The combined unidirectional and local coupling in a spatially one-dimensional model of oscillatory metal electrodissolution. Patch-adaptive simulation study

Abstract

Experimentally observed effects of a spatially localised external laser forcing, on the oscillatory current of the electrodissolution of an iron ring electrode in sulfuric acid, can be reproduced qualitatively by means of a simple, spatially one-dimensional model, expressed by partial differential equations for the double layer potential drop and hydrogen ions concentration, coupled with an ordinary differential equation for the coverage fraction by the passivating hydroxide. These model equations can be solved efficiently and economically by means of the patch-adaptive finite-difference strategy, that automatically concentrates the spatial and temporal grids in the critical regions. The analysis of the model solutions reveals that activation caused by the forcing occurs via accelerating moving fronts, resulting in spatially non-homogeneous distributions of the dynamical variables. When the oscillator is predominantly in the passive state, then a one-dimensional discrete map can be constructed, based on single perturbation simulations, which predicts, with a good quantitative agreement, the temporal behaviour of the electric current simulated under conditions of periodic forcing. However, when the oscillator is not predominantly in the passive state, a more complex spatio-temporal behaviour is revealed by the simulations. The spatial non-homogeneity of the dynamic variables is observed in the most profound way for the concentration which lacks any relaxation characteristics. This suggests that it is not only the double layer potential drop, but also the ionic concentrations, which may play a role in the development of spatio-temporal patterns in electrochemical systems.