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

L. G. StantonA. A. Golovin — 2008

Mathematical Modelling of Natural Phenomena

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.

Marangoni Convection in a Photo-Chemically Reacting Liquid

A. A. GolovinV. A. Volpert — 2008

Mathematical Modelling of Natural Phenomena

Marangoni convection caused by a photochemical reaction of the type A h ν B in a deep liquid layer is studied. Linear stability analysis is performed and the conditions for Marangoni convection to occur are obtained. It is shown that increasing the rate of the direct reaction, for example, by increasing the light intensity, destabilizes the steady state and causes convective motion of the fluid, whereas increasing the rate of the inverse reaction stabilizes the steady state. A weakly nonlinear analysis...

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