Pore Network Modeling of Multiphase Transport in Polymer ... · In this thesis, pore network modeling was used to study how the microstructure of the polymer electrolyte membrane

Pore Network Modeling of Multiphase Transport in Polymer

Electrolyte Membrane Fuel Cell Gas Diffusion Layers

by

Mohammadreza Fazeli

A thesis submitted in conformity with the requirements

for the degree of Master of Applied Science

Department of Mechanical and Industrial Engineering

University of Toronto

© Copyright by Mohammadreza Fazeli 2015

ii

Pore Network Modeling of Multiphase Transport in Polymer Electrolyte

Membrane Fuel Cell Gas Diffusion Layers

Mohammadreza Fazeli

Master of Applied Science

Department of Mechanical and Industrial Engineering

University of Toronto

2015

Abstract

In this thesis, pore network modeling was used to study how the microstructure of the polymer

electrolyte membrane (PEM) fuel cell gas diffusion layer (GDL) influences multiphase transport

within the composite layer. An equivalent pore network of a GDL was used to study the effects

of GDL/catalyst layer condensation points and contact quality on the spatial distribution of liquid

water in the GDL. Next, pore networks extracted from synchrotron-based micro-computed

tomography images of compressed GDLs were employed to simulate liquid water transport in

GDL materials over a range of compression pressures, and favorable GDL compression values

for preferred liquid water distributions were found for two commercially available GDL

materials. Finally, a technique was developed for calculating the oxygen diffusivity in carbon

paper substrates with a microporous layer (MPL) coating through pore network modeling. A

hybrid network was incorporated into the pore network model, and effective diffusivity

predictions of MPL coated GDL materials were obtained.

iii

Acknowledgements

This work would have not been possible without the supervision, guidance, and never ending

support from my supervisor, Professor Aimy Bazylak. I would like to express my sincere

gratitude to her for providing me with the unique opportunity of working on this project.

I would like to thank all the amazing people I had the pleasure to meet in Toronto. I greatly

appreciate the support of the members of Thermofluids for Energy and Advanced Materials

(TEAM) Laboratory, who I had the pleasure to work with over the last two years. I am especially

grateful to James Hinebaugh for his valuable assistance throughout my study. His input and

support has been invaluable and helped me produce the best possible results.

I would like to thank the Natural Sciences and Engineering Research Council of Canada

(NSERC), the NSERC Collaborative Research and Training Experience (CREATE) Program in

Distributed Generation for Remote Communities, the NSERC Canada Research Chairs Program,

the Canadian Foundation for Innovation (CFI), and the Ontario Ministry of Research and

Innovation Early Researcher Award for their generous financial support.

Finally, I would like to thank my caring, loving family who encouraged me to make it through

this process. You have been there for me my entire life, and the value of your support and of

your belief in me is immeasurable.

Thank you all.

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Table of Contents

Acknowledgements ........................................................................................................................ iii

Table of Contents ........................................................................................................................... iv

List of Tables ................................................................................................................................ vii

List of Figures .............................................................................................................................. viii

1 Introduction ............................................................................................................................. 1

1.1 Preamble ........................................................................................................................... 1

1.2 Objective .......................................................................................................................... 2

1.3 Contributions .................................................................................................................... 3

1.4 Organization of Thesis ..................................................................................................... 4

2 Background and Literature Review ......................................................................................... 6

2.1 Introduction ...................................................................................................................... 6

2.2 Polymer Electrolyte Membrane Fuel Cells ...................................................................... 6

2.2.1 Operation Principles.................................................................................................. 7

2.3 Gas Diffusion Layer ......................................................................................................... 7

2.4 Microporous Layer ........................................................................................................... 8

2.5 Pore Network Modeling ................................................................................................... 9

2.6 Liquid Water Inlet Conditions........................................................................................ 10

2.7 PEM Fuel Cell Compression .......................................................................................... 12

2.8 Modeling GDL Compression ......................................................................................... 12

2.9 Multiphase Transport in Compressed GDLs .................................................................. 13

2.10 Oxygen Effective Diffusivity ......................................................................................... 16

2.11 Figures ............................................................................................................................ 19

3 Liquid Water Inlet Conditions ............................................................................................... 23

3.1 Introduction .................................................................................................................... 23

3.2 Motivation and Objective ............................................................................................... 23

3.3 Methodology .................................................................................................................. 25

3.3.1 Imaging ................................................................................................................... 25

3.3.2 Pore Network Modeling .......................................................................................... 25

3.3.3 Invasion Simulation ................................................................................................ 26

v

3.3.4 Inlet Boundary Conditions ...................................................................................... 28

3.3.5 GDL/CL Contact ..................................................................................................... 30

3.4 Results and Discussion ................................................................................................... 31

3.4.1 Inlet Conditions ....................................................................................................... 31

3.4.2 Simulated Delamination of the GDL ...................................................................... 33

3.5 Conclusions .................................................................................................................... 35

3.6 Tables ............................................................................................................................. 36

3.7 Figures ............................................................................................................................ 37

4 GDL Compression ................................................................................................................. 46

4.1 Introduction .................................................................................................................... 46


4.3 Methodology .................................................................................................................. 48

4.3.1 Materials ................................................................................................................. 48

4.3.2 Synchrotron Tomography ....................................................................................... 48

4.3.3 Image Segmentation................................................................................................ 49

4.3.4 Network Extraction ................................................................................................. 51

4.3.5 Boundary Conditions .............................................................................................. 52

4.3.6 Water Percolation Simulation ................................................................................. 53


4.4.1 Toray TGP-H-090 ................................................................................................... 54

4.4.2 SGL Sigracet 25BC................................................................................................. 55

4.4.3 Significance of the microporous layer .................................................................... 56

4.5 Conclusions .................................................................................................................... 57

4.6 Figures ............................................................................................................................ 59

5 MPL/substrate Oxygen Diffusivity ....................................................................................... 69

5.1 Introduction .................................................................................................................... 69


5.3 Methodology .................................................................................................................. 71

5.3.1 Stochastic Network Generation .............................................................................. 71

5.3.2 Pore Network Extraction......................................................................................... 72

5.3.3 MPL Image Processing ........................................................................................... 73

vi

5.3.4 Transport Equations ................................................................................................ 74

5.3.5 Resistance Network Model ..................................................................................... 79

5.3.6 Analytical Diffusivity Calculations ........................................................................ 80


5.4.1 Comparison with Analytical Solutions ................................................................... 84

5.4.2 Mesh Resolution Study ........................................................................................... 86

5.4.3 Pore Diffusion Length at the Interface .................................................................... 88

5.5 Conclusions .................................................................................................................... 89

5.6 Tables ............................................................................................................................. 91

5.7 Figures ............................................................................................................................ 92

6 Conclusions ......................................................................................................................... 101

7 Future Work ......................................................................................................................... 104

References ................................................................................................................................... 106

vii

List of Tables

Table ‎3.1 Average saturation levels for Case 1 and Case 2 with various inlet conditions ........... 36

Table ‎5.1 Specifications of Samples A, B, and C. ........................................................................ 91

viii

List of Figures

Figure ‎2.1 Schematic of PEM fuel cell electrode arrangement and operation. ............................ 19

Figure ‎2.2 SEM image of a Toray GDL at (a) 25x, (b) 100, and (c) 500x magnifications. ......... 20

Figure ‎2.3 SEM image of the MPL coating in a SGL GDL at (a) 25x, (b) 100x, and (c) 500x

magnifications. .............................................................................................................................. 21

Figure ‎2.4 Schematic representation of (a) a porous material and (b) the pore network describing

the pore space of the material. ...................................................................................................... 22

Figure ‎3.1 (a) 3D trinary image of SGL Sigracet 25BC, where the three material phases are MPL

(yellow), fiber (red), and void (transparent) and (b) the extracted pore space of the material.

Yellow, red, and blue represent MPL, fiber, and pore space, respectively. ................................. 37

Figure ‎3.2 Side view and top view of the boundary conditions for liquid water entering the

material: (a) uniform pressure, (b) distributed uniform pressure, and (c) uniform flux. .............. 38

Figure ‎3.3 (a) Region considered for simulating poor contact quality at the GDL/CL interface

(Case 1). (b) The first through-plane slice of this region, which is equivalent to the MPL/CL

interface......................................................................................................................................... 39

Figure ‎3.4 (a) Region considered for simulating ideal contact quality at the GDL/CL interface


interface......................................................................................................................................... 40

Figure ‎3.5 Mean saturation values at breakthrough for (a) Case 1 and (b) Case 2. Case 1

describes a situation where the CL is experiencing delamination, and Case 2 simulates full

contact between the CL and the GDL. Through-plane position values are normalized to the

sample thickness. .......................................................................................................................... 41

Figure ‎3.6 Liquid water distribution at breakthrough for Case 1 which simulates poor GDL/CL

contact quality with (a) uniform pressure (b) distributed uniform pressure (100 reservoirs) and

(c) uniform flux boundary conditions. The red pores indicate the breakthrough locations. ......... 42

Figure ‎3.7 Liquid water distribution at breakthrough for Case 2 which simulates ideal GDL/CL


(c) uniform flux boundary conditions. The red pores indicate the breakthrough locations. ......... 43

Figure ‎3.8 Fiber, water, MPL, and void content in each slice of the material after simulation is

performed for Case 1 with (a) uniform pressure boundary condition, (b) distributed uniform

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pressure boundary condition (100 reservoirs), and (c) uniform flux boundary condition. Through-

plane position values are normalized to the sample thickness. ..................................................... 44




plane position values are normalized to the sample thickness. ..................................................... 45

Figure ‎4.1 (a) Grey-scale and (b) trinary images of compressed SGL Sigracet 25B. The three

phases in the trinary image are solid (dark grey), MPL (light grey), and void space (black). ..... 59

Figure ‎4.2 (a) Segmented image of Toray TGP-H-090 at 10% compression and (b) its pore

space. (c) Segmented image of Toray TGP-H-090 at 30% compression and (d) its pore space.

GDL samples were approximately 1.8 × 2 mm. ........................................................................... 60

Figure ‎4.3 (a) Segmented image of SGL Sigracet 25BC at 10% compression and (b) its pore

space. (c) Segmented image of SGL Sigracet 25BC at 30% compression and (d) its pore space.

GDL samples were approximately 1.8 × 2 mm. ........................................................................... 61

Figure ‎4.4 Water distribution in Toray TGP-H-90 at (a) 0%, (b) 10%, (c) 20%, and (d) 30%

compression with 100 condensation points at the inlet (GDL/CL interface). .............................. 62

Figure ‎4.5 Breakthrough saturation profiles for Toray TPG-H-090 at various compression states

and with (a) 20 reservoirs, (b) 40 reservoirs, (c) 100 reservoirs, and (d) 300 reservoirs

stochastically placed at the inlet. .................................................................................................. 63

Figure ‎4.6 Average saturations and saturation values at the GDL inlet (GDL/CL interface) for

Toray TPG-H-090 at various compression states and with (a) 20 reservoirs, (b) 40 reservoirs, (c)

100 reservoirs, and (d) 300 reservoirs stochastically placed at the inlet. ..................................... 64

Figure ‎4.7 Water distribution in SGL Sigracet 25BC at (a) 0%, (b) 10%, (c) 20%, and (d) 30%

compression with 100 condensation points at the inlet (GDL/CL interface). .............................. 65

Figure ‎4.8 Breakthrough saturation profiles for SGL Sigracet 25BC at various compression states


stochastically placed at the inlet. .................................................................................................. 66


SGL Sigracet 25BC at various compression states and with (a) 20 reservoirs, (b) 40 reservoirs,

(c) 100 reservoirs, and (d) 300 reservoirs stochastically placed at the inlet. ................................ 67

Figure ‎4.10 (a) Toray TPG-H-090 and (b) SGL Sigracet 25BC porosity profiles at various

compression states. The MPL microporosity is assumed to be 50%. ........................................... 68

x

Figure ‎5.1 2D schematic representation of the image processing steps. (a) Extracted pore space

and solid MPL. (b) Extracted pore space and refined MPL. (c) Expanded pore space and refined

MPL. (d) Final network with all identified connections. Circles and squares represent pores and

MPL elements, respectively, and connections are shown with solid lines. .................................. 92

Figure ‎5.2 (a) The original 3D material created stochastically which has 3 phases: MPL, fiber,

and‎void‎space.‎The‎material‎dimensions‎are‎266‎μm‎×‎266‎μm‎×‎248‎μm.‎(b)‎The‎hybrid‎

network‎of‎spherical‎pores‎representing‎the‎void‎space‎and‎cubic‎elements‎with‎a‎length‎of‎7‎μm‎

representing the MPL phase.......................................................................................................... 93

Figure ‎5.3 Schematic representation of the three types of node connections in the network and

their equivalent diffusion conduits. (a) Pore/pore connections. (b) MPL element/MPL element

connections. (c) Pore/MPL element connections. ......................................................................... 94

Figure ‎5.4 (a) The first in-plane slice of sample A which consists of a numerically created SGL

Sigracet 25BA substrate and a flat sheet-type MPL. (b) The first in-plane slice of sample B

which consists of a numerically created SGL Sigracet 25BA substrate and a sinusoidal sheet-type

MPL. The equivalent resistance network of each sample is presented. ........................................ 95

Figure ‎5.5 Through-plane effective diffusion coefficients of sample A for various MPL

thicknesses calculated both analytically and numerically. Numerical results are calculated with

MPL element sizes of 9.5 microns (5 voxels) and 13.2 microns (7 voxels). ................................ 96

Figure ‎5.6 Through-plane effective diffusion coefficients of sample B for various MPL


MPL element sizes of 9.5 microns (5 voxels) and 13.2 microns (7 voxels). ................................ 97

Figure ‎5.7 Predicted effective diffusion coefficients in the through-plane direction of a

numerically created SGL25BA with an MPL coating for various computational element sizes in

the MPL region. ............................................................................................................................ 98

Figure ‎5.8 Total number of computational nodes in the network for various MPL element sizes.

....................................................................................................................................................... 99

Figure ‎5.9 Schematic representation of distinct diffusion pathways for oxygen diffusion where

one pathway passes through an MPL/void interface. ................................................................. 100

1

1 Introduction

1.1 Preamble

Polymer electrolyte membrane (PEM) fuel cells are electrochemical energy conversion devices

that have received considerable attention in the last decade owing to their high efficiency, zero-

local emissions, and rapid start-up capability. PEM fuel cells convert the chemical energy stored

in hydrogen fuel into electricity in a single step, producing only water and heat as by-products.

This technology is a viable alternative for environmentally friendly and efficient power

generation with a wide range of potential applications. PEM fuel cells are a suitable replacement

for‎internal‎combustion‎engines.‎The‎world’s‎leading‎motor‎companies‎including‎Daimler,‎Ford,‎

General Motors, Nissan, Hyundai, and Toyota have developed and demonstrated fuel cell

vehicles powered by PEM fuel cells and have announced plans for commercialization [1]. This

technology is also practical for distributed and portable power generation. Companies such as

Samsung, Sony, and Toshiba are developing PEM fuel cells for portable applications such as fuel

cell powered recharging devices for laptops and mobile phones [2]. Back-up power systems

developed by companies such as Hydrogenics, Ballard Power Systems and Plug Power are

available in the market that can be used for residential application or back-up power in banks,

hospitals or telecom companies [2].

To make this technology commercially viable on a massive scale, factors such as efficiency,

durability, and cost need to be addressed. Significant improvements of PEM fuel cell efficiency

and durability are possible with the development of new water management strategies derived

2

from a strong fundamental understanding of mass transport mechanisms within various

components of the PEM fuel cell [3].

1.2 Objective

The main objective of this study is to investigate the effects of PEM fuel cell gas diffusion layer

(GDL) microstructure on the mass transport characteristics of the GDL. This will be

accomplished by developing and implementing pore network modeling techniques able to

describe two phase phenomena in this unique domain. A primary focus is the simulation of liquid

water transport in the GDL under various conditions, including varying distribution and number

of condensation points at the GDL/catalyst layer (CL) interface and a range of GDL compression

states. By using numerical simulations for predicting the spatial distribution of liquid water in the

GDL under different scenarios, the optimum configuration of the GDL for effective water

management characteristics can be identified.

In addition, a hybrid network based modeling technique is introduced for mass transport

calculations in porous materials with multi-scale porosities, where finely porous regions are

represented as block elements. The feasibility of incorporating this hybrid network into our pore

network modeling software for calculating the oxygen diffusivity in carbon paper substrates with

a microporous layer (MPL) coating is investigated. The results of this model are validated

through comparisons with analytical calculations, and the limiting element size that accurately

predicts the effective diffusivity of the material while maintaining the physical features of the

MPL is identified.

3

1.3 Contributions

The results of this thesis have led to the following contributions:

Chapter 3 was previously published in the Journal of the Electrochemical Society. Chapter 5 has

been submitted to the Journal of Materials Chemistry A, and Chapter 4 is being prepared for

submission to the Electrochimica Acta. Professor Aimy Bazylak was a co-author on all journal

articles prepared for publication.

James Hinebaugh was a co-author on the publication resulting from Chapter 3, and the submitted

manuscript associated with Chapter 5. James provided the extraction algorithm employed to

create 3D pore network models of GDL materials in both studies and led the development of the

stochastic network generation algorithm employed for creating bilayer GDLs.

Zachary Fishman and James Hinebaugh were co-authors on the manuscript associated with

Chapter 4. Zachary and James developed the image segmentation algorithm, and Zachary

performed the image segmentation process for creating binary/trinary images of each material.

Professor Ingo Manke from Institute of Applied Materials at Helmholtz Zentrum Berlin,

Germany was a co-author on the manuscript associated with Chapter 4. A research group led by

Professor Manke performed synchrotron-based X-ray imaging of GDL samples at various

compression states, and the 3D tomograms of the materials were employed for performing the

studies presented in Chapter 4.

4

The following is an overview of the contributions of this thesis:

Fazeli,‎M.,‎Hinebaugh,‎J.,‎Bazylak,‎A.‎(2015)‎“Investigating‎Inlet‎Condition‎Effects‎on‎

PEMFC‎GDL‎Liquid‎Water‎Transport‎through‎Pore‎Network‎Modeling”‎Journal‎of‎the‎

Electrochemical Society, 162(7), F661-F668

Fazeli,‎M.,‎Hinebaugh,‎J.,‎Bazylak,‎A.‎(2015)‎“Determining‎Oxygen‎Diffusivity‎in‎MPL‎

coated‎GDLs‎for‎PEM‎Fuel‎Cells‎through‎Pore‎Network‎Modeling”‎Journal‎of‎Materials‎

Chemistry A, (Submitted August 5, 2015)

Fazeli, M., Hinebaugh, J., Fishman, Z., Tötzke, C., Lehnert, W., Manke, I., Bazylak, A.

“Pore‎Network‎Modeling‎to‎Explore‎the‎Effects‎of‎Compression‎on‎Liquid‎Water‎

Transport‎in‎Polymer‎Electrolyte‎Membrane‎Fuel‎Cell‎Gas‎Diffusion‎Layers”‎(In

preparation)

1.4 Organization of Thesis

This thesis is organized into seven chapters. In this chapter a brief description of the PEM fuel

cell technology and the motivation and objective of this thesis are given. Chapter 2 provides

details regarding the operating principles of PEM fuel cells and the role of the macro-scale

substrate and the MPL, as well as an introduction to pore network modeling. In addition, a

review of the previous studies on liquid water inlet conditions, oxygen diffusion through the

GDL, and the effect of compression on water transport through the GDL and PEM fuel cell

performance are provided. In Chapter 3, the influence of liquid water condensation at the

GDL/CL interface on liquid water distribution within a commercially available GDL is studied.

The 3D microstructure of the GDL is represented with a pore network model, informed by

micro-scale computed tomography imaging of the GDL. Invasion percolation is used to simulate

5

liquid water transport in the material with varying inlet conditions. An alternative boundary

condition is introduced which attempts to mimic the formation of individual water clusters at the

GDL/CL interface. In Chapter 4, the effect of compression on liquid water transport in two

commercial GDL materials is investigated. For each material, favorable GDL compression

values for preferred liquid water distributions are reported. The role of an MPL coating in water

management in the GDL is also presented. In Chapter 5, a novel hybrid network is introduced for

simulating oxygen diffusion in GDL materials with MPL coatings, and through-plane diffusivity

values are calculated for stochastically created GDL materials to validate this technique. Finally,

conclusions and highlighted future works are presented in Chapters 6 and 7, respectively.

6

2 Background and Literature Review

2.1 Introduction

In this chapter, polymer electrolyte membrane (PEM) fuel cells are introduced and the details of

the hydrogen based electrochemical energy generation process are described. Descriptions of two

critical porous layers of the PEM fuel cell, the macro-scale substrate and the microporous layer

(MPL), are presented. Finally, an overview of pore network modeling and a review of the

existing literature on mass transport within the gas diffusion layer (GDL) are provided.

2.2 Polymer Electrolyte Membrane Fuel Cells

The PEM fuel cell is an electrochemical energy conversion technology that directly converts the

chemical energy stored in hydrogen to electrical energy. Hydrogen gas is supplied at the anode

as the fuel, oxygen or air is supplied at the cathode as the oxidant, and the cell generates

electricity with water and heat as the only by-products. PEM fuel cells have several advantages

compared to conventional power sources, including high efficiencies and zero-local emissions,

and are considered a viable alternative for stationary and portable electricity production. PEM

fuel cells can supply high power densities (~0.7‎‎W⁄cm2 ) [4] with efficiencies that can reach as

high as 60% in electricity generation and over 80% in co-generation of electrical and thermal

energies with more than 90% reduction in pollutants [2]. Furthermore, PEM fuel cells run at

relatively low operating temperatures (70 - 80 ) compared to other fuel cell types, allowing the

cell to quickly reach steady state conditions and operate with little noise. However, there are

barriers such as cost, durability, and reliability that prevent the full commercialization of this

7

technology [5]. In particular, the accumulation and transport of liquid water in the cathode GDL

remains a significant issue that influences the operation and performance of the cell [6].

2.2.1 Operation Principles

In a PEM fuel cell, hydrogen and oxygen are fed continuously to the anode and the cathode,

respectively, during operation. Figure 2.1 shows a schematic diagram of the electrode

arrangement and the electrochemical energy generation process. In the anode, each hydrogen

molecule is catalytically broken down into protons, H+, and electrons, e-. Protons flow through

the membrane to the cathode side and electrons travel to the cathode through an external circuit

in the form of electricity. Equation (2.1) shows the anode half-cell reaction.

(2.1)

In the cathode, protons and electrons meet with the oxygen molecules, and through the oxygen

reduction reaction, oxygen, protons, and electrons combine producing water and heat. Equations

(2.2) and (2.3) show the cathode half-cell reaction and the overall reaction, respectively.

(2.2)

(2.3)

2.3 Gas Diffusion Layer

During PEM fuel cell operation, both electrons and reactant gasses travel through a conductive,

porous material named the gas diffusion layer (GDL) to reach the reaction sites. The GDL

typically consists of a paper-like, highly porous, carbon fiber substrate, coated with

polytetrafluoroethyene (PTFE) to render the material hydrophobic. This porous medium plays a

8

critical role in fuel cell performance. The GDL is responsible for maintaining open diffusion

pathways for reactants between the gas channels and the reaction sites. It is also the primary

pathway for conducting the electrical current and heat produced at the catalyst layer (CL) to the

current collector plates while providing sufficient mechanical strength for protecting the

membrane electrode assembly. Finally, the GDL is responsible for passively managing the water

produced in the electrochemical reaction, balancing the need for a well hydrated membrane and

clear pathways for gas diffusion. The focus of water management is on the cathode GDL, which

is the key contributor to mass transport limitations due to the blockage of diffusion pathways by

the electrochemically produced liquid water. This management is controlled by both the

microstructural and thermal properties of the GDL. Figure 2.2 includes a scanning electron

microscopy (SEM) image of a commercially available Toray GDL at 25x, 100, and 500x

magnifications, illustrating the anisotropic nature of the GDL.

2.4 Microporous Layer

The microporous layer (MPL) is a thin, porous layer that is commonly made of carbon black and

PTFE with pore sizes ranging between 20 and 300 nm [7]. This hydrophobic, finely porous

material is added to the GDL to decrease GDL water accumulation, thereby increasing oxygen

diffusivity in wet operating conditions. Recent studies have shown that the addition of a

hydrophobic MPL to one face of the carbon fiber substrate can improve the fuel cell performance

under high current density operation [8,9], but the precise mass transport mechanisms within the

MPL are not fully understood. Some studies [10,11] conclude that the MPL improves water

removal from the cathode GDL by acting as a capillary barrier to water entering the substrate and

encourages water to back diffuse from the cathode to the anode, while other studies report that

9

the MPL has no impact on back diffusion[12,13]. The MPL is either used as a sheet at the

interface between the CL and the substrate or is directly coated onto the substrate. In the latter

case, the MPL coating can take on a complex structure within the GDL, which necessitates a

sophisticated mass transport model for resolving the interactions between the nano-scale pores of

the MPL and the micro-scale pores of the substrate. Figure 2.3 shows a SEM image of the MPL

coating in a commercially available SGL GDL at 25x, 100x, and 500x magnifications.

2.5 Pore Network Modeling

Pore network modeling (PNM) is a pore-scale, numerical modeling approach for studying

multiphase transport in porous media. This method has become widely popular for studying

transport phenomena in the porous layers of PEM fuel cell due to its computational efficiency.

PNM has the ability to represent porous media as a simplified network of pores (nodes)

connected with throats (bonds), where pores represent locations of large void spaces and throats

represent the local constrictions that connect adjacent pores. A schematic representation of a

porous material and the pore network describing the pore space of the material is illustrated in

Figure 2.4. A distinct advantage of this modeling approach is that it does not require knowledge

of the multiphase transport properties as it examines the material properties at the pore level.

This method was initially developed and employed for petroleum-related applications, studying

the distribution of fluids in porous rocks [14]. The PNM method has been successfully applied to

study the pore-scale distribution of liquid water and gas in the GDL [15-25]. Sinha et al. [16]

were among the first researchers who developed pore network models describing the pore-scale

physics of liquid water transport in the GDL. They reported that the capillary number, defined as

the ratio of viscous and capillary forces, is a fundamental parameter determining the mechanisms

10

of liquid water transport in the GDL. In an operating fuel cell, liquid water transport in the GDL

occurs at extremely low capillary numbers, and is governed by fractal capillary fingering which

cannot be described by two-phase Darcy's law [16]. Gostick et al. [15] developed a pore network

model to identify the pore-scale distribution of water and gas in the GDL and computed the

relative permeability of water and gas and the effective gas diffusivity as a function of water

saturation. In addition, the continuum models of relative permeability and diffusivity were shown

to overestimate mass transport in the gas phase [15].

Recently pore network models have been employed to investigate the effects of the presence of

the MPL on water transport in the GDL [26-28]. Gostick et al. [26] used PNM with invasion

percolation to simulate the breakthrough process and predicted that the presence of an MPL

significantly reduces the GDL steady state water saturation. Wu et al. [27] employed PNM to

find the preferred values of MPL thickness, wettability and connectivity for minimum water

saturation in the GDL. The effects of MPL defects on water transport in the GDL was also

investigated by previous PNM researchers [29,30], and the cracks within the MPL were shown to

be the dominant pathways for liquid water transport, maintaining a reduced saturation level in

the GDL.

2.6 Liquid Water Inlet Conditions

The introduction of water into the cathodic GDL occurs through a variety of mechanisms:

electro-osmotic water transport across the membrane, water production from the oxygen

reduction reaction, water vapor condensation within the bulk of the GDL, and condensation near

the low temperature ribs of the flow field [31,32]. The overall GDL saturation (fraction of pore

volume occupied by liquid water) as well as the precise spatial distribution of the liquid water

11

depends on how liquid water is introduced to this porous layer [16,18,19,25,27,33-35]. However,

the precise configuration of liquid water inlets into this material is not well understood.

Many authors have provided valuable insight into how inlet conditions heavily influence the

spatial distribution of liquid water in the material [16,18,19,25,27,33-35]. Two types of boundary

conditions have been generally considered in isolation for studying liquid water transport in the

GDL: uniform pressure boundary condition [16,35] and uniform flux boundary condition [18].

For the uniform pressure condition, all inlet pores along the GDL/CL interface are assumed to be

connected to a single continuous water reservoir. For the uniform flux boundary condition, each

inlet pore along the GDL/CL interface is connected to a separate water reservoir. The uniform

pressure assumption applies to the case where there is negligible hydraulic resistance between

sources of water at the GDL/CL interface. The uniform flux assumption applies to the case

where there is negligible hydraulic connectivity between sources of water at the GDL/CL

interface. Lee et al. [19] found that the maximum saturation at the GDL/CL interface can vary by

0.44 when comparing the uniform pressure to uniform flux boundary condition.

Wu et al. [27] were the first to introduce an alternative, hybrid inlet boundary condition in an

effort to simulate experimental observations. Their boundary condition consisted of a structured

array of same-sized water clusters that were assumed to form between the CL and the GDL,

which consisted of a simulated MPL and a macro-porous substrate. They showed that changing

the water cluster size and the coverage fraction alters the shape of the water saturation profile

within the gas diffusion media.

Although substantial effort has been made to study the effects of inlet conditions on liquid water

transport and flooding within the GDL, most studies are limited to uniform pressure and uniform

12

flux inlet conditions which are not validated conditions for liquid water entering the GDL during

PEM fuel cell operation. Therefore, there is a strong demand for fundamental understanding

regarding the influence of liquid water inlet conditions on two-phase behavior within the GDL,

and the introduction of more realistic inlet conditions.

2.7 PEM Fuel Cell Compression

In a fuel cell stack, cell components are compressed under high compression loads to ensure

contact quality and minimize transport contact resistance between the layered fuel cell materials.

However, over-compression of the GDL can affect cell performance [36]. Therefore, an

optimum compression rate is expected to exist for maximized PEM fuel cell performance.

Several authors have explored the use of analytical [37], experimental [38] and numerical [39]

methods for investigating the effects of compression on the performance of the PEM fuel cell.

Numerical methods have been used extensively for analyzing PEM fuel cell performance. In

particular, commercial computational fluid dynamics (CFD) software packages have been

utilized frequently to develop multidimensional models of the PEM fuel cell for studying the

performance of the cell under compression loads [40]. For these models, the values applied

throughout the non-uniform distribution of transport properties are taken from ex-situ

measurements, where the entire GDL is compressed to varying degrees [40].

2.8 Modeling GDL Compression

The non-uniform compression of the GDL significantly modifies the microstructure of this

porous layer which should be accounted for in multiphase simulations of the GDL. Various

techniques have been developed and employed for modeling the compression of the GDL.

13

Traditionally, finite element methods were used to simulate the deformation of the GDL under

compression [41], and the results were then coupled with a continuum model to analyze the

transport of species in the modeled domain. Schulz et al. [42] simulated the compression of the

GDL using a reduced model of compression. In this model the macroscopic behavior of the GDL

structure under compression was transferred into the unidirectional morphological displacement

of solid voxels with the assumption of negligible transverse strain. In another study, Froning et

al. [43] used a simple compression model to simulate compression in a stochastically created

fibrous GDL and employed a Lattice Boltzmann model for mass transport simulations. In this

model, adjacent layers of the material were merged to simulate GDL compression. Recently,

Gaiselmann et al. [44] introduced a parameterized model that virtually generates the

microstructure of compressed fibrous materials. In this model, fibers are translated with a vector

field which depends on the locations of fibers and the rate of compression. These compression

models can be applied to stochastically created or reconstructed images of commercial GDL

materials to investigate multiphase transport in compressed GDLs.

The use of micro-computed tomography is an alternative approach to generate microstructural

representations of compressed GDLs [45-47]. This technique has the advantage of intrinsically

capturing an accurate representation of the compressed domain, while avoiding any simplifying

assumptions associated with a numerical model.

2.9 Multiphase Transport in Compressed GDLs

The performance of PEM fuel cells is closely related to the mass transport capabilities of the

GDL. The non-uniform compression of the GDL due to its contact with the rib and channel

structured flow field alters the microstructure of the material and the dynamics of liquid water

14

transport through the GDL. This, in turn, affects the reactant diffusion pathways and

consequently the performance of the PEM fuel cell [36].

Experimental and numerical measurements of the effective transport properties, e.g. oxygen

diffusivity and thermal conductivity, of compressed GDLs have been the concentration of a

number of studies [48]. In addition, imaging techniques such as X-ray computed tomography

have been utilized to analyze the effects of uniform and non-uniform compression on the

microstructure and transport properties of commercial GDL materials, including porosity,

tortuosity, and permeability [45,49]. Finally, capillary pressure – saturation relations and liquid

water breakthrough pressure were measured for commercial GDL materials at various

compression states [50].

Several attempts have been made in visualization and quantification of liquid water distribution

in compressed GDLs. These include experimental methods, such as fluorescence microscopy

[51,52], X-ray computed tomography [46], and synchrotron radiography [53], among others

[54].

In addition, continuum models have been employed to numerically investigate liquid water

flooding in deformed GDLs [55]. Commercial CFD software packages have been frequently

used to investigate water transport in compressed GDLs [56]. Chippar et al. [56] investigated the

effects of non-uniform GDL compression on liquid water transport in the GDL, as well as its

effect on the performance of the cell using the STAR-CD CFD package. They predicted that in a

compressed GDL, more water will accumulate near the ribs due to the reduced porosity and

permeability in that region. Olesen et al. [57] developed and utilized a 3-D model in the CFX 13

(ANSYS Inc.) CFD package to investigate the effect of GDL compression on the distribution of

15

liquid water and oxygen in the cathode side of a PEM fuel cell. They predicted a decrease in the

oxygen transport rate near the rib due to the compression of the GDL, which subsequently

decreased liquid water production in the CL under the rib. Wan and Chen [58] used the Fluent

CFD package to solve two-phase transport equations and studied the distribution of liquid water

in a fuel cell with a compressed GDL, and determined that land compression can substantially

lower the liquid water saturation under the land. While the traditional continuum-based models

are widely used for simulating water transport in the GDL, their use may lead to inaccurate

approximations of water distribution in this porous layer. These models do not incorporate pore-

scale physics into their simulations and assume smooth distributions of water throughout the

material. This is in stark contrast to the discrete liquid water clusters predicted by pore-scale

models [16,19,28,59], and directly visualized with in-situ X-ray computed tomography [60-62].

In addition, continuum models require prior knowledge of multiphase transport properties as

inputs to the model.

In an attempt to incorporate pore-scale physics into the simulation of liquid water in compressed

GDLs, Mukherjee et al. [63] applied the compression model developed in [42] to stochastically

generated non-woven carbon paper GDLs, and they investigated liquid water distributions in the

GDL at various compression states using a two-phase Lattice Boltzmann model. This

compression model was also used with a single-phase Lattice Boltzmann model to study the

effect of compression on the permeability of numerically reconstructed Toray TGPH-090 and

SGL Sigracet 10BA GDL materials [64]. They reported that GDL compression exhibits

enhanced resistance to liquid water transport in the in-plane direction due to the change in the

GDL microstructure leading to increased tortuosity. However, simulations were performed on a

16

relatively small GDL domain, since incorporating a large region of the GDL in an LBM

simulation would be computationally intensive.

2.10 Oxygen Effective Diffusivity

The effective diffusivity of the GDL is a unique characteristic of the material expressed as a

function of the GDL microstructure and the bulk diffusivity [65]. This property is described as:

(2.4)

where is the effective diffusivity of the GDL, is the GDL effective diffusion coefficient,

and is the bulk oxygen diffusivity in air. There is a strong interest in characterizing the

diffusive resistance of various GDL materials as a decrease in the effective diffusion coefficient

from unity, results in a decrease in the Nernst potential of the cell which in turn increases the

concentration polarization. Therefore, modeling techniques capable of accurately predicting the

mass transport limitations of GDL materials are required in order to design GDL materials with

high effective diffusion coefficients. Many analytical and theoretical correlations are available in

the literature that can be used to estimate the effective diffusion coefficient of the GDL [66-69];

however, these expressions may over-predict the effective diffusion coefficient [70], since they

are mainly formulated for porous media that are simplifications of the GDL.

Several authors have explored the use of ex-situ and in-situ experimental methods for measuring

the effective diffusivity of GDL materials. These techniques include using a diffusion bridge [71-

73], a Loschmidt cell [70,74,75], and a limiting-current method [76-78], among others [79,80].

17

Experimental methods have been used to directly measure the mass transport properties of

MPL/substrate materials [73,74,81-83]. In some studies, the properties of the plain substrate and

the MPL/substrate assembly were measured separately, and the MPL properties were inferred by

subtracting the properties of the substrate [74]. Despite the large volume of available

experimental results, the experimental measurements of GDL diffusivity exhibit high

measurement uncertainty and remain expensive and time consuming to conduct. In addition, it is

difficult to resolve and explain the impact of the heterogeneous microstructure of the GDL

through experimental approaches. Therefore, numerical techniques have been highly valuable for

investigating the microstructure of the substrate and its effect on gas transport through this

porous medium [83-87].

Numerical methods have been utilized to investigate gas diffusion in the MPL [83,88-94].

Becker et al. [95] developed a multi-scale model for determining the binary diffusion coefficient

of MPL/substrate materials accounting for Knudsen diffusion. They found that the presence of

the MPL had a larger effect on oxygen diffusion in the through-plane direction compared to the

in-plane direction. Using a similar technique Zamel et al. [96] investigated the effect of MPL

thickness, porosity, and its penetration depth into the substrate on the effective diffusivity of the

MPL/substrate assembly. Wargo et al. [97] applied X-ray computed tomography and focused ion

beam-scanning electron microscopy (FIB-SEM) to obtain the microstructure of the material and

employed numerical methods to calculate the mass transport characteristics of MPL/substrate

assemblies. They found that the addition of the MPL caused a decrease of ~50% in the effective

diffusion coefficient of the MPL/substrate assembly.

Despite the large number of numerical and experimental attempts to predict the effective

diffusion coefficient of MPL/substrate materials, these studies did not account for the non-

18

uniform penetration of the MPL into the substrate that is observed in GDL materials that have an

MPL coating. Therefore, there is a critical need for developing accurate numerical models for

predicting the diffusivity characteristics of MPL coated GDL materials which aids the design of

MPL/substrate assemblies with preferred gas transport qualities.

19

2.11 Figures

Figure ‎2.1 Schematic of PEM fuel cell electrode arrangement and operation.

20

Figure 2.2 SEM image of a Toray GDL at (a) 25x, (b) 100, and (c) 500x magnifications.

21

Figure 2.3 SEM image of the MPL coating in a SGL GDL at (a) 25x, (b) 100x, and (c) 500x

magnifications.

22

(a) (b)

Figure 2.4 Schematic representation of (a) a porous material and (b) the pore network describing

the pore space of the material.

23

3 Liquid Water Inlet Conditions

3.1 Introduction

In this chapter, the influence of the liquid water inlet boundary conditions at the gas diffusion

layer (GDL)/catalyst layer (CL) interface on the spatial distribution of liquid water within the

GDL was studied. Pore network modeling with invasion percolation was used to simulate liquid

water transport in a commercially available GDL, where the detailed, 3D microstructure of the

GDL was obtained through X-ray imaging. Three inlet boundary conditions were studied:

uniform pressure (single reservoir), uniform flux (completely discretized reservoirs), and

distributed uniform pressure (random spatial- and size-distributions of reservoirs). The

distributed uniform pressure boundary condition was presented as a more realistic inlet, where

inlets are randomly distributed reservoirs that are connected to multiple inlet pores. It was found

that the overall saturation ranged from 6% to 28% when the number of inlets ranged from 20 to

300; however, the GDL/CL delamination dominated water transport behavior. The results of this

chapter are published in the Journal of the Electrochemical Society.

3.2 Motivation and Objective

PEM fuel cells are promising electrochemical energy conversion devices; however, at high

current densities they are prone to the accumulation of excess liquid water (flooding) in the

cathode GDL. This excess water leads to problems such as reduced oxygen transport pathways to

the CL, performance degradation, and reduced efficiency. Unfortunately, the mechanisms of

liquid water formation within the CL and the GDL/CL interface are difficult to observe during

PEM fuel cell operation. However, using direct visualization in an operating fuel cell, Zhang et

24

al. [98] revealed that during operation the GDL/CL interface is covered with several independent

water clusters.

While several researchers have developed and applied pore network models to study the

distribution of liquid water in the GDL and the effects of various inlet conditions on water

saturation [16,18,19,27,33-35], most work has been performed on regular, cubic pore networks.

Alternatively, a number of 3D irregular pore networks have been developed, which provide a

better approximation of real material structure of the GDL. Gostick presented a 3D irregular pore

network based on Voronoi and Delaunay tessellations [99]. In another study, Putz et al.

generated random pore network topologies using an open source pore network modeling

framework named OpenPNM [100]. Luo et al. demonstrated that pore network modeling can be

performed on equivalent pore networks extracted from 3D reconstructions of the GDL [101].

Equivalent networks inherently account for all microstructural characteristics of GDL materials,

which facilitate a better understanding of how liquid water invades various GDL configurations.

The objective of this study is to investigate the effect of various boundary conditions on the

resulting saturation of an equivalent pore network of a GDL. The equivalent pore network is

generated using 3D X-ray images of SGL Sigracet 25BC, and invasion percolation is employed

to simulate liquid water transport in the material with varying inlet conditions. A new boundary

condition is introduced whereby various sized independent water reservoirs are stochastically

placed at the GDL inlet to mimic the formation of water clusters of various sizes at the CL. In

addition, two scenarios are considered in this study for the GDL/CL contact quality. The first

scenario mimics a slight delamination between the GDL and the CL, and the second mimics full

contact between the GDL and the CL. Inlet condition effects are studied for both scenarios and

25

breakthrough saturation profiles are compared as a means to compare the impact of these

boundary conditions on water management in the GDL.

3.3 Methodology

3.3.1 Imaging

X-ray micro-computed‎tomography‎(μCT)‎imaging‎was‎performed‎(40‎kV,‎Skyscan‎1172,‎

Belgium) for uncompressed SGL Sigracet 25BC paper GDL with 5 wt % polytetrafluoroethylene

(PTFE) and treated with an MPL coating [102]. The resulting tomograms were obtained with a

voxel‎resolution‎of‎2.44‎μm,‎and‎once‎stacked‎together,‎created‎a‎3D‎greyscale‎image.‎The‎full‎

image was cropped to a square subsection of 1025 × 1025 voxels (2.5 × 2.5 mm). The 3D

greyscale image was converted into a trinary image using a technique similar to the method

described in [103].‎The‎μCT‎resolution‎was‎not‎sufficient‎to‎visualize‎the‎MPL‎micro-pores, but

it was sufficient to reveal the larger cracks and holes of the MPL described in [104], which are

assumed to be the dominating pathways for liquid water transport through the hydrophobic MPL.

3.3.2 Pore Network Modeling

After a 3D trinary image of the material was obtained (see Figure 3.1a), the pore space was

analyzed to extract a topologically equivalent pore network (see Figure 3.1b). A customized

watershed algorithm [105] written in C++ was utilized to extract the pore networks. In this

method, the distance of each void voxel to the nearest solid voxel was calculated, creating a

distance map of the pore space. Then, the voxels within the pore space were grouped into

clusters based on the watershed of this distance map, and each pair of adjacent pores was

connected by throat voxels. Over-segmentation (the process by which the segmented pores are

themselves segmented into subcomponents due to image noise) was reduced with a median filter

26

on the distance map. Additionally, a search was performed to find pores connected to throats of

equivalent size. Such pores were combined with these neighboring throats and pores. The Purcell

toroid model was used to account for the converging-diverging geometry of the throats [99].

Figure 3.1b shows the locations and relative sizes of pores represented by spheres. The pore

diameter distribution on the top surface of the GDL was determined by the void space at the

GDL outlet which did not affect the liquid water distribution in the GDL, since water movement

was assumed to stop when water reached the outlet pores. The through-plane morphological

changes were intrinsically captured in this model due to the use of a μCT scanned image as the

domain. Due to the imperfections in the segmentation algorithm, a number of fiber voxels at the

top of the material were marked as MPL voxels. Also the extracted pore volume of the network

was represented with spheres which might not cover the entire pore space of the actual extracted

pore. Therefore, some of the MPL material is visible in Figure 3.1b, which has no effect on the

results of this study.

3.3.3 Invasion Simulation

Invasion percolation without trapping as defined by Wilkinson and Willemsen [106] was

performed to simulate the movement of liquid water within the GDL. Invasion percolation is a

two-phase invasion simulation that advances invading fluid based on pore and throat capillary

entry pressures. This algorithm allows individual water clusters to fluctuate in capillary pressure

depending on their local interface conditions. The invasion process was simulated with the

following assumptions:

the process was quasi-static,

the viscous forces were negligible,

27

the system was isothermal at 25 ,

the domain was uniformly hydrophobic (it was assumed that the PTFE coated the entire

GDL, and there was a uniform contact angle of 110 ),

flow field ribs were hydrophilic and were assumed to cover 50% of the outlet,

when a breakthrough event occurred, defined as the instant a liquid water cluster reached

the outlet surface of the GDL (either rib or channel), the liquid water cluster did not

continue to grow within the GDL,

clusters grew simultaneously at uniform volumetric rates,

the GDL was initially dry,

liquid water at the gas channel was not considered, and

thin film of air persisted in invaded pores and throats which prevented trapping.

Due to the assumption that the invasion process was quasi-static with negligible viscous forces,

the final saturation distribution became deterministic, independent of the assumed water flux.

Additionally, each isolated water cluster in the network can be assumed to be at a specific

uniform pressure at every simulation step, dictated by the entry pressure of the current

pore/throat being invaded. This means that cluster pressures, although spatially uniform at a

given point in time, fluctuated throughout the invasion process.

The simulation was initialized by locating all pores at the GDL/CL interface in contact with any

assumed water reservoirs in the region. For each reservoir, all such pores, labeled inlet pores,

were initiated as fully saturated with liquid water, belonging to a single water cluster, and all

neighboring throats were defined as the interfacial throats of that cluster. In this algorithm,

clusters were developed simultaneously; therefore, at each step of the simulation, the interface of

28

a cluster was advanced through its interfacial throat with the lowest capillary entry pressure, and

the adjacent pore was fully saturated, if not already invaded.

Simulation steps were ordered based on the filling volume of these pores and throats, assuming

that all original clusters grow at a uniform volumetric rate. During this process, when a throat

separating two water clusters was invaded, the clusters were merged creating a new cluster with

a volumetric growth rate equal to the sum of the original clusters. This process was repeated until

breakthrough occurred for each cluster in the network.

A liquid water cluster that reached the flow field rib was also considered to have reached a stable

configuration as the pore space adjacent to the hydrophilic rib would have a lower capillary

pressure barrier than those in the bulk of the hydrophobic GDL. At the completion of each

simulation, the breakthrough saturation was calculated for each planar subsection of the material.

Saturation at the flow field surface of the GDL was not considered. Saturation is defined for this

study as the volume of liquid water divided by the volume of available void space. It should be

noted that this definition of saturation does not account for the unresolved void space within the

MPL.

3.3.4 Inlet Boundary Conditions

Various inlet conditions were considered to represent a variety of condensation conditions that

are expected to occur during fuel cell operation. Since the accurate condensation conditions are

not clearly understood in the literature, previous researchers have considered various

assumptions for condensation points at the GDL/CL interface for studying liquid water transport

in the GDL, particularly the assumptions of uniform pressure and uniform flux which are

fundamentally different [18].

29

Schematics of the three boundary conditions used in this study are shown in Figure 3.2. Figure

3.2a and Figure 3.2c show the side and top views of the uniform pressure and uniform flux

boundary conditions, respectively. To create a uniform pressure boundary condition, the

simulation was initiated with one liquid water reservoir in contact with all inlet pores, creating a

single water cluster spanning the entire inlet face of the network. Therefore, at each simulation

step, the entire inlet face is at a spatially uniform pressure. To create the uniform flux boundary

condition, liquid water was injected into the network through many independent water reservoirs

located adjacent to each of the ~2000 pores at the GDL/CL boundary, leading to ~2000

independent water reservoirs and as many independent clusters at the start of the simulation. A

single, arbitrary flow rate was assigned to each such cluster. Using this boundary condition, the

overall water flux is approximately uniform across the entire inlet face.

The distributed uniform pressure boundary condition proposed in this study is shown in Figure

3.2b. This boundary condition was used for simulating the formation of water clusters with a

range of sizes at the CL, which is expected to occur during fuel cell operation. For this boundary

condition 20, 40, 100, and 300 water reservoirs were considered at the GDL inlet. Figure 3.2b

displays 300 reservoirs stochastically placed with a uniform distribution at the GDL inlet in this

boundary condition. According to in-situ visualizations of micro-droplet formation on the

cathode CL [98], the diameter of each circular reservoir was randomly chosen from a uniform

distribution between 7.5 to 60 microns. Due to the stochastic placement of water reservoirs at the

inlet, some inlet pores may not be covered by a reservoir, while a reservoir with a large diameter

may cover multiple inlet pores.

30

3.3.5 GDL/CL Contact

Two cases for GDL/CL contact quality were considered. In Case 1, the GDL was ~90%

delaminated from the CL surface, representing poor contact quality. The 90% delamination was

arbitrarily selected to create a large void volume at the GDL/CL interface representing an

extreme case of delamination. In Case 2, the GDL is in full contact with the CL, representing

ideal contact quality. To simulate ideal contact quality the cross section with the lowest through-

plane porosity was chosen to be the GDL inlet to avoid large void regions at the GDL/CL

interface which can be occupied by liquid water blocking oxygen diffusion to the CL. In order to

simulate these two scenarios, the µCT image of an uncompressed GDL was cropped, removing

varying amounts of the rough MPL surface from the domain. Figure 3.3a displays the cropped

region considered for Case 1, where delamination was simulated. In this region, the inlet face

became the through-plane cross-section of the GDL where the local porosity of the material first

reached 90%. The first through-plane slice of this region, which is equivalent to the interface

between the GDL inlet (MPL region) and the CL, is shown in Figure 3.3b. This high local

porosity at the GDL/CL interface is expected to facilitate the formation of a large reservoir of

water. Figure 3.4a displays the cropped region considered for Case 2, where ideal GDL/CL

contact was simulated. Here, the inlet face became the through-plane cross section at the first

local porosity minimum, representing the first plane of the original image that was wholly within

the bulk of the MPL. This region described a situation where the GDL was in full contact with

the CL. Figure 3.4b shows that the MPL cracks are completely visible at the inlet of this region.

To visualize the spatial distributions of liquid water in each domain, saturation profiles were

created where the local saturation of each through-plane slice of the domain was calculated. In

31

the case of the distributed uniform pressure inlet, each saturation profile was the average of 10

saturation profiles obtained from 10 stochastic distributions of reservoirs at the inlet.

3.4 Results and Discussion

In this study, liquid water transport through a commercial GDL material was simulated using the

invasion percolation algorithm described above. The material was SGL Sigracet 25BC which

contained an MPL coating and PTFE treatment. After the pore network extraction, invasion

simulations were conducted with various inlet conditions and for the two cases of GDL/CL

contact quality.

3.4.1 Inlet Conditions

Figure 3.5 displays the breakthrough saturation profiles for simulations where the uniform

pressure boundary condition, uniform flux boundary condition, and distributed uniform pressure

boundary condition were applied to the two contact assumptions (Case 1 and 2) under

investigation.

In both cases of simulated contact quality, comparatively low average saturations were

associated with the uniform pressure boundary condition. The simulations with this boundary

condition reached breakthrough at an overall saturation of 15% in Case 1 (poor GDL/CL contact

quality) and 3% in Case 2 (ideal GDL/CL contact quality). The uniform flux boundary condition

reached the highest average saturations, with 18% overall saturation in Case 1 and 38% in Case

2. Also, the overall saturations for 20 water reservoirs at the inlet were 15% in Case 1 and 6% in

Case 2, while the overall saturations for 300 water reservoirs increased to 17% in Case 1 and

28% in Case 2 (See Table 3.1). This shows that when the distributed uniform pressure boundary

32

condition was considered, the average saturation was positively correlated to the number of

water reservoirs. Therefore, considering various sized independent water reservoirs at the inlet

may be necessary to achieve realistic saturation levels across a variety of operational set points.

In the distributed uniform pressure boundary condition, only one inlet throat per water reservoir

was invaded at the first simulation step, which is similar to the uniform pressure boundary

condition. Also, the presence of more than one reservoir at the inlet can be modeled with the

uniform flux boundary condition. Therefore, the distributed uniform pressure boundary condition

presented here results in liquid water distributions that are a balance between these two extreme

assumptions (uniform pressure and uniform flux), which are typically accepted in fuel cell

studies [18]. The number of reservoirs at the GDL inlet is predicted to correspond to the rate of

water production in the CL, which can be correlated to the current density of the cell. As

capillary forces are expected to dominate the invasion process, flow rates are not relevant for our

simulations. Considering typical operating current densities, flow rates only affect the invasion

time, and they do not impact the invasion pattern. The liquid water pressure of each cluster is

determined by the capillary pressure of the interfacial throats; therefore in this model, there is no

relation between the current density of the cell and water flow rate and pressure. However,

higher current densities might lead to higher concentrations of water vapor in the gas phase,

leading to more condensation sites. The saturation profiles of Figure 3.5 demonstrate that the

overall saturation is an increasing function of the number of inlet water reservoirs. Both the

uniform flux boundary condition and the distributed uniform pressure boundary condition have

various water clusters simultaneously penetrating the GDL. However, the number of original

water clusters with the uniform flux boundary condition is higher, since each inlet pore is

covered with a separate inlet water reservoir, and the network has ~2000 inlet pores. While in the

33

distributed uniform pressure boundary condition the number of original water clusters in the

network is limited to the maximum number of non-overlapping reservoirs at the GDL inlet that

cover at least one inlet pore, which is ~1000 reservoirs when considering the average reservoir

diameter. If the number of water reservoirs passes this limit, reservoirs with very small diameters

will be placed at the GDL inlet, which have a small chance of covering an inlet pore; hence, the

saturation profiles with the distributed uniform pressure boundary condition will not converge

towards the uniform flux saturation profiles even if the number of inlet water reservoirs is very

high.

3.4.2 Simulated Delamination of the GDL

The difference in the saturation levels and liquid water distributions between Case 1 and Case 2

can be explained as follows. The region considered for Case 1 had a large, connected pore space

at the inlet due to the high levels of porosity at the inlet. When water was introduced into this

region, the inlet became flooded, as water clusters initially advanced laterally throughout this

delaminated region. In this situation separate water clusters at the inlet tended to coalesce,

resulting in a boundary condition that resembled the uniform pressure boundary condition.

Therefore, saturation profiles did not vary significantly, even as the number of reservoirs

increased (Figure 3.5a). Figure 3.6 shows the liquid water distribution at breakthrough in the

delaminated GDL with various boundary conditions. It was observed that water distributions in

this region did not vary significantly with the boundary conditions studied.

In Case 2, the MPL cracks created directed pathways through which water percolated into the

bulk of the GDL. In this case, the separate inlet water reservoirs will typically independently

penetrate the bulk of the material; hence, there was a significant difference between the

breakthrough saturation profiles associated with inlet conditions studied (Figure 3.5b). Figure 3.7

34

shows the liquid water distribution at breakthrough in this region with various boundary

conditions, and the liquid water distribution in this region depended heavily on the type of inlet

boundary condition.

Although, the inlet was fully saturated in the uniform pressure boundary condition, only one

water cluster percolated through the GDL. This explains why the saturation levels with this

boundary condition followed the same trend in both cases (poor and ideal GDL/CL contact) and

also why they exhibited the lowest levels of saturation when compared to the other inlet

conditions.

Overall saturations were higher in Case 2 when the uniform flux boundary condition and

distributed uniform pressure boundary condition (with 100 and 300 reservoirs) were employed,

but the saturation profiles in this region were evenly distributed into the bulk of the material,

while in Case 1, a wall of liquid water formed in the delaminated region which would

significantly inhibit oxygen diffusion to the reaction sites. This is displayed in Figure 3.8 and

Figure 3.9 where the material content in each through plane position is shown for Case 1 and

Case 2, respectively. In these figures, void and MPL (with 50% porosity) are permeable to

oxygen. Figure 3.8 shows that in Case 1 oxygen diffusion pathways were blocked by liquid

water at the inlet, whereas Figure 3.9 shows that a clear pathway was available for oxygen

diffusion in Case 2. Thus, it is predicted that Case 2 represented a better performing fuel cell,

even though its cathodic GDL often exhibited higher total saturations.

35

3.5 Conclusions

In this study an equivalent pore network was created using X-ray based images of a commercial

GDL material, SGL Sigracet 25BC. Invasion simulations were conducted with varying inlet

boundary conditions, and the contact quality of the GDL/CL interface was varied. An alternative

boundary condition was introduced in this study which attempts to mimic the formation of

individual water clusters at the CL in operating PEM fuel cells. Saturation distributions were

recorded at the assumed steady state configuration, and mean saturation values were compared.

It was found that the region simulating ideal GDL/CL contact would provide for a better

performing GDL, while it often led to higher average saturations compared to the case with some

delamination. However, saturation profiles of the region simulating ideal GDL/CL contact were

significantly affected by the type of boundary condition.

This study emphasizes the impact of inlet conditions and the GDL/CL contact surface on

breakthrough saturation levels in SGL Sigracet 25BC. This study also suggests that the uniform

pressure boundary condition and the uniform flux boundary condition are extreme cases for

liquid water entering the GDL, while the distributed uniform pressure boundary condition may

be a more realistic inlet condition that is expected to account for a variety of fuel cell operating

conditions.

36

3.6 Tables

Table ‎3.1 Average saturation levels for Case 1 and Case 2 with various inlet conditions

Inlet Condition Saturation for Case 1 Saturation for Case 2

Uniform Pressure 0.15 0.03

20 Reservoirs 0.15 0.06




Uniform Flux 0.18 0.38

37

3.7 Figures

Figure ‎3.1 (a) 3D trinary image of SGL Sigracet 25BC, where the three material phases are MPL

(yellow), fiber (red), and void (transparent) and (b) the extracted pore space of the material.

Yellow, red, and blue represent MPL, fiber, and pore space, respectively.

38

Figure ‎3.2 Side view and top view of the boundary conditions for liquid water entering the

material: (a) uniform pressure, (b) distributed uniform pressure, and (c) uniform flux.

39

Figure ‎3.3 (a) Region considered for simulating poor contact quality at the GDL/CL interface


interface.

40

Figure ‎3.4 (a) Region considered for simulating ideal contact quality at the GDL/CL interface


interface.

41

Figure ‎3.5 Mean saturation values at breakthrough for (a) Case 1 and (b) Case 2. Case 1

describes a situation where the CL is experiencing delamination, and Case 2 simulates full

contact between the CL and the GDL. Through-plane position values are normalized to the

sample thickness.

42

Figure ‎3.6 Liquid water distribution at breakthrough for Case 1 which simulates poor GDL/CL


(c) uniform flux boundary conditions. The red pores indicate the breakthrough locations.

43

Figure ‎3.7 Liquid water distribution at breakthrough for Case 2 which simulates ideal GDL/CL


(c) uniform flux boundary conditions. The red pores indicate the breakthrough locations.

44




plane position values are normalized to the sample thickness.

45




plane position values are normalized to the sample thickness.

46

4 GDL Compression

4.1 Introduction

In this chapter, equivalent pore networks of commercial gas diffusion layer (GDL) materials

were employed to analyze the impact of compression on liquid water transport in the GDL. Two

types of carbon paper GDLs were compressed, and at each compression value, three-dimensional

X-ray tomography images of the samples were obtained. The resulting greyscale images were

segmented into three phases, solid, microporous solid, and void, using a novel segmentation

algorithm. Equivalent pore networks were obtained of each segmented image through a

watershed-based pore segmentation algorithm. There was no need for numerical modeling of

GDL compression as the morphological changes due to compression were intrinsically captured

by X-ray imaging. An invasion percolation algorithm was employed to identify the distribution

of liquid water in each material over the range of compression states. After analysis of predicted

saturation distributions, favorable GDL compression values for preferred liquid water

distributions were found for Toray TGP-H-090 (20%) and SGL Sigracet 25BC (30%). The

predicted liquid water distributions varied significantly between the two material types, which

was attributed to the presence of a microporous layer (MPL) coating in SGL Sigracet 25BC.


Excess liquid water in the gas diffusion layers (GDL) of the PEM fuel cell can block oxygen

diffusion pathways to the catalyst layer (CL) and hinder cell performance. In addition, cell

components are assembled under compressive loads to ensure contact quality between the

layered fuel cell materials; however, the effects of high GDL compression on liquid water

47

behavior and related cell performance are unknown. Understanding how compression affects the

distribution of liquid water in the GDL is vital for informing the design of improved porous

materials for effective water management strategies.

While traditional continuum models have been used to simulate the distribution of liquid water in

compressed GDLs [55], these models do not describe the observed capillary fingering regime in

the GDL [20]. In the past decade, pore network modeling has become widely popular for

studying multiphase transport in the GDL. This method has been used extensively for studying

liquid water transport in the porous layers of the PEM fuel cell [15-17,23,24,107]. Rebai and Prat

[20] used a cubic pore network model to calculate liquid water saturation at breakthrough under

the land and channel at various compression values, where the compression of the GDL under

the land region was simulated using a compression coefficient (a number between 0 and 1)

applied to the diameter of pores and throats under the land regions. Although the authors have

successfully analyzed liquid water transport in a compressed GDL using pore network modeling,

the study has been performed on a regular, cubic pore network. Therefore, more work is required

to harness the full potential of pore network modeling and accurately simulate the distribution of

liquid water in GDL materials under compression, which should aid the evaluation of the cell

performance under compression.

The objective of this study is to understand the distribution of liquid water in the GDL under

compressive loads using pore network modeling. The specific distribution of liquid water in the

GDL is influenced by a combination of operating condition-sensitive condensation scenarios and

the capillary pressure dominated percolation of any such water clusters to the adjacent gas

channels. The water distributions resulting from a variety of assumed condensation scenarios can

be predicted using the pore network modeling approach. Pore networks extracted from

48

synchrotron-based micro-computed tomography images of compressed GDLs were employed to

simulate liquid water transport in GDL materials over a range of compression pressures. The

analysis conducted in this chapter provides a deeper knowledge of how compression and the

GDL microstructure affect the movement of liquid water.

4.3 Methodology

4.3.1 Materials

Two GDL materials were used in this study: Toray TGP-H-090, and SGL Sigracet 25BC. TGP-

H-090 is a carbon-based material produced by Toray Industries which has an uncompressed

thickness of 280 µm, an average porosity of 78 %, and no MPL coating. Sigracet 25BC is a GDL

material produced by the SGL group which has an uncompressed thickness of 235 µm, average

porosity of 80 %, 5 wt % PTFE, and MPL coating.

4.3.2 Synchrotron Tomography

The synchrotron tomography measurements were performed by Dr. Ingo Manke (Institute of

Applied Materials at Helmholtz Zentrum Berlin, Germany) at the BAMline beamline which is

located at the synchrotron source BESSY, a third-generation synchrotron facility at the

Helmholtz-Zentrum Berlin research center. Dr.‎Manke’s‎group‎prepared‎all‎samples‎and‎

acquired the raw images, which were captured with a PCO camera (4008 × 2672 pixels) used in

combination‎with‎a‎lens‎system‎and‎a‎20‎μm‎thick‎CWO‎scintillator. The field of view of 3.6 ×

2.3 mm2 corresponds‎to‎an‎image‎pixel‎size‎of‎0.876‎μm‎and‎a‎respective‎physical‎spatial‎

resolution‎of‎about‎2‎μm‎[45]. Using a W-Si multilayer monochromator, a monochromatic X-ray

beam with energy of 15 keV and an energy resolution of about 200 eV was produced. Circular

49

GDL samples with a diameter of 3 mm were rotated for in equidistant steps, and the

resulting radiographs were reconstructed to 3D volumes.

The samples were compressed using a compression device as the sample holder [45], which

provided accurate compression rates and acceptable X-ray beam attenuation. The device

included a circular base platform with an adjustable compression unit fastened on top of the base

unit. Each circular sample was placed on the base unit with the compression unit applying a

specific compression rate on the sample. An adjusting screw with an ultra-fine-pitch thread

allowed‎for‎an‎adjustment‎precision‎of‎±5‎μm [49]. The compression unit had a channel cut-out

with a width of 0.8 mm and a depth of 1 mm, mimicking one flow field channel and two ribs on

each sample. This device simulated the inhomogeneous GDL compression that occurs during

fuel cell assembly.

4.3.3 Image Segmentation

At the University of Toronto, the grey-scale images of all samples were cropped to a rectangular

subsection of 1.8 × 2.0 mm. When the greyscale tomograms of compressed GDL materials with

an MPL were segmented, three phases were taken into account: solid, microporous material, and

void. The solid phase was considered to be all materials associated with the carbon fiber

substrate, i.e. carbon fibers, carbonized binder, and any PTFE coating on the substrate. The sub-

micron pores of the MPL were below the image resolution, and therefore the bulk MPL material

was considered a secondary, microporous, material phase. The void phase was assumed to

contain no material. The compression device material was manually removed from the image,

and replaced with greyscale values representative of the void region.

50

In the tomograms employed in this study, the greyscale values (arbitrarily rescaled to values

between 0 and 1) correlate to the relative attenuation associated with each cubic voxel-sized

volume of the original material; the higher the greyscale value, the more of the X-ray light can be

assumed to have been attenuated by that region through absorption or scattering. Ideally, the

three phases would have three distinct attenuation levels to be segmented by clean threshold

values. However, because the greyscale values associated with the solid, microporous, and void

phases were not clearly distinct, clean greyscale thresholds could not be used to segment the

image. Instead an algorithm similar to [102] was employed that took into account the intrinsic

structure of the GDL. The roughly cylindrical carbon fibers were observed to be the brightest

greyscale values in the tomogram. The binder and PTFE present in the substrate were assumed to

have behaved as a wetting fluid during application onto the fibers. Also, the solid and

microporous phases were each assumed to be contiguous volumes.

To accurately estimate the volumetric fractions of the respective phases in the domains, material

density, areal weight, and domain size were considered. Accounting for the densities of the

constituent components, the voxels determined to represent the solid phase were assumed to be

of a density of 1.95 g/cm3, and the voxels determined to represent of the microporous material

phase, were assumed to be of a density of 0.67 g/cm3. With reported areal weight values of the

plain substrate (SGL Sigracet 25BA), and the MPL coated substrate (SGL Sigracet 25BC) being

40 g/m2 and 86 g/m

2 respectively, it was determined that the segmented solid and microporous

material phases should approximately occupy areal volumes of 20.5 cm3/m

2 and 68.3 cm

3/m

2,

respectively. Similarly, with the MPL-free material (Toray TGP-H 090), due to an areal weight

of 142 g/m2, the solid phase was predicted to occupy approximately 72.8 cm

3/m

2. These values

51

were then combined with the planar area of each domain to calculate the required volume of each

phase.

After a bilateral filter was applied to each greyscale stack for noise reduction, the above

assumptions were incorporated into the segmentation algorithm in three major steps. In the first

major step, voxels deemed likely to reside in the solid phase, due to their greyscale values, were

identified, and temporarily removed from the image, such that they would not be considered

during the microporous phase segmentation. Then the microporous phase was isolated from the

remaining image. Finally, the solid phase was carefully segmented from any voxels not

identified as the microporous phase. During each of the steps above, after an initial threshold was

performed, a number of binary image operations were performed to ensure that each solid phase

was contiguous, smooth, and of an appropriate number of voxels. For the Toray TGP-H-090

materials, with no MPL, only the final major step was performed.

Figure 4.1 provides a comparison between a through-plane slice of the original greyscale

tomogram of SGL Sigracet 25BC with that of the resulting segmented image, where the three

phases within the porous material have been elucidated.

4.3.4 Network Extraction

After the void and material spaces were separated, the void space was analyzed to obtain an

equivalent network representation of the material, which would describe the void space as pores

connected by throats. In this process, a distance transform was first obtained for the void space,

representing the Euclidean distance between each void voxel and the nearest material voxel. The

void voxels were then grouped into “pores”‎using an inverse watershed algorithm performed on

the distance transform. Finally, voxels at pore interfaces were labeled as “throats” [107]. The

52

information obtained from the image and distance transform included pore location, pore

connectivity, pore volume, pore radius and throat radius. Throat lengths were assumed to be on

the order of a fiber diameter, while throat volumes were assumed to be approximately zero, as

the spherical representations of connecting pores in such materials tend to overlap [25].

Therefore, a constant length of 7.7 μm was assigned to each throat in the network. Figures 4.2

and 4.3 display the 3D segmented images and the 3D extracted networks of Toray TGP-H-090

and SGL Sigracet 25BC, respectively, at 10% and 30% compression.

4.3.5 Boundary Conditions

The configuration of liquid water in the porous GDL has been shown to depend on how precisely

liquid water enters this porous layer [107]. During operation, water is introduced to the fuel cell

through humidified reactants and is produced during the electrochemical reactions at the cathode

CL. Water vapor concentrations can be assumed to be at maximum values near the cathode

GDL/CL interface, while temperatures can be assumed to be assumed to be at minimum values

at the flow field ribs, due to coolant fluid circulated within the flow field plates. These factors

provide reason to assume that condensation of water would be primarily located near either the

GDL/CL interface, or the GDL/rib interface, or both.

In order to simulate the formation of independent liquid water clusters at the GDL/CL interface,

various sized liquid water reservoirs were stochastically placed, without overlap, at the GDL/CL

boundary according to uniform distributions in both planar dimensions. In addition, reservoirs

that did not meet an inlet pore were expanded until they reached an inlet pore or they coalesced

with another water reservoir. Therefore, while all inlet reservoirs were necessarily connected to

some inlet pores, not all inlet pores were connected to an inlet reservoir.

53

In this model, different numbers of water reservoirs were considered at the GDL/CL interface,

which was assumed to be related to the rate of liquid water production (i.e. current density) in the

fuel cell. This allows for the simulation of a variety of operational conditions. At the GDL outlet,

the ribs of the flow field were assumed to have roughly the same wetting properties as the fibers

of the GDL, and condensation near the ribs was not considered; therefore, liquid water can only

exit the GDL through the gas channel.

4.3.6 Water Percolation Simulation

The configuration of liquid water in the porous layers of the PEM fuel cell can be realistically

simulated using the invasion percolation algorithm described by Wilkinson and Willemsen [106]

as the liquid water invasion of these media is a quasi-static process dominated by capillary forces

[16,18,20]. For liquid water percolation through SGL Sigracet 25BC, only the macro-pores, such

as cracks and holes of the MPL were considered as viable percolation pathways. It was assumed

that each material was entirely coated with PTFE, and the domain was uniformly hydrophobic

with a contact angle of 110 . Furthermore, both GDLs were assumed to be initially dry and

isothermal at 25 , and liquid water at the gas channel was not considered.

Each simulation was initiated by labeling any pores at the GDL/CL interface connected to a

water reservoir as inlet pores. Inlet pores were initiated as fully saturated with liquid water. Any

inlet pores in contact with the same water reservoir were grouped together to form inlet clusters.

At each stage of the simulation, clusters individually advanced through the largest uninvaded

throat available to them, following invasion percolation logic, without considering trapped air.

Clusters were assumed to grow simultaneously at uniform volumetric rates and the order of

cluster filling was chosen according to this assumption. This process continued until each cluster

reached a breakthrough event, defined as the moment a liquid water cluster reached the gas

54

channel (the outlet surface of the GDL). When breakthrough occurred, the liquid water cluster

was assumed to be in a stable configuration and no longer allowed to continue growing within

the GDL. Each simulation was repeated 10 times with 10 stochastic distributions of water

reservoirs at the inlet, and the saturation levels were recorded at each planar subsection of the

material. The reported saturations are the average of the 10 saturation profiles obtained for each

inlet condition studied.


In this study, pore network models were generated for two types of GDL materials to study

liquid water transport using a capillary force dominated percolation simulation. At each

compression state, 20, 40, 100, and 300 condensation points were considered at the GDL/CL

interface of each material.

4.4.1 Toray TGP-H-090

The top and side views of breakthrough water distributions in Toray TGP-H-090 across the

studied compression states are shown in Figure 4.4. The inlet condition represented by Figure 4.4

is 100 reservoirs, and the brightness of each pixel corresponds to the amount of liquid water

present in the material in that location. Figure 4.5 displays the distribution of breakthrough

saturations in the through-plane direction of the material across the compression states and inlet

conditions studied. According to this figure, the saturation is generally a decreasing function

from inlet to outlet, with saturation levels above 60% at the inlet. Figure 4.6 shows both the

average and inlet saturations predicted for Toray TGP-H-090 across the compression states and

inlet conditions studied. Although, the lowest average saturation was associated with the

uncompressed sample, the high levels of water saturation near the inlet are predicted to shield

55

large portions of the CL to oxygen diffusion. Therefore, in general GDL compression appears to

decrease the possibilities of GDL flooding (accumulation of excess liquid water) near the CL.

Being that the 20% compressed sample had the lowest amount of saturation at the inlet, the

authors predict that Toray TGP-H-090 would have the best performance at 20% compression

even though it had higher average saturations than less compressed samples.

Figure 4.6 also demonstrates that both the average and inlet saturation values increase with the

number of reservoirs at the inlet. This trend is expected as more condensation sites will be

available at the GDL/CL interface, leading to increased amounts of liquid water in the material.

As shown in Figure 4.6(a), the inlet saturation decreases with increasing compression; however,

the number of inlet reservoirs has a dominating impact on inlet saturation as the number of inlets

increases (Figure 4.6(b-d). This indicates that the effect of compression on the amount of liquid

water at the GDL/CL interface is more significant at moderate operational conditions.

4.4.2 SGL Sigracet 25BC

The top and side views of breakthrough water distributions in SGL Sigracet 25BC across the

studied compression values are shown in Figure 4.7, corresponding to the case of 100 inlet

reservoirs. Figure 4.8 contains the breakthrough saturation distributions in the through-plane

direction. According to Figure 4.8, a local saturation minimum is generally observed near the

inlet face of the GDL at the MPL/substrate interface. This drop in the saturation level is

associated with the hydrophobic nano-pores of the MPL, which were assumed to stay free of

water during the percolation process, due to their extremely high capillary entry pressures. For

this material, the predicted saturations for the 30% compressed sample were the most uniformly

distributed through the thickness of the material except for the peak near the gas channel (outlet

face of the GDL). This rise in the saturation level is associated with the reduced porosity under

56

the land region, imposed by compression, which increases the capillary barrier of throats under

the land leading to the buildup of liquid water in this region. Also the predicted saturations for

the 30% compressed sample had the lowest values near the CL (inlet face of the GDL). Figure

4.9 shows the average and inlet saturation values over the range of compression states and inlet

conditions for this material. It was observed that neither compression nor inlet conditions had a

significant effect on the average saturation values. However, the 30% compressed sample, which

had slightly higher average saturations, exhibited significantly lower saturation values at the inlet

face (advantageous for oxygen diffusion to the CL). Therefore, the 30% compressed material

may lead to better performance compared to other compression rates.

4.4.3 Significance of the microporous layer

The MPL consists of carbon black particles and PTFE and is usually coated onto the fibrous

substrate. The microporous and hydrophobic structure of the MPL resulted in lower saturation

levels in this region, which is beneficial for the diffusion of oxygen to the CL. Comparing the

saturation profiles and the average saturation values in the materials considered in this study

showed that with the same inlet conditions less liquid water accumulated in SGL Sigracet 25 BC

compared to Toray TGP-H-090. It was assumed that liquid water will not penetrate the nano-

pores of the MPL and only percolates through the MPL cracks and holes; therefore, the nano-

pores of the MPL provide pathways for oxygen diffusion that aid cell performance.

Figure 4.10 shows the through-plane porosity distributions for both materials at various

compression states. In porosity calculations of SGL Sigracet 25BC, it was assumed that the

voxels associated with the MPL coating had a porosity of 50% [95]. The addition of an MPL

coating in SGL Sigracet 25BC decreases the porosity and permeability of the material [108].

This is evident from Figure 4.10 as the porosity near the inlet (first 10% of the thickness) is

57

substantially lower for SGL Sigracet 25BC compared to Toray TGP-H-090. The steep negative

slope in porosity levels near the inlets of both materials should promote lateral water cluster

growth, according to previous studies [24]. However, the crack and holes of the MPL which are

the dominating pathways for liquid water transport in the MPL [104,109] are only a fraction of

the MPL void space and have little lateral connectivity. Therefore, as the nano-pores of the MPL

were not occupied by liquid water, the overall saturation near the inlet of SGL Sigracet 25BC

was lower than that of Toray TGP-H-090.

4.5 Conclusions

In this study, the effects of compression on liquid water transport in two commercially available

GDL materials were investigated through the method of pore network simulations on equivalent

networks. GDL materials were compressed using a compression device with an integrated

channel profile simulating the inhomogeneous compression induced by the rib/channel structure

of the flow-field during fuel cell assembly. Synchrotron-based X-ray images provided the 3D

structure of the materials at each compression state which was used to create an equivalent pore

network of each sample. Invasion percolation simulation was performed on the corresponding

network of each sample, and for each material an optimum compression state was identified with

respect to water management and associated fuel cell performance.

In both GDL materials, the lowest average saturation was associated with the uncompressed

sample. However, high levels of water saturation observed near the inlet face of the

uncompressed samples are expected to shield large portions of the CL to oxygen diffusion. Since

less water accumulated near the inlet of the compressed samples, GDL compression is expected

to decrease the possibilities of GDL flooding near the CL. The favorable compression value for

58

Toray TGP-H-090 was predicted to be 20% as this sample had the lowest amount of saturation at

the inlet, though it had slight higher average saturations than less compressed samples. For SGL

Sigracet 25BC, the 30% compressed sample had the lowest levels of saturation near the inlet face

of the GDL, and was found to be the best performing GDL, although it resulted in higher levels

of saturation near the outlet (GDL/gas channel interface).

In addition, this study highlights the role of the MPL on liquid water transport in the GDL and

ultimately the performance of the cell. It was shown that the presence of an MPL coating in SGL

Sigracet 25BC reduces liquid water accumulation in this material and provides more pathways

for oxygen to diffuse to the reaction cites during flooding conditions, which will increase the

performance of the cell. The technique of capturing the morphological changes of GDL materials

using X-ray imaging and converting this information to equivalent networks for multiphase

simulations can be applied to other commercial GDL materials to understand the effect of

compression on a wide range of materials.

59

4.6 Figures

Figure ‎4.1 (a) Grey-scale and (b) trinary images of compressed SGL Sigracet 25B. The three

phases in the trinary image are solid (dark grey), MPL (light grey), and void space (black).

(a)

(b)

60

Figure ‎4.2 (a) Segmented image of Toray TGP-H-090 at 10% compression and (b) its pore

space. (c) Segmented image of Toray TGP-H-090 at 30% compression and (d) its pore space.

GDL samples were approximately 1.8 × 2 mm.

(a)

(b)

(c)

(d)

61

Figure ‎4.3 (a) Segmented image of SGL Sigracet 25BC at 10% compression and (b) its pore

space. (c) Segmented image of SGL Sigracet 25BC at 30% compression and (d) its pore space.

GDL samples were approximately 1.8 × 2 mm.

(a)

(b)

(c)

(d)

62

Figure ‎4.4 Water distribution in Toray TGP-H-90 at (a) 0%, (b) 10%, (c) 20%, and (d) 30%

compression with 100 condensation points at the inlet (GDL/CL interface).

63

Figure ‎4.5 Breakthrough saturation profiles for Toray TPG-H-090 at various compression states


stochastically placed at the inlet.

64


Toray TPG-H-090 at various compression states and with (a) 20 reservoirs, (b) 40 reservoirs, (c)

100 reservoirs, and (d) 300 reservoirs stochastically placed at the inlet.

65

Figure ‎4.7 Water distribution in SGL Sigracet 25BC at (a) 0%, (b) 10%, (c) 20%, and (d) 30%

compression with 100 condensation points at the inlet (GDL/CL interface).

66

Figure ‎4.8 Breakthrough saturation profiles for SGL Sigracet 25BC at various compression states


stochastically placed at the inlet.

67


SGL Sigracet 25BC at various compression states and with (a) 20 reservoirs, (b) 40 reservoirs,

(c) 100 reservoirs, and (d) 300 reservoirs stochastically placed at the inlet.

68

Figure ‎4.10 (a) Toray TPG-H-090 and (b) SGL Sigracet 25BC porosity profiles at various

compression states. The MPL microporosity is assumed to be 50%.

69

5 MPL/substrate Oxygen Diffusivity

5.1 Introduction

In this chapter, a novel technique is introduced for calculating the oxygen diffusivity in a

polymer electrolyte membrane (PEM) fuel cell microporous layer (MPL) through pore network

modeling. The composite gas diffusion layer (GDL) with an MPL was modeled with a hybrid

network of block MPL elements with assigned bulk properties, combined with a network of

larger, discrete pores present in the remainder of the GDL. This hybrid network was incorporated

into our pore network model, and effective diffusivity predictions of GDL materials with MPL

coatings were obtained. Through-plane diffusivity values were calculated for stochastically

generated GDL materials to validate this technique. The predicted diffusivity values were in

excellent agreement with analytically calculated effective diffusivities for numerically generated

materials. Upon conducting a mesh sensitivity study, it was determined that a maximum MPL

element size of could be employed, resulting in a maximum error of 1%. The effective

diffusion coefficient of the numerically generated material was predicted to be 0.48 using an

MPL element size of . The results of this chapter are submitted to the Journal of Materials

Chemistry A.


The performance of the PEM fuel cell is strongly influenced by the diffusion resistance of the

GDL, as the Nernst potential of the cell is directly related to the oxygen concentration at the

reaction sites. Therefore, a full understanding of GDL mass transport limitations, especially at

high current densities, is crucial for informing preferred GDL design for optimum cell

70

performance. Gas transport through the GDL occurs in both in-plane and through-plane

directions; however, the addition of an MPL layer has a major effect on oxygen diffusion in the

through-plane direction [95]. Fishman and Bazylak [102,110] found that in commercial GDL

materials where the MPL is coated onto the substrate, the MPL penetrates the substrate non-

uniformly. Thus the MPL and the substrate cannot be assumed to be separate, distinct layers,

which further emphasizes the need to examine the transport properties of the material as a

composite.

Pore network modeling is a powerful tool for studying gas diffusion in porous media. This

method has been used to investigate oxygen diffusion in MPL/substrate assemblies under dry

and wet conditions [26,30,111]. However, previous PNM and other numerical estimations of the

MPL/substrate effective diffusion coefficient have not accounted for the non-uniform MPL

intrusion into the substrate. While pore network modeling boasts the ability to incorporate pore-

scale physics into its simulations, explicitly describing the nano-pores within the MPL would

pose a high computational burden on the system. Since the mean MPL pore size is two to three

orders of magnitude smaller than that of pores in the macro-scale substrate, there would be

several thousand times as many nano-pores as there are pores in the substrate for a full pore

network used to explicitly describe the MPL-coated GDL.

The purpose of this work is to create a pore network model for predicting the mass transport

characteristics of bilayer GDL materials where the MPL merges with the substrate in the absence

of a distinct separating boundary. To accomplish this, a modified pore network model is

introduced for investigating the through-plane oxygen diffusion in an MPL-coated GDL

material. A hybrid network of continuum MPL elements and discrete pores is created for

transport calculations. The through-plane diffusivity values of sample materials are calculated

71

both analytically and numerically to validate the results of this model. Finally, the preferred MPL

element size for obtaining accurate results with the least computational burden is introduced.

5.3 Methodology

In order to create topologically representative pore networks of a GDL with an MPL, images of

GDL materials were employed, where images had three distinct phases: MPL, fibers, and void.

While the 3D representation of a material could be created either stochastically or using micro-

computed tomography (micro-CT) techniques, stochastic methods were employed here to

achieve arbitrarily high resolutions of the MPL structure. To create an equivalent network of the

material for diffusivity calculations without increasing the number of modeling elements by

several orders of magnitude, the MPL was treated as an arrangement of uniform, cubic,

continuum elements. Additionally, this hybrid network was necessary as the resolution of current

micro-CT devices is not yet capable of capturing the MPL pore space.

5.3.1 Stochastic Network Generation

Pore network simulations were performed on stochastically generated numerical models of

carbon paper substrates with and without MPL coatings. The modeled GDLs were both

compressed and uncompressed and exhibited macroscopically homogenous porosities. Straight,

cylindrical fibers of uniform length and diameter were iteratively placed in the material domain

until the specific bulk porosity of the simulating material was achieved. Fibers centers were

prescribed random x-, y-, and z-coordinates, where z-coordinates were prescribed from

experimentally measured through-plane material distributions. In addition, a random planar angle

and pitch (also chosen from experimentally measured distributions) were assigned to each fiber.

Finally all coordinates were converted to the units of voxels. Fibers were allowed to intersect in

72

this model, which is a commonly employed assumption in the literature used to produce realistic

results [85,86,96,112]. Binder and PTFE were added to the material assuming that they behave

as wetting fluids.

The substrate modeling algorithm described above was employed to create two material samples.

The first material represented a compressed SGL Sigracet 25BA substrate, and the second

represented an uncompressed SGL Sigracet 25BA substrate. A sheet-type, non-penetrating MPL

was digitally applied to the compressed sample. A more realistic, penetrating MPL was digitally

applied to the uncompressed sample using an invasion simulation, referred to as morphological

image opening, described by Gostick [99].

The penetrating MPL was assumed to have an average thickness of 70 µm, 50 µm of which was

assumed to exist outside of the extent of the substrate. To represent crack-like defects that

puncture the MPL surface, vertical columns of rhombus cross sections were removed from the

MPL until 3.5% of the surface was covered in cracks-like defects.

5.3.2 Pore Network Extraction

Once the 3D image of the material was created, a pore network extraction algorithm described in

[107] was used to extract a topologically equivalent network of the void space. Using this

method the pore space of the material was characterized with a network of pores and throats,

where pores were represented with spheres, and throats were represented with cylinders. The

information obtained from the void phase of the 3D image included pore location, pore

connectivity, pore volume, pore radius and throat radius.

73

5.3.3 MPL Image Processing

After the pore space was identified, the 3D images of stochastically created materials were

analyzed to represent the MPL phase with a continuous network of cubic elements. A script

written in MATLAB was used to create this MPL network. Figure 5.1 shows a schematic

representation of the steps taken for creating a continuous network of the MPL. Each high

resolution 3D image was segmented into cubic elements of equivalent size, except for the

smaller edge and corner elements should the image dimensions not be whole multiples of such

cubes. Then, an element was marked as either MPL or non-MPL, depending on whether at least

a certain percentage of its volume was occupied by MPL voxels. This percentage was initially set

to 50%, and it was modified until the total MPL element volume matched the initial MPL

volume with a deviation of less than 1.5%. A schematic representation of this refining step is

shown in Figure 5.1b.

As shown in Figure 5.1b, refining the MPL phase and creating MPL elements involves the

removal of some of the original MPL voxels at the interface between the MPL and other regions

(solid and void space). This step leads to a disconnection between the MPL phase from the other

void and solid phases. In order to restore these connections, the void and solid regions of the

original image were dilated until they extended to the edge of the MPL network. This image

processing step did not alter the originally extracted geometric features of the pores and throats

in the substrate. Figure 5.1c shows the result of this procedure, which is the expanded pore space

fully connected to the MPL network.

Finally, the connections between MPL elements and their neighboring macro-pores were

identified. The interfacial area between each MPL element and the connecting pores was

calculated based on the number of pore voxels that were in contact with each MPL element. In

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addition, the total MPL/void interfacial area of the network was compared to the original MPL

surface area, and a correction factor was applied to the area of all interfacial connections in the

network so that the original MPL surface area was obtained. A search was performed to locate

any small pores that might have been fully covered by large MPL elements, and these pores were

connected to their neighboring MPL elements. A schematic representation of the final network

with all identified connections is shown in Figure 5.1d. In this figure, circles and squares

represent pores and MPL elements, respectively, and connections are shown with solid lines.

Figure 5.2 shows the stochastically created uncompressed SGL Sigracet 25BA GDL with a

penetrating MPL coating and the equivalent pore network. In Figure 5.2a, the stochastically

created fibers and the solid MPL are shown. Figure 5.2b displays the locations and relative sizes

of pores represented by spheres and MPL elements represented by cubes. A magnified view of

the network showing pore and MPL element connections is also shown in the inset of Figure

5.2b.

5.3.4 Transport Equations

It is assumed that oxygen transport in the GDL occurs via diffusion. The effective diffusivity of a

material‎can‎be‎calculated‎using‎Fick’s‎law:

( )

(5.1)

where is the diffusion length, is the oxygen flux, is the diffusion area, and and

are the inlet and outlet oxygen concentrations, respectively.

75

The oxygen concentration values applied at the GDL inlet and outlet are the boundary conditions

for the simulation. With these boundary conditions, the oxygen flux in the network was

calculated by applying the mass conservation equation to each node in the network:

∑ ( )

(5.2)

where is the total number of neighbors of node , is the diffusive conductance between

node and node , and and are the oxygen concentration in nodes and , respectively.

The formula for calculating for each connection was determined based on the connection

type. Three connection types existed in the MPL/substrate network: 1) pore/pore connections, 2)

MPL element/MPL element connections, and 3) pore/MPL element connections. All transport

calculations were performed using the open source pore network modeling framework,

OpenPNM [100], which provides pore/pore conductance models. Additional functionalities were

added for calculating the diffusive conductance of MPL element/MPL element and pore/MPL

element connections. An additional module was also created for OpenPNM capable of importing

a hybrid network of pores and MPL elements.

Figure 5.3a shows a schematic representation of pore/pore connections and the cylindrical

conduits considered for diffusion calculations in these connections. Because oxygen diffusion

was modeled as travelling from pore center to pore center, the diffusive conductance of the

conduit connecting two neighboring pores, i and j, was calculated based on the diffusive

conductance of the half-pores ( ) and ( ) and that of their connecting throat ( ) as

follows:

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(

)

(5.3)

The diffusive conductance of each half-pore was defined as:

(5.4)

and the conductance of throat was calculated as:

(5.5)

In equations (5.4) and (5.5), ⁄ , which is the oxygen bulk diffusivity in air

calculated at 298 K and 1 atm using the Fuller model [113]. and are the cross-sectional

areas of half-pore and throat , which were calculated assuming cylindrical conduits:

(5.6)

(5.7)

where and are the diameters of pore and throat , respectively. and are the

length of half-pore and throat , respectively, determined as follows:

(5.8)

(5.9)

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where is the Euclidean distance between pores and .

Pore networks directly extracted from images sometimes contain overlapping neighboring pores

where the distance between the pore centers is less than the sum of the pore radii, creating throats

with unphysical, negative lengths.

In these cases, this was addressed by assigning a length of to , and the remaining length

between the pore centers ( ) was assigned to and proportionally to their

corresponding diameters.

Figure 5.3b shows a schematic representation of an MPL element/MPL element connection,

along with the cubic conduits considered for conductance calculations. Similar to the situation

for pores, oxygen diffusion was modeled as travelling from MPL element center to MPL element

center. Therefore, the diffusive conductivity between two neighboring MPL elements was

calculated as:

(

)

(5.10)

where the diffusive conductivity of each MPL half-element was defined as:

, (5.11)

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where is the interface area between MPL elements and , is the effective diffusion

coefficient of each MPL element, and is the diffusion length of MPL half-element . The

variables and were calculated as

(5.12)

(5.13)

where is the cube length of each MPL element. The dry through-plane effective diffusion

coefficients reported in the literature for various MPL materials range from 0.04 to 0.22

[7,91,92]. Hence, an MPL effective diffusion coefficient of was considered for this study.

Figure 5.3c shows a schematic representation of a pore/MPL element connections and the half-

pore and MPL half-element conduits considered for conductance calculations. The diffusive

conductivity between an MPL element and a pore was calculated as:

(

)

(5.14)

The diffusive conductivity of the half-pore was calculated as

(5.15)

and the diffusive conductivity of the MPL half-element was defined as

(5.16)

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where is the interfacial area between the pore and MPL element. In Equation (5.15), the

pore diffusion length ( ) was calculated as

, (5.17)

where is the Euclidian distance between pore and MPL element .

5.3.5 Resistance Network Model

The stochastically modeled materials of compressed SGL Sigracet 25BA substrate, with a sheet-

type MPL were essentially multiple layers in series with the details of each region explained in

Section 5.4.1. This section introduces the resistance network model used for calculating the

overall through-plane diffusivity of samples consisting of multiple layers in series, assuming

one-dimensional diffusion [65,74,96]. This assumption was applied because sample thickness

was much smaller than their length and width.

Once the effective diffusivity of each layer was determined, a resistance network of multiple

layers was considered for analytically calculating the overall diffusivity of the sample.

∑

(5.18)

where is the total resistance, is the total number of layers in series and is the diffusion

resistance through each layer. The resistance of each layer was:

(5.19)

where is the diffusion length, is the diffusion area, is the effective diffusivity of the layer.

Combining equations (5.18) and (5.19) yields:

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∑

(5.20)

For through-plane diffusion, the diffusion area was identical for all layers in series:

(5.21)

and the length of the sample was the sum of the lengths of all regions:

∑

(5.22)

Combining equations (5.20), (5.21), and (5.22), the effective diffusivity of the sample was

obtained as follows

∑

∑

(5.23)

Using Equation (2.4) the effective diffusion coefficient of the sample was obtained as

∑

∑

(5.24)

5.3.6 Analytical Diffusivity Calculations

The effective diffusion coefficients of two sample GDLs (Samples A and B) were predicted

using analytical calculations. The samples consisted of sheet-type MPLs placed in series with a

substrate; therefore, the effective diffusivity of these GDLs could be calculated analytically. The

properties of Samples A and B are summarized in Table 5.1. The results of analytical

calculations were compared with the results of pore network simulations. Figure 5.4 shows the

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first through-plane cross section of Samples A and B and the resistance network model for each

sample. Sample A consisted of a substrate and a flat MPL sheet, creating two distinct regions. In

Sample B, the substrate was placed on top of a sheet MPL with a sinusoidal surface, producing

three separate regions: the substrate, the sinusoidal interface, and the bulk MPL. In order to

calculate the effective diffusion coefficients of Samples A and B, the effective diffusion

coefficients of each layer were calculated. Once the effective diffusion coefficients of each layer

were calculated, the overall diffusivities of each sample were calculated using Equation (5.24).

The substrate in both samples was stochastically generated using the characteristics of a 2 mm ×

2 mm SGL Sigracet 25BA substrate, with a thickness of 76‎μm. To calculate the effective

diffusion coefficient of the SGL Sigracet 25BA substrate, an equivalent pore network of the

substrate was created using the algorithm explained in Section 5.3.2. This network consisted of

spherical pores and cylindrical throats only; therefore, the transport equations for pore/pore

connections as explained in Section 5.3.4 were sufficient for calculating the effective diffusivity

of the substrate.

To calculate the effective diffusivity of the interface region in Sample B, it was assumed that

diffusion in this region was one-dimensional and only occurred in the z-direction. This

assumption was applied because the thickness of this region ( ) was much smaller

than its length ( ) and width ( ); however, the assumption may lead to the

slight overestimation in diffusive resistance of the interface, since oxygen is artificially forced to

diffuse in a single direction. With this assumption, the equivalent diffusive conductance of the

interface is the sum of the conductance of the parallel, infinitesimal elements in this region.

These elements have an area of and a height of , where a fraction of this height is void and

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the remainder is MPL. The resistance of the MPL and the void column were calculated in terms

of the local height of the MPL, as follows:

(5.25)

(5.26)

In the above equations, is the total height of each element or the thickness of the interface

region, is the bulk diffusion coefficient, is the cross-sectional area of the element which is

available for diffusion, and is the effective diffusion coefficient of the MPL, which is

assumed to be . The sinusoidal MPL surface was created by setting as a function of the

location of the element:

( ) ( ) ( ) (5.27)

where,

( ) (

) ⁄ (5.28)

( ) (

) ⁄ (5.29)

and and are the length and width of the material, respectively.

The diffusive resistance of each infinitesimal element consisting of a void column and an MPL

column was calculated using the resistance network theory explained in Section 5.3.5 (Equation

(5.18))

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( ⁄ )

(5.30)

The diffusive conductance of each element was the inverse of its diffusive resistance:

( ⁄ ) (5.31)

Combining equations (5.27) and (5.31) and knowing that , the conductance of each

infinitesimal element ( ) became

( ( ⁄ ) ( ) ( )) (5.32)

Having the diffusive conductance of each infinitesimal element in the interface, the diffusive

conductance of the interface was calculated with the following integration:

∫ ∬

( ( ⁄ ) ( ) ( )) (5.33)

With the domains of integration being and , the above double integral is

solved to obtain the diffusive conductance of the interface. Then, the effective diffusivity of the

interface was calculated as follows

(5.34)

where

(5.35)

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Using Equation (2.4), the effective diffusion coefficient of the interface was obtained as follows

(5.36)

Once the effective diffusion coefficient of each layer was obtained, Equation (5.24) was used to

obtain the effective diffusion coefficient of each sample. The equivalent resistance network of

Samples A and B is shown in Figure 5.4.


5.4.1 Comparison with Analytical Solutions

The effective diffusion coefficient of each layer in Samples A and B was calculated using the

methodology explained in Section 5.3.6. The effective diffusion coefficient of the SGL Sigracet

25BA substrate in both samples was predicted to be 0.32, and the effective diffusion coefficient

of the bulk MPL in both samples was set to 0.15. Finally, the effective diffusion coefficient of

the interface in Sample B was predicted to be .

The effective diffusion coefficient of Sample A with various MPL thicknesses was calculated

both numerically using pore network modeling and analytically using Equation (5.24), and the

results are presented in Figure 5.5. The MPL thickness ranged from 38‎μm (20 voxels) to 76‎μm

(40 voxels). Figure 5.5 provides a comparison between the numerical and analytical results,

where the numerical effective diffusion coefficients were obtained using networks with MPL

element sizes of 9.5‎μm (5 voxels) and 13.2‎μm (7 voxels). It is evident from Figure 5.5 that a

network with MPL elements as large as 13.2‎μm can correctly predict the effective diffusion

coefficient of the material, since the values were in good agreement with analytical calculations.

85

From Figure 5.5, a slight change in the numerically calculated effective diffusion coefficients of

Sample A can be observed when the element size was increased from 9.5‎μm (5 voxels) to 13.2

μm (7 voxels). This change in the calculated effective diffusion coefficients is attributed to a

calculation artifact resulting from the discrete segmentation of the MPL. When applying the

segmentation technique to sheet-type MPL domains, this segmentation will either overestimate

or underestimate the MPL thickness, unless the chosen element size evenly divides into the

original thickness. For example, the effective diffusion coefficient of the sample with an MPL

thickness of 57‎μm (30 voxels) was higher when an element size of 7 voxels was utilized. With

an element size of 7 voxels, the thickness of the MPL (30 voxels) was divided into 4 MPL

elements of length 7 voxels. Therefore, in this process, 2 voxel layers of the MPL were removed

(compared to the case with an element size of 5 voxels), which resulted in decreasing the oxygen

diffusion barrier and caused a jump in the numerically calculated effective diffusion coefficient.

On the contrary, the effective diffusion coefficient of Sample A with an MPL thickness of 66‎μm

(35 voxels) was nearly identical with both element sizes (5 voxels and 7 voxels), as 35 is

divisible by both 5 and 7.

Figure 5.6 shows the results of numerical and analytical diffusivity calculations for Sample B

with the same range of MPL thicknesses as Sample A. The MPL thickness in this sample was

considered the sum of the thicknesses of the bulk MPL region and the interfacial region. The

numerical results were calculated with MPL element sizes of 9.5‎μm (5 voxels) and 13.2‎μm (7

voxels). It is evident from Figure 5.6 that the numerically calculated diffusivities of Sample B

with various MPL thicknesses were in good agreement with analytical calculations. The

assumption of one-dimensional diffusion in deriving the analytical expressions led to

overestimating the effective diffusion coefficient; therefore, the analytically calculated effective

86

diffusion coefficients were slightly higher than the numerical approximations as shown in

Figures 5.5 and 5.6.

Figures 5.5 and 5.6 show that creating a continuum network of the MPL connected to a pore

network of the substrate is a suitable technique for predicting the effective diffusion coefficient

of materials that have multiple layers with widely varying mean pore sizes. These results also

show that the equivalent continuum network of the MPL is an excellent model for simulating all

the diffusion-related physical features of the MPL phase. Also from Figures 5.5 and 5.6, the

effective diffusion coefficients of Samples A and B with an MPL thickness of 76‎μm (40 voxels)

were as low as 0.19 and 0.23, respectively since these samples had a compressed substrate with a

porosity of 0.73 and thickness of only 76‎μm.

5.4.2 Mesh Resolution Study

To account for more complex MPL geometries that exist in commercial GDL materials, such as

where the MPL penetrates the substrate non-uniformly, the diffusivity of a stochastically created

SGL Sigracet 25BA with an MPL coating (Sample C) was calculated using the proposed model.

This sample had dimensions of 266‎μm‎× 266‎μm × 248‎μm‎, and an image resolution of 1

μm/voxel. The properties of Sample C are summarized in Table 5.1. In this section, the effect of

MPL element size (mesh resolution) on the predicted effective diffusion coefficient in the

through-plane direction of the sample material was investigated. The through-plane diffusivity

was calculated with various MPL element sizes to ensure that the results were mesh-independent,

and the predicted values are presented in Figure 5.7. From Figure 5.7, the material effective

diffusion coefficient is shown to increase steadily as the mesh resolution of the MPL phase is

refined. A coarser MPL mesh prevents the resolution of some of the fine features that exist in a

complex MPL geometry, but this does not alter the void space as the pore network is created

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prior to the MPL meshing stage. Therefore losing MPL features reduces the diffusion pathways

through the MPL and leads to lower predicted effective diffusion coefficients. As seen in Figure

5.7, the effective diffusion coefficients nearly plateau at an MPL element size of 7‎μm, so an

element size of 7‎μm was deemed sufficient for capturing all MPL features and accurately

predicting the effective diffusivity of the material. The predicted effective diffusion coefficient

with an element size of 7‎μm deviated by just 1% from the value calculated with an element size

of 3‎μm. The SGL Sigracet 25BA substrate generated for the composite material was

uncompressed and had an average porosity of ~0.90; therefore, the effective diffusion

coefficients calculated for the material were relatively high.

The ability to capture all the physical properties of the MPL with a coarser MPL mesh is crucial,

as a fine MPL mesh produces a large number of computational nodes making a simulation

quickly computationally prohibitive. The 3D image of the sample used in this study contained

MPL voxels, which resulted in MPL elements with an MPL element

size of 1. Comparing MPL elements to the 492 pores in the void space shows that

considering each voxel in the MPL phase as a computational node introduces a large

computational burden. Figure 5.8 shows the total number of computational nodes (pores and

MPL elements) in the network for each MPL element size. The number of pores was constant as

the extracted pore network of the void space remains unchanged regardless of the MPL element

size. Figure 5.8 shows that increasing the MPL element size reduced the number of

computational nodes in the network significantly. Therefore, it is important to find the largest

element size that preserves all the physical features of the MPL, in order to reduce the

computational expense of the simulation. An alternative approach for keeping all MPL features

88

is to use an adaptive mesh by considering a finer grid at the MPL edges while leaving the other

MPL regions at lower grid resolution. This will be considered in future studies.

5.4.3 Pore Diffusion Length at the Interface

When considering the pore/MPL conductance calculations, some unrealistic scenarios manifest

from the utilization of Equation (5.14). Figure 5.9 illustrates two possible scenarios during

oxygen diffusion at the interface. In Figure 5.9a, consider oxygen travelling from MPL Element

1 to MPL Element 3. This figure shows that oxygen can first diffuse from MPL Element 1 to

MPL Element 2 through two distinct pathways. In the solid pathway, oxygen travels directly

from MPL Element 1 to MPL Element 2, and in the dashed pathway, oxygen travels from the

center of MPL Element 1 to the center of Pore 4 and back to the center of MPL Element 2.

However, in reality when oxygen molecules leave MPL Element 1, most would follow the path

of least diffusion resistance; therefore, they would follow the path adjacent to MPL elements

rather than traveling to the center of the pore and back to MPL Element 2. Considering the entire

pore diffusion length for oxygen diffusion in this elongated case would lead to the

underestimation of diffusive conductance of the dashed pathway. It might seem logical to

eliminate the diffusion length associated with the pore for this journey; however, neglecting this

elongated (dashed) pore diffusion length is equivalent to directly connecting MPL Elements 1

and 3, which would be unrealistic.

Another possible scenario is displayed in Figure 5.9b, where there are two distinct pathways for

oxygen diffusion from Pore 1 to Pore 3. In the solid pathway, oxygen travels directly from Pore

1 to Pore 3, and in the dashed pathway, oxygen travels from Pore 1 to MPL Element 2 and then

to Pore 3. In this case, the diffusion length in Pores 1 and 3 are required to accurately describe

the transport from Pore 1 to MPL Element 2 and from MPL Element 2 to Pore 3.

89

It should also be noted that omitting the pore diffusion length may have a minor effect on oxygen

diffusion, since the diffusivity of the void region ( ) is 6.7 times larger than that of the

MPL ( ).

5.5 Conclusions

In this chapter, the feasibility of using a hybrid network model of MPL elements with bulk

properties and discrete pores for predicting the effective diffusion coefficient of MPL/substrate

assemblies was investigated. The hybrid pore network model was utilized to perform diffusivity

measurements on stochastically created 3D trinary images of MPL-coated GDL materials. In

order to apply the mass conservation law over each node in the network, special conductance

values were formed for the three types of network connections: pore/pore, pore/MPL, and

MPL/MPL. 3D micro-computed tomography images of GDL materials can also be used to

predict the material diffusivity using this model. The values predicted by this model were

compared to analytical calculations for validation, which showed that this method is highly

promising for studying the influence of the geometrical features of MPL-coated GDLs on

oxygen diffusion through the porous medium.

A mesh resolution study was performed on a 266‎μm‎× 266‎μm × 248‎μm MPL/substrate

assembly where the MPL invaded the substrate non-uniformly. The results showed that an MPL

element size of 7 μm is small enough for maintaining all of the physical features of the MPL.

This hybrid pore network modeling technique can be applied for estimating the transport

properties of more complex systems, such as rocks with multi-scale porosities e.g. carbonates,

where the nano-pores of the system are not captured due to the limited spatial resolution of

90

micro-CT techniques. In addition, this method can be coupled with an invasion percolation

model to predict mass transport rates in partially saturated materials with porous features across

multiple length scales.

91

5.6 Tables

Table ‎5.1 Specifications of Samples A, B, and C.

Sample Length

(μm)

Width

(μm)

Substrate

Thickness

(μm)

MPL

Thickness

(μm)

Total

Thickness

(μm)

Substrate

Porosity

Resolution

(μm/voxel) MPL Type

A 2000 2000 76 38 - 76 114 - 152 0.73 1.89 Sheet (Flat)

B 2000 2000 76 38 - 76 114 - 152 0.73 1.89 Sheet

(Sinusoidal)

C 266 266 - - 248 0.9* 1 Coated

*The substrate porosity in Sample C is calculated without the digitally added MPL coating

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5.7 Figures

Figure ‎5.1 2D schematic representation of the image processing steps. (a) Extracted pore space

and solid MPL. (b) Extracted pore space and refined MPL. (c) Expanded pore space and refined

MPL. (d) Final network with all identified connections. Circles and squares represent pores and

MPL elements, respectively, and connections are shown with solid lines.

93

Figure ‎5.2 (a) The original 3D material created stochastically which has 3 phases: MPL, fiber,

and‎void‎space.‎The‎material‎dimensions‎are‎266‎μm‎×‎266‎μm‎×‎248‎μm.‎(b)‎The‎hybrid‎

network‎of‎spherical‎pores‎representing‎the‎void‎space‎and‎cubic‎elements‎with‎a‎length‎of‎7‎μm‎

representing the MPL phase.

94

Figure ‎5.3 Schematic representation of the three types of node connections in the network and

their equivalent diffusion conduits. (a) Pore/pore connections. (b) MPL element/MPL element

connections. (c) Pore/MPL element connections.

95

Figure ‎5.4 (a) The first in-plane slice of sample A which consists of a numerically created SGL

Sigracet 25BA substrate and a flat sheet-type MPL. (b) The first in-plane slice of sample B

which consists of a numerically created SGL Sigracet 25BA substrate and a sinusoidal sheet-type

MPL. The equivalent resistance network of each sample is presented.

96

Figure ‎5.5 Through-plane effective diffusion coefficients of sample A for various MPL


MPL element sizes of 9.5 microns (5 voxels) and 13.2 microns (7 voxels).

97

Figure ‎5.6 Through-plane effective diffusion coefficients of sample B for various MPL


MPL element sizes of 9.5 microns (5 voxels) and 13.2 microns (7 voxels).

98

Figure ‎5.7 Predicted effective diffusion coefficients in the through-plane direction of a

numerically created SGL25BA with an MPL coating for various computational element sizes in

the MPL region.

99

Figure ‎5.8 Total number of computational nodes in the network for various MPL element sizes.

100

Figure ‎5.9 Schematic representation of distinct diffusion pathways for oxygen diffusion where

one pathway passes through an MPL/void interface.

101

6 Conclusions

In this thesis, the effect of the PEM fuel cell GDL microstructure on multiphase transport within

this layer was studied using pore network modeling. An in-depth literature review on the role of

both the macro-scale substrate and the MPL on liquid water percolation and oxygen diffusion in

the PEM fuel cell was presented. A comprehensive description of analytical, experimental, and

numerical methods employed for predicting the distribution of liquid water and oxygen gas in the

substrate and the MPL was included, highlighting the main techniques used in these studies.

In Chapter 3, liquid water transport through an SGL Sigracet 25BC GDL material was simulated

using the invasion percolation algorithm, and the effects of GDL/CL condensation points and

contact quality on the spatial distribution of liquid water in the material was studied. An

equivalent pore network model, extracted from an X-ray micro-computed tomography image of

the GDL material, was used in this study. An alternative boundary condition was introduced to

mimic the formation of individual water clusters at the CL in an operating PEM fuel cell. The

breakthrough saturation profiles in the through-plane direction were recorded, and it was found

that an ideal GDL/CL contact quality would significantly reduce liquid water accumulation at the

interface. This ideal contact would provide more diffusion pathways to the reaction sites, even

though higher average saturations were generally observed compared to the case with some

delamination. Saturation profiles of the region representing the ideal GDL/CL contact were

significantly affected by the condensation site assumptions. This study shows that accurate

modeling of the boundary condition of liquid water entering the GDL is a prerequisite to

predicting a realistic spatial distribution of liquid water in the material.

102

In Chapter 4, synchrotron-based micro-computed tomography images of two commercially

available GDL materials at various compression states were used to create equivalent pore

networks. PNM along with invasion percolation was used to simulate liquid water transport in

the GDL materials over a range of compression pressures, and favorable GDL compression

values for preferred liquid water distributions were found for Toray TGPH-090 and SGL

Sigracet 25BC GDL materials. It was found that the non-uniform compression of the GDL

significantly alters the microstructure, and consequently, the dynamics of liquid water transport

through the GDL. The through-plane saturation profiles in both GDL materials were generally

observed to be a decreasing function of the through-plane location from the catalyst layer to the

gas channels with high levels of water saturation present at the GDL/catalyst layer interface. In

general, GDL compression appeared to decrease the accumulation of excess liquid water near the

catalyst layer, which is predicted to keep large portions of the catalyst layer available for oxygen

diffusion. In addition, the presence of an MPL coating in the SGL material was found to have a

favorable effect on liquid water saturation, as lower levels of liquid water were present in this

material compared to the Toray substrate-only material.

In Chapter 5, a numerical technique capable of predicting the oxygen diffusivity in carbon paper

substrates with an MPL coating was developed. A network of MPL elements with bulk

properties was incorporated into a traditional pore network with discrete pores, and the effective

diffusivity of bilayer GDL materials were obtained. The mass conservation law was applied over

each node in the network with special conductance values formed for the three types of

connection in the hybrid network: pore/pore, pore/MPL, and MPL/MPL. Two samples with

relatively simple geometries were used to compare the diffusivity values predicted by this model

with analytical calculations. This comparison showed a good agreement between the results of

103

the proposed model and the analytical model, demonstrating that this method is highly promising

for studying the influence of the geometrical features of MPL-coated GDLs on oxygen diffusion

through the porous medium. A mesh resolution study was performed on a stochastically created

MPL/substrate assembly where the MPL invaded the substrate non-uniformly, and an MPL

element‎size‎of‎7μm‎was‎shown‎to‎be‎small enough for maintaining all of the physical features of

the MPL. The introduced hybrid network provides a new methodology for estimating the

transport properties of materials with multi-scale porosities.

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7 Future Work

The findings of this thesis can be investigated further to improve the accuracy of mass transport

simulations and to create a full electrochemical simulation of the PEM fuel cell using modified

pore network models of liquid, gas, and charge transfer in various components of cell.

In the existing pore network model, the system was assumed to be isothermal at . While the

distribution of temperature has a minor effect on capillary pressure calculations, it can heavily

influence the distribution of condensation points in the domain. A more realistic simulation of

liquid and gas distribution within various porous layers of the PEM fuel cell can be achieved by

considering a distribution of condensation points based on a realistic temperature map of the

domain. Condensation points should be located at regions with low temperature or high

concentration of oxygen leading to more electrochemical water production. For example,

condensation points should be considered at the GDL/rib interface since it is a region with a

relatively low temperature within the GDL. In addition, future work can include an initial non-

uniform concentration of oxygen and water vapor in the system.

In this thesis, only two commercial GDL materials were assessed for studying compression

effects on mass transport within the GDL. Future work should include a larger number of

materials to provide a comprehensive report of mass transport behavior of GDL materials under

realistic stack compression.

In future studies, the breakthrough densities seen in percolation simulations can be compared

with the available experimental visualizations of breakthrough density in various GDL materials

to identify the most realistic distribution of condensation points and GDL/catalyst layer contact

quality.

105

Physical features such as contact angle and surface tension of pores and throats near the ribs

must be modified to simulate hydrophilic ribs and capture breakthrough points at the edge of the

ribs.

The proposed hybrid network can be used to calculate the effective diffusivity of saturated GDLs

at various saturation levels and under various compression states to introduce GDL materials

with preferred water management characteristics. This model can also be used on various pore

scales to model the full membrane electrode assembly (MEA) including the membrane, the

catalyst layer, the MPL, and the substrate. This multiscale model could be used to simulate liquid

water percolation, oxygen diffusion, and electron transport in the MEA. Using such a model, the

performance of the PEM fuel cell can be accurately predicted under various operating conditions.

106

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Pore Network Modeling of Multiphase Transport in Polymer ... · In this thesis, pore network modeling was used to study how the microstructure of the polymer electrolyte membrane