Electrokinetics-Driven Anodic Oxide Pore Formation: Linear and Weakly Nonlinear Analysis

Anodization of aluminum in an acidic medium facilitates the formation of well-ordered nanoporous anodic oxide films. The mechanism of pore formation is investigated as a morphological instability using a simplified model. The model accounts for the high field conduction law and field-assisted reactions (oxide formation/dissolution) only at the oxide-solution interface. The role of Butler-Volmer electrokinetics, electrolyte pH, anodic efficiency, and interface curvature on reaction kinetics are taken into account. Linear stability analysis suggests that the oxide film is unstable to well-defined wavelengths in specific ranges of parameters such as anodizing efficiency, applied voltage and electrolyte pH. Subsequently, a weakly nonlinear analysis is carried out to determine the nature of bifurcation beyond the stability threshold. Our findings indicate that the instability exhibits a subcritical nature, well in agreement with experimental observations.