̅�𝑛𝑒𝑡[𝑡𝑒𝑛𝑑], represents the scaling factor that would need to be
multiplied to each pixel of 𝐼𝑛𝑒𝑡[𝑥,𝑦, 𝑡𝑒𝑛𝑑] to make the first and last frames comparable.
Additionally, the function, 𝑓[𝑡], represents this scaling factor for each time step between 𝑡0 and
𝑡𝑒𝑛𝑑, where 𝑓[𝑡𝑒𝑛𝑑] = 𝑓𝑒𝑛𝑑 and 𝑓0 = 𝑓[𝑡0] = 1. The possible water in the images keeps us from
being able to similarly calculate 𝑓[𝑡] for all the images in the series, therefore we assume a linear
transition from 𝑓0 and 𝑓𝑒𝑛𝑑, and interpolate to find 𝑓[𝑡] for all points between.
145
The intensity data of each image in the sequence is scaled to be comparable to the original
image:
𝐼𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑[𝑥,𝑦, 𝑡] = 𝑓[𝑡] 𝐼𝑛𝑒𝑡[𝑥,𝑦, 𝑡]. B.2
B.3 Beam Position Correction
The vertical position of the X-ray beam fluctuates with time. To account for this unsteady
source, for each image of 𝐼𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑[𝑥,𝑦, 𝑡] five dry state images were found with comparable
beam positions, using the technique described in Chapter 7. These five images were averaged,
and associated with the time stamp of their corresponding 𝐼𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑[𝑥, 𝑦, 𝑡] image, generating a
data set denoted as 𝐼𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑,𝑑𝑟𝑦[𝑥,𝑦, 𝑡] with the same dimensions as 𝐼𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑[𝑥,𝑦, 𝑡].
B.4 Flat Field Normalization
The thickness of liquid water can now be quantified using the Beer-Lambert Law as:
𝜒𝑤𝑎𝑡𝑒𝑟[𝑥,𝑦, 𝑡] =
ln(𝐼𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑[𝑥,𝑦,𝑡]
𝐼𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑,𝑑𝑟𝑦[𝑥,𝑦,𝑡])
−𝜇𝑤𝑎𝑡𝑒𝑟, B.3
which takes into account the beam intensity distribution, fuel cell components, and the
heterogeneities in the scintillator and detector.