Water management in proton-exchange membrane fuel cells (PEFCs) has a large impact on the performance of the device, as liquid water affects the transport properties of the gas diffusion layer (GDL). In this study, we develop an ensemble-based model of the liquid water distribution inside the GDL. Based on a water injection experiment, the wet structure of the porous medium is inspected via X-ray tomographic microscopy and, after an image segmentation process, a voxel-based meshing of the fiber, air, and water domains is obtained. Starting from the obtained dry fiber structure, a Metropolis-Hastings Monte Carlo algorithm is used to obtain the equilibrium distribution of liquid water that minimizes the surface free energy of the ensemble. The different water distributions from the Monte Carlo (MC) simulation and water injection experiment are identified as solution for different physical mechanisms both of which are present in a running fuel cell. The wet structure is then used to calculate saturation-dependent effective transport properties using the software geodict. Thereby, a strong influence of the saturation gradient on the macrohomogeneous transport properties is found.

References

1.
Wargo
,
E.
,
Kotaka
,
T.
,
Tabuchi
,
Y.
, and
Kumbur
,
E.
,
2013
, “
Comparison of Focused Ion Beam Versus Nano-Scale X-Ray Computed Tomography for Resolving 3-D Microstructures of Porous Fuel Cell Materials
,”
J. Power Sources
,
241
, pp.
608
618
.
2.
Russ
,
J.
,
2010
,
The Image Processing Handbook
,
CRC Press, Boca Raton, FL
.
3.
Lee
,
J.
,
Jeon
,
S.
,
Yoon
,
J.
,
Byun
,
S.
, and
Shin
,
M.
,
2009
, “
A Numerical Simulation of a Flow in Pem Fuel Cell Stack Using Lattice Boltzmann Method
,”
Fluid Machinery and Fluid Mechanics
,
Springer
, Berlin, pp.
191
194
.
4.
Niu
,
X.
,
Munekata
,
T.
,
Hyodo
,
S.
, and
Suga
,
K.
,
2007
, “
An Investigation of Water-Gas Transport Processes in the Gas-Diffusion-Layer of a PEM Fuel Cell by a Multiphase Multiple-Relaxation-Time Lattice Boltzmann Model
,”
J. Power Sources
,
172
(
2
), pp.
542
552
.
5.
Hao
,
L.
, and
Cheng
,
P.
,
2010
, “
Lattice Boltzmann Simulations of Water Transport in Gas Diffusion Layer of a Polymer Electrolyte Membrane Fuel Cell
,”
J. Power Sources
,
195
(
12
), pp.
3870
3881
.
6.
Chen
,
S.
, and
Doolen
,
G.
,
1998
, “
Lattice Boltzmann Method for Fluid Flows
,”
Ann. Rev. Fluid Mech.
,
30
(
1
), pp.
329
364
.
7.
Succi
,
S.
,
2001
,
The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond
,
Oxford University Press/Clarendon Press
, Oxford, UK.
8.
Körner
,
C.
,
Pohl
,
T.
,
Rüde
,
U.
,
Thürey
,
N.
, and
Zeiser
,
T.
,
2006
, “
Parallel Lattice Boltzmann Methods for CFD Applications
,”
Numerical Solution of Partial Differential Equations on Parallel Computers
,
Springer
, Berlin, pp.
439
466
.
9.
Kim
,
S.
,
Pitsch
,
H.
, and
Boyd
,
I.
,
2008
, “
Slip Velocity and Knudsen Layer in the Lattice Boltzmann Method for Microscale Flows
,”
Phys. Rev. E
,
77
(
2
), p.
026704
.
10.
Sterling
,
J.
, and
Chen
,
S.
,
1996
, “
Stability Analysis of Lattice Boltzmann Methods
,”
J. Comp. Phys.
,
123
(
1
), pp.
196
206
.
11.
Toschi
,
F.
, and
Succi
,
S.
,
2005
, “
Lattice Boltzmann Method at Finite Knudsen Numbers
,”
Europhys. Lett.
,
69
(
4
), p.
549
.
12.
Quan
,
P.
,
Zhou
,
B.
,
Sobiesiak
,
A.
, and
Liu
,
Z.
,
2005
, “
Water Behavior in Serpentine Micro-Channel for Proton Exchange Membrane Fuel Cell Cathode
,”
J. Power Sources
,
152
, pp.
131
145
.
13.
Raeini
,
A.
,
Blunt
,
M.
, and
Bijeljic
,
B.
,
2012
, “
Modelling Two-Phase Flow in Porous Media at the Pore Scale Using the Volume-of-Fluid Method
,”
J. Comp. Phys.
,
231
(
17
), pp.
5653
5668
.
14.
Hirt
,
C.
, and
Nichols
,
B.
,
1981
, “
Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries
,”
J. Comp. Phys.
,
39
(
1
), pp.
201
225
.
15.
Kopanidis
,
A.
,
Theodorakakos
,
A.
,
Gavaises
,
M.
, and
Bouris
,
D.
,
2011
, “
Pore Scale 3D Modelling of Heat and Mass Transfer in the Gas Diffusion Layer and Cathode Channel of a PEM Fuel Cell
,”
Int. J. Therm. Sci.
,
50
(
4
), pp.
456
467
.
16.
Pisani
,
L.
,
Valentini
,
M.
, and
Murgia
,
G.
,
2003
, “
Analytical Pore Scale Modeling of the Reactive Regions of Polymer Electrolyte Fuel Cells
,”
J. Electrochem. Soc.
,
150
(
12
), pp.
A1549
A1559
.
17.
Gerlach
,
D.
,
Tomar
,
G.
,
Biswas
,
G.
, and
Durst
,
F.
,
2006
, “
Comparison of Volume-of-Fluid Methods for Surface Tension-Dominant Two-Phase Flows
,”
Int. J. Heat Mass Transfer
,
49
(
3
), pp.
740
754
.
18.
Huang
,
H.
,
Meakin
,
P.
, and
Liu
,
M.
,
2005
, “
Computer Simulation of Two-Phase Immiscible Fluid Motion in Unsaturated Complex Fractures Using a Volume of Fluid Method
,”
Water Resour. Res.
,
41
(
12
), p. W12413.
19.
Sussman
,
M.
, and
Puckett
,
E.
,
2000
, “
A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows
,”
J. Comput. Phys.
,
162
(
2
), pp.
301
337
.
20.
Nam
,
J.
, and
Kaviany
,
M.
,
2003
, “
Effective Diffusivity and Water-Saturation Distribution in Single- and Two-Layer PEMFC Diffusion Medium
,”
Int. J. Heat Mass Transfer
,
46
(24), pp.
4595
4611
.
21.
Gostick
,
J.
,
Ioannidis
,
M.
,
Fowler
,
M.
, and
Pitzker
,
M.
,
2007
, “
Pore Network Modeling of Fibrous Gas Diffusion Layers for Polymer Electrolyte Membrane Fuel Cells
,”
J. Power Sources
,
173
(
1
), pp.
277
290
.
22.
Sinha
,
P.
, and
Wang
,
C.
,
2007
, “
Pore-Network Modeling of Liquid Water Transport in Gas Diffusion Layer of a Polymer Electrolyte Fuel Cell
,”
Electrochim. Acta
,
52
(
28
), pp.
7936
7945
.
23.
El Hannach
,
M.
,
Pauchet
,
J.
, and
Prat
,
M.
,
2011
, “
Pore Network Modeling: Application to Multiphase Transport Inside the Cathode Catalyst Layer of Proton Exchange Membrane Fuel Cell
,”
Electrochim. Acta
,
56
(
28
), pp.
10796
10808
.
24.
Kuttanikkad
,
S. P.
,
Prat
,
M.
, and
Pauchet
,
J.
,
2011
, “
Pore-Network Simulations of Two-Phase Flow in a Thin Porous Layer of Mixed Wettability: Application to Water Transport in Gas Diffusion Layers of Proton Exchange Membrane Fuel Cells
,”
J. Power Sources
,
196
(
3
), pp.
1145
1155
.
25.
Chapuis
,
O.
,
Prat
,
M.
,
Quintard
,
M.
,
Chane-Kane
,
E.
,
Guillot
,
O.
, and
Mayer
,
N.
,
2008
, “
Two-Phase Flow and Evaporation in Model Fibrous Media. Application to the Gas Diffusion Layer of PEM Fuel Cells
,”
J. Power Sources
,
178
(1), pp.
258
268
.
26.
Rebai
,
M.
, and
Prat
,
M.
,
2009
, “
Scale Effect and Two-Phase Flow in a Thin Hydrophobic Porous Layer. Application to Water Transport in Gas Diffusion Layers of Proton Exchange Membrane Fuel Cells
,”
J. Power Sources
,
192
(2), pp.
534
543
.
27.
Kang
,
J.
,
Kim
,
K.
,
Nam
,
J.
, and
Kim
,
C.
,
2012
, “
Visualization Experiments and Pore Network Simulations for Invasion-Percolation Transport of a Non-Wetting Fluid Through Multiple Porous Layers
,”
Int. J. Hydrogen Energy
,
37
(
2
), pp.
1642
1652
.
28.
Pauchet
,
J.
,
Prat
,
M.
,
Schott
,
P.
, and
Kuttanikkad
,
S.
,
2012
, “
Performance Loss of Proton Exchange Membrane Fuel Cell Due to Hydrophobicity Loss in Gas Diffusion Layer: Analysis by Multiscale Approach Combining Pore Network and Performance Modelling
,”
Int. J. Hydrogen Energy
,
37
(
2
), pp.
1628
1641
.
29.
Wu
,
R.
,
Liao
,
Q.
,
Zhu
,
X.
, and
Wang
,
H.
,
2012
, “
Impacts of the Mixed Wettability on Liquid Water and Reactant Gas Transport Through the Gas Diffusion Layer of Proton Exchange Membrane Fuel Cells
,”
Int. J. Heat Mass Transfer
,
55
(
9–10
), pp.
2581
2589
.
30.
Seidenberger
,
K.
,
Wilhelm
,
F.
,
Haußmann
,
J.
,
Markötter
,
H.
,
Manke
,
I.
, and
Scholta
,
J.
,
2013
, “
Grand Canonical Monte Carlo Study on Water Agglomerations Within a Polymer Electrolyte Membrane Fuel Cell Gas Diffusion Layer
,”
J. Power Sources
,
239
, pp.
628
641
.
31.
Seidenberger
,
K.
,
Wilhelm
,
F.
,
Schmitt
,
T.
,
Lehnert
,
W.
, and
Scholta
,
J.
,
2011
, “
Estimation of Water Distribution and Degradation Mechanisms in Polymer Electrolyte Membrane Fuel Cell Gas Diffusion Layers Using a 3D Monte Carlo Model
,”
J. Power Sources
,
196
(
12
), pp.
5317
5324
.
32.
Krüger
,
P.
,
Markötter
,
H.
,
Haußmann
,
J.
,
Klages
,
M.
,
Arlt
,
T.
,
Banhart
,
J.
,
Hartnig
,
C.
,
Manke
,
I.
, and
Scholta
,
J.
,
2011
, “
Synchrotron X-Ray Tomography for Investigations of Water Distribution in Polymer Electrolyte Membrane Fuel Cells
,”
J. Power Sources
,
196
(
12
), pp.
5250
5255
.
33.
Eller
,
J.
,
Rosén
,
T.
,
Marone
,
F.
,
Stampanoni
,
M.
,
Wokaun
,
A.
, and
Büchi
,
F.
,
2011
, “
Progress in In Situ X-Ray Tomographic Microscopy of Liquid Water in Gas Diffusion Layers of PEFC
,”
J. Electrochem. Soc.
,
158
(
8
), pp.
B963
B970
.
34.
Tötzke
,
C.
,
Gaiselmann
,
G.
,
Osenberg
,
M.
,
Bohner
,
J.
,
Arlt
,
T.
,
Markötter
,
H.
,
Hilger
,
A.
,
Wieder
,
F.
,
Kupsch
,
A.
,
Müller
,
B. R.
, Hentschel, M. P., Banhart, J., Schmidt, V., Lehnert, W., and Manke, I.,
2014
, “
Three-Dimensional Study of Compressed Gas Diffusion Layers Using Synchrotron X-Ray Imaging
,”
J. Power Sources
,
253
, pp.
123
131
.
35.
Attig
,
N.
,
Binder
,
K.
,
Grubmuller
,
H.
, and
Kremer
,
K.
,
2004
,
Computational Soft Matter: From Synthetic Polymers to Proteins
,
John von Neumann Institute for Computing (NIC)
,
Juelich, Germany
.
36.
Weber
,
A. Z.
, and
Newman
,
J.
,
2006
, “
Coupled Thermal and Water Management in Polymer Electrolyte Fuel Cells
,”
J. Electrochem. Soc.
,
153
(
12
), p.
A2205
.
37.
Kim
,
S.
, and
Mench
,
M. M.
,
2009
, “
Investigation of Temperature-Driven Water Transport in Polymer Electrolyte Fuel Cell: Phase-Change-Induced Flow
,”
J. Electrochem. Soc.
,
156
(
3
), p.
B353
.
38.
Das
,
P. K.
,
Grippin
,
A.
,
Kwong
,
A.
, and
Weber
,
A. Z.
,
2012
, “
Liquid-Water-Droplet Adhesion-Force Measurements on Fresh and Aged Fuel-Cell Gas-Diffusion Layers
,”
J. Electrochem. Soc.
,
159
(
5
), pp.
B489
B496
.
39.
Packard
,
N. H.
, and
Wolfram
,
S.
,
1985
, “
Two-Dimensional Cellular Automata
,”
J. Stat. Phys.
,
38
(
5–6
), pp.
901
946
.
40.
Allen
,
M. P.
, and
Tildesley
,
D. J.
,
1989
,
Computer Simulation of Liquids
,
Oxford University Press
, Oxford, UK.
41.
Huang
,
K.
,
2009
,
Introduction to Statistical Physics
,
CRC Press
, Boca Raton, FL.
42.
Chib
,
S.
, and
Greenberg
,
E.
,
1995
, “
Understanding the Metropolis-Hastings Algorithm
,”
Am. Stat.
,
49
(
4
), pp.
327
335
.
43.
Billera
,
L. J.
, and
Diaconis
,
P.
,
2001
, “
A Geometric Interpretation of the Metropolis-Hastings Algorithm
,”
Stat. Sci.
, 16(4), pp.
335
339
.
44.
Landau
,
D. P.
, and
Binder
,
K.
,
2014
,
A Guide to Monte Carlo Simulations in Statistical Physics
,
Cambridge University Press
, New York.
45.
Reichl
,
L. E.
, and
Prigogine
,
I.
,
1980
,
A Modern Course in Statistical Physics
, Vol.
71
,
University of Texas Press
,
Austin, TX
.
46.
Liu
,
J. S.
,
2008
,
Monte Carlo Strategies in Scientific Computing
,
Springer Science & Business Media
, New York.
47.
Adamson, A. W., 1976,
Physical Chemistry of Surfaces
, Wiley, Hoboken, NJ.
48.
Cassie
,
A.
, and
Baxter
,
S.
,
1944
, “
Wettability of Porous Surfaces
,”
Trans. Faraday Soc.
,
40
, pp.
546
551
.
49.
Wenzel
,
R. N.
,
1949
, “
Surface Roughness and Contact Angle
,”
J. Phys. Chem.
,
53
(
9
), pp.
1466
1467
.
50.
Lu
,
N.
,
Zeidman
,
B. D.
,
Lusk
,
M. T.
,
Willson
,
C. S.
, and
Wu
,
D. T.
,
2010
, “
A Monte Carlo Paradigm for Capillarity in Porous Media
,”
Geophys. Res. Lett.
,
37
(
23
), p. L23402.
51.
Kawasaki
,
K.
,
1972
, “
Kinetics of Ising Models
,”
Phase Transitions and Critical Phenomena
, Vol.
2
, Academic Press, New York, pp.
443
501
.
52.
Berg
,
B. A.
, and
Billoire
,
A.
,
2008
,
Markov Chain Monte Carlo Simulations
,
Wiley
, New York.
53.
Chatterjee
,
J.
,
2007
, “
Prediction of Coupled Menisci Shapes by Young–Laplace Equation and the Resultant Variability in Capillary Retention
,”
J. Colloid Interface Sci.
,
314
(
1
), pp.
199
206
.
54.
Roura
,
P.
, and
Fort
,
J.
,
2004
, “
Local Thermodynamic Derivation of Young's Equation
,”
J. Colloid Interface Sci.
,
272
(
2
), pp.
420
429
.
55.
Lamibrac
,
A.
,
Roth
,
J.
,
Toulec
,
M.
,
Marone
,
F.
,
Stampanoni
,
M.
, and
Büchi
,
F.
,
2016
, “
Characterization of Liquid Water Saturation in Gas Diffusion Layers by X-Ray Tomographic Microscopy
,”
J. Electrochem. Soc.
,
163
(
3
), pp.
F202
F209
.
56.
Thiedmann
,
R.
,
Hartnig
,
C.
,
Manke
,
I.
,
Schmidt
,
V.
, and
Lehnert
,
W.
,
2009
, “
Local Structural Characteristics of Pore Space in GDLs of PEM Fuel Cells Based on Geometric 3D Graphs
,”
J. Electrochem. Soc.
,
156
(
11
), pp.
B1339
B1347
.
57.
Stenzel
,
O.
,
Pecho
,
O.
,
Holzer
,
L.
,
Neumann
,
M.
, and
Schmidt
,
V.
,
2016
, “
Predicting Effective Conductivities Based on Geometric Microstructure Characteristics
,”
AIChE J.
,
62
(5), pp. 1834–1843.
58.
García-Salaberri
,
P. A.
,
Hwang
,
G.
,
Vera
,
M.
,
Weber
,
A. Z.
, and
Gostick
,
J. T.
,
2015
, “
Effective Diffusivity in Partially-Saturated Carbon-Fiber Gas Diffusion Layers: Effect of Through-Plane Saturation Distribution
,”
Int. J. Heat Mass Transfer
,
86
, pp.
319
333
.
59.
García-Salaberri
,
P. A.
,
Gostick
,
J. T.
,
Hwang
,
G.
,
Weber
,
A. Z.
, and
Vera
,
M.
,
2015
, “
Effective Diffusivity in Partially-Saturated Carbon-Fiber Gas Diffusion Layers: Effect of Local Saturation and Application to Macroscopic Continuum Models
,”
J. Power Sources
,
296
, pp.
440
453
.
60.
Schulz
,
V. P.
,
Mukherjee
,
P. P.
,
Becker
,
J.
,
Wiegmann
,
A.
, and
Wang
,
C.-Y.
,
2006
, “
Numerical Evaluation of Effective Gas Diffusivity-Saturation Dependence of Uncompressed and Compressed Gas Diffusion Media in PEFCs
,”
ECS Trans.
,
3
(
1
), pp.
1069
1075
.
61.
Wiegmann
,
A.
,
2007
,
Computation of the Permeability of Porous Materials
,
Fraunhofer ITWM
, Kaiserslautern, Germany.
You do not currently have access to this content.