Geodesic
Solitary Structures Sustained by Marangoni Flow
L.M. Pismen1
1 Department of Chemical Engineering and Minerva Center for Nonlinear Physics of Complex Systems, Technion, 32000 Haifa, Israel
Mathematical modelling of natural phenomena, Tome 6 (2011) no. 1, pp. 48-61.

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We construct interfacial solitary structures (spots) generated by a bistable chemical reaction or a non-equilibrium phase transition in a surfactant film. The structures are stabilized by Marangoni flow that prevents the spread of a state with a higher surface tension when it is dynamically favorable. In a system without surfactant mass conservation, a unique radius of a solitary spot exists within a certain range of values of the Marangoni number and of the deviation of chemical potential from the Maxvell construction, but multiple spots attract and coalesce. In a conservative system, there is a range of stable spot sizes, but solitary spots may exist only in a limited parametric range, beyond which multiple spots nucleate. Repeated coalescence and nucleation leads to chaotic dynamics of spots observed computationally in Ref. .
DOI : 10.1051/mmnp/20116103

L.M. Pismen 1

1 Department of Chemical Engineering and Minerva Center for Nonlinear Physics of Complex Systems, Technion, 32000 Haifa, Israel 
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L.M. Pismen. Solitary Structures Sustained by Marangoni Flow. Mathematical modelling of natural phenomena, Tome 6 (2011) no. 1, pp. 48-61. doi : 10.1051/mmnp/20116103. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20116103/

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