Analytical 3D migration model of steady-state metal anodizing: the velocity fields and trajectories of inert tracers, metal and oxygen ions

A mathematical model is proposed that describes the velocity fields of metal and oxygen ions and inert tracers in the steady-state porous metal oxidation. The 3D migration model is based on the theory of field-assisted dissolution of oxide at the pore bottom and migration of ions in strong spherical electric fields. The ion motion at a constant velocity in the direction of anodic film growth and their migration in the radial direction (along the electric field lines) are taken into consideration. The effect of mechanical stresses on the motion of ions and inert tracers is ignored. The oxide flows both from the oxide/electrolyte interface and from the oxide/metal interface to the boundary between the barrier and porous layers. These two flows form the porous oxide layers adjacent to the pores and afar from them. A ratio between the volumes of these layers is determined by the transport numbers and oxide porosity. The calculated tracer trajectories agree with the experimental results of Garcia-Vergara et al. on the oxide flow in the barrier layer of porous anodic alumina film. (C) 2016 Elsevier Ltd. All rights reserved.