A stability criterion for accurate simulation of electrochemical diffusion-kinetic phenomena at the rotating disk electrode and implications for simulation of diffusion-migration and other problems
A stability criterion for accurate simulation of electrochemical diffusion-kinetic phenomena at the rotating disk electrode and implications for simulation of diffusion-migration and other problems
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DOI：
10.1016/0022-0728(96)04625-6
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发表时间：
1996-09-12
影响因子：
4.5
通讯作者：
Rudolph, M
中科院分区：
文献类型：
--
作者：
Feldberg, SW;Goldstein, CI;Rudolph, M
开发了一种稳定、准确且高效的全隐式有限差分算法，用于模拟旋转盘电极 (RDE) 的电化学行为。开发了方便的表达式，用于准确评估垂直于圆盘的溶液的流体动力速度分布、扩散层的厚度以及模拟中必须考虑的溶液的最小厚度。该模拟算法使用指数扩展的空间网格来有效且准确地模拟涉及均相化学反应的系统，其反应层可能比RDE扩散层小得多。在不存在均质动力学的情况下，RDE 模拟的稳定性分析产生了一个简单的标准，该标准精确地界定了稳定和准确的模拟所需的表征指数膨胀空间网格的参数值（即体积元素的密度和膨胀率）。 RDE 模拟算法被纳入通用循环伏安模拟器中，这使我们能够模拟涉及异质和均质（一级和/或二级）反应的各种组合的复杂系统的 RDE 响应：相同的稳定性标准就足够了。还讨论了扩散迁移问题的有限差分模拟分析的含义。
A stable, accurate, and efficient fully implicit finite difference algorithm is developed for the simulation of electrochemical behavior at a rotating disk electrode (RDE). Convenient expressions are developed for accurate evaluations of the hydrodynamic velocity profile of the solution normal to the disk, of the thickness of the diffusion layer, and of the minimum thickness of solution which must be considered in a simulation. The simulation algorithm uses an exponentially expanding space grid to effect efficient and accurate simulation of systems involving homogeneous chemical reactions with reaction layers that may be much smaller than the RDE diffusion layer. Stability analysis of the RDE simulation in the absence of homogeneous kinetics produces a simple criterion which precisely delimits the values of the parameters which characterize the exponentially expanding space grid (i.e. the density of the volume elements and the rate of expansion) required for stable and accurate simulations. The RDE simulation algorithm was incorporated into a generalized cyclic voltammetric simulator which allowed us to simulate RDE responses for complex systems involving various combinations of heterogeneous and homogeneous (first- and or second-order) reactions: the same stability criterion sufficed. Implications of the analysis for finite difference simulations of diffusion-migration problems are also discussed.