Nonlinear Analysis Of Three-Dimensions Electeode

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,n₂/n₁ 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.