Weakly Nonlinear Analysis of Flow-Driven Porous Anodic Oxide

Abstract

Porous anodic oxide (PAO) films are formed by the electrochemical oxidation of metals such as titanium, aluminum, and other metals in acidic solutions. The optimal selection of parameters leads to the formation of submicron-sized pores arranged in a parallel hexagonal array within these films. Porous anodic oxide has enormous industrial applications in the development of functional nanodevices. The present study builds upon the flow-driven porous anodic oxide model proposed by Mishra and Hebert. They have shown through a linear stability analysis of the model that the inter-pore distance in PAO is successfully determined by the competition between stabilizing oxide formation and destabilizing viscous flow. In this work, we investigate the weakly nonlinear analysis of the model to determine the nature of instability arising in flow-driven porous anodic films beyond the stability threshold. For formation of well- developed pores, the nature of instability must be subcritical. However, the results of weakly nonlinear analysis show that the solutions resulting from neutral stability exhibit a supercritical nature for the practical range of anodizing control parameters as shown in Figure 1. Thus, in order to make accurate nonlinear predictions about the formation of pores, it is imperative to incorporate additional physics into the viscous flow model. We also determine the Hadamard stability criteria by tracking the neutral wavenumber to ascertain the regions of well- posedness of the viscous flow model. Figure 1