5. Optimization of the flow-field pattern
5.4 Conclusion
We have investigated the effects of the flow-field pattern and flow configuration on the performance of a polymer-electrolyte-membrane water electrolysis (PEMWE) at high temperatures, and concluded the following:
1. The cathode flow-field pattern affects only the ohmic resistance. A serpentine flow-field pattern provides the lowest ohmic resistance by creating an under-rib flow that wets the polymer-electrolyte membrane.
2. The anode flow-field pattern significantly affects the overpotential by liquid water depletion. A cascade flow-field pattern provides better electrolysis performance than serpentine and parallel flow-field patterns.
3. The flow configuration has little impact on the electrolysis performance.
4. Using cascade and serpentine flow-field patterns in the anode and cathode, respectively, provides the minimum electrolysis voltage of 1.69 V at 120 and 0.3 MPa.
105
Figures and tables.
(a) Serpentine flow field pattern
(b) Parallel flow field pattern
(c) Cascade flow field pattern
Figure 5.1 Flow field patterns examined in this study.
0.5mm
1mm
Vertical flow channel Parallel flow channel
106
(a) Co-flow
(b) Counter flow
Figure 5.2 The two conventional flow configurations use in this study.
107
(a) I-V characteristics
(b) I-HFR characteristics
108
(c) Non-linear overpotential characteristics
Figure 5.3 Impact of the cathode flow field patterns on electrolysis performance.
109
(a) Serpentine and cascade flow fields
(b) Parallel flow field
Figure 5.4 Under-rib flow in different cathode flow field patterns.
110
(a) I-V characteristics
(b) I-HFR characteristics
111
(c) Non-linear overpotential characteristics
(d) O bubble departure from the interface between the ACC and flow channel.
Figure 5.5 Impact of the anode flow field patterns on electrolysis performance.
112
(a) I-V characteristics
(b) I-HFR characteristics
Figure 5.6 Impact of the flow configuration on the electrolysis performance.
113
References
[1]. Chiwoong Choi, Dongin Yu, Moohwan Kim. Water Flow Boiling Behaviors in Hydrophilic and Hydrophobic Microchannels. ECI International Conference on Boiling Heat Transfer. Florianópolis-SC-Brazil, 3-7 May 2009.
[2]. Peng L., Mai J. Hu P., Lai X., and Lin Z., “Optimum Design of the Slotted-interdigitated Channels Flow Field for Proton Exchange Membrane Fuel Cells with Consideration of Gas Diffusion Layer Intrusion,” Renewable Energy, Volume 36, Issue 5, May 2011, Pages 1413–1420.
[3]. Anders Christian Olesen and Sϕren Knudsen Kӕr. Flow Maldistribution in the Anode of a Polymer Electrolyte Membrane water electrolysis cell employing interdigitated channels. The 55th Conference on Simulation and Modelling (SIMS 55) 21-22 October, 2014. Aalborg, Denmark.
[4]. H. Ito, T. Maeda, A. Nakano, Y. Hasegawa, N. Yokoi, C.M. Hwang, M. Ishida, A.
Kato, T. Yoshida. Effect of flow regime of circulating water on a proton exchange membrane electrolyzer. International Journal of Hydrogen Energy 35 (2010) 9550-9560.
[5]. A.P. Manso, F.F. Marzo, J. Barranco, X. Garikano, M. Garmendia Mujika. Influence of Gemetric Parameters of the Flow Fields on the Performance of a PEM Fuel Cell. A review. International Journal of Hydrogen Energy 37 (2012) 15256-15287.
[6].Ararimeh Aiyejina, M. K. S. Sastry. PEMFC Flow Channel Geometry Optimization:
A Review. Journal of Fuel Cell Science and Technology (2012), Vol.9, 011011-1~24.
[7]. Xianguo Li, Imran Sabir. Review of bipolar plates in PEM fuel cells: Flow-field designs. International Journal of Hydrogen Energy 30 (2005) 359 – 371.
[8]. Ferng, Y. H., Su, A., and Lu, S. M., “Experiment and Simulation Investigations for Effects of Flow field patterns on the PEMFC Performance,” Int. J. Energy Res.(2008),
114
32, pp. 12–23.
[9]. Lobato, J., Cañizares, P., Rodrigo, M. A., Pinar, F. J., Mena, E., and Úbeda, D.,
“Three-Dimensional Model of a 50 cm2 High Temperature PEM Fuel Cell. Study of the Flow Channel Geometry Influence,” Int. J. Hydrogen Energy (2010), 35, pp. 5510–5520.
[10]. Lobato, J., Cañizares, P., Rodrigo, M. A., Pinar, F. J., and Úbeda, D., “Study of Flow Channel Geometry Using Current Distribution Measurement in a High Temperature Polymer Electrolyte Membrane Fuel Cell,” J. Power Sources (2011), 196, pp. 4209–4217.
[11]. Jang, J. H., Yan, W. M., Li, H. Y., and Tsai, W. C., “Three-Dimensional Numerical Study on Cell Performance and Transport Phenomena of PEM Fuel Cells With Conventional Flow Fields,” Int. J. Hydrogen Energy (2008), 33, pp. 156–164.
[12]. Wang, X. D., Zhang, Z. Z., Yan, W. M., Lee, D. J., and Su, A., “Determination of the Optimal Active Area for Proton Exchange Membrane Fuel Cells With Parallel, Interdigitated or Serpentine Designs,” Int. J. Hydrogen Energy (2009), 34, pp. 3823–3832.
[13]. Wang, X. D., Duan, Y. Y., Yan, W. M., and Peng, X. F., “Local Transport Phenomena and Cell Performance of PEM Fuel Cells with Various Serpentine Flow Field Designs,” J. Power Sources (2008), 175, pp. 397–407.
[14]. F. Barreras, A. Lozano, L. Valiño, R. Mustata, C. Marín, Fluid dynamics performance of different bipolar plates Part I. Velocity and pressure fields, Journal of Power Sources, 175 (2008), 841–850.
[15]. F. Barreras, A. Lozano, L. Valiño, R. Mustata, C. Marín, Fluid dynamics performance of different bipolar plates Part II. Flow through the diffusion layer, Journal of Power Sources 179 (2008) 711–722.
[16]. Scholta J, Haüssler F, Zhang W, Küppers L, Jörissen L, Lehnert W. Development of a stack having an optimized flow field structure with low cross transport effects.
115
Journal of Power Sources 2006;155:60-5.
[17] Nguyen TV. A gas distributor design for proton-exchange membrane fuel cells.
Journal of Electrochemical Society 1996;143:L103e5.
[18] He W, Yi JS, Nguyen TV. Two-phase flow model of the cathode of PEM fuel cells using interdigitated flow fields. AIChE Journal 1999;46:2053-64.
[19] Feser JP, Prasad AK, Advani SG. Experimental characterization of in-plane permeability of gas diffusion layers. Journal of Power Sources 2006;161:404-12.
[20] Nam Jin Hyun, Lee Kyu-Jin, Sohn Sangho, Kim Charn-Jung. Multi-pass serpentine flow-fields to enhance under-rib convection in polymer electrolyte membrane fuel cells:
design and geometrical characterization. Journal of Power Sources 2009;188:14-23.
[21] Wang Lin, Liu Hongtan. Performance studies of PEM fuel cells with interdigitated flow fields. J Power Sources 2004; 134:185-96.
[22] Hsieh Shou-Shing, Yang Sheng-Huang, Kuo Jenn-Kun, Huang Chin-Feng, Tsai Huang-Hsiu. Study of operational parameters on the performance of micro PEMFCs with different flow fields. Energy Conversion and Management 2006;47:1868-78.
[23] Hu Guilin, Fan Jianren, Chen Song, Liu Yongjiang, Cen Kefa. Three-dimensional numerical analysis of proton exchange membrane fuel cells (PEMFCs) with conventional and interdigitated flow fields. Journal of Power Sources 2004;136:1-9.
[24]. Wu Xu, Keith Scott, Suddhasatwa Basu. Performance of a high temperature polymer electrolyte membrane water electrolyser. Journal of Power Soures 2011;196: 8918-8924.
[25]. Antonucci V, Di Blasi A, Baglio V, Ornelas R, Matteucci F, Ledesma-Garcia J, Arriaga LG, Aricò AS. High temperature operation of a composite membrane-based solid polymer electrolyte water electrolyser. Electrochimica Acta 2008;53:7350-7356.
[26]. Xiaojin Li, Shuguo Qu, Hongmei Yu, Ming Hou, Zhigang Shao, Baolian Yi.
116
Membrane water-flow rate in electrolyzer cells with a solid polymer electrolyte (SPE).
Journal of Power Sources 190 (2009) 534–537.
[27]. Paul Majsztrik, Andrew Bocarsly, and Jay Benziger. Water Permeation through Nafion Membranes: The Role of Water Activity. J. Phys. Chem. B 2008, 112, 16280–
16289.
[28]. Qiao Zhao, Paul Majsztrik, and Jay Benziger. Diffusion and Interfacial Transport of Water in Nafion. J. Phys. Chem. B 2011, 115, 2717–2727.
[29]. Brian Kientiz, Haruhiko Yamada, Nobuaki Nonoyama, Adam Z. Weber. Interfacial Water Transport Effects in Proton-Exchange Membranes. Journal of Fuel Cell Science and Technology FEBRUARY 2011, Vol. 8 / 011013-1~7.
[30]. Makoto Adachi, Titichai Navessin, Zhong Xie, Barbara Frisken, and Steven Holdcroft. Correlation of In Situ and Ex Situ Measurements of Water Permeation Through Nafion NRE211 Proton Exchange Membranes. Journal of The Electrochemical Society, 156 (6) B782-B790 (2009).
[31]. Huaneng Su, Vladimir Linkov, Bernard Jan Bladergroen. Membrane electrode assemblies with low noble metal loadings for hydrogen production from solid polymer electrolyte water electrolysis. International journal of hydrogen energy 38 (2013) 9601-9608.
[32]. K.C. Neyerlin, Hubert A. Gasteiger, Cortney K. Mittelsteadt, Jacob Jorne and Wenbin Gu. Effect of Relative Humidity on Oxygen Reduction Kinetics in a PEMFC. J. Electrochem. Soc. 2005, volume 152, issue 6, A1073-A1080.
[33]. K. C. Neyerlin, Wenbin Gu, Jacob Jorne and Hubert A. Gasteiger. Determination of Catalyst Unique Parameters for the Oxygen Reduction Reaction in a PEMFC. J.
Electrochem. Soc. 2006, volume 153, issue 10, A1955-A1963.
117
[34]. K. C. Neyerlin, Wenbin Gu, Jacob Jorne, Alfred Clark Jr. and Hubert A. Gasteiger.
Cathode Catalyst Utilization for the ORR in a PEMFC Analytical Model and Experimental Validation. J. Electrochem. Soc. 2007volume 154, issue 2, B279-B287.
[35]. K. C. Neyerlin, Wenbin Gu, Jacob Jorne and Hubert A. Gasteiger. Study of the Exchange Current Density for the Hydrogen Oxidation and Evolution Reactions. J.
Electrochem. Soc. 2007volume 154, issue 7, B631-B635.
[36] Hu Mingruo, Gu Anzhong, Wang Minghua, Zhu Xinjian, Yu Lijun. Three dimensional, two phase flow mathematical model for PEM fuel cell: part I. model development. Energy Conversion and Management 2004;45:1861-82.
[37] Hu Mingruo, Zhu Xinjian, Wang Minghua, Gu Anzhong, Yu Lijun. Three dimensional, two phase flow mathematical model for PEM fuel cell: Part II. Analysis and discussion of the internal transport mechanisms. Energy Conversion and Management 2004;45:1883-1916.
[38] Wang Xiao-Dong, Xu Jin-Liang, Yan Wei-Mon, Lee Duu-Jong, Su Ay. Transient response of PEM fuel cells with parallel and interdigitated flow field designs.
International Journal of Heat and Mass Transfer 2011;54:2375-2386.
[39]. Weilin Qu, Issam Mudawar. Prediction and measurement of incipient boiling heat flux in micro-channel heat sinks. International Journal of Heat and Mass Transfer 45 (2002) 3933-3945
[40]. Satish G. Kandlikar. Fundamental issues related to flow boiling in minichannels and microchannels. Experimental Thermal and Fluid Science 26 (2002) 389–407.
[41]. John R. Thome. Boiling in microchannels: a review of experiment and theory.
International Journal of Heat and Fluid Flow 25 (2004) 128–139.
[42]. S.A. Grigoriev, A. A. Kalinnikov, P. Millet, V. I. Porembsky, V. N. Fateev.
118
Mathematical modeling of high-pressure PEM water electrolysis. J. Appl. Electrochem (2010) 40:921-932.
[43]. K. H. Loo, K. H. Wong, Y. M. Lai, S. C. Tan and Chi K. Tse. Derivation of a Fast Mathematical Model of PEM Fuel Cell With Two-Phase Water Transport. IEEE Transactions on Energy conversion, vol. 26, 2011.
[44]. Marcelo Carmo, David L. Fritz, Jürgen Mergel, Detlef Stolten. A comprehensive review on PEM water electrolysis. International Journal of Hydrogen Energy, 38 (2013), 4901-4934.
[45]. Ishanka Dedigama, Pangiota Angeli, Nicholas van Dijk, Jason Millichamp, Dimitrios Tsaoulidis, Paul R. Shearing, Daniel J.L. Brett, Current density mapping and optical flow visualisation of a polymer electrolyte membrane water electrolyser. Journal of Power Sources, 265, 97-103 (2014).
[46]. Peter Berg, Keith Promislow, Jean St. Pierre, Jürgen Stumper, and Brian Wetton.
Water Management in PEM Fuel Cells. Journal of The Electrochemical Society, 151 (3) A341-A353 (2004).
[47]. Huaneng Su, Vladimir Linkov, Bernard Jan Bladergroen. Membrane electrode assemblies with low noble metal loadings for hydrogen production from solid polymer electrolyte water electrolysis. International journal of hydrogen energy 38 (2013) 9601-9608.
[48]. Huaneng Su, Bernard Jan Bladergroen,Vladimir Linkov, Sivakumar Pasupathi, Shan Ji. Study of catalyst sprayed membrane under irradiation method to prepare high performance membrane electrode assemblies for solid polymer electrolyte water electrolysis. International journal of hydrogen energy 36 (2011) 15081-15088.
[49]. Huaneng Su, Bernard Jan Bladergroen, Sivakumar Pasupathi, Vladimir Linkov,
119
Shan Ji. Performance Investigation of Membrane Electrode Assemblies for Hydrogen Production by Solid Polymer Electrolyte Water Electrolysis. International Journal of Electrochemical Science (2012) 4223-4234.
[50]. Junyuan Xu, Ruiying Miao, Tingting Zhao, Jun Wu, Xindong Wang. A novel catalyst layer with hydrophilic-hydrophobic meshwork and pore structure for solid polymer electrolyte water electrolysis. Electrochemistry Communications 13 (2011) 437-439.
[51]. J. C. Cruz, V. Baglio, S. Siracusano, R. Ornelas, L.Ortiz-Frade, L. G. Arriaga, V.
Antonucci, A. S. Aricò. Nanosized IrO2 electrocatalysts for oxygen evolution reaction in an SPE electrolyzer. J Nanopart Res (2011) 13: 1639-1646.
[52]. Jinbin Cheng, Huamin Zhang, Haipeng Ma, Hexiang Zhong, Yi Zou. Study of carbon-supported IrO2 and RuO2 for use in the hydrogen evolution reaction in a solid polymer electrolyte electrolyzer. Electrochimica Acta 55 (2010) 1855–1861.
[53]. S.A. Grigoriev, P. Millet, V.N. Tattev. Evaluation of carbon-supported Pt and Pd nanoparticles for the hydrogen evolution in PEM water electrolysers. Journal of Power Sources 177 (2008) 281-285.
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Chapter 6 Summary
The PEMWEs operated at conventional temperatures ( 80 ), bring us benefits with generating high purity hydrogen in massive scale compared to other types of water electrolysis. High temperature operation, such as 120 , will improve the electrolysis performance by reducing the overpotential, leading to high current density operation.
Thereby, the high temperature PEMWE (HT-PEMWE) is more attractive to us. This study improves and perfects the HT-PEMWE system based on mechanical engineering approaches, the efforts consist of optimizing the operation conditions, structural properties of current collectors and flow field patterns.
Firstly, this study optimizes the operation condition by investigating the effect of operation pressure, temperature and water flow rate on electrolysis performance. The results show that elevating temperature enlarges overpotential by liquid water depletion, but increasing water flow rate and operating pressure can suppress the increase of the overpotential due to elevating temperature. These findings suggest that a vapor/liquid two-phase flow in cell should be maintained through careful controlling the operating pressure and temperature, so that elevating temperature contributes to reduce electrolysis voltage.
After optimizing the operation condition, this study investigates the effect of
121
structural properties of both anode and cathode current collector on water transport and overpotential by liquid water depletion. Results show that the effect of the ACC properties on the electrolysis cell performance at conventional temperature ( 80 °C) are not entirely the same at high temperature ( 100 °C). At high temperature, the contact angle and thickness of the ACC affect the electrolysis voltage mainly through a change in the overpotential by liquid water depletion and the HFR value. Smaller contact angle and thinner ACC promise lowering the HFR value and overpotential by liquid water depletion in the range of 0-120 ° and 200-300 μm. At the same time, the average pore diameter of CCC also has an effect on non-linear overpotential through affecting the water evaporation rate.
Finally, we confirm the effect of flow configurations, anode and cathode flow field pattern on the electrolysis performance. The cathode flow field pattern impacts on only the ohmic overpotential, but the anode flow field pattern impacts on both the ohmic overpotential and the overpotential by liquid water depletion. The flow configuration has little impact on the electrolysis performance. The final result shows that using cascade flow field pattern in the anode and the serpentine in the cathode can promise the lowest electrolysis voltage.
In a nutshell, this study suggests a strategy for optimizing the HT-PEMWE systems.
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The PEMWE finally reaches 1.69 V at 2 A/cm2 under 120 and 0.3 MPa with using cascade flow field pattern and CC4 (20 μm average pore diameter, 200 μm thickness) in the anode, while using the serpentine flow field pattern and CC6 (15 μm average pore diameter, 300 μm thickness) in the cathode.
Besides of aforementioned efforts, other parameters of the catalyst layer, such as the crystal phase of IrO2 and the ionomer content in anode and cathode catalyst layer, also have significant impact on electrolysis performance. To further improve the performance of HT-PEMWE, we plan to optimize the catalyst layer in the future.
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Appendix
A. Theoretical analysis for the effect of anode flow field patterns on the electrolysis performance.
A mathematical model is developed to quantitatively clarify the impact of the anode flow field pattern on electrolysis voltage. Efforts in this modeling concentrates on anode side. This is because anodic activation overpotential dominates the major part in overpotentials [1-8]. The domains of modeling is illustrated in Fig. A.1(a) and A.1(b), which consists of anode components: flow channel, anode current collector (ACC) and catalyst layer. Fig. A.1(c) illustrates a force balance to an oxygen bubble, which leaves from the surface of the ACC. Liquid water is supplied at the inlet of the channel, and both liquid water and oxygen bubble drain at the outlet. This model is applicable only to the cases of serpentine and parallel channel of which shapes can be treated to be straight duct.
The velocity of liquid water can be simply estimated in straight duct. The simulation procedure is shown as followings:
(1) Calculate the Reynolds number of the gas/liquid two-phase flow in channel, to judge flow regime (laminar or turbulent flow).
(2) Calculate the diameter of oxygen bubble when it departs from the surface of the ACC. The calculation is based on the force balance on an oxygen bubble
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along flow channel direction shown in Fig. A.1(c).
(3) Calculate the oxygen gas saturation ( ) in the ACC near the interface between ACC and flow channel. As shown in Fig. 1(c), (the bubble gas pressure in the channel) is assumed to be equal with (the bubble gas pressure in the ACC) [4-8].
(4) Calculate the liquid water saturation ( ) in the ACC pore near the interface between the flow channel and the ACC. Also, the liquid water saturation at the interface between the ACC and catalyst layer ( ) is calculated according to mass transport through the ACC.
(5) Calculate the anode overpotential. The activation overpotential, which is expressed in the Tafel-like equation, is modified to consider the impact of liquid water saturation ( ). Then, the anode overpotential due to water mass transport can be derived from the modified activation overpotential.
Step 1. Judging the flow regime based on Reynolds number.
In the beginning, molar flow rate of each component in channel is quantified to determine the Reynolds number of the gas/liquid two-phase flow in the channel. When electrolysis current is applied, oxygen gas is produced:
4 1
125
where is the mass flow rate of oxygen gas in flow channel, is the current density, A is the area of the catalyst layer, is the molar weight of oxygen gas, F is the Faraday constant.
At the same time, the liquid water supplied is consumed as the result of water electrolysis:
2 2
Where, is the molar weight of water. In addition, the liquid water supplied is carried with proton from anode to cathode due to the osmosis drag. The electro-osmosis drag coefficient is [6]:
0.0134 0.03 3
Where, T is the cell temperature. Then molar flow rate of water dragged by electro-osmosis force is:
4
A representative volumetric flow rate of the liquid water in each flow channel is:
5
where is the mass flow rate of liquid water at inlet, and is the number of flow channels, is the density of liquid water. This number becomes 1 in the case of serpentine channel, and 17 in the case of parallel channel. At the same time, a
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representative volumetric flow rate of the gas phase in each flow channel is:
6
The obtained molar flow rate of liquid water and gas are converted into Reynolds number. According to experimental and numerical analysis under similar working condition with this study, the flow phase in channel is bubbly flow under low current density and slug flow under high current density [7]. In the two-phase flow, which is shown in Fig. A.1(b), gas phase takes a part of the cross section of flow channel. The cross section taken by liquid water should be:
7
As shown in Fig. A.1 (b), is the width of flow channel, is the height of flow channel. The average velocity of liquid ( ) and gas phase ( ) can be calculated as:
8
ch ch
9
Finally, these velocities give the Reynolds number of each phase, , in the flow channel with a rectangular shape as shown Fig. A.1(b).
10 where the subscript x represents liquid phase (l) or gas phase (g). is Dynamic
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viscosity of liquid water or oxygen, is the hydraulic diameter and can be expressed as follows:
4 4
2
2 11
The density of oxygen gas ( ) can be calculated as:
273 12
The Reynolds numbers of gas and liquid water are listed in Table A.1. These Reynolds numbers are calculated with fluid properties.
Step 2. Calculating the diameter of oxygen bubble when it departs from the ACC.
These specific Reynolds numbers contribute to determine flow regime and flow velocity distribution in channel, and leads to estimate the representative liquid water velocity surrounding oxygen bubble. Since Reynolds numbers for liquid and gas in serpentine and parallel channel, as shown in Table A.1, is far smaller than 2300, the flow regime is laminar flow [9, 10]. Analytical distribution for liquid water velocity in horizontal direction at different height can be described as follows [8, 11]:
6 13
As shown in Fig. A.1(a), 0 is the vertical coordinate along the channel height direction. The diameter of oxygen bubble is quite small compared with the height of channel, and Eq. 13 is re-expressed in a simplified manner.
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6 14
Though normalizing the liquid water velocity ( ) in the region from the surface of the ACC to the top of bubble (y = 2 ), the average velocity of liquid water surrounding bubble ( ) can be derived from Eq.14 [8, 11]:
2 2
3
2 15
Release of oxygen bubbles from the surface of ACC is determined by the force balance on the bubble along the channel flow direction. As illustrated in Fig. A.1(c), the drag force on the bubble balances to the attaching force, which is originated in surface tension. The drag force is a function of water velocity surrounding the bubble, which can be represented by in Eq. 14([11]):
1
2 16
Where, is the factor of the resistivity when bubble moves on the surface of porous media in the PEMWE [8]. is the project area of bubble to the flow direction, and
is drag coefficient and can be calculated as follows [11]:
24 17
When the bubble is going to departure from the surface of ACC, the project area of bubble is [11]:
18
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In Eq. 17, is the bubble Reynolds number which is defined with liquid water velocity surrounding bubble [11]:
2 19
When a bubble appears on the surface of ACC, the attaching force originated from surface tension works against the drag force, so that the bubble keeps to stay at the appeared position. The attaching force is expressed by [11]:
1
4 20
Where, is the empirical coefficient, and are the advancing and receding contact angle of the ACC, respectively. is the length of the contact line. and is the empirical coefficient given by [11]:
2 21 58
5 0.14 22
Where is the surface tension of liquid water to air. is the contact angle, which effectively expresses water angle on the ACC.
The relationship between , , and , is shown as following [11]. The receding contact angle is expressed with,
10° 23 In this study, is smaller than 10° because the ACC is super hydrophilic, but the
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will not be negative in fact, then,
0° 24
The θ can be calculated as following [11]:
10° 25
Therefore, Eq. 20 can rewritten as following for short.
1.2 θ 26
As mentioned, the radius of oxygen gas bubbles, when the bubble releases from the surface of ACC, is determined by the force balance on the bubble along the channel flow direction. The force balance equation is described as the drag force is equal to the attaching force,
27
Substituting Eq. 16 and Eq. 26 into Eq. 27, this balance equation yields the bubble radius.
2 θ
15 28
Step 3. Calculate the liquid water saturation value at the interface between the flow channel and ACC ( ). According to Fig. A.1(c), should be equal to because in the same bubble. This relationship can be used to calculate the as following methodology.
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The pressure is capillary pressure in the bubble on ACC, which can be calculated based on Laplace law:
2 29
According to reference [8] with being 4 and Eq. 28, Eq. 29 can be described as following:
120 30
The capillary pressure of the bubble ( ) is the difference between pressure of gas in the bubble ( ) and the pressure of liquid water around the bubble ( ) [5].
31
Thus, the pressure of gas in the bubble can be written as:
32
The derived as the Eq. 30 is utilized to derive oxygen gas saturation near the surface in the ACC in the following.
The capillary pressure in ACC depends on gas saturation and porous properties such as wettability (contact angle). Different gas saturation causes different capillary pressure. The capillary pressure in the ACC near the interface between the flow channel and ACC can be expressed with the gas saturation there [5]:
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1.417 2.12 1.26 33
where is the permeability of ACC, is the porosity of ACC. Gas saturation is defined as the fraction of gas volume in pore of ACC. When saturation is 100%, pore of ACC is completely occupied by gas. The gas saturation in ACC near the interface between channel and ACC, , is very close to 0 in PEMWE, because the interface positions next to the liquid water flow in channel. Thus, Eq. 33 can be simplified as follows [8]:
1.417 θ 34
This capillary pressure in ACC at the interface between the ACC and catalyst layer is the pressure difference between the gas phase ( ) and the liquid phase near the interface ( ) [5].
35
Therefore, the gas phase can be written as
36
The gas pressure at the channel side ( ) should balance to the gas pressure in the ACC side ( ).
37 Substituting Eq. 32 and 36 into 37, we obtain,
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38
The water pressure at the channel side ( ) is approximately equal to that in the
ACC ( ).
39
Substituting Eq. 39 to Eq. 38, we obtain a capillary pressure balance between the capillary pressure in the flow channel and capillary pressure in the ACC.
40
Finally, substituting Eq. 30 and 34 into Eq. 40 yields the gas saturation near the interface .
15.492 41
This equation shows that high invites high , and the detail reason is explained as follows. Eq. 41 shows the high water velocity allows oxygen gas bubble departs from the ACC with a small diameter. Small oxygen gas bubble means high gas pressure in the bubble. Because the bubble departure is a continuous process, therefore, the bubble in the ACC is also small and invites high gas pressure. According to the Ref. [5], high gas pressure in ACC promises high gas saturation ( ). Therefore, the higher water velocity is, the higher gas saturation will be.
According to aforementioned analysis, the overpotential is directly related to the
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flow velocity. Although the velocity can be slowed down through decreasing the water flow rate, but this method changes the water utilization. When water utilization is changed, only the analysis of the capillary pressure cannot explain the impact from the change of water flow rate on the electrolysis performance clearly. Therefore, only decreasing the water flow rate may not help decrease the overpotential when serpentine flow field pattern is used.
The gas saturation near the interface can be converted into the liquid saturation at the same position, , with the relationship of 1.
1 42
Step 4. Calculating the value of liquid water saturation at the interface between the catalyst layer and ACC ( ) according to structural properties of ACC.
In the PEMWE, the molar density of liquid water in the catalyst layer affects electrolysis voltage. Molar density of water in liquid phase is thousands of times larger than that in vapor phase. Thus, liquid water saturation near the catalyst layer, , should be carefully addressed in this modeling. There are a series of methods on calculating the liquid water saturation at catalyst layer [8-11]. Among them, the mass transport driven by liquid water saturation gradient (Ref. [4]) can be used to calculate the saturation. It is assumed that the liquid water saturation in the ACC in through-plane direction has a linear