Current and potential distributions, satisfying Laplace's equation and obtained by superposition of ring sources, are developed and discussed for a cylinder electrode embedded in an infinite insulating cylinder. For the primary distribution, the resistance and the coefficient describing how the current density goes to infinity at the edge of the electrode are presented as functions of the aspect ratio of the electrode. For a uniform current density on the electrode, the maximum potential variation on the electrode is presented as a function of the aspect ratio. For linear electrode kinetics, the condition for nearly uniform electrode current density is quantified, and the ratio of edge to center current densities is developed for kinetic parameters that lead toward the primary distribution. Current and potential distributions on the electrode and the adjoining insulator are presented for these three cases, and some asymptotic formulas are developed for high and low aspect ratios. This geometry is of interest in applications of cathodic protection
Current and Potential Distributions on A Cylinder Electrode
Grabowski, AJ., & Newman, J. (1993). Current and Potential Distributions on A Cylinder Electrode. Journal of the Electrochemical Society, 140(6), 1625-1631.