A Hybrid Model for Electrokinetic and Stress-Induced Flow Mechanisms in Porous Anodic Oxide Formation

A hybrid model is developed to investigate pore initiation and growth in anodic oxides, incorporating both the viscous oxide flow and the electrokinetic dissolution mechanisms. Linear stability analysis reveals that the instability arises from the combined destabilizing effects of stress-induced oxide flow and field-assisted electrochemical reaction kinetics, counteracted by the stabilizing effects of electrochemical oxide formation and surface energy. Notably, both stress-driven flow and electrokinetic effects play a significant role in the early stages of pore formation, as revealed by the linear stability analysis results. Accounting only for electrokinetics-driven instability growth leads to a significant overestimation of the pore spacing. The model is shown to be well-posed and predicts a long-wave instability across all parameter ranges. Further, the Weighted-Residual Integral Boundary Layer (WRIBL) method, based on the long-wave approximation, is employed to derive the evolution equations for the metal-oxide and oxide-electrolyte interfaces. The predictions of the WRIBL model agree with the linear stability analysis of the long-wave equations. Numerical simulations reveal a subcritical nature of instability leading to the initiation and deepening of pores, with oxide flow directed from pore base to pore walls, in agreement with previous tracer experiments.