Ohmic model for electrodeposition of metallic ions

An ohmic model to describe the electrodeposition of metallic ions on the electrodes is proposed. We assume that the ionic distribution is homogeneous across the electrolytic cell, and that the ionic current is due to the bulk electric field. The nucleation in the electrodeposition is supposed to be well described by a kinetic equation at the electrode, taking into account the neutralization of metallic ions on the electrodes. Two cases are considered. In the first case the characteristic time describing the neutralization of the ions is supposed to be negligible with respect to the flight time of the ions across the cell. In this framework the bulk electric field coincides with the external electric field, and our analysis gives analytical formulae for the surface density of deposited ions and for the electric current in the external circuit. The case where the two characteristic times are comparable, and the effective electric field in the bulk depends on the surface deposition, is considered too. In this case the ordinary differential equations describing the ionic distribution and the adsorption phenomenon have to be solved numerically. The agreement between the presented model and the experimental results published by several groups is reasonably good.