Multi-scale modeling of diffusion and electrochemical reactions in porous micro-electrodes

•A diffusion and electrochemical reaction model in a porous electrode is proposed.•A macroscale model operating at the electrode scale is obtained by upscaling.•The macroscale model is validated by direct numerical simulation and experiments.

A multi-scale model of diffusion/reaction at play in a porous electrode is developed and solutions to the physico-electro-chemical coupled problem are provided. This represents a key step to progress in the optimization of new efficient and innovative micro-electro-devices that needs to be addressed from a chemical engineering point of view. The pore-scale model based on Fickian diffusion in the porous medium and Nernstian layer and the electrochemical reaction governed by the Buttler-Volmer equation is upscaled using volume averaging to obtain a macroscopic model that describes the process on an effective equivalent medium. The validity and accuracy of the macroscopic model is successfully checked through the comparison with direct numerical simulations of the initial microscale model for amperometry tests. Predictions obtained from the upscaled model on the current intensity versus the scanning potential during voltammetry reveal to be in very good agreement with experimental results reported in the literature. These results show the capability of the macroscopic model to analyze the behavior of the porous electrode. In particular, it provides an efficient tool to study the dependence of the current intensity on the microstructure of the porous material and on the electrochemical parameters with the perspective of optimizing the electrode efficiency.