Development and application of the quasi-potential transformation

Abstract

The quasi-potential transformation, based on the Kirchhoff transformation, reduces the equations governing mass-transfer in a steady-state, nonconvective electrolytic system into two independent parts. The geometry-specific part involves the solution of Laplace's equation subject to the relevant boundary conditions. The system-specific part involves the solution of a set of coupled first-order, nonlinear, ordinary differential equations. We develop a theoretical basis for the quasi-potential transformation using potential theory. The major assumption on which the quasi-potential transformation is based is that the concentrations can be written as single-valued functions of the electrostatic potential. We see how the system-specific part of the calculation is developed. Boundary conditions are outlined, and the geometry-specific calculations for the disk and hemisphere electrodes are developed. We combine the system-specific calculations for the binary and acidic copper sulfate solutions with these geometry-specific calculations to obtain complete concentration profiles, potential distributions, and current density distributions for these systems. We also investigate the effect of migration on limiting currents.