Flow Instability Mechanism for Formation of Self-Ordered Porous Anodic Oxide Films

Abstract

Experimental studies have suggested that oxide flow plays an important role in the growth of porous anodic oxide films on reactive metals. Here a mathematical model for anodic oxide formation is presented that includes viscous flow of oxide, along with high-field ionic conduction and interfacial oxygen transfer and metal dissolution reactions. Flow is driven by near-surface compressive stress, as has been detected by measurements of residual stress distributions in anodic alumina. Linear stability analysis of the model shows that pattern formation at the solution interface is possible near the critical value of a parameter expressing competition between stabilizing electrochemical oxide formation and destabilizing flow. According to the critical parameter value, pattern formation requires that the Faradaic efficiency for oxygen transfer at the solution interface must be close to the transport number for electrical migration of oxygen ions across the film. This relationship between efficiency and transport number is indeed suggested by experimental data. A scaling ratio of pore separation to voltage, as characteristically found in anodic films, is predicted by the wavelength at the critical point.