旁流式多孔电极非稳态行为数学分析

根据 Newman 的多孔电极理论,本文给出旁流式多孔电极非稳态行为数学模型。该模型涉及三个区域,即:液相主体、多孔区和界面。为了获得解析解,该模型被化简为两个较简单的模型:多孔区模型和液相主体模型。前者仅考虑多孔区的积累项,属于微分方程的本征值问题;后者仅考虑液相主体的积累项,属于非稳态的 Leveque 问题。文中给出旁流式多孔电极内进行 Br_2/Br-氧化还原反应时非稳态行为的计算实例。该实例表明:本文给出的简单模型的解析解,在处理更复杂问题时,可用于判断所使用技巧的正确性。

An Analysis of the Time-dependent Behavior of a Flow-by Porous Electrode

A mathematical model is presented for the time-dependent behavior of a flow-by porous electrode according to Newman's porous electrode theory. The model includes three regions(i.e.,the porous region and the inter- face),and can be simplified into two simple models which consider the accumulation in the porous and the accumulation in the bulk region inde- pendently.The two simple models belong to the eigenvalue problem and the time-dependent leveque problem respectively,and can be solved analytically. Predictions of time-dependent currents for a flow-by porous electrode with the Br_2/Br~- redox reaction are presented.These predictions show that exact analytical solutions obtained here may serve as a reliable reference to check techniques developed for the treatment of more complicated problems.