Analytical solution for the steady-state diffusion and migration. Application to the identification of Butler-Volmer electrode reaction parameters

An analytical solution for the one-dimensional steady-state transport of ions in an electrolyte between two planar electrodes has been obtained. This electrolyte contains one electroactive species and any number of non-reacting species. The mass and charge transport equations give rise to an implicit form of a set of non-linear algebraic equations which must be solved numerically. It has been shown that the same set of equations, with only a very small modification, can easily be used to solve the stagnant boundary layer problem. The solution is generally applicable and can deal with any kind of overpotential relation at both anode and cathode. The analytical solution for the stagnant boundary layer has been used to determine the diffusion coefficient for the reacting ion and the kinetic parameters in the Butler-Volmer overpotential relation for the electrodeposition of copper from a 0.01 M CuSO4 + 0.1 M H2SO4 solution. The resulting parameters are in good agreement with the values found in the literature. Analytical results obtained with these parameters match very well with the experimental data for current densities ranging from secondary up to limiting current values and for different values of the rotation speed (100, 500 and 1000 rev min(-1)). Also, it has been shown that neglecting migration can lead to an overestimation of the diffusion coefficient of about 15%.