Oxygen electrode design criteria and performance characteristics: recessed cathode.

A computer simulation of the steady-state operation of recessed (Whalen-type) polarographic oxygen electrodes has been developed to give the design factors important for performance optimization. The simulation makes use of a specially formulated three-dimensional orthogonal coordinate system with the geometry identical to the actual recessed cathode and gives the oxygen concentration field induced by it in the surrounding medium. Equations are presented which allow one to calculate, for any recessed cathode, the current sensitivity, maximum stirring artifact, measurement error, and time constant. Comparisons with analytically obtained expressions for the corresponding quantities for idealized, spherosymmetric cathodes demonstrate the unique aspects of recessed-cathode performance. For commonly used electrodes, a recess length-to-cathode diameter ratio of greater than 10 is found to give a negligible stirring artifact, a negligible measurement error, and a rapid response.