NUMERICAL−SIMULATION OF THE TIME−DEPENDENT CURRENT TO MEMBRANE−COVERED OXYGEN SENSORS .1. THE SWITCH−ON TRANSIENT

Abstract

We have examined the nature of the diffusion processes and determined the transient current characteristics of membrane-covered Clark-type oxygen sensors by solving the axially symmetric two-dimensional diffusion equation. Correction for a singularity at the edge of the cathode allows us to achieve a numerical solution which we demonstrate to be accurate to 1%. Earlier one-dimensional theories based on linear or hemispherical diffusion are shown to be grossly inadequate for predicting the variation in behaviour with cathode radius and electrolyte layer thickness. The calculated depletion patterns give insight into the ways in which t