Abstract

Redox flow batteries (RFBs) are an emerging electrochemical technology suitable for energy-intensive grid storage, but further cost reductions are needed for broad deployment. Overcoming cell performance limitations through improvements in the design and engineering of constituent components represent a promising pathway to lower system costs. Of particular relevance, but limited in study, are the porous carbon electrodes whose surface composition and microstructure impact multiple aspects of cell behavior. Here, we systematically investigate woven carbon cloth electrodes based on identical carbon fibers but arranged into different weave patterns (plain, 8-harness satin, 2 × 2 basket) of different thicknesses to identify structure–function relations and generalizable descriptors. We first evaluate the physical properties of the electrodes using a suite of analytical methods to quantify structural characteristics, accessible surface area, and permeability. We then study the electrochemical performance in a diagnostic flow cell configuration to elucidate resistive losses through polarization and impedance analysis and to estimate mass transfer coefficients through limiting current measurements. Finally, we combine these findings to develop power law relations between relevant dimensional and dimensionless quantities and to calculate extensive mass transfer coefficients. These studies reveal nuanced relationships between the physical morphology of the electrode and its electrochemical and hydraulic performance and suggest that the plain weave pattern offers the best combination of these attributes. More generally, this study provides physical data and experimental insights that support the development of purpose-built electrodes using a woven materials platform.

References

References
1.
Chu
,
S.
, and
Majumdar
,
A.
,
2012
, “
Opportunities and Challenges for a Sustainable Energy Future
,”
Nature
,
488
(
7411
), pp.
294
303
. 10.1038/nature11475
2.
Ibrahim
,
H.
,
Ghandour
,
M.
,
Dimitrova
,
M.
,
Ilinca
,
A.
, and
Perron
,
J.
,
2011
, “
Integration of Wind Energy Into Electricity Systems: Technical Challenges and Actual Solutions
,”
Energy Procedia
,
6
, pp.
815
824
. 10.1016/j.egypro.2011.05.092
3.
Denholm
,
P.
,
Ela
,
E.
,
Kirby
,
B.
, and
Milligan
,
M.
,
2010
, “
The Role of Energy Storage With Renewable Electricity Generation
,”
Technical Report
, p.
61
.
4.
Resch
,
M.
,
Bühler
,
J.
,
Schachler
,
B.
,
Kunert
,
R.
,
Meier
,
A.
, and
Sumper
,
A.
,
2019
, “
Technical and Economic Comparison of Grid Supportive Vanadium Redox Flow Batteries for Primary Control Reserve and Community Electricity Storage in Germany
,”
Int. J. Energy Res.
,
43
(
1
), pp.
337
357
. 10.1002/er.4269
5.
Noack
,
J.
,
Wietschel
,
L.
,
Roznyatovskaya
,
N.
,
Pinkwart
,
K.
, and
Tübke
,
J.
,
2016
, “
Techno-Economic Modeling and Analysis of Redox Flow Battery Systems
,”
Energies
,
9
(
8
), p.
627
. 10.3390/en9080627
6.
Li
,
Z.
,
Pan
,
M. S.
,
Su
,
L.
,
Tsai
,
P.-C.
,
Badel
,
A. F.
,
Valle
,
J. M.
,
Eiler
,
S. L.
,
Xiang
,
K.
,
Brushett
,
F. R.
, and
Chiang
,
Y.-M.
,
2017
, “
Air-Breathing Aqueous Sulfur Flow Battery for Ultralow-Cost Long-Duration Electrical Storage
,”
Joule
,
1
(
2
), pp.
306
327
. 10.1016/j.joule.2017.08.007
7.
Weber
,
A. Z.
,
Mench
,
M. M.
,
Meyers
,
J. P.
,
Ross
,
P. N.
,
Gostick
,
J. T.
, and
Liu
,
Q.
,
2011
, “
Redox Flow Batteries: A Review
,”
J. Appl. Electrochem.
,
41
(
10
), p.
1137
1164
. 10.1007/s10800-011-0348-2
8.
Wang
,
W.
,
Luo
,
Q.
,
Li
,
B.
,
Wei
,
X.
,
Li
,
L.
, and
Yang
,
Z.
,
2013
, “
Recent Progress in Redox Flow Battery Research and Development
,”
Adv. Funct. Mater.
,
23
(
8
), pp.
970
986
. 10.1002/adfm.201200694
9.
Ponce de León
,
C.
,
Frías-Ferrer
,
A.
,
González-García
,
J.
,
Szánto
,
D. A.
, and
Walsh
,
F. C.
,
2006
, “
Redox Flow Cells for Energy Conversion
,”
J. Power Sources
,
160
(
1
), pp.
716
732
. 10.1016/j.jpowsour.2006.02.095
10.
Whitehead
,
A. H.
,
Rabbow
,
T. J.
,
Trampert
,
M.
, and
Pokorny
,
P.
,
2017
, “
Critical Safety Features of the Vanadium Redox Flow Battery
,”
J. Power Sources
,
351
, pp.
1
7
. 10.1016/j.jpowsour.2017.03.075
11.
Lüth
,
T.
,
König
,
S.
,
Suriyah
,
M.
, and
Leibfried
,
T.
,
2018
, “
Passive Components Limit the Cost Reduction of Conventionally Designed Vanadium Redox Flow Batteries
,”
Energy Procedia
,
155
, pp.
379
389
. 10.1016/j.egypro.2018.11.040
12.
Kim
,
K. J.
,
Park
,
M.-S.
,
Kim
,
Y.-J.
,
Kim
,
J. H.
,
Dou
,
S. X.
, and
Skyllas-Kazacos
,
M.
,
2015
, “
A Technology Review of Electrodes and Reaction Mechanisms in Vanadium Redox Flow Batteries
,”
J. Mater. Chem. A
,
3
(
33
), pp.
16913
16933
. 10.1039/C5TA02613J
13.
Bortolin
,
S.
,
Toninelli
,
P.
,
Maggiolo
,
D.
,
Guarnieri
,
M.
, and
Col
,
D. D.
,
2015
, “
CFD Study on Electrolyte Distribution in Redox Flow Batteries
,”
J. Phys. Conf. Ser.
,
655
(
1
), p.
012049
. 10.1088/1742-6596/655/1/012049
14.
Xu
,
Q.
, and
Zhao
,
T. S.
,
2013
, “
Determination of the Mass-Transport Properties of Vanadium Ions Through the Porous Electrodes of Vanadium Redox Flow Batteries
,”
Phys. Chem. Chem. Phys.
,
15
(
26
), p.
10841
. 10.1039/c3cp51944a
15.
Ke
,
X.
,
Prahl
,
J. M.
,
Alexander
,
J. I. D.
,
Wainright
,
J. S.
,
Zawodzinski
,
T. A.
, and
Savinell
,
R. F.
,
2018
, “
Rechargeable Redox Flow Batteries: Flow Fields, Stacks and Design Considerations
,”
Chem. Soc. Rev.
,
47
(
23
), pp.
8721
8743
. 10.1039/C8CS00072G
16.
Sun
,
B.
, and
Skyllas-Kazacos
,
M.
,
1992
, “
Chemical Modification of Graphite Electrode Materials for Vanadium Redox Flow Battery Application—Part II. Acid Treatments
,”
Electrochim. Acta
,
37
(
13
), pp.
2459
2465
. 10.1016/0013-4686(92)87084-D
17.
Tian
,
C.-H.
,
Chein
,
R.
,
Hsueh
,
K.-L.
,
Wu
,
C.-H.
, and
Tsau
,
F.-H.
,
2011
, “
Design and Modeling of Electrolyte Pumping Power Reduction in Redox Flow Cells
,”
Rare Met.
,
30
(
S1
), pp.
16
21
. 10.1007/s12598-011-0229-1
18.
Greco
,
K. V.
,
Forner-Cuenca
,
A.
,
Mularczyk
,
A.
,
Eller
,
J.
, and
Brushett
,
F. R.
,
2018
, “
Elucidating the Nuanced Effects of Thermal Pretreatment on Carbon Paper Electrodes for Vanadium Redox Flow Batteries
,”
ACS Appl. Mater. Interfaces
,
10
(
51
), pp.
44430
44442
. 10.1021/acsami.8b15793
19.
Milshtein
,
J. D.
,
Tenny
,
K. M.
,
Barton
,
J. L.
,
Drake
,
J.
,
Darling
,
R. M.
, and
Brushett
,
F. R.
,
2017
, “
Quantifying Mass Transfer Rates in Redox Flow Batteries
,”
J. Electrochem. Soc.
,
164
(
11
), pp.
E3265
E3275
. 10.1149/2.0201711jes
20.
Gerhardt
,
M. R.
,
Wong
,
A. A.
, and
Aziz
,
M. J.
,
2018
, “
The Effect of Interdigitated Channel and Land Dimensions on Flow Cell Performance
,”
J. Electrochem. Soc.
,
165
(
11
), pp.
A2625
A2643
. 10.1149/2.0471811jes
21.
Barton
,
J. L.
,
Milshtein
,
J. D.
,
Hinricher
,
J. J.
, and
Brushett
,
F. R.
,
2018
, “
Quantifying the Impact of Viscosity on Mass-Transfer Coefficients in Redox Flow Batteries
,”
J. Power Sources
,
399
, pp.
133
143
. 10.1016/j.jpowsour.2018.07.046
22.
Sun
,
B.
, and
Skyllas-Kazacos
,
M.
,
1992
, “
Modification of Graphite Electrode Materials for Vanadium Redox Flow Battery Application—I. Thermal Treatment
,”
Electrochim. Acta
,
37
(
7
), pp.
1253
1260
. 10.1016/0013-4686(92)85064-R
23.
Houser
,
J.
,
Pezeshki
,
A.
,
Clement
,
J. T.
,
Aaron
,
D.
, and
Mench
,
M. M.
,
2017
, “
Architecture for Improved Mass Transport and System Performance in Redox Flow Batteries
,”
J. Power Sources
,
351
, pp.
96
105
. 10.1016/j.jpowsour.2017.03.083
24.
Zhou
,
X. L.
,
Zhao
,
T. S.
,
Zeng
,
Y. K.
,
An
,
L.
, and
Wei
,
L.
,
2016
, “
A Highly Permeable and Enhanced Surface Area Carbon-Cloth Electrode for Vanadium Redox Flow Batteries
,”
J. Power Sources
,
329
, pp.
247
254
. 10.1016/j.jpowsour.2016.08.085
25.
He
,
Z.
,
Chen
,
Z.
,
Meng
,
W.
,
Jiang
,
Y.
,
Cheng
,
G.
,
Dai
,
L.
, and
Wang
,
L.
,
2016
, “
Modified Carbon Cloth as Positive Electrode With High Electrochemical Performance for Vanadium Redox Flow Batteries
,”
J. Energy Chem.
,
25
(
4
), pp.
720
725
. 10.1016/j.jechem.2016.04.002
26.
Tenny
,
K. M.
,
Lakhanpal
,
V. S.
,
Dowd
,
R. P.
,
Yarlagadda
,
V.
, and
Van Nguyen
,
T.
,
2017
, “
Impact of Multi-Walled Carbon Nanotube Fabrication on Carbon Cloth Electrodes for Hydrogen-Vanadium Reversible Fuel Cells
,”
J. Electrochem. Soc.
,
164
(
12
), pp.
A2534
A2538
. 10.1149/2.1151712jes
27.
Forner-Cuenca
,
A.
,
Penn
,
E. E.
,
Oliveira
,
A. M.
, and
Brushett
,
F. R.
,
2019
, “
Exploring the Role of Electrode Microstructure on the Performance of Non-Aqueous Redox Flow Batteries
,”
J. Electrochem. Soc.
,
166
(
10
), pp.
A2230
A2241
. 10.1149/2.0611910jes
28.
Ishmael
,
N.
,
Fernando
,
A.
,
Andrew
,
S.
, and
Taylor
,
L. W.
,
2017
, “
Textile Technologies for the Manufacture of Three-Dimensional Textile Preforms
,”
Res. J. Text. Apparel
,
21
(
4
), pp.
342
362
.
29.
El-kharouf
,
A.
,
Mason
,
T. J.
,
Brett
,
D. J. L.
, and
Pollet
,
B. G.
,
2012
, “
Ex-Situ Characterisation of Gas Diffusion Layers for Proton Exchange Membrane Fuel Cells
,”
J. Power Sources
,
218
, pp.
393
404
. 10.1016/j.jpowsour.2012.06.099
30.
Jiang
,
H. R.
,
Zeng
,
Y. K.
,
Wu
,
M. C.
,
Shyy
,
W.
, and
Zhao
,
T. S.
,
2019
, “
A Uniformly Distributed Bismuth Nanoparticle-Modified Carbon Cloth Electrode for Vanadium Redox Flow Batteries
,”
Appl. Energy
,
240
, pp.
226
235
. 10.1016/j.apenergy.2019.02.051
31.
Milshtein
,
J. D.
,
Kaur
,
A. P.
,
Casselman
,
M. D.
,
Kowalski
,
J. A.
,
Modekrutti
,
S.
,
Zhang
,
P. L.
,
Harsha Attanayake
,
N.
,
Elliott
,
C. F.
,
Parkin
,
S. R.
,
Risko
,
C.
,
Brushett
,
F. R.
, and
Odom
,
S. A.
,
2016
, “
High Current Density, Long Duration Cycling of Soluble Organic Active Species for Non-Aqueous Redox Flow Batteries
,”
Energy Environ. Sci.
,
9
(
11
), pp.
3531
3543
. 10.1039/C6EE02027E
32.
Su
,
L.
,
Ferrandon
,
M.
,
Kowalski
,
J. A.
,
Vaughey
,
J. T.
, and
Brushett
,
F. R.
,
2014
, “
Electrolyte Development for Non-Aqueous Redox Flow Batteries Using a High-Throughput Screening Platform
,”
J. Electrochem. Soc.
,
161
(
12
), pp.
A1905
A1914
. 10.1149/2.0811412jes
33.
Milshtein
,
J. D.
,
Barton
,
J. L.
,
Darling
,
R. M.
, and
Brushett
,
F. R.
,
2016
, “
4-Acetamido-2,2,6,6-Tetramethylpiperidine-1-Oxyl as a Model Organic Redox Active Compound for Nonaqueous Flow Batteries
,”
J. Power Sources
,
327
, pp.
151
159
. 10.1016/j.jpowsour.2016.06.125
34.
35.
Pierson
,
H. O.
,
1994
,
Handbook of Carbon, Graphite, Diamonds and Fullerenes—Properties, Processing and Applications
,
Noyes
,
New Jersey
.
36.
Su
,
L.
,
Badel
,
A. F.
,
Cao
,
C.
,
Hinricher
,
J. J.
, and
Brushett
,
F. R.
,
2017
, “
Toward an Inexpensive Aqueous Polysulfide–Polyiodide Redox Flow Battery
,”
Ind. Eng. Chem. Res.
,
56
(
35
), pp.
9783
9792
. 10.1021/acs.iecr.7b01476
37.
Darling
,
R. M.
, and
Perry
,
M. L.
,
2013
, “
Pseudo-Steady-State Flow Battery Experiments
,”
ECS Transactions Abstract
,
480
.
38.
Darling
,
R. M.
, and
Perry
,
M. L.
,
2014
, “
The Influence of Electrode and Channel Configurations on Flow Battery Performance
,”
J. Electrochem. Soc.
,
161
(
9
), pp.
A1381
A1387
. 10.1149/2.0941409jes
39.
Ritzoulis
,
G.
,
Papadopoulos
,
N.
, and
Jannakoudakis
,
D.
,
1986
, “
Densities, Viscosities, and Dielectric Constants of Acetonitrile + Toluene at 15, 25, and 35 .Degree.C
,”
J. Chem. Eng. Data
,
31
(
2
), pp.
146
148
. 10.1021/je00044a004
40.
León y León
,
C.
,
1998
, “
New Perspectives in Mercury Porosimetry
,”
Adv. Colloid Interface Sci.
,
76
(
77
), pp.
341
372
. 10.1016/S0001-8686(98)00052-9
41.
Zhang
,
Y.
,
Wang
,
H. P.
, and
Chen
,
Y. H.
,
2006
, “
Capillary Effect of Hydrophobic Polyester Fiber Bundles With Noncircular Cross Section
,”
J. Appl. Polym. Sci.
,
102
(
2
), pp.
1405
1412
. 10.1002/app.24261
42.
Carniglia
,
S. C.
,
1986
, “
Construction of the Tortuosity Factor From Porosimetry
,”
J. Catal.
,
102
(
2
), pp.
401
418
. 10.1016/0021-9517(86)90176-4
43.
Ghanbarian
,
B.
,
Hunt
,
A. G.
,
Ewing
,
R. P.
, and
Sahimi
,
M.
,
2013
, “
Tortuosity in Porous Media: A Critical Review
,”
Soil Sci. Soc. Am. J.
,
77
(
5
), pp.
1461
1477
. 10.2136/sssaj2012.0435
44.
Rashapov
,
R.
,
Imami
,
F.
, and
Gostick
,
J. T.
,
2015
, “
A Method for Measuring In-Plane Effective Diffusivity in Thin Porous Media
,”
Int. J. Heat Mass Transfer
,
85
, pp.
367
374
. 10.1016/j.ijheatmasstransfer.2015.01.101
45.
Eifert
,
L.
,
Banerjee
,
R.
,
Jusys
,
Z.
, and
Zeis
,
R.
,
2018
, “
Characterization of Carbon Felt Electrodes for Vanadium Redox Flow Batteries: Impact of Treatment Methods
,”
J. Electrochem. Soc.
,
165
(
11
), pp.
A2577
A2586
. 10.1149/2.0531811jes
46.
Castañeda
,
L. F.
,
Walsh
,
F. C.
,
Nava
,
J. L.
, and
Ponce de León
,
C.
,
2017
, “
Graphite Felt as a Versatile Electrode Material: Properties, Reaction Environment, Performance and Applications
,”
Electrochim. Acta
,
258
, pp.
1115
1139
. 10.1016/j.electacta.2017.11.165
47.
Pezeshki
,
A. M.
,
Clement
,
J. T.
,
Veith
,
G. M.
,
Zawodzinski
,
T. A.
, and
Mench
,
M. M.
,
2015
, “
High Performance Electrodes in Vanadium Redox Flow Batteries Through Oxygen-Enriched Thermal Activation
,”
J. Power Sources
,
294
, pp.
333
338
. 10.1016/j.jpowsour.2015.05.118
48.
Park
,
S.-K.
,
Shim
,
J.
,
Yang
,
J. H.
,
Jin
,
C.-S.
,
Lee
,
B. S.
,
Lee
,
Y.-S.
,
Shin
,
K.-H.
, and
Jeon
,
J.-D.
,
2014
, “
The Influence of Compressed Carbon Felt Electrodes on the Performance of a Vanadium Redox Flow Battery
,”
Electrochim. Acta
,
116
, pp.
447
452
. 10.1016/j.electacta.2013.11.073
49.
Schneider
,
J.
,
Bulczak
,
E.
,
El-Nagar
,
G. A.
,
Gebhard
,
M.
,
Kubella
,
P.
,
Schnucklake
,
M.
,
Fetyan
,
A.
,
Derr
,
I.
, and
Roth
,
C.
,
2019
, “
Degradation Phenomena of Bismuth-Modified Felt Electrodes in VRFB Studied by Electrochemical Impedance Spectroscopy
,”
Batteries
,
5
(
1
), p.
16
. 10.3390/batteries5010016
50.
Trasatti
,
S.
, and
Petrii
,
O. A.
,
1992
, “
Real Surface Area Measurements in Electrochemistry
,”
J. Electroanal. Chem.
,
327
(
1
), pp.
353
376
. 10.1016/0022-0728(92)80162-W
51.
Naderi
,
M.
,
2015
, “Chapter Fourteen—Surface Area: Brunauer–Emmett–Teller (BET),”
Progress in Filtration and Separation
,
S.
Tarleton
, ed.,
Academic Press
,
Oxford
, pp.
585
608
.
52.
Han
,
L.
,
Karthikeyan
,
K. G.
,
Anderson
,
M. A.
, and
Gregory
,
K. B.
,
2014
, “
Exploring the Impact of Pore Size Distribution on the Performance of Carbon Electrodes for Capacitive Deionization
,”
J. Colloid Interface Sci.
,
430
, pp.
93
99
. 10.1016/j.jcis.2014.05.015
53.
Hahn
,
M.
,
Kötz
,
R.
,
Gallay
,
R.
, and
Siggel
,
A.
,
2006
, “
Pressure Evolution in Propylene Carbonate Based Electrochemical Double Layer Capacitors
,”
Electrochim. Acta
,
52
(
4
), pp.
1709
1712
. 10.1016/j.electacta.2006.01.080
54.
Urita
,
K.
,
Urita
,
C.
,
Fujita
,
K.
,
Horio
,
K.
,
Yoshida
,
M.
, and
Moriguchi
,
I.
,
2017
, “
The Ideal Porous Structure of EDLC Carbon Electrodes With Extremely High Capacitance
,”
Nanoscale
,
9
(
40
), pp.
15643
15649
. 10.1039/C7NR05307J
55.
Zhao
,
Y.
,
Zhao
,
Z.
,
Zhang
,
J.
,
Wei
,
M.
,
Xiao
,
L.
, and
Hou
,
L.
,
2018
, “
Distinctive Performance of Gemini Surfactant in the Preparation of Hierarchically Porous Carbons via High-Internal-Phase Emulsion Template
,”
Langmuir
,
34
(
40
), pp.
12100
12108
. 10.1021/acs.langmuir.8b02562
56.
Endo
,
M.
,
Maeda
,
T.
,
Takeda
,
T.
,
Kim
,
Y. J.
,
Koshiba
,
K.
,
Hara
,
H.
, and
Dresselhaus
,
M. S.
,
2001
, “
Capacitance and Pore-Size Distribution in Aqueous and Nonaqueous Electrolytes Using Various Activated Carbon Electrodes
,”
J. Electrochem. Soc.
,
148
(
8
), p.
A910
. 10.1149/1.1382589
57.
Koh
,
A. R.
,
Hwang
,
B.
,
Roh
,
K. C.
, and
Kim
,
K.
,
2014
, “
The Effect of the Ionic Size of Small Quaternary Ammonium BF4 Salts on Electrochemical Double Layer Capacitors
,”
Phys. Chem. Chem. Phys.
,
16
(
29
), pp.
15146
15151
. 10.1039/c4cp00949e
58.
Kok
,
M. D. R.
,
Khalifa
,
A.
, and
Gostick
,
J. T.
,
2016
, “
Multiphysics Simulation of the Flow Battery Cathode: Cell Architecture and Electrode Optimization
,”
J. Electrochem. Soc.
,
163
(
7
), pp.
A1408
A1419
. 10.1149/2.1281607jes
59.
Mosch
,
H. L. K. S.
,
Akintola
,
O.
,
Plass
,
W.
,
Höppener
,
S.
,
Schubert
,
U. S.
, and
Ignaszak
,
A.
,
2016
, “
Specific Surface Versus Electrochemically Active Area of the Carbon/Polypyrrole Capacitor: Correlation of Ion Dynamics Studied by an Electrochemical Quartz Crystal Microbalance With BET Surface
,”
Langmuir
,
32
(
18
), pp.
4440
4449
. 10.1021/acs.langmuir.6b00523
60.
Jung
,
S.
,
McCrory
,
C. C. L.
,
Ferrer
,
I. M.
,
Peters
,
J. C.
, and
Jaramillo
,
T. F.
,
2016
, “
Benchmarking Nanoparticulate Metal Oxide Electrocatalysts for the Alkaline Water Oxidation Reaction
,”
J. Mater. Chem. A
,
4
(
8
), pp.
3068
3076
. 10.1039/C5TA07586F
61.
Holze
,
R.
, and
Vielstich
,
W.
,
1984
, “
Double-Layer Capacity Measurements as a Method to Characterize Porous Fuel Cell Electrodes
,”
Electrochim. Acta
,
29
(
5
), pp.
607
610
. 10.1016/0013-4686(84)87118-2
62.
Escalante-García
,
I. L.
,
Wainright
,
J. S.
,
Thompson
,
L. T.
, and
Savinell
,
R. F.
,
2015
, “
Performance of a Non-Aqueous Vanadium Acetylacetonate Prototype Redox Flow Battery: Examination of Separators and Capacity Decay
,”
J. Electrochem. Soc.
,
162
(
3
), pp.
A363
A372
. 10.1149/2.0471503jes
63.
Katinas
,
V.
,
Gecevicius
,
G.
, and
Marciukaitis
,
M.
,
2018
, “
An Investigation of Wind Power Density Distribution at Location With Low and High Wind Speeds Using Statistical Model
,”
Appl. Energy
,
218
, pp.
442
451
. 10.1016/j.apenergy.2018.02.163
64.
Binyu
,
X.
,
Jiyun
,
Z.
, and
Jinbin
,
L.
,
2013
, “
Modeling of an All-Vanadium Redox Flow Battery and Optimization of Flow Rates
,”
2013 IEEE Power Energy Society General Meeting
, pp.
1
5
.
65.
Darcy
,
H
.,
1803
–1858, 1856, “
Les fontaines publiques de la ville de Dijon: exposition et application des principes à suivre et des formules à employer dans les questions de distribution d’eau…/ par Henry Darcy,…
,”
Distrib. Eau
, p.
659
.
66.
Carman
,
P. C.
,
1997
, “
Fluid Flow Through Granular Beds
,”
Chem. Eng. Res. Des.
,
75
, pp.
S32
S48
. 10.1016/S0263-8762(97)80003-2
67.
Deen
,
D.
, and
William
,
M.
,
2012
,
Analysis of Transport Phenomena
,
Oxford University Press
,
NY
.
68.
Forchheimer
,
P. H.
,
1901
, “
Wasserbewegung Durch Boden
,”
Z. Acker-Pflanzenbau
,
45
, pp.
1782
1788
.
69.
Sobieski
,
W.
, and
Trykozko
,
A.
,
2014
, “
Darcy’s and Forchheimer’s Laws in Practice. Part 1. The Experiment
,”
Tech. Sci.
,
17
(
4
), pp.
321
335
.
70.
Gostick
,
J. T.
,
Fowler
,
M. W.
,
Pritzker
,
M. D.
,
Ioannidis
,
M. A.
, and
Behra
,
L. M.
,
2006
, “
In-Plane and Through-Plane Gas Permeability of Carbon Fiber Electrode Backing Layers
,”
J. Power Sources
,
162
(
1
), pp.
228
238
. 10.1016/j.jpowsour.2006.06.096
71.
Geertsma
,
J.
,
1974
, “
Estimating the Coefficient of Inertial Resistance in Fluid Flow Through Porous Media
,”
Soc. Pet. Eng. J.
,
14
(
5
), pp.
445
450
. 10.2118/4706-PA
72.
Zeng
,
Z.
, and
Grigg
,
R.
,
2006
, “
A Criterion for Non-Darcy Flow in Porous Media
,”
Transp. Porous Media
,
63
(
1
), pp.
57
69
. 10.1007/s11242-005-2720-3
73.
Ma
,
H.
, and
Ruth
,
D. W.
,
1993
, “
The Microscopic Analysis of High Forchheimer Number Flow in Porous Media
,”
Transp. Porous Media
,
13
(
2
), pp.
139
160
. 10.1007/BF00654407
74.
Feser
,
J. P.
,
Prasad
,
A. K.
, and
Advani
,
S. G.
,
2006
, “
Experimental Characterization of In-Plane Permeability of Gas Diffusion Layers
,”
J. Power Sources
,
162
(
2
), pp.
1226
1231
. 10.1016/j.jpowsour.2006.07.058
75.
Rama
,
P.
,
Liu
,
Y.
,
Chen
,
R.
,
Ostadi
,
H.
,
Jiang
,
K.
,
Gao
,
Y.
,
Zhang
,
X.
,
Brivio
,
D.
, and
Grassini
,
P.
,
2011
, “
A Numerical Study of Structural Change and Anisotropic Permeability in Compressed Carbon Cloth Polymer Electrolyte Fuel Cell Gas Diffusion Layers
,”
Fuel Cells
,
11
(
2
), pp.
274
285
. 10.1002/fuce.201000037
76.
Ozgumus
,
T.
,
Mobedi
,
M.
, and
Ozkol
,
U.
,
2014
, “
Determination of Kozeny Constant Based on Porosity and Pore to Throat Size Ratio in Porous Medium With Rectangular Rods
,”
Eng. Appl. Comput. Fluid Mech.
,
8
(
2
), pp.
308
318
.
77.
Tomadakis
,
M. M.
, and
Sotirchos
,
S. V.
,
1991
, “
Effective Kundsen Diffusivities in Structures of Randomly Overlapping Fibers
,”
AIChE J.
,
37
(
1
), pp.
74
86
. 10.1002/aic.690370107
78.
Tomadakis
,
M. M.
, and
Sotirchos
,
S. V.
,
1993
, “
Effective Diffusivities and Conductivities of Random Dispersions of Nonoverlapping and Partially Overlapping Unidirectional Fibers
,”
J. Chem. Phys.
,
99
(
12
), pp.
9820
9827
. 10.1063/1.465464
79.
Tomadakis
,
M. M.
, and
Sotirchos
,
S. V.
,
1993
, “
Ordinary and Transition Regime Diffusion in Random Fiber Structures
,”
AIChE J.
,
39
(
3
), pp.
397
412
. 10.1002/aic.690390304
80.
Tomadakis
,
M. M.
, and
Robertson
,
T. J.
,
2005
, “
Viscous Permeability of Random Fiber Structures: Comparison of Electrical and Diffusional Estimates With Experimental and Analytical Results
,”
J. Compos. Mater.
,
39
(
2
), pp.
163
188
. 10.1177/0021998305046438
81.
Karakashov
,
B.
,
Toutain
,
J.
,
Achchaq
,
F.
,
Legros
,
P.
,
Fierro
,
V.
, and
Celzard
,
A.
,
2019
, “
Permeability of Fibrous Carbon Materials
,”
J. Mater. Sci.
,
54
(
21
), pp.
13537
13556
.
82.
Bruggeman
,
D. A. G.
,
1935
, “
Berechnung Verschiedener Physikalischer Konstanten von Heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus Isotropen Substanzen
,”
Ann. Phys.
,
416
(
7
), pp.
636
664
. 10.1002/andp.19354160705
83.
van Brakel
,
J.
, and
Heertjes
,
P. M.
,
1974
, “
Analysis of Diffusion in Macroporous Media in Terms of a Porosity, a Tortuosity and a Constrictivity Factor
,”
Int. J. Heat Mass Transfer
,
17
(
9
), pp.
1093
1103
. 10.1016/0017-9310(74)90190-2
84.
Tjaden
,
B.
,
Cooper
,
S. J.
,
Brett
,
D. J.
,
Kramer
,
D.
, and
Shearing
,
P. R.
,
2016
, “
On the Origin and Application of the Bruggeman Correlation for Analysing Transport Phenomena in Electrochemical Systems
,”
Curr. Opin. Chem. Eng.
,
12
, pp.
44
51
. 10.1016/j.coche.2016.02.006
85.
You
,
X.
,
Ye
,
Q.
, and
Cheng
,
P.
,
2017
, “
The Dependence of Mass Transfer Coefficient on the Electrolyte Velocity in Carbon Felt Electrodes: Determination and Validation
,”
J. Electrochem. Soc.
,
164
(
11
), pp.
E3386
E3394
. 10.1149/2.0401711jes
86.
Ma
,
X.
,
Zhang
,
H.
, and
Xing
,
F.
,
2011
, “
A Three-Dimensional Model for Negative Half Cell of the Vanadium Redox Flow Battery
,”
Electrochim. Acta
,
58
, pp.
238
246
. 10.1016/j.electacta.2011.09.042
87.
Cooper
,
S. J.
,
Bertei
,
A.
,
Shearing
,
P. R.
,
Kilner
,
J. A.
, and
Brandon
,
N. P.
,
2016
, “
TauFactor: An Open-Source Application for Calculating Tortuosity Factors From Tomographic Data
,”
SoftwareX
,
5
, pp.
203
210
. 10.1016/j.softx.2016.09.002
88.
Carta
,
R.
,
Palmas
,
S.
,
Polcaro
,
A. M.
, and
Tola
,
G.
,
1991
, “
Behaviour of a Carbon Felt Flow by Electrodes Part I: Mass Transfer Characteristics
,”
J. Appl. Electrochem.
,
21
(
9
), pp.
793
798
. 10.1007/BF01402816
89.
Kinoshita
,
K.
, and
Leach
,
S. C.
,
1982
, “
Mass-Transfer Study of Carbon Felt, Flow-Through Electrode
,”
J. Electrochem. Soc.
,
129
(
9
), pp.
1993
1997
. 10.1149/1.2124338
90.
Schmal
,
D.
,
Van Erkel
,
J
, and
Van Duin
,
P. J.
,
1986
, “
Mass Transfer at Carbon Fibre Electrodes
,”
J. Appl. Electrochem.
,
16
(
3
), pp.
422
430
. 10.1007/BF01008853
91.
Newman
,
J.
, and
Tiedemann
,
W.
,
1978
, “
Flow-Through Porous Electrodes
,”
Adv. Electrochem. Electrochem. Eng.
,
11
, pp.
353
435
.
92.
Recio
,
F. J.
,
Herrasti
,
P.
,
Vazquez
,
L.
,
Ponce de León
,
C.
, and
Walsh
,
F. C.
,
2013
, “
Mass Transfer to a Nanostructured Nickel Electrodeposit of High Surface Area in a Rectangular Flow Channel
,”
Electrochim. Acta
,
90
, pp.
507
513
. 10.1016/j.electacta.2012.11.135
93.
Kok
,
M. D. R.
,
Jervis
,
R.
,
Tranter
,
T. G.
,
Sadeghi
,
M. A.
,
Brett
,
D. J. L.
,
Shearing
,
P. R.
, and
Gostick
,
J. T.
,
2019
, “
Mass Transfer in Fibrous Media With Varying Anisotropy for Flow Battery Electrodes: Direct Numerical Simulations with 3D X-Ray Computed Tomography
,”
Chem. Eng. Sci.
,
196
, pp.
104
115
. 10.1016/j.ces.2018.10.049
94.
Moressi
,
M. B.
, and
Fernández
,
H.
,
1994
, “
The Use of Ultramicroelectrodes for the Determination of Diffusion Coefficients
,”
J. Electroanal. Chem.
,
369
(
1–2
), pp.
153
159
. 10.1016/0022-0728(94)87093-4
95.
Bergner
,
B. J.
,
Schürmann
,
A.
,
Peppler
,
K.
,
Garsuch
,
A.
, and
Janek
,
J.
,
2014
, “
TEMPO: A Mobile Catalyst for Rechargeable Li-O2 Batteries
,”
J. Am. Chem. Soc.
,
136
(
42
), pp.
15054
15064
. 10.1021/ja508400m
96.
Nutting
,
J. E.
,
Rafiee
,
M.
, and
Stahl
,
S. S.
,
2018
, “
Tetramethylpiperidine N-Oxyl (TEMPO), Phthalimide N-Oxyl (PINO), and Related N-Oxyl Species: Electrochemical Properties and Their Use in Electrocatalytic Reactions
,”
Chem. Rev.
,
118
(
9
), pp.
4834
4885
. 10.1021/acs.chemrev.7b00763
97.
Saha
,
K. C.
, and
Mandal
,
P. C.
,
2002
, “
Electrochemical Oxidation and Reduction of Nitroxides: A Cyclic Voltammetric and Simulation Study
,”
Indian J. Chem.
,
41A
(
11
), pp.
2231
2237
.
98.
Yen
,
H. T. H.
,
2014
, “
Electrochemical Investigations of the Diffusion Coefficients and the Heterogeneous Electron Transfer Rates of Organic Redox Couples Measured in Ionic Liquids
,”
Dissertation
,
Technischen Universität Gra
.
99.
Aris
,
R.
,
1989
,
Elementary Chemical Reactor Analysis
,
Dover
,
New York
.
100.
Green
,
L. J.
, and
Duwez
,
P.
,
1951
, “
Fluid Flow Through Porous Media
,”
J Appl. Mech
,
18
(
1
), pp.
39
45
.
101.
Berg
,
C. F.
,
2014
, “
Permeability Description by Characteristic Length, Tortuosity, Constriction and Porosity
,”
Transp. Porous Media
,
103
(
3
), pp.
381
400
. 10.1007/s11242-014-0307-6
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