三维电极的非线性分析
摘要
三维电极是电化学反应器中的工作电极,对工作电极的过程分析是电化学反应系统分析的源头,能够了解系统内过程的基本特征。与传统的两维电极相比,三维电极具有大的电极比表面积和高的传质速率,能在相对低的电极极化下,达到较高的表观电流密度,故广泛应用于能源(燃料电池)、电合成、环境等多个领域,对三维电极理论的需求也日趋迫切。填充床电极(packed bed electrode)和多孔电极(porous electrode)是两种常见的三维电极。在三维电极内部,存在着两维电极所没有的、耦联的超电势和浓度等动力学参量的空间分布,反应表面电荷转移过程与空隙中传质过程的耦联,是三维电极的主要特征。把这个学术观点进行理论上的数学表达,寻找相适应的求解新方法,是目前国内外研究者尚未完全解决的前沿性理论研究工作。
本文根据电化学反应工程的基本原理,通过与多相催化工程理论的交叉、类比,从电化学反应工程的“源头”出发,寻找出三维电极工程理论的创新点。通过对填充床电极微分反应器(PBEDR)中典型有机电合成复合反应过程的理论分析,建立了动力学普遍化非线性理论模型,归纳出量纲1准数,探讨了各参数对总选择性的影响规律;针对质子膜燃料电池(PEMFC)多孔电极微结构的特征,提出了两尺度理论分析的新方法,建立了多孔电极内反应和传递过程耦联的普遍化非线性理论模型,描述电极中浓度和超电势分布,考察了量纲1准数及诸工程参数对浓度分布、电势分布、效率因子和极化曲线的影响;采用新的解析计算工具—Adomian分解法(ADM),对所建立的非线性常微分方程(组)的边值问题进行求解,以多项式形式给出数模的逼近解析解;以硝基苯电化学还原制对氨基苯酚为例,验证了填充床电极反应器的理论模型,并优化了反应器的关键尺寸;给出了氢质子膜燃料电池多孔阴极的实例,对多孔电极的两尺度普遍化模型进行验证。本文的主要研究内容及结论如下:
1.建立了填充床电极微分反应器中典型有机电化学复合反应过程的动力学普遍化的非线性理论模型,描述床层内超电势横向分布及超电势横向分布对选择性的影响。归纳出表征电极极化和副反应影响的量纲1准数μ、ω。普遍化数模中的量纲1准数,不但对于理论分析,而且对于更复杂实际过程的相似分析,都是十分重要的。给出了超电势分布和总选择性S与数模中μ、ω、n_2/n_1等量纲1准数的理论关系,详细讨论了各准数对S的影响。有机电合成最值得关注的问题是反应总选择性S ,对于特定的复合反应体系,μ-S关系最为重要,μ- S曲线能为选择PBEDR主要操作条件(外加超电势η)和优化反应器主要尺寸(填充床电极厚度l)提供理论依据。
2.对质子膜燃料电池多孔电极进行多尺度的理论分析,以便从理论上分析宏观尺度平均可能带入的误差,更加准确地理解和描述多孔电极内反应和传递耦联的过程。建立了能够同时在团簇微观和电极宏观两尺度上描述多孔电极内反应和传递耦联过程的非线性理论模型,研究内容处于电化学反应工程理论研究的前沿,是对传统研究方法的突破。给出了浓度分布、电势分布、效率因子曲线及量纲1表观极化曲线和表观极化曲线,讨论了量纲1准数s和v~2、多孔催化层厚度l、量纲1表面超电势Φ_0、多孔电极比表面积a等对浓度分布、电势分布、效率因子以及极化曲线的影响。文中提出的两尺度新方法也可被其它相似的多相催化反应系统理论分析所借鉴。
3. ADM分解法是一个非线性数模逼近解析的有效方法。采用ADM对所建立的非线性常微分方程(组)的边值问题进行求解,给出数模逼近解析解的代数表达式,能够连续描述模型的非线性规律,简单地进行定量计算,为反应器的分析、设计和优化提供有价值的理论依据。
4.以硝基苯电还原制对氨基苯酚为例,对填充床电极反应器理论模型进行验证。将μ-S关系的理论计算结果与实验数据进行了对比,结果令人满意,并优化了反应器关键尺寸(填充床电极厚度)。
5.给出了氢质子膜燃料电池(PEMFC)多孔阴极的计算实例,与电极单尺度模型相比,两尺度模型的预测值与极化实验数据能更好相符,从而验证了包含微团尺度传质影响的理论模型更加合理、准确。
Three-dimensions electrode is the working electrode in electrochemical reactor. Its process is analyzed as the source of analysis of electrochemical reaction system so that the basic characteristic is realized in electrochemical reaction system. Compared with conventional two-dimensions electrode, three-dimensions electrode provides a large electrode surface area per unit of reaction volume and presents very good mass transport velocity, hence it can reach higher current density at relatively low electrode polarization. So it is used widely in energy(fuel cell), electrosynthesis and environmental treatment etc. Three-dimensions electrode theories are required urgently. Packed bed electrode and porous electrode are two kinds of familiar three-dimensions electrodes. There is space distribution of kinetics parameters or couple overpotential and concentration in three-dimensions electrode, whereas there is no in two-dimensions electrode. The main characteristic of three-dimensions electrode is that surface charge transfer and mass transport in interspace are coupled. Establishing mathematical model and seeking appropriate new solving method are of challenges that still have been not solved entirely by domestic and external pursuers.
In this dissertation, basing on basic theory of electrochemical reaction engineering and starting with source of electrochemical reaction engineering, the innovation of three-dimensions electrode engineering theory was educed by comparison and analogue with heterogeneous catalysis engineering theory. First, the typical process of electro-organic synthesis in a differential reactor of packed bed electrode (PBEDR) was theoretically analyzed and a generalized nonlinear kinetics mathematical model was developed, dimensionless variables were derived from modeling, the effect of variables on the reaction selectivity was researched. Second, aiming at the character of microstructure of porous electrode in Proton Exchange Membrane Fuel Cell (PEMFC), a novel two-scale method was presented, the generalized nonlinear theoretical model of coupled reaction-transport process in porous electrode was developed to describe the distribution of overpotential and concentration, the effect of dimensionless variables and engineering parameters on distribution of overpotential and concentration, effectiveness factor, polarization curve was discussed. Then, a novel analytical method–Adomian Decomposition Method (ADM) was used for solving a boundary problem of nonlinear differential equation or a set of nonlinear differential equations derived from dissertation, it can give the approximate analytical solutions in a form of polynomial. Furthermore, an analysis of electrochemical reduction of nitrobenzene to p-aminophenol in a PBEDR was presented, the theoretical model of PBEDR was validated, and the key size of the reactor was theoretically optimized. Finally, an example of porous cathode in PEMFC was given to verify two-scale generalized model of porous electrode. The contents and conclusions of this dissertation are as follows:
1. A generalized nonlinear kinetics theoretical model for the typical complex reaction process of electro-organic synthesis in a PBEDR was developed to describe the lateral distribution of overpotential and the effect of the lateral distribution of overpotential on selectivity. Dimensionless variablesμand ? that characterize the polarization and influence of side electrode reaction in the system, were derived from modeling. Dimensionless variables in generalized model are very important not only for theoretical analysis but also for analogical analysis of more complicated practical process. The theoretical relation between distribution of overpotential, selectivityS and dimensionless variablesμ,ω,n_2/n_1 was presented. Selectivity is paid specially attention in electro-organic synthesis. The relation betweenμand S is important to given complex reaction system, it can provide theoretical foundation for selecting main operation condition of PBEDR and optimizing primary size of the reactor.
2. Two-scale method was presented for the theoretical analysis of porous electrode in PEMFC so as to analyze possible error caused by macro scale average method, understand and describe exactly coupled reaction-transport process in porous electrode. The nonlinear theoretical model was developed to simultaneity describe the coupled reaction-transport process on both scales of the micro cluster and macro size of electrode. The study is in forward position of electrochemical reaction engineering, and is of challenge to conventional research method. The distribution of overpotential and concentration, effectiveness factor, dimensionless polarization and macro polarization curves were given. The influence of dimensionless variables, thickness of catalyst layer, dimensionless overpotential and specific area of porous electrode on the distribution of overpotential and concentration, effectiveness factor and polarization curve was researched. The two-scale method here may be used for the theory analysis of reaction system of heterogeneous catalysis.
3. ADM is an effective approximate analytical method solving nonlinear mathematical model. It was used for solving a boundary problem of nonlinear differential equation or a set of nonlinear differential equations derived from dissertation, and gave the approximate analytical solutions in a form of algebraic expressions. It can describe continuously nonlinear disciplinarian of model and calculate ration. It provides valuable theoretical foundation for analysis, design and optimization of reactors.
4. As a example of electrochemical reduction of nitrobenzene to p-aminophenol , the theoretical model of PBEDR was verified. The results show that the calculated results ofμ-S are consistent with experimental data satisfactorily. The key size of the reactor, namely the thickness of the packed bed electrode, was theoretically optimized.
5. A computation example of porous cathode in PEMFC was presented. Compared with conventional one-scale model of electrode, the computation results of two-scale model are consistent better with experimental data of polarization. It is validated that the theoretical model considering the influence of mass transport in micro cluster is more reasonable and accurate.
本文根据电化学反应工程的基本原理,通过与多相催化工程理论的交叉、类比,从电化学反应工程的“源头”出发,寻找出三维电极工程理论的创新点。通过对填充床电极微分反应器(PBEDR)中典型有机电合成复合反应过程的理论分析,建立了动力学普遍化非线性理论模型,归纳出量纲1准数,探讨了各参数对总选择性的影响规律;针对质子膜燃料电池(PEMFC)多孔电极微结构的特征,提出了两尺度理论分析的新方法,建立了多孔电极内反应和传递过程耦联的普遍化非线性理论模型,描述电极中浓度和超电势分布,考察了量纲1准数及诸工程参数对浓度分布、电势分布、效率因子和极化曲线的影响;采用新的解析计算工具—Adomian分解法(ADM),对所建立的非线性常微分方程(组)的边值问题进行求解,以多项式形式给出数模的逼近解析解;以硝基苯电化学还原制对氨基苯酚为例,验证了填充床电极反应器的理论模型,并优化了反应器的关键尺寸;给出了氢质子膜燃料电池多孔阴极的实例,对多孔电极的两尺度普遍化模型进行验证。本文的主要研究内容及结论如下:
1.建立了填充床电极微分反应器中典型有机电化学复合反应过程的动力学普遍化的非线性理论模型,描述床层内超电势横向分布及超电势横向分布对选择性的影响。归纳出表征电极极化和副反应影响的量纲1准数μ、ω。普遍化数模中的量纲1准数,不但对于理论分析,而且对于更复杂实际过程的相似分析,都是十分重要的。给出了超电势分布和总选择性S与数模中μ、ω、n_2/n_1等量纲1准数的理论关系,详细讨论了各准数对S的影响。有机电合成最值得关注的问题是反应总选择性S ,对于特定的复合反应体系,μ-S关系最为重要,μ- S曲线能为选择PBEDR主要操作条件(外加超电势η)和优化反应器主要尺寸(填充床电极厚度l)提供理论依据。
2.对质子膜燃料电池多孔电极进行多尺度的理论分析,以便从理论上分析宏观尺度平均可能带入的误差,更加准确地理解和描述多孔电极内反应和传递耦联的过程。建立了能够同时在团簇微观和电极宏观两尺度上描述多孔电极内反应和传递耦联过程的非线性理论模型,研究内容处于电化学反应工程理论研究的前沿,是对传统研究方法的突破。给出了浓度分布、电势分布、效率因子曲线及量纲1表观极化曲线和表观极化曲线,讨论了量纲1准数s和v~2、多孔催化层厚度l、量纲1表面超电势Φ_0、多孔电极比表面积a等对浓度分布、电势分布、效率因子以及极化曲线的影响。文中提出的两尺度新方法也可被其它相似的多相催化反应系统理论分析所借鉴。
3. ADM分解法是一个非线性数模逼近解析的有效方法。采用ADM对所建立的非线性常微分方程(组)的边值问题进行求解,给出数模逼近解析解的代数表达式,能够连续描述模型的非线性规律,简单地进行定量计算,为反应器的分析、设计和优化提供有价值的理论依据。
4.以硝基苯电还原制对氨基苯酚为例,对填充床电极反应器理论模型进行验证。将μ-S关系的理论计算结果与实验数据进行了对比,结果令人满意,并优化了反应器关键尺寸(填充床电极厚度)。
5.给出了氢质子膜燃料电池(PEMFC)多孔阴极的计算实例,与电极单尺度模型相比,两尺度模型的预测值与极化实验数据能更好相符,从而验证了包含微团尺度传质影响的理论模型更加合理、准确。
Three-dimensions electrode is the working electrode in electrochemical reactor. Its process is analyzed as the source of analysis of electrochemical reaction system so that the basic characteristic is realized in electrochemical reaction system. Compared with conventional two-dimensions electrode, three-dimensions electrode provides a large electrode surface area per unit of reaction volume and presents very good mass transport velocity, hence it can reach higher current density at relatively low electrode polarization. So it is used widely in energy(fuel cell), electrosynthesis and environmental treatment etc. Three-dimensions electrode theories are required urgently. Packed bed electrode and porous electrode are two kinds of familiar three-dimensions electrodes. There is space distribution of kinetics parameters or couple overpotential and concentration in three-dimensions electrode, whereas there is no in two-dimensions electrode. The main characteristic of three-dimensions electrode is that surface charge transfer and mass transport in interspace are coupled. Establishing mathematical model and seeking appropriate new solving method are of challenges that still have been not solved entirely by domestic and external pursuers.
In this dissertation, basing on basic theory of electrochemical reaction engineering and starting with source of electrochemical reaction engineering, the innovation of three-dimensions electrode engineering theory was educed by comparison and analogue with heterogeneous catalysis engineering theory. First, the typical process of electro-organic synthesis in a differential reactor of packed bed electrode (PBEDR) was theoretically analyzed and a generalized nonlinear kinetics mathematical model was developed, dimensionless variables were derived from modeling, the effect of variables on the reaction selectivity was researched. Second, aiming at the character of microstructure of porous electrode in Proton Exchange Membrane Fuel Cell (PEMFC), a novel two-scale method was presented, the generalized nonlinear theoretical model of coupled reaction-transport process in porous electrode was developed to describe the distribution of overpotential and concentration, the effect of dimensionless variables and engineering parameters on distribution of overpotential and concentration, effectiveness factor, polarization curve was discussed. Then, a novel analytical method–Adomian Decomposition Method (ADM) was used for solving a boundary problem of nonlinear differential equation or a set of nonlinear differential equations derived from dissertation, it can give the approximate analytical solutions in a form of polynomial. Furthermore, an analysis of electrochemical reduction of nitrobenzene to p-aminophenol in a PBEDR was presented, the theoretical model of PBEDR was validated, and the key size of the reactor was theoretically optimized. Finally, an example of porous cathode in PEMFC was given to verify two-scale generalized model of porous electrode. The contents and conclusions of this dissertation are as follows:
1. A generalized nonlinear kinetics theoretical model for the typical complex reaction process of electro-organic synthesis in a PBEDR was developed to describe the lateral distribution of overpotential and the effect of the lateral distribution of overpotential on selectivity. Dimensionless variablesμand ? that characterize the polarization and influence of side electrode reaction in the system, were derived from modeling. Dimensionless variables in generalized model are very important not only for theoretical analysis but also for analogical analysis of more complicated practical process. The theoretical relation between distribution of overpotential, selectivityS and dimensionless variablesμ,ω,n_2/n_1 was presented. Selectivity is paid specially attention in electro-organic synthesis. The relation betweenμand S is important to given complex reaction system, it can provide theoretical foundation for selecting main operation condition of PBEDR and optimizing primary size of the reactor.
2. Two-scale method was presented for the theoretical analysis of porous electrode in PEMFC so as to analyze possible error caused by macro scale average method, understand and describe exactly coupled reaction-transport process in porous electrode. The nonlinear theoretical model was developed to simultaneity describe the coupled reaction-transport process on both scales of the micro cluster and macro size of electrode. The study is in forward position of electrochemical reaction engineering, and is of challenge to conventional research method. The distribution of overpotential and concentration, effectiveness factor, dimensionless polarization and macro polarization curves were given. The influence of dimensionless variables, thickness of catalyst layer, dimensionless overpotential and specific area of porous electrode on the distribution of overpotential and concentration, effectiveness factor and polarization curve was researched. The two-scale method here may be used for the theory analysis of reaction system of heterogeneous catalysis.
3. ADM is an effective approximate analytical method solving nonlinear mathematical model. It was used for solving a boundary problem of nonlinear differential equation or a set of nonlinear differential equations derived from dissertation, and gave the approximate analytical solutions in a form of algebraic expressions. It can describe continuously nonlinear disciplinarian of model and calculate ration. It provides valuable theoretical foundation for analysis, design and optimization of reactors.
4. As a example of electrochemical reduction of nitrobenzene to p-aminophenol , the theoretical model of PBEDR was verified. The results show that the calculated results ofμ-S are consistent with experimental data satisfactorily. The key size of the reactor, namely the thickness of the packed bed electrode, was theoretically optimized.
5. A computation example of porous cathode in PEMFC was presented. Compared with conventional one-scale model of electrode, the computation results of two-scale model are consistent better with experimental data of polarization. It is validated that the theoretical model considering the influence of mass transport in micro cluster is more reasonable and accurate.
引文
[1] D. Pletcher and F. C. Walsh. Industrial Electrochemistry, 2nd ed. London : Chapman & Hall, 1990: 3
[2]许文林.固定床电化学反应器基础研究[学位论文].上海:华东化工学院,1991
[3] K. Scott. Electrochemical Processes for Clean Technology. London : The Royal Society of Chemistry, 1995: 2-6
[4] Newman J S. Electrochemical Systems. New Jersey: Prentice Hall. Inc., 1973
[5] Bockris J. Modern Electrochemistry Vol.12. New York: Plennum press, 1970
[6]Б.Б.达马斯金,O.A.佩特里.电化学动力学导论.北京:科学出版社,1989
[7]查全性.电极过程动力学导论,第三版.北京:科学出版社,2002
[8]许文林,刘河洲,袁渭康.固定床电化学反应器研究(Ⅰ).化工学报, 1993, 44(2):383-388
[9] Sun Y P , Xu W L , Scott K. An efficient method for solving the model equations of a two dimensional packed bed electrode. J. Appl Electrochem., 1995, 25: 755-763
[10]许文林,刘河洲,袁渭康.固定床电化学反应器研究.自然科学进展,1993,(2): 181-186
[11]孙彦平,许文林,袁渭康.固定床电化学反应器研究(Ⅱ)..化工学报, 1993, 44(4): 389-394
[12] Scott K, Sun Y P. Approximate analytical solutions for models of three-dimensional electrodes by Adomian’s decomposition method. Modern Aspects of Electrochemistry 41. New York: Springer, 2007: 221-304.
[13]张兴芳,孙彦平.填充床电极反应器中典型有机电合成反应系统的选择性分析.化工学报, 2008,59(5): 1165-1170.
[14]马淳安,褚有群,童少平等.对氨基苯酚的绿色电化学合成及其工业化.化工学报,2004, 55(12): 1971-1975
[15] Sun Yanping, Xu Wenlin and Scott Keith. A study the electrochemical reduction of nitrobenzene to p-aminophenol in a packed bed electrode reactor. Electro Chimica Acta, 1993, 38(13): 1753-1759
[16] Nolen T R. Fedkiw P S. Kinetic study of the electroreduction of nitrobenzene. Journal of Applied Electrochemistry, 1990, 20: 370-376
[17] Sun Yan Ping, Scott Keith. An analysis of the influence of mass transfer on porous electrode performance. Chemical Engineering Journal, 2004,1024(1): 83-91
[18] Sun Y P , Scott K. The influence of mass transfer on a porous fuel cell electrode. Fuel Cell ,2004,4(1-2): 30-38
[19]孙彦平.关于多孔电极理论数模及非线性分析[J].化工学报, 2007,58(9): 2161-2168
[20] Sun Y P, Liu S B Scott K. Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by the decomposition method. Chemical Engineering Journal, 2004,102 (1):1-10
[21]孙彦平. DMFC多孔Pt-Ru阳极甲醇氧化宏观动力学模型化[J].化工学报, 2009,60(1): 55-68
[22] Sun Y P, Qiu O,. Xu W L, Scott K. A study of the performance of a sparged packed bed electrode reactor for the direct electrochemical oxidation of propylene. Journal of Electroanalytical Chemistry, 2001, 503: 36–44
[23]范山湖,余向阳,湛社霞等.循环流动固定床光催化反应器动力学数学模拟.物理化学学报, 2001, 17(11): 1000-1005
[24] Latifi M. A, Laurent A, Wild G, Storck A. Wall-to-liquid mass transfer in a packed-bed reactor: influence of Schmidt number. Chemical Engineering and Processing, 1994, 33,(3): 189-192
[25] Walsh. F.C. Electrochemical technology for environmental treatment and clean energy conversion. Pure Appl. Chem., Vol. 73, No. 12, pp. 1819–1837, 2001.
[26] Paca J., Halecky M., Barta J., etc. Aerobic biodegradation of 2,4-DNT and 2,6-DNT: Performance characteristicsand biofilm composition changes in continuous packed-bed bioreactors. Journal of Hazardous Materials, 2009, 163( 2-3): 848-854
[27] Leonidia Maria, Castro Daniel, Eloísa Pozzi, etc. Removal of ammonium via simultaneous nitrification–denitrification nitrite-shortcut in a single packed-bed batch reactor. Bioresource Technology, 2009, 100(3): 1100-1107
[28] Enrique J., Mammarella, Amelia C., etc. Effect of biocatalyst swelling on the operation of packed-bed immobilized enzyme bioreactor. Process Biochemistry, 2009, 44(2): 183-190
[29] Gómez-De Jesús A., Romano-Baez F.J., Leyva-Amezcua L. Biodegradation of 2,4,6-trichlorophenol in a packed-bed biofilm reactor equipped with an internal net draft tube riser for aeration and liquid Circulation. Journal of Hazardous Materials, 2009, 161(2-3): 1140-1149
[30] Eugen Magyari. Steady thermal regimes of a parallel-plane packed bed reactor with an organized structure. Chemical Engineering Journal, 2009, 146(1): 136-142
[31] Lyubomir Chalakov, Liisa K., Rihko-Struckmann, etc. Oxidative dehydrogenation of ethane in an electrochemical packed-bed membrane reactor: Model and experimental validation. Chemical Engineering Journal, 2009, 145(3): 385-392
[32] Wang Lizhang, Zhao Yuemin, Fu Jianfeng. The influence of TiO2 and aeration on the kinetics of electrochemical oxidation of phenol in packed bed reactor. Journal of Hazardous Materials, 2008, 160(2-3): 608-613
[33] Galiasso Tailleur R., Hernandez Jesus, Rojas Alejandra. Selective hydrogenation of olefins with mass transfer control in a structured packed bed reactor. Fuel, 2008, 87(17-18): 3694-3705
[34] Jafari A., Zamankhan P., Mousavi S.M., etc. Modeling and CFD simulation of flow behavior and dispersivity through randomly packed bed reactors. Chemical Engineering Journal, 2008, 144(3): 476-482
[35] Francisco J., Trujillo, Kelfin M., etc. Catalytic decomposition of H2S in a double-pipe packed bed membrane reactor: Numerical simulation studies. Chemical Engineering Journal, 2008, 143(1-3): 273-281
[36] Güven? Altan, Tar?k Pekel A., Mete Ko?kar ?. The experimental optimization of the electrosynthesis of manganese(III) acetate in a bipolar packed-bed reactor. Chemical Engineering Journal, 2004, 99(3): 257-263
[37] An Taicheng, Zhang Wenbing, Xiao Xianming, etc. Photoelectrocatalytic degradation of quinoline with a novel three-dimensional electrode-packed bed photocatalytic reactor. Journal of Photochemistry and Photobiology A: Chemistry, 2004, 161(2-3): 233-242
[38] Chen Fengtao, Ma Hongzhu, Wang Bo. Simple and effective synthesis of methoxy-dimethylbenzene from electrochemical oxidation of p-xylene in methanol solvent catalyzed by SO4 2?/ZrO2-MxOy. Journal of Hazardous Materials, 2009, 162 (2-3): 668–673.
[39] Zhang Xin-Sheng, Wu Guo-Bin, Ding Ping, etc. Studies on paired packed-bed electrode reactor: Modeling and experiments. Chemical Engineering Science, 1999, 54(13-14): 2969-2977
[40] Xu Wen-Lin, Ding Ping, Yuan Wei-Kang. The behavoir of packed bed electrode reactor. Chemical Engineering Science, 1992, 47(9-11): 2307-2312
[41] Latifi M. A., Midoux N., Storck A., etc. The use of micro-electrodes in the study of the flow regimes in a packed bed reactor with single phase liquid flow. Chemical Engineering Science, 1989, 44(11): 2501-2508
[42] Fleischmann M.,. Jansson R. E. W. The reaction engineering of electrochemical cells—I. Axial packed bed electrodes. Electrochimica Acta, 1982, 27(8): 1023-1028
[43] Wang Yung-Yun, Lu Shu-Hua, Wan Chi-Chao. Effect of particle conductivity of a packed bed reactor on the electrowinning of copper. Hydrometallurgy, 1982, 8(3): 231-239
[44] ?ener Engin, Ersin Karag?zler A. Tarik Pekel A. Simplex optimization of reaction variables in the production of cobalt(II1) acetate in a bipolar packed-bed reactor. Analytica Chimica Acta, 1996, 335(1-2): 35-40
[45] Ruiyun Wu, Mark J. McCready, Arvind Varma. Influence of mass transfer coefficient fluctuation frequency on performance of three-phase packed-bed reactors. Chemical Engineering Science, 1995, 50(21): 3333-3344
[46] Tran Tri D., Londner Igal, Langer Stanley H. Electrogenerative oxidation of dissolved alcohols with platinum—graphite packed bed catalysts. Electrochimica Acta, 1993, 38(2-3): 221-234
[47] Fleischmann M., Jansson R. E. W. The reaction engineering of electrochemical cells—II. Packed bed electrodes with orthogonal flow of current and solution. Electrochimica Acta, 1982, 27(8): 1029-1034
[48] Kreysa G. Kinetic behaviour of packed and fluidised bed electrodes. Electrochimica Acta, 1978,23(12): 1351-1359
[49]李玉明,邢向军,周集体等.三维固定床电极法降解焦化废水.环境科学与技术, 2006, 29(4): 82-84
[50]王立章,傅剑锋,乔启成.三维电极体系降解有机污染物的数学模型.化学工程, 2006, 34(12): 54-57
[51]陈武,梅平,吴伍涛.三维电极电化学方法处理含锌废水的试验研究.长江大学学报(自科版), 2006, 3(3): 35-37
[52]薛松宇,孙宝盛,于冰.三维电极反应器处理染料废水的研究.天津工业大学学报, 2005, 24(3): 24-27
[53] Doherty, T., Sunderland, J.G., Roberts, E.P.L., etc. An improved model of potential and currentdistribution within a flow-through porous electrode. Electrochim. Acta, 1996, 41 (4): 519–526
[54] Madhusudana Rao R, Bhattacharyya D, Rengaswamy R, Choudhury S R. A two-dimensional steady model including the effect of liquid water for a PEM fuel cell cathode. Journal of Power Sources, 2007,173 (1): 375-393
[55] Wang Qianpu, Song Datong, Navessin Titichai, Holdcroft Steven, Liu Zhongsheng. A mathematical model and optimization of the cathode catalyst layer structure in PEM fuel cells. Electrochimica Acta, 2004,50: 725-730
[56] Marr Curtis, Li Xiangguo. Composition and performance modeling of catalyst layer in a proton exchange membrane fuel cell. Journal of Power Sources, 1999,77: 17-27
[57] Newman J S. Electrochemical Systems,.3rd ed. New Jersey: Prentice Hall. Inc., 2004
[58] Scott K. Electrochemical Reaction Engineering. London: Academic Press, 1991: 56
[59] Bard A J. Encyclopedia of Electro Chemistry, Volume 8, Organic Electrochemistry. USA: Wiley-VCH,2004
[60] Scott K. Reactor engineering models of complex electrochemical reaction schemes - II. Electrochim. Acta, 1985, 30(2): 245-251
[61] Scott K. Electrochemical Reaction Engineering. London: Aademic Press, 1991
[62] Enriquez-Granados M. A., D. Storck Hutin, A. The behaviour of porous electrodes in a flow-by regime—II. experimental study Electrochimica Acta, 1982, 27(2): 303-311
[63] Mauvy F., Lalanne C., Bassat J.M. Oxygen reduction on porous Ln2NiO4+δelectrodes. Journal of the European Ceramic Society, 2005, 25(12): 2669-2672
[64] Van Berkel Gary J., Kertesz Vilmos, Ford Michael J. etc. Efficient analyte oxidation in an electrospray ion source using a porous flow-through electrode emitter. Journal of the American Society for Mass Spectrometry, 2004, 15(12): 1755-1766
[65] Norlin A., Pan J., Leygraf C. Investigation of Pt, Ti, TiN, and nano-porous carbon electrodes for implantable cardioverter-defibrillator applications. Electrochimica Acta, 2004, 49(22-23): 4011-4020
[66] Scott K., Argyropoulos P. A current distribution model of a porous fuel cell electrode. Journal of Electroanalytical Chemistry, 2004, 567(1): 103-109
[67]马淳安.有机电化学合成导论.北京:科学出版社,2002
[68] Bennion, D.N., Newman, J. Electrochemical removal of copper ions from very dilute solutions. J. Appl. Electrochem, 1972, 2: 113–122.
[69] Lanza, M.R.V., Bertazzoli, R. Removal of Zn(II) from chloride médium using a porous electrode: current penetration withing the cathode. J. Appl. Electrochem, 2000, 30 (1): 61–70
[70] Hwang J.J., Chen P.Y. Heat/mass transfer in porous electrodes of fuel cells. International Journal of Heat and Mass Transfer, 2006, 49(13-14): 2315-2327
[71] Zhang Qi, White Ralph E. Comparison of approximate solution methods for the solid phase diffusion equation in a porous electrode model. Journal of Power Sources, 2007, 165(2): 880-886
[72] Masliy A.I., Poddubny N.P., Medvedev A.Zh.,etc. Modeling of the dynamics of metal deposition inside a flow-through porous electrode with low initial conductivity. Journal of Electroanalytical Chemistry, 2007, 600(1): 180-190
[73] Park, M. Matsubara J., Li X. Application of lattice Boltzmann method to a micro-scale flow simulation in the porous electrode of a PEM fuel cell. Journal of Power Sources, 2007, 173(1): 404-414
[74] Song Zhang, Dean Edwards. Three-dimensional conductivity model for porous electrodes in lead acid batteries. Journal of Power Sources, 2007, 172(2): 957-961
[75] Reddy Ravinder, Reddy Ramana G. Analytical solution for the voltage distribution in one-dimensional porous electrode subjected to cyclic voltammetric (CV) conditions. Electrochimica Acta, 2007, 53(2): 575-583
[76] Masliy A.I., Poddubny N.P., Medvedev A.Zh., etc. Electrodeposition on a porous electrode with low initial conductivity: Effect of the oxidant on the dynamics of the cathode deposit mass. Journal of Electroanalytical Chemistry, 2008, 623(2): 155-164
[77] Meyers Jeremy P., Newman J. Simulation of the direct methanol fuel cellⅡmodeling and data analysis of transport and kinetic phenomena. J. Electrochem. Soc., 2002, 149(6): A717-A728
[78]刘世斌.直接甲醇燃料电池中电催化反应工程关键问题的研究[学位论文].太原:太原理工大学,2006
[79]衣宝廉.燃料电池-原理、技术、应用.北京:化学工业出版社, 2003
[80]李瑛,王林山.燃料电池.北京:冶金工业出版社, 2000
[81]张成光,缪娟,符德学.三维电极电化学处理废水的研究进展.焦作大学学报, 2006(3): 61-62
[82] Tennakoon C. L. Electro-chemical treatment of human waste in a packed-bed reaction. Appl. Electrochem., 1996, 26: 18-29
[83] JP0416286
[84] Euler W. Nonnenmacher Stromverteilung in por?sen elektroden Electrochimica Acta, 1960(2) : 268-286
[85] Alkire Richard, Ng Patrick. Two-dimensional current distribution within a packed-bed electrochemical flow reactor. ,J. Electrochem. Soc, 1974, 121: 95-103
[86] Alkire Richard, Ng Patrick. Studies on flow-by porous electrode having perpendicular directions of current and electrolyte flow. J. Electrochem. Soc, 1977, 124: 1220-1227
[87] Enriquez Granados M. A., Hutin D., Storck A. The behavior of porous electrode in a flow-by regime-I theoretical study. Electrochimica Acta, 1982, 27: 293-303
[88] Enriquez Granados M. A., Hutin D., Storck A. The behavior of porous electrode in a flow-by regime-II experimental study , Electrochimica Acta, 1982, 27: 303-311
[89] Langlois S., Coeuret F. Flow-through and flow-by porous electrodes of nickel foam Part III: theoretical electrode potential distribution in the flow-by configuration. Journal of Applied Electrochemistry, 1990, 20: 740-748
[90] R. de Levie. Electrochem. Electrochem. Eng., 1961, 1: 329-336
[91] Newman John, Tobias Charles W. Theoretical analysis of current distribution in porous electrode ; J. Electrochem. Soc, 1962, 109: 1183-1191
[92] Risch Tim and Newman John. A theoretical comparison of flow-through and flow-by Porous electrode at the limiting. J. Electrochem. Soc, 1984, 131: 2551-2556
[93] Eikerling M., Kornyshev A. Modeling the performance of the cathode catalyst layer of polymer electrolyte fuel cell. J. of Electroanal. Chem., 1998, 453: 89-106
[94] Bernardi Dawn M., Verbrugge Mark W. A mathematical model of the solid-polymer-electrolyte fuel cell. J. Electrochem. Soc, 1992, 139: 2477-2491
[95] Springer T.E., Zawodkinski T.A., Gottesfeld S. Polymer Electrolyte Fuel Cell Model. J. Electrochem. Soc, 1991, 138: 2334-2342
[96] Fuller Thomas F., Newman John. Water and thermal management in solid-polymer-electrolyte fuelcells. J. Electrochem. Soc, 1993, 140: 1218-1225
[97] Nguyen Trung V., White R.E. A water and heat management model for proton-exchange-membrane. J. Electrochem. Soc, 1993, 140: 2178-2186
[98] Baxter S. F., Battaglia V. S., White R.E. Methanol fuel cell model: anode. J. Electrochem. Soc, 1999, 146: 437-447
[99] Kulikovsky A.A. Analytical model of the anode side of DMFC: the effect of non-Tafel kinetics on cell performance. Electrochemistry Communications, 2003, 5: 530–538
[100] Ge Jiabin, Liu Hongtan. A three-dimensional mathematical model for liquid-fed direct methanol fuel cells. Journal of Power Sources, 2006, 160(1): 413-421
[101] Pehr Bjornbom. Modelling of a double-layered Pt fe-bonded oxygen electrode. Electrochimica Acta,1987, 32: 115-119
[102] Paulin M., Hutin D., Coeuret F. Theoretical and experimental study of flow-through porous electrode. J. Electrochem. Soc, 1977, 124: 180-188
[103] Scott K. The influence of mass transfer on the effectiveness of particulate bed electrodes. Electrochimica Acta, 1983, 28: 1191-1200
[104]李静海,郭慕孙.过程工程量化的科学途径-多尺度法.自然科学进展, 1999, 9(12): 1073-1078
[105]李洪钟.聚集结构、界面与多尺度问题,开辟化学工程的新里程.过程工程学报, 2006, 6(6): 991-996
[106] Glimm J., Sharp D. H. Multiscale science: A challenge for the twenty-first century. SIAM, 1997, 30(8): 1-7
[107]柴立和.多尺度科学的研究进展.化学进展, 2005, 17(2): 186-191
[108]康毅力,李前贵,张箭等.多尺度科学及其在油气田开发中的应用研究.西南石油大学学报, 2007, 29(5): 177-180
[109]郭慕孙,胡英.物质转化过程中的多尺度效应.黑龙江哈尔滨:黑龙江教育出版社, 2002
[110] Aris R. Mathematical theory of diffusion and reaction in permeable catalyst. Oxford: Clarendon Press, 1975
[111] Finlayson B A. Nonlinear analysis in chemical engineering. New York: Mc Graw-Hill Inc, 1980
[112] Newman John. Numerical solution of coupled, ordinary differential equation Ind.Eng.Chem.Fundam,1967, 7: 514-517
[113] Adomian G. Stochastic systems. New York: Academic Press, 1983
[114] Adomian G. Solving frontier problems of physics: the Decomposition Method. Boston: Kluwer, 1994
[115]方锦清.逆算符理论方法及其在非线性物理中的应用.物理学进展, 1993, 13(4): 441-558
[116] Liu S B, Sun Y P, Scott K. Analytic solution of diffusion reaction in spherical porous catalyst. Chem. Eng. Technol., 2003, 26 (1): 87-95
[117]黄倬,屠海令,张冀强等.质子交换膜燃料电池的研究开发与应用.北京:冶金工业出版社,2000
[118] Barbir F. PEM Fuel Cells: Theory and Practice. New York: Academic Press, 2005
[119] Bennion Douglas N. Modeling and reaction simulation. AIChE Symposium Series, 1983, 79: 25-36
[120]侯宝林,孙彦平. ADM机械化求解反应工程数模中非线性常微分方程边值问题.计算机与应用化学, 2006, 23(3): 256-259
[121] Sattersfield C N., Sherwood T K. The role of diffusion in catalysis. Massachusetts: Addison-Wesley, 1963
[122] Levenspiel O. Chemical Reaction Engineering, 3rd Edition. New York: John Wiley, 1999
[2]许文林.固定床电化学反应器基础研究[学位论文].上海:华东化工学院,1991
[3] K. Scott. Electrochemical Processes for Clean Technology. London : The Royal Society of Chemistry, 1995: 2-6
[4] Newman J S. Electrochemical Systems. New Jersey: Prentice Hall. Inc., 1973
[5] Bockris J. Modern Electrochemistry Vol.12. New York: Plennum press, 1970
[6]Б.Б.达马斯金,O.A.佩特里.电化学动力学导论.北京:科学出版社,1989
[7]查全性.电极过程动力学导论,第三版.北京:科学出版社,2002
[8]许文林,刘河洲,袁渭康.固定床电化学反应器研究(Ⅰ).化工学报, 1993, 44(2):383-388
[9] Sun Y P , Xu W L , Scott K. An efficient method for solving the model equations of a two dimensional packed bed electrode. J. Appl Electrochem., 1995, 25: 755-763
[10]许文林,刘河洲,袁渭康.固定床电化学反应器研究.自然科学进展,1993,(2): 181-186
[11]孙彦平,许文林,袁渭康.固定床电化学反应器研究(Ⅱ)..化工学报, 1993, 44(4): 389-394
[12] Scott K, Sun Y P. Approximate analytical solutions for models of three-dimensional electrodes by Adomian’s decomposition method. Modern Aspects of Electrochemistry 41. New York: Springer, 2007: 221-304.
[13]张兴芳,孙彦平.填充床电极反应器中典型有机电合成反应系统的选择性分析.化工学报, 2008,59(5): 1165-1170.
[14]马淳安,褚有群,童少平等.对氨基苯酚的绿色电化学合成及其工业化.化工学报,2004, 55(12): 1971-1975
[15] Sun Yanping, Xu Wenlin and Scott Keith. A study the electrochemical reduction of nitrobenzene to p-aminophenol in a packed bed electrode reactor. Electro Chimica Acta, 1993, 38(13): 1753-1759
[16] Nolen T R. Fedkiw P S. Kinetic study of the electroreduction of nitrobenzene. Journal of Applied Electrochemistry, 1990, 20: 370-376
[17] Sun Yan Ping, Scott Keith. An analysis of the influence of mass transfer on porous electrode performance. Chemical Engineering Journal, 2004,1024(1): 83-91
[18] Sun Y P , Scott K. The influence of mass transfer on a porous fuel cell electrode. Fuel Cell ,2004,4(1-2): 30-38
[19]孙彦平.关于多孔电极理论数模及非线性分析[J].化工学报, 2007,58(9): 2161-2168
[20] Sun Y P, Liu S B Scott K. Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by the decomposition method. Chemical Engineering Journal, 2004,102 (1):1-10
[21]孙彦平. DMFC多孔Pt-Ru阳极甲醇氧化宏观动力学模型化[J].化工学报, 2009,60(1): 55-68
[22] Sun Y P, Qiu O,. Xu W L, Scott K. A study of the performance of a sparged packed bed electrode reactor for the direct electrochemical oxidation of propylene. Journal of Electroanalytical Chemistry, 2001, 503: 36–44
[23]范山湖,余向阳,湛社霞等.循环流动固定床光催化反应器动力学数学模拟.物理化学学报, 2001, 17(11): 1000-1005
[24] Latifi M. A, Laurent A, Wild G, Storck A. Wall-to-liquid mass transfer in a packed-bed reactor: influence of Schmidt number. Chemical Engineering and Processing, 1994, 33,(3): 189-192
[25] Walsh. F.C. Electrochemical technology for environmental treatment and clean energy conversion. Pure Appl. Chem., Vol. 73, No. 12, pp. 1819–1837, 2001.
[26] Paca J., Halecky M., Barta J., etc. Aerobic biodegradation of 2,4-DNT and 2,6-DNT: Performance characteristicsand biofilm composition changes in continuous packed-bed bioreactors. Journal of Hazardous Materials, 2009, 163( 2-3): 848-854
[27] Leonidia Maria, Castro Daniel, Eloísa Pozzi, etc. Removal of ammonium via simultaneous nitrification–denitrification nitrite-shortcut in a single packed-bed batch reactor. Bioresource Technology, 2009, 100(3): 1100-1107
[28] Enrique J., Mammarella, Amelia C., etc. Effect of biocatalyst swelling on the operation of packed-bed immobilized enzyme bioreactor. Process Biochemistry, 2009, 44(2): 183-190
[29] Gómez-De Jesús A., Romano-Baez F.J., Leyva-Amezcua L. Biodegradation of 2,4,6-trichlorophenol in a packed-bed biofilm reactor equipped with an internal net draft tube riser for aeration and liquid Circulation. Journal of Hazardous Materials, 2009, 161(2-3): 1140-1149
[30] Eugen Magyari. Steady thermal regimes of a parallel-plane packed bed reactor with an organized structure. Chemical Engineering Journal, 2009, 146(1): 136-142
[31] Lyubomir Chalakov, Liisa K., Rihko-Struckmann, etc. Oxidative dehydrogenation of ethane in an electrochemical packed-bed membrane reactor: Model and experimental validation. Chemical Engineering Journal, 2009, 145(3): 385-392
[32] Wang Lizhang, Zhao Yuemin, Fu Jianfeng. The influence of TiO2 and aeration on the kinetics of electrochemical oxidation of phenol in packed bed reactor. Journal of Hazardous Materials, 2008, 160(2-3): 608-613
[33] Galiasso Tailleur R., Hernandez Jesus, Rojas Alejandra. Selective hydrogenation of olefins with mass transfer control in a structured packed bed reactor. Fuel, 2008, 87(17-18): 3694-3705
[34] Jafari A., Zamankhan P., Mousavi S.M., etc. Modeling and CFD simulation of flow behavior and dispersivity through randomly packed bed reactors. Chemical Engineering Journal, 2008, 144(3): 476-482
[35] Francisco J., Trujillo, Kelfin M., etc. Catalytic decomposition of H2S in a double-pipe packed bed membrane reactor: Numerical simulation studies. Chemical Engineering Journal, 2008, 143(1-3): 273-281
[36] Güven? Altan, Tar?k Pekel A., Mete Ko?kar ?. The experimental optimization of the electrosynthesis of manganese(III) acetate in a bipolar packed-bed reactor. Chemical Engineering Journal, 2004, 99(3): 257-263
[37] An Taicheng, Zhang Wenbing, Xiao Xianming, etc. Photoelectrocatalytic degradation of quinoline with a novel three-dimensional electrode-packed bed photocatalytic reactor. Journal of Photochemistry and Photobiology A: Chemistry, 2004, 161(2-3): 233-242
[38] Chen Fengtao, Ma Hongzhu, Wang Bo. Simple and effective synthesis of methoxy-dimethylbenzene from electrochemical oxidation of p-xylene in methanol solvent catalyzed by SO4 2?/ZrO2-MxOy. Journal of Hazardous Materials, 2009, 162 (2-3): 668–673.
[39] Zhang Xin-Sheng, Wu Guo-Bin, Ding Ping, etc. Studies on paired packed-bed electrode reactor: Modeling and experiments. Chemical Engineering Science, 1999, 54(13-14): 2969-2977
[40] Xu Wen-Lin, Ding Ping, Yuan Wei-Kang. The behavoir of packed bed electrode reactor. Chemical Engineering Science, 1992, 47(9-11): 2307-2312
[41] Latifi M. A., Midoux N., Storck A., etc. The use of micro-electrodes in the study of the flow regimes in a packed bed reactor with single phase liquid flow. Chemical Engineering Science, 1989, 44(11): 2501-2508
[42] Fleischmann M.,. Jansson R. E. W. The reaction engineering of electrochemical cells—I. Axial packed bed electrodes. Electrochimica Acta, 1982, 27(8): 1023-1028
[43] Wang Yung-Yun, Lu Shu-Hua, Wan Chi-Chao. Effect of particle conductivity of a packed bed reactor on the electrowinning of copper. Hydrometallurgy, 1982, 8(3): 231-239
[44] ?ener Engin, Ersin Karag?zler A. Tarik Pekel A. Simplex optimization of reaction variables in the production of cobalt(II1) acetate in a bipolar packed-bed reactor. Analytica Chimica Acta, 1996, 335(1-2): 35-40
[45] Ruiyun Wu, Mark J. McCready, Arvind Varma. Influence of mass transfer coefficient fluctuation frequency on performance of three-phase packed-bed reactors. Chemical Engineering Science, 1995, 50(21): 3333-3344
[46] Tran Tri D., Londner Igal, Langer Stanley H. Electrogenerative oxidation of dissolved alcohols with platinum—graphite packed bed catalysts. Electrochimica Acta, 1993, 38(2-3): 221-234
[47] Fleischmann M., Jansson R. E. W. The reaction engineering of electrochemical cells—II. Packed bed electrodes with orthogonal flow of current and solution. Electrochimica Acta, 1982, 27(8): 1029-1034
[48] Kreysa G. Kinetic behaviour of packed and fluidised bed electrodes. Electrochimica Acta, 1978,23(12): 1351-1359
[49]李玉明,邢向军,周集体等.三维固定床电极法降解焦化废水.环境科学与技术, 2006, 29(4): 82-84
[50]王立章,傅剑锋,乔启成.三维电极体系降解有机污染物的数学模型.化学工程, 2006, 34(12): 54-57
[51]陈武,梅平,吴伍涛.三维电极电化学方法处理含锌废水的试验研究.长江大学学报(自科版), 2006, 3(3): 35-37
[52]薛松宇,孙宝盛,于冰.三维电极反应器处理染料废水的研究.天津工业大学学报, 2005, 24(3): 24-27
[53] Doherty, T., Sunderland, J.G., Roberts, E.P.L., etc. An improved model of potential and currentdistribution within a flow-through porous electrode. Electrochim. Acta, 1996, 41 (4): 519–526
[54] Madhusudana Rao R, Bhattacharyya D, Rengaswamy R, Choudhury S R. A two-dimensional steady model including the effect of liquid water for a PEM fuel cell cathode. Journal of Power Sources, 2007,173 (1): 375-393
[55] Wang Qianpu, Song Datong, Navessin Titichai, Holdcroft Steven, Liu Zhongsheng. A mathematical model and optimization of the cathode catalyst layer structure in PEM fuel cells. Electrochimica Acta, 2004,50: 725-730
[56] Marr Curtis, Li Xiangguo. Composition and performance modeling of catalyst layer in a proton exchange membrane fuel cell. Journal of Power Sources, 1999,77: 17-27
[57] Newman J S. Electrochemical Systems,.3rd ed. New Jersey: Prentice Hall. Inc., 2004
[58] Scott K. Electrochemical Reaction Engineering. London: Academic Press, 1991: 56
[59] Bard A J. Encyclopedia of Electro Chemistry, Volume 8, Organic Electrochemistry. USA: Wiley-VCH,2004
[60] Scott K. Reactor engineering models of complex electrochemical reaction schemes - II. Electrochim. Acta, 1985, 30(2): 245-251
[61] Scott K. Electrochemical Reaction Engineering. London: Aademic Press, 1991
[62] Enriquez-Granados M. A., D. Storck Hutin, A. The behaviour of porous electrodes in a flow-by regime—II. experimental study Electrochimica Acta, 1982, 27(2): 303-311
[63] Mauvy F., Lalanne C., Bassat J.M. Oxygen reduction on porous Ln2NiO4+δelectrodes. Journal of the European Ceramic Society, 2005, 25(12): 2669-2672
[64] Van Berkel Gary J., Kertesz Vilmos, Ford Michael J. etc. Efficient analyte oxidation in an electrospray ion source using a porous flow-through electrode emitter. Journal of the American Society for Mass Spectrometry, 2004, 15(12): 1755-1766
[65] Norlin A., Pan J., Leygraf C. Investigation of Pt, Ti, TiN, and nano-porous carbon electrodes for implantable cardioverter-defibrillator applications. Electrochimica Acta, 2004, 49(22-23): 4011-4020
[66] Scott K., Argyropoulos P. A current distribution model of a porous fuel cell electrode. Journal of Electroanalytical Chemistry, 2004, 567(1): 103-109
[67]马淳安.有机电化学合成导论.北京:科学出版社,2002
[68] Bennion, D.N., Newman, J. Electrochemical removal of copper ions from very dilute solutions. J. Appl. Electrochem, 1972, 2: 113–122.
[69] Lanza, M.R.V., Bertazzoli, R. Removal of Zn(II) from chloride médium using a porous electrode: current penetration withing the cathode. J. Appl. Electrochem, 2000, 30 (1): 61–70
[70] Hwang J.J., Chen P.Y. Heat/mass transfer in porous electrodes of fuel cells. International Journal of Heat and Mass Transfer, 2006, 49(13-14): 2315-2327
[71] Zhang Qi, White Ralph E. Comparison of approximate solution methods for the solid phase diffusion equation in a porous electrode model. Journal of Power Sources, 2007, 165(2): 880-886
[72] Masliy A.I., Poddubny N.P., Medvedev A.Zh.,etc. Modeling of the dynamics of metal deposition inside a flow-through porous electrode with low initial conductivity. Journal of Electroanalytical Chemistry, 2007, 600(1): 180-190
[73] Park, M. Matsubara J., Li X. Application of lattice Boltzmann method to a micro-scale flow simulation in the porous electrode of a PEM fuel cell. Journal of Power Sources, 2007, 173(1): 404-414
[74] Song Zhang, Dean Edwards. Three-dimensional conductivity model for porous electrodes in lead acid batteries. Journal of Power Sources, 2007, 172(2): 957-961
[75] Reddy Ravinder, Reddy Ramana G. Analytical solution for the voltage distribution in one-dimensional porous electrode subjected to cyclic voltammetric (CV) conditions. Electrochimica Acta, 2007, 53(2): 575-583
[76] Masliy A.I., Poddubny N.P., Medvedev A.Zh., etc. Electrodeposition on a porous electrode with low initial conductivity: Effect of the oxidant on the dynamics of the cathode deposit mass. Journal of Electroanalytical Chemistry, 2008, 623(2): 155-164
[77] Meyers Jeremy P., Newman J. Simulation of the direct methanol fuel cellⅡmodeling and data analysis of transport and kinetic phenomena. J. Electrochem. Soc., 2002, 149(6): A717-A728
[78]刘世斌.直接甲醇燃料电池中电催化反应工程关键问题的研究[学位论文].太原:太原理工大学,2006
[79]衣宝廉.燃料电池-原理、技术、应用.北京:化学工业出版社, 2003
[80]李瑛,王林山.燃料电池.北京:冶金工业出版社, 2000
[81]张成光,缪娟,符德学.三维电极电化学处理废水的研究进展.焦作大学学报, 2006(3): 61-62
[82] Tennakoon C. L. Electro-chemical treatment of human waste in a packed-bed reaction. Appl. Electrochem., 1996, 26: 18-29
[83] JP0416286
[84] Euler W. Nonnenmacher Stromverteilung in por?sen elektroden Electrochimica Acta, 1960(2) : 268-286
[85] Alkire Richard, Ng Patrick. Two-dimensional current distribution within a packed-bed electrochemical flow reactor. ,J. Electrochem. Soc, 1974, 121: 95-103
[86] Alkire Richard, Ng Patrick. Studies on flow-by porous electrode having perpendicular directions of current and electrolyte flow. J. Electrochem. Soc, 1977, 124: 1220-1227
[87] Enriquez Granados M. A., Hutin D., Storck A. The behavior of porous electrode in a flow-by regime-I theoretical study. Electrochimica Acta, 1982, 27: 293-303
[88] Enriquez Granados M. A., Hutin D., Storck A. The behavior of porous electrode in a flow-by regime-II experimental study , Electrochimica Acta, 1982, 27: 303-311
[89] Langlois S., Coeuret F. Flow-through and flow-by porous electrodes of nickel foam Part III: theoretical electrode potential distribution in the flow-by configuration. Journal of Applied Electrochemistry, 1990, 20: 740-748
[90] R. de Levie. Electrochem. Electrochem. Eng., 1961, 1: 329-336
[91] Newman John, Tobias Charles W. Theoretical analysis of current distribution in porous electrode ; J. Electrochem. Soc, 1962, 109: 1183-1191
[92] Risch Tim and Newman John. A theoretical comparison of flow-through and flow-by Porous electrode at the limiting. J. Electrochem. Soc, 1984, 131: 2551-2556
[93] Eikerling M., Kornyshev A. Modeling the performance of the cathode catalyst layer of polymer electrolyte fuel cell. J. of Electroanal. Chem., 1998, 453: 89-106
[94] Bernardi Dawn M., Verbrugge Mark W. A mathematical model of the solid-polymer-electrolyte fuel cell. J. Electrochem. Soc, 1992, 139: 2477-2491
[95] Springer T.E., Zawodkinski T.A., Gottesfeld S. Polymer Electrolyte Fuel Cell Model. J. Electrochem. Soc, 1991, 138: 2334-2342
[96] Fuller Thomas F., Newman John. Water and thermal management in solid-polymer-electrolyte fuelcells. J. Electrochem. Soc, 1993, 140: 1218-1225
[97] Nguyen Trung V., White R.E. A water and heat management model for proton-exchange-membrane. J. Electrochem. Soc, 1993, 140: 2178-2186
[98] Baxter S. F., Battaglia V. S., White R.E. Methanol fuel cell model: anode. J. Electrochem. Soc, 1999, 146: 437-447
[99] Kulikovsky A.A. Analytical model of the anode side of DMFC: the effect of non-Tafel kinetics on cell performance. Electrochemistry Communications, 2003, 5: 530–538
[100] Ge Jiabin, Liu Hongtan. A three-dimensional mathematical model for liquid-fed direct methanol fuel cells. Journal of Power Sources, 2006, 160(1): 413-421
[101] Pehr Bjornbom. Modelling of a double-layered Pt fe-bonded oxygen electrode. Electrochimica Acta,1987, 32: 115-119
[102] Paulin M., Hutin D., Coeuret F. Theoretical and experimental study of flow-through porous electrode. J. Electrochem. Soc, 1977, 124: 180-188
[103] Scott K. The influence of mass transfer on the effectiveness of particulate bed electrodes. Electrochimica Acta, 1983, 28: 1191-1200
[104]李静海,郭慕孙.过程工程量化的科学途径-多尺度法.自然科学进展, 1999, 9(12): 1073-1078
[105]李洪钟.聚集结构、界面与多尺度问题,开辟化学工程的新里程.过程工程学报, 2006, 6(6): 991-996
[106] Glimm J., Sharp D. H. Multiscale science: A challenge for the twenty-first century. SIAM, 1997, 30(8): 1-7
[107]柴立和.多尺度科学的研究进展.化学进展, 2005, 17(2): 186-191
[108]康毅力,李前贵,张箭等.多尺度科学及其在油气田开发中的应用研究.西南石油大学学报, 2007, 29(5): 177-180
[109]郭慕孙,胡英.物质转化过程中的多尺度效应.黑龙江哈尔滨:黑龙江教育出版社, 2002
[110] Aris R. Mathematical theory of diffusion and reaction in permeable catalyst. Oxford: Clarendon Press, 1975
[111] Finlayson B A. Nonlinear analysis in chemical engineering. New York: Mc Graw-Hill Inc, 1980
[112] Newman John. Numerical solution of coupled, ordinary differential equation Ind.Eng.Chem.Fundam,1967, 7: 514-517
[113] Adomian G. Stochastic systems. New York: Academic Press, 1983
[114] Adomian G. Solving frontier problems of physics: the Decomposition Method. Boston: Kluwer, 1994
[115]方锦清.逆算符理论方法及其在非线性物理中的应用.物理学进展, 1993, 13(4): 441-558
[116] Liu S B, Sun Y P, Scott K. Analytic solution of diffusion reaction in spherical porous catalyst. Chem. Eng. Technol., 2003, 26 (1): 87-95
[117]黄倬,屠海令,张冀强等.质子交换膜燃料电池的研究开发与应用.北京:冶金工业出版社,2000
[118] Barbir F. PEM Fuel Cells: Theory and Practice. New York: Academic Press, 2005
[119] Bennion Douglas N. Modeling and reaction simulation. AIChE Symposium Series, 1983, 79: 25-36
[120]侯宝林,孙彦平. ADM机械化求解反应工程数模中非线性常微分方程边值问题.计算机与应用化学, 2006, 23(3): 256-259
[121] Sattersfield C N., Sherwood T K. The role of diffusion in catalysis. Massachusetts: Addison-Wesley, 1963
[122] Levenspiel O. Chemical Reaction Engineering, 3rd Edition. New York: John Wiley, 1999