Modeling Diffusion and Migration in Dilute Electrochemical Systems Using the Quasi-Potential Transformation
The quasi-potential transformation, based on the Kirchhoff transformation, simplifies the equations governing mass transfer in steady-state, nonconvective electrolytic systems. The major assumption is that the species concentrations can be written as single-valued functions of the electrostatic potential. Methods are developed, based on a theorem presented by Gibbs, to solve the system-specific calculations, those calculations that are dependent only on the specific chemical system used. Results are presented for the binary aqueous copper sulfate system with variable transport properties and for the acidic aqueous copper sulfate system accounting for variations in the dissociation constant of the bisulfate ions. These results are combined with solutions of Laplace's equation for some simple boundary conditions to give complete solutions for the disk and hemisphere electrodes. The effect of migration on limiting currents is discussed
Pillay, B., & Newman, J. (1993). Modeling Diffusion and Migration in Dilute Electrochemical Systems Using the Quasi-Potential Transformation. Journal of the Electrochemical Society, 140(2), 414-420.