填充床电极二维模型的逼近解析

Approximate analytic solutions for two-dimensional mathematic model of packed bed electrode

建立了填充床电极普遍化二维数学模型,用以描述电极内超电势、浓度以及电流密度的分布。该模型包含了填充床电极内横向返混和纵向对流传质的影响,为非线性的椭圆和抛物线形耦联偏微分方程组。用Ado-mian分解法求解模型获得其逼近解析解,简要介绍了求解方法并给出了两维分布计算结果的图形实例。本文对填充床电极二维模型的分析不仅能为该类电极的设计、优化操作提供理论依据,也可为其他催化反应工程系统的理论分析所借鉴。

A generalized mathematical model for the packed bed electrode （PBE） was developed to describe the two-dimensional distributions of overpotential, reactant concentration and current density in the electrode. The model included the influences of lateral dispersion and vertical convection in the packed bed between electrode feeder and membrane, and was in a form of coupled elliptical and parabolic nonlinear partial differential equations. The model was solved by using Adomian decomposition method （ ADM ） to obtain the approximate analytic solutions, and the solving procedure was presented. Furthermore typical computation examples of the two-dimensional distributions in PBE were given by figures to show the distribution nonlinearities. The prediction of the model would provide a theoretical idea for the design or operation optimizing of PBE, and the presented method might also be used for the analysis of heterogeneous catalysis engineering system.