An Integral Equation Solution for the Steady-State Current at a Periodic Array of Surface Microelectrodes

An integral equation approach is developed for the problem of determining the steady-state current to a periodic array of microelectrodes imbedded in an otherwise insulating plane. The formulation accounts for both surface electrode and bulk fluid reactions, and evaluates the Green’s functions for periodic systems using convergence acceleration techniques. Numerical results are presented for disc-shaped microelectrodes at the center of rectangular periodic cells for a large range of dimensionless surface and bulk reaction rates and periodic cell sizes.