Effect of Electrostriction on the Self-organization of Porous Nanostructures in Anodized Aluminum Oxide

Authors: L. G. Stanton  and A. A. Golovin

Reference: Mathematical Modelling of Natural Phenomena,  Volume 3, 2008

The self-organization of porous nanostructures in anodic metal oxide is considered. A mathematical model which incorporates the chemical reactions at the metal-oxide and oxide-electrolyte interfaces and elastic stress caused by the electrostrictive effects is developed. It is shown through linear stability analysis, that a short-wave instability exists in certain parameter regimes which can lead to the formation of hexagonally ordered pores observed in anodized aluminum oxide.

Solidification of free liquid films

Authors: A. M. Anderson and S. H. Davis

Reference: Journal of Fluid Mechanics, Volume 617, 2008

We examine steady longitudinal freezing of a two-dimensional single-component free liquid film.  In the liquid, there are thermocapillary and volume-change flows as a result of temperature gradients along the film and density change upon solidification.  We examine these flows, heat transfer, and interfacial shapes using an asymptotic analysis which is valid for thin films with small aspect rations.  These solutions depend sensitively on contact conditions at the tri-junctions.  In particular, when the sum of the angles formed in the solid and liquid phases falls below a critical value, the existence of steady solutions is lost and the liquid film cannot be continuous, suggesting the breakage of the film owing to freezing.  The solutions are relevant to the freezing of foams of metals or ceramics, materials unaffected by surface active agents.