Geodesic
Solitary Structures Sustained by Marangoni Flow
L.M. Pismen1
1Department 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 
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
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