微型直接甲醇燃料电池的性能模拟与分析
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摘要
直接甲醇燃料电池是直接利用甲醇水溶液作为燃料,氧或空气作为氧化剂的一种燃料电池,其具有低污染、高效率、燃料补充方便且安全性高等优点,适宜成为笔记本电脑、手机等便携式电子产品的小型移动电源供应系统。为了深入理解发生在直接甲醇燃料电池中的物理化学现象和限制其性能的各因素,本文建立了沿着膜电极厚度方向的稳态数学模型进行数值模拟分析,从而确定理想的结构设计和操作条件。
本文首先综述了直接甲醇燃料电池数学模型的国内外研究现状,详细阐述了微型直接甲醇燃料电池各组件的工作机理,并建立了相应的模型。其中多组分气相扩散现象是以Maxwell-Stefan方程来描述的;假定模型内的燃料为粘性不可压缩流体,用Navier-Stokes方程来描述其基本传输;质子在多孔材料中的传递现象以Nernst-Plack方程来描述;多孔介质内的流体流动采用修正的Schlogl方程来描述;电池内部电化学反应采用Butler-Volmer方程来描述。
本文对直接甲醇燃料电池微流场结构进行仿真分析,为电池极板设计提供了可靠的依据。对直接甲醇燃料电池在不同操作条件下对其性能的影响进行了模拟分析,研究中发现以下性质:工作电流密度较小时,电池操作温度越高性能越差,而工作电流密度较大时,电流操作温度越高性能越好;阴极侧空气进料压力越大其性能越好;甲醇浓度在2molL-1时,输出功率密度最大;催化层和扩散层的孔隙率的大小影响着极限电流密度。最后将理论结果与实验数据进行了比较,进一步验证了模型的准确性。
Direct methanol fuel cell is the direct use of methanol as fuel, oxygen or air as an oxidant a fuel cell, having some advantages, such as clean, efficient, convenient and safe, which are suitable for notebook computers, mobile phones and other portable product and the small mobile electronics power supplying system. In order to better understand the processes and phenomena that determine the performance of a liquid feed DMFC, an isothermal, steady-state, mathematical model of DMFC is established.
This paper reviews the model of direct methanol fuel cell at home and abroad, and describes the components of working mechanism and the establishment of the corresponding model. The diffusive mass flux of gas is described using the Maxwell-Stefan equation. The fluid flow in the anode channel is modeled with the momentum and continuity equations (the Navier-Stokes equations). The proton through the portentous electrodes can be described by Nernst-Plack equations. The fluid within portentous electrodes is described by modified Schlogl equations. The electrode reaction in the active catalyst layers are described by Butler-Volmer equations.
In this paper, the flow microchannel of DMFC is simulated and analyzed which provides a reliable basis for designing flow channel. The performance of DMFC is simulated with different operating conditions. It is found that the performance of DMFC decrease as the operating temperature increase in the low current density. Moreover as the operating temperature increasing, the performance of DMFC also increases in the high current density. In cathode, the performance of DMFC increases as the operating pressure of outlet. The output power density is largest with the concentration of methanol at 2molL-1. The porosity of diffusion layer and catalyst layer has effects on the ultimate current density. Finally, theoretical results agree with the experimental data that verify the accuracy of the model.
本文首先综述了直接甲醇燃料电池数学模型的国内外研究现状,详细阐述了微型直接甲醇燃料电池各组件的工作机理,并建立了相应的模型。其中多组分气相扩散现象是以Maxwell-Stefan方程来描述的;假定模型内的燃料为粘性不可压缩流体,用Navier-Stokes方程来描述其基本传输;质子在多孔材料中的传递现象以Nernst-Plack方程来描述;多孔介质内的流体流动采用修正的Schlogl方程来描述;电池内部电化学反应采用Butler-Volmer方程来描述。
本文对直接甲醇燃料电池微流场结构进行仿真分析,为电池极板设计提供了可靠的依据。对直接甲醇燃料电池在不同操作条件下对其性能的影响进行了模拟分析,研究中发现以下性质:工作电流密度较小时,电池操作温度越高性能越差,而工作电流密度较大时,电流操作温度越高性能越好;阴极侧空气进料压力越大其性能越好;甲醇浓度在2molL-1时,输出功率密度最大;催化层和扩散层的孔隙率的大小影响着极限电流密度。最后将理论结果与实验数据进行了比较,进一步验证了模型的准确性。
Direct methanol fuel cell is the direct use of methanol as fuel, oxygen or air as an oxidant a fuel cell, having some advantages, such as clean, efficient, convenient and safe, which are suitable for notebook computers, mobile phones and other portable product and the small mobile electronics power supplying system. In order to better understand the processes and phenomena that determine the performance of a liquid feed DMFC, an isothermal, steady-state, mathematical model of DMFC is established.
This paper reviews the model of direct methanol fuel cell at home and abroad, and describes the components of working mechanism and the establishment of the corresponding model. The diffusive mass flux of gas is described using the Maxwell-Stefan equation. The fluid flow in the anode channel is modeled with the momentum and continuity equations (the Navier-Stokes equations). The proton through the portentous electrodes can be described by Nernst-Plack equations. The fluid within portentous electrodes is described by modified Schlogl equations. The electrode reaction in the active catalyst layers are described by Butler-Volmer equations.
In this paper, the flow microchannel of DMFC is simulated and analyzed which provides a reliable basis for designing flow channel. The performance of DMFC is simulated with different operating conditions. It is found that the performance of DMFC decrease as the operating temperature increase in the low current density. Moreover as the operating temperature increasing, the performance of DMFC also increases in the high current density. In cathode, the performance of DMFC increases as the operating pressure of outlet. The output power density is largest with the concentration of methanol at 2molL-1. The porosity of diffusion layer and catalyst layer has effects on the ultimate current density. Finally, theoretical results agree with the experimental data that verify the accuracy of the model.
引文
1衣宝廉.燃料电池——原理·技术·应用.化学工业出版社, 2003: 13~15
2贺华,赵景联.燃料电池的开发现状及其发展前景.石化技术与应用. 2001, 3: 205~209
3 K. Scott, W. Taama, J. Cruickshank. Performance and Modeling of a Direct Methanol Solid Polymer Electrolyte Fuel Cell. Journal of Power Sources. 1997, 65(1/2): 159~171
4 K. Scott, P. Argtropoulos, K. SundMacher. A Model for the Liquid Feed Direct Methanol Fuel Cell. Journal of Electroanalytical Chemistry. 1999, 477(2): 97~110
5 P. Argtropoulos, K. Scott, WM. Taama. One Dimensional Thermal Model for Direct Methanol Fuel Cell Stacks Part I. Model development. Journal of Power Sources. 1999, 79(2): 169~183
6 P. Argtropoulos, K. Scott, WM. Taama. Pressure Drop Modeling for Liquid Feed Direct Methanol Fuel Cells Part I. Model Development. Chemical Engineering Journal. 1999, 73(3): 217~227
7 G. Murgiag, L. Pisanil, A. K. Shukla et al. A Numerical Model of a Liquid Feed Solid Polymer Electrolyte DMFC and its Experimental Validation. Journal of the Electrochemical Society. 2003, 150(9): A1231~A1245
8 K. Scott, P. Argtropoulos. A One Dimensional Model of a Methanol Fuel Cell Anode. Journal of Power Sources. 2004, 137(2): 228~238
9 A. A. Kulikovsky. Two Dimensional Numerical Modeling of a Direct Methanol Fuel Cell. Journal of Applied Electrochemistry. 2000, 30(9): 1005~1014
10 A. A. Kulikovsky, J. Divisek, A. A. Kornyshew. Two Dimensional Simulation of Direct Methanol Fuel Cell a New (Embedded) Type of Current Collector. Journal of the Electrochemical Society. 2000, 147(3): 953~959
11 A. A. Kulikovsky. 1D+1D Model of a DMFC: Localized Solutions and Mixed Potential. Electrochemistry Communications. 2004, 6(12): 1259~1265
12 J. Divisek, J. Fuhrmann, K. Gartner et al. Performance Modeling of a Direct Methanol Fuel Cell. Journal of the Electrochemical Society. 2003, 150(6): A811~A825
13 Z. H. Wang, C. Y. Wang. Mathematical Modeling of Liquid-Feed DirectMethanol Fuel Cells. Journal of the Electrochemical Society. 2003, 150(4): A508~A519
14 S. F. Baxter, V. S. Battaglia, R. E. White. Methanol Fuel Cell Model: Anode. Journal of the Electrochemical Society. 1999, 146(2): 437~447
15 J. P. Meyers, J. Newman. Simulation of the Direct Methanol Fuel Cell-I. Thermodynamic Framework for a Multicomponent Membrane. Journal of the Electrochemical Society. 2002, 149(6): A710~A717
16 A. Z. Weber, J. Newman. Transport in Polymer-Electrolyte Membranes-I. Physical Model. Journal of the Electrochemical Society. 2003, 150(7): A1008~A1015
17 A. Z. Weber, J. Newman. Transport in Polymer-Electrolyte Membranes-II. Mathematical Model. Journal of the Electrochemical Society. 2004, 151(2): A311~A325
18 A. A. Kulikovsky. Model of the Flow with Bubbles in the Anode Channel and Performance of a Direct Methanol Fuel Cell. Electrochemistry Communications. 2005, 7 (2): 237~243
19 G. B. Jung, A. Su, C. H. Tu et al. Effects of Flow Fields on Direct Methanol Fuel Cell-Simulation Study. Journal of Power Sources. 2007, 171(1): 212~217
20毛庆,孙公权,杨少华等.直接甲醇燃料电池模型研究进展.电源技术. 2005, 29(12): 840~843
21 A. A. Kulikovsky. Bubbles in the Anode Channel and Performance of a DMFC: Asymptotic Solutions. Electrochimica Acta. 2006, 51(10): 2003~2011
22 G. Q. Lu, C. Y. Wang. Electrochemical and Flow Characterization of a Direct Methanol Fuel Cell. Journal of Power Sources. 2004,134(1): 33~40
23 H. Yang, T. S. Zhao, Q. Ye. Addition of Non-Reacting Gases to the Anode Flow Field of DMFCs Leading to Improved Performance. Electrochemistry Communications. 2004, 6(11): 1098~1103
24 S. Waelchli, P. R. Rohr. Two-Phase Flow Characteristics in Gas-Liquid Microreactors. International Journal of Multiphase Flow. 2006, 32(7): 791~806
25 G. Murgia, L. Pisani, A. K. Shukla et al. A Numerical Model of a Liquid-Feed Solid Polymer Electrolyte DMFC and its Experimental Validation. Journal of the Electrochemical Society. 2003, 150(9): A1231~A1245
26 A. A. Kulikovsky. Two-Dimensional Numerical Modeling of a Direct Methanol Fuel Cell. Journal of Applied Electrochemistry. 2000, 30(9): 1005~1014
27 J. Divisek, J. Fuhrmann, K. Gartner et al. Performance Modeling of a Direct Methanol Fuel Cell. Journal of the Electrochemical Society. 2003, 150(6): A811~A825
28 E. Birgersson, J. Nordlund, H. Ekstrom et al. Reduced Two-Dimensional One-Phase Model for Analysis of the Anode of a DMFC. Journal of the Electrochemical Society. 2003, 150(10): A1368~A1376
29 A. A. Kulikovsky. Analytical Model of the Anode Side of DMFC: the Effect of Non-Tafel Kinetics on Cell Performance. Electrochemistry Communications. 2003, 5(7): 530~538
30 X. M. Ren, P. Zelenay, S. Thomas et al. Recent Advances in Direct Methanol Fuel Cells at Los Alamos National Laboratory. Journal of Power Sources. 2000, 86(1/2): 111~116
31 K. Scott, W. Taama, J. Cruickshank. Performance and Modeling of a Direct Methanol Solid Polymer Electrolyte Fuel Cell. Journal of Power Sources. 1997, 65(1/2): 159~171
32 A. K. Shukla, C. L. Jackson, K. Scott et al. A Solid-Polymer Electrolyte Direct Methanol Fuel Cell with a Mixed Reactant and Air Anode. Journal of Power Sources. 2002, 111(1): 43~51
33 D. M. Bernardi, M. W. Vebrugge. A Mathematical Model of the Solid-Polymer-Electrolyte Fuel Cell. Journal of the Electrochemical Society. 1992, 139(9): 2477~2491
34 A. Heinzel, V. M. Barragan. A Review of the State-of-the-Art of the Methanol Crossover in Direct Methanol Fuel Cells. Journal of Power Sources. 1999, 84(1): 70~74
35 V. S. Silva, A. Mendes, L. M. Madeira et al. Proton Exchange Membranes for Direct Methanol Fuel Cells: Properties Critical Study Concerning Methanol Crossover and Proton Conductivity. Journal of Membrane Science. 2006, 276(1/2): 126~134
36 K. C. Yu, W. J. Kim, C. H. Chung. Utilization of Pt/Ru Catalysts in MEA for Fuel Cell Application by Breathing Process of Proton Exchange Membrane. Journal of Power Sources. 2006, 163(1): 34~40
37詹姆斯·拉米尼,安德鲁·迪克斯.燃料电池系统——原理、设计、应用.朱红,衣宝廉译.第二版.科学出版社, 2006: 119~126
38查全性.燃料电池技术的发展与我国应有的对策.应用化学. 1993, 10(5):38~42
39黄已立,雷声,郭玉宝.化学反应生成物浓度预测、控制数学模型的研究.大学数学. 2005, 21(5): 30~36
40 D. H. Jung, C. H. Lee, C. S. Kim. Electrochemical Cell with Fluid Distribution Layer Having Integral Sealing Capability. Journal of Power Sources. 2002, 71(1/2): 169~173
41 K. Scott, P. Argyropoulos. A Current Distribution Model of a Porous Fuel Cell Electrode. Journal of Electroanalytical Chemistry. 2004, 567(1): 103~109
42 Y. H. Chan, T. S. Zhao, R. Chen et al. A Self-Regulated Fuel-Feed System for Passive Direct Methanol Fuel Cells. Journal of Power Sources. 2008, 176(1): 183~190
43 R. Z. Jiang, D. Chu. Voltage-Time Behavior of a Polymer Electrolyte Membrane Fuel Cell Stack at Constant Current Discharge. Journal of Power Sources. 2001, 92(1/2): 193~198
44 A. Vincenzo. Direct Methanol Fuel Cells for Mobile Applications: a Strategy for the Future. Fuel Cells Bulletin. 1999, 2(7): 6~8
45 S. C. Kelley, G. A. Deluga, W. H. Smyrl. Miniature Methanol/Air Polymer Electrolyte Fuel Cell. Electrochemical Solid-State Letters. 2000, 3(9): 407~409
46于景荣,衣宝廉,张华民等.微型燃料电池的研究与发展.电源技术. 2004, 28(8): 515~519
47 P. Costamagna,S. Srinivasan. Quantum Jumps in the PEMFC Science and Technology form the 1960s to the Year 2000: Part I. Fundamental Scientific Aspects. Journal of Power Source. 2001, 102(1/2): 242~252
48 K. Scott, P. Argyropoulos, K. Sundmacher. A Model for Liquid Feed Direct Methanol Fuel Cell. Journal of Electroanalytical Chemistry. 1999,477(2): 97~110
49 R. B. Bird, W. Stewart, E. Lightfoot. Genesis of Transport Phenomena. Chemical & Engineering News. 1995, 73(48): 32
50 F. Jaouen, G. Lindbergh, G. Sundholm. Investigation of Mass Transport Limitations in the Solid Polymer Fuel Cell Cathode I. Mathematical Model. Journal of the Electrochemical Society. 2002, 149(4): A437~A447
51 T. Vidakovic, M. Christov, K. Sundmacher. Rate Expression for Electrochemical Oxidation of Methanol on a Direct Methanol Fuel Cell Anode. Journal of Electroanalytical Chemistry. 2005, 580(1): 105~121
2贺华,赵景联.燃料电池的开发现状及其发展前景.石化技术与应用. 2001, 3: 205~209
3 K. Scott, W. Taama, J. Cruickshank. Performance and Modeling of a Direct Methanol Solid Polymer Electrolyte Fuel Cell. Journal of Power Sources. 1997, 65(1/2): 159~171
4 K. Scott, P. Argtropoulos, K. SundMacher. A Model for the Liquid Feed Direct Methanol Fuel Cell. Journal of Electroanalytical Chemistry. 1999, 477(2): 97~110
5 P. Argtropoulos, K. Scott, WM. Taama. One Dimensional Thermal Model for Direct Methanol Fuel Cell Stacks Part I. Model development. Journal of Power Sources. 1999, 79(2): 169~183
6 P. Argtropoulos, K. Scott, WM. Taama. Pressure Drop Modeling for Liquid Feed Direct Methanol Fuel Cells Part I. Model Development. Chemical Engineering Journal. 1999, 73(3): 217~227
7 G. Murgiag, L. Pisanil, A. K. Shukla et al. A Numerical Model of a Liquid Feed Solid Polymer Electrolyte DMFC and its Experimental Validation. Journal of the Electrochemical Society. 2003, 150(9): A1231~A1245
8 K. Scott, P. Argtropoulos. A One Dimensional Model of a Methanol Fuel Cell Anode. Journal of Power Sources. 2004, 137(2): 228~238
9 A. A. Kulikovsky. Two Dimensional Numerical Modeling of a Direct Methanol Fuel Cell. Journal of Applied Electrochemistry. 2000, 30(9): 1005~1014
10 A. A. Kulikovsky, J. Divisek, A. A. Kornyshew. Two Dimensional Simulation of Direct Methanol Fuel Cell a New (Embedded) Type of Current Collector. Journal of the Electrochemical Society. 2000, 147(3): 953~959
11 A. A. Kulikovsky. 1D+1D Model of a DMFC: Localized Solutions and Mixed Potential. Electrochemistry Communications. 2004, 6(12): 1259~1265
12 J. Divisek, J. Fuhrmann, K. Gartner et al. Performance Modeling of a Direct Methanol Fuel Cell. Journal of the Electrochemical Society. 2003, 150(6): A811~A825
13 Z. H. Wang, C. Y. Wang. Mathematical Modeling of Liquid-Feed DirectMethanol Fuel Cells. Journal of the Electrochemical Society. 2003, 150(4): A508~A519
14 S. F. Baxter, V. S. Battaglia, R. E. White. Methanol Fuel Cell Model: Anode. Journal of the Electrochemical Society. 1999, 146(2): 437~447
15 J. P. Meyers, J. Newman. Simulation of the Direct Methanol Fuel Cell-I. Thermodynamic Framework for a Multicomponent Membrane. Journal of the Electrochemical Society. 2002, 149(6): A710~A717
16 A. Z. Weber, J. Newman. Transport in Polymer-Electrolyte Membranes-I. Physical Model. Journal of the Electrochemical Society. 2003, 150(7): A1008~A1015
17 A. Z. Weber, J. Newman. Transport in Polymer-Electrolyte Membranes-II. Mathematical Model. Journal of the Electrochemical Society. 2004, 151(2): A311~A325
18 A. A. Kulikovsky. Model of the Flow with Bubbles in the Anode Channel and Performance of a Direct Methanol Fuel Cell. Electrochemistry Communications. 2005, 7 (2): 237~243
19 G. B. Jung, A. Su, C. H. Tu et al. Effects of Flow Fields on Direct Methanol Fuel Cell-Simulation Study. Journal of Power Sources. 2007, 171(1): 212~217
20毛庆,孙公权,杨少华等.直接甲醇燃料电池模型研究进展.电源技术. 2005, 29(12): 840~843
21 A. A. Kulikovsky. Bubbles in the Anode Channel and Performance of a DMFC: Asymptotic Solutions. Electrochimica Acta. 2006, 51(10): 2003~2011
22 G. Q. Lu, C. Y. Wang. Electrochemical and Flow Characterization of a Direct Methanol Fuel Cell. Journal of Power Sources. 2004,134(1): 33~40
23 H. Yang, T. S. Zhao, Q. Ye. Addition of Non-Reacting Gases to the Anode Flow Field of DMFCs Leading to Improved Performance. Electrochemistry Communications. 2004, 6(11): 1098~1103
24 S. Waelchli, P. R. Rohr. Two-Phase Flow Characteristics in Gas-Liquid Microreactors. International Journal of Multiphase Flow. 2006, 32(7): 791~806
25 G. Murgia, L. Pisani, A. K. Shukla et al. A Numerical Model of a Liquid-Feed Solid Polymer Electrolyte DMFC and its Experimental Validation. Journal of the Electrochemical Society. 2003, 150(9): A1231~A1245
26 A. A. Kulikovsky. Two-Dimensional Numerical Modeling of a Direct Methanol Fuel Cell. Journal of Applied Electrochemistry. 2000, 30(9): 1005~1014
27 J. Divisek, J. Fuhrmann, K. Gartner et al. Performance Modeling of a Direct Methanol Fuel Cell. Journal of the Electrochemical Society. 2003, 150(6): A811~A825
28 E. Birgersson, J. Nordlund, H. Ekstrom et al. Reduced Two-Dimensional One-Phase Model for Analysis of the Anode of a DMFC. Journal of the Electrochemical Society. 2003, 150(10): A1368~A1376
29 A. A. Kulikovsky. Analytical Model of the Anode Side of DMFC: the Effect of Non-Tafel Kinetics on Cell Performance. Electrochemistry Communications. 2003, 5(7): 530~538
30 X. M. Ren, P. Zelenay, S. Thomas et al. Recent Advances in Direct Methanol Fuel Cells at Los Alamos National Laboratory. Journal of Power Sources. 2000, 86(1/2): 111~116
31 K. Scott, W. Taama, J. Cruickshank. Performance and Modeling of a Direct Methanol Solid Polymer Electrolyte Fuel Cell. Journal of Power Sources. 1997, 65(1/2): 159~171
32 A. K. Shukla, C. L. Jackson, K. Scott et al. A Solid-Polymer Electrolyte Direct Methanol Fuel Cell with a Mixed Reactant and Air Anode. Journal of Power Sources. 2002, 111(1): 43~51
33 D. M. Bernardi, M. W. Vebrugge. A Mathematical Model of the Solid-Polymer-Electrolyte Fuel Cell. Journal of the Electrochemical Society. 1992, 139(9): 2477~2491
34 A. Heinzel, V. M. Barragan. A Review of the State-of-the-Art of the Methanol Crossover in Direct Methanol Fuel Cells. Journal of Power Sources. 1999, 84(1): 70~74
35 V. S. Silva, A. Mendes, L. M. Madeira et al. Proton Exchange Membranes for Direct Methanol Fuel Cells: Properties Critical Study Concerning Methanol Crossover and Proton Conductivity. Journal of Membrane Science. 2006, 276(1/2): 126~134
36 K. C. Yu, W. J. Kim, C. H. Chung. Utilization of Pt/Ru Catalysts in MEA for Fuel Cell Application by Breathing Process of Proton Exchange Membrane. Journal of Power Sources. 2006, 163(1): 34~40
37詹姆斯·拉米尼,安德鲁·迪克斯.燃料电池系统——原理、设计、应用.朱红,衣宝廉译.第二版.科学出版社, 2006: 119~126
38查全性.燃料电池技术的发展与我国应有的对策.应用化学. 1993, 10(5):38~42
39黄已立,雷声,郭玉宝.化学反应生成物浓度预测、控制数学模型的研究.大学数学. 2005, 21(5): 30~36
40 D. H. Jung, C. H. Lee, C. S. Kim. Electrochemical Cell with Fluid Distribution Layer Having Integral Sealing Capability. Journal of Power Sources. 2002, 71(1/2): 169~173
41 K. Scott, P. Argyropoulos. A Current Distribution Model of a Porous Fuel Cell Electrode. Journal of Electroanalytical Chemistry. 2004, 567(1): 103~109
42 Y. H. Chan, T. S. Zhao, R. Chen et al. A Self-Regulated Fuel-Feed System for Passive Direct Methanol Fuel Cells. Journal of Power Sources. 2008, 176(1): 183~190
43 R. Z. Jiang, D. Chu. Voltage-Time Behavior of a Polymer Electrolyte Membrane Fuel Cell Stack at Constant Current Discharge. Journal of Power Sources. 2001, 92(1/2): 193~198
44 A. Vincenzo. Direct Methanol Fuel Cells for Mobile Applications: a Strategy for the Future. Fuel Cells Bulletin. 1999, 2(7): 6~8
45 S. C. Kelley, G. A. Deluga, W. H. Smyrl. Miniature Methanol/Air Polymer Electrolyte Fuel Cell. Electrochemical Solid-State Letters. 2000, 3(9): 407~409
46于景荣,衣宝廉,张华民等.微型燃料电池的研究与发展.电源技术. 2004, 28(8): 515~519
47 P. Costamagna,S. Srinivasan. Quantum Jumps in the PEMFC Science and Technology form the 1960s to the Year 2000: Part I. Fundamental Scientific Aspects. Journal of Power Source. 2001, 102(1/2): 242~252
48 K. Scott, P. Argyropoulos, K. Sundmacher. A Model for Liquid Feed Direct Methanol Fuel Cell. Journal of Electroanalytical Chemistry. 1999,477(2): 97~110
49 R. B. Bird, W. Stewart, E. Lightfoot. Genesis of Transport Phenomena. Chemical & Engineering News. 1995, 73(48): 32
50 F. Jaouen, G. Lindbergh, G. Sundholm. Investigation of Mass Transport Limitations in the Solid Polymer Fuel Cell Cathode I. Mathematical Model. Journal of the Electrochemical Society. 2002, 149(4): A437~A447
51 T. Vidakovic, M. Christov, K. Sundmacher. Rate Expression for Electrochemical Oxidation of Methanol on a Direct Methanol Fuel Cell Anode. Journal of Electroanalytical Chemistry. 2005, 580(1): 105~121