Extensions of the Koutecky–Levich Equation to Channel Electrodes

An analytical solution is herein presented for the current at a channel-type electrode associated with a simple first-order (in the reactant) heterogeneous electron transfer process involving a solution phase species. Assuming a fixed cell geometry, electrolyte composition, and temperature, a series expansion of this solution revealed that in the limit of small values of , where is the first-order kinetic rate constant and is the fluid velocity in the center of the channel, the reciprocal of the measured current, , where and are the kinetic and diffusion limited currents, respectively, and . This equation bears striking resemblance to that reported by Koutecky and Levich for a rotating disk electrode, except that β in the latter case is unity. Rather surprisingly, and in agreement with recent findings [ Electrochim. Acta , 52 , 4124 (2007)] , a plot of vs was found to be close to linear, with a slope reaching values slightly higher than β as the magnitude of increased.