Math. Model. Nat. Phenom.
Volume 6, Number 1, 2011Instability and patterns. Issue dedicated to the memory of A. Golovin
|Page(s)||48 - 61|
|Published online||09 June 2010|
Solitary Structures Sustained by Marangoni Flow
Department of Chemical Engineering and Minerva Center for Nonlinear Physics
of Complex Systems, Technion, 32000
1 Email: email@example.com
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. .
Mathematics Subject Classification: 76D45 / 76V05
Key words: solitary structures / Marangoni convection / coalescence / nucleation
© EDP Sciences, 2010
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