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Marangoni Convection in a Photo-ChemicallyReacting Liquid

Published online by Cambridge University Press:  17 July 2008

A. A. Golovin  and
V. A. Volpert
A. A. Golovin
Affiliation:
Department of Engineering Sciences and Applied Mathematics Northwestern University, Evanston, IL 60208, USA
V. A. Volpert*
Affiliation:
Department of Engineering Sciences and Applied Mathematics Northwestern University, Evanston, IL 60208, USA
*
v-volpert@northwestern.edu
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Abstract

Marangoni convection caused by a photochemical reaction of the type A $\stackrel{h\nu}{\rightleftharpoons}$ B in a deep liquid layer is studied. Linear stability analysis is performed and the conditionsfor Marangoni convection to occur are obtained. It is shown that increasing the rate of thedirect reaction, for example, by increasing the light intensity, destabilizes the steady stateand causes convective motion of the fluid, whereas increasing the rate of the inverse reactionstabilizes the steady state. A weakly nonlinear analysis of the problem is performed thatgives conditions for hexagonal convective patters to occur. It is shown that, in the case ofsmall light absorption length, the hexagonal cells correspond to "down"-hexagons.

Keywords

Marangoni convectionphotochemical reactionstability analysisnonlinearanalysis
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 3 , Issue 1: Interfacial phenomena in fluids , 2008 , pp. 27 - 54
Copyright
© EDP Sciences, 2008

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