ANALYTICAL 3D MIGRATION MODEL OF STEADY-STATE METAL ANODIZING: THE VELOCITY FIELDS AND TRAJECTORIES OF MIGRATING TRACERS

Mathematical 3D migration model of the motion of tracers migrating in the electric field is developed for the steady-state porous metal oxidation. Tracers can be introduced into the metal or solution for research purposes. In this work, the impurities in the anodized metal and the main electrolyte anions are also considered as tracers, if their content in the AOF is so small that a fraction of ionic current of their migration may be ignored, i.e. the entire ionic current is carried only by the main metal and oxygen ions. The tracers can migrate in the direction of oxygen ion motion or in the opposite direction. It is shown that the tracer migration can be taken into account by introducing the effective transport number. The effect of the direction and velocity of tracer migration on their trajectory is studied within the mathematic model developed. The phenomenon of oxide flow, which was discovered in the works of Garcia-Vergara, Skeldon, Thompson, Habazaki, is explained within a concept that the oxide flow is a result of oxide growth in the direction normal to the substrate and the migration of basic ions in the radial direction in the strong spherical electric field with no considerable effect of mechanical stresses. The calculated arrangement of tracers agrees well with the experimental data of many works, where the tracers were introduced from the metal and electrolyte. The model offers possibilities of experimental determination of transport numbers of metal and oxygen in the steady-state processes of anodic porous oxidation of metals.