Mathematical modeling of interdigitated electrode arrays in finite electrochemical cells

• Analysis of interdigitated array of electrodes subject to a finite geometry cell.
• Fourier representation of the concentration as a function of the current density.
• Calculation of the response time of the concentration to a current step.
• Obtention of a lower bound for the limiting current in a finite geometry cell.
• Conditions for obtaining finite and semi-infinite cells with comparable behaviors.

Accurate theoretical results for interdigitated array of electrodes (IDAE) in semi-infinite cells can be found in the literature. However, these results are not always applicable when using finite cells. In this study, theoretical expressions for IDAE in a finite geometry cell are presented. At known current density, transient and steady state concentration profiles were obtained as well as the response time to a current step. Concerning the diffusion limited current, a lower bound was derived from the concentration profile and an upper bound was obtained from the limiting current of the semi-infinite case. The lower bound, which is valid when Kirchhoff’s current law applies to the unit cell, can be useful to ensure a minimum current level during the design of the electrochemical cell. Finally, a criterion was developed defining when the behaviors of finite and semi-infinite cells are comparable. This allows to obtain higher current levels in finite cells, approaching that of the semi-infinite case. Examples with simulations were performed in order to illustrate and validate the theoretical results.