Perspectives On Newman'S Work On Resistance For Flow Of Current To A Disk

In order to obtain the concentration and activation overpotential for a rotating disk electrodde it is necessary to subtract from between the reference electrode probe and the disk. The ohmic drop for a small disk is concentrated in the solution near the disk Fig. Rather than try to put the probe from a reference electrode very near the surface and thus distort the potential and velocity distributions one can estimate the ohmic drop form the reistance between is disk imbeddd in the surface of an insulator and a counter electrode at infinity. This procedure does not account for deviations from the primary current distributions.For the purpose of calculating the potential distribution from Laplaco's equation, we use rotational elliptic coordinates it and related to cylindrical coordinates byf = phi(1) at xi = 0 (on the disk electrode)partial derivative phi/partial derivative eta = 0 at eta = 0 (on the insulating annulus)phi = 0 at xi =infinity (far from the disk)phi well behaved at eta = 1 (on the axis of the disk)} (3)To obtain a solution by the method of seperation of variables we setphi = P(eta)Q(xi) {4}The differential equations for P and Q ared/d(eta) [(1-eta(2) dP/d(n)] + nP = theta(c)d/d xi [(1 + xi) dQ/d xi] - nQ - 0 {5}