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Math. Model. Nat. Phenom. Vol. 3, No. 1, 2008, pp. 27-54
DOI: 10.1051/mmnp:2008032
Marangoni Convection in a Photo-Chemically Reacting Liquid
A.A. Golovin and V.A. VolpertDepartment of Engineering Sciences and Applied Mathematics Northwestern University, Evanston, IL 60208, USA
v-volpert@northwestern.edu
Published online: 17 July 2008
Abstract
Marangoni convection caused by a photochemical reaction of the type A
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 of the problem is performed that
gives conditions for hexagonal convective patters to occur. It is shown that, in the case of
small light absorption length, the hexagonal cells correspond to "down"-hexagons.
Mathematics Subject Classification. 76E06, 76E17, 76E30
Key words: Marangoni convection -- photochemical reaction -- stability analysis -- nonlinear analysis