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Solitary Structures Sustained by Marangoni Flow

Published online by Cambridge University Press:  09 June 2010

L.M. Pismen
L.M. Pismen*
Affiliation:
Department of Chemical Engineering and Minerva Center for Nonlinear Physics of Complex Systems, Technion, 32000 Haifa, Israel
*
1 Email: [email protected]
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Abstract

We construct interfacial solitary structures (spots) generated by a bistable chemicalreaction or a non-equilibrium phase transition in a surfactant film. The structures arestabilized by Marangoni flow that prevents the spread of a state with a higher surfacetension when it is dynamically favorable. In a system without surfactant massconservation, a unique radius of a solitary spot exists within a certain range of valuesof the Marangoni number and of the deviation of chemical potential from the Maxvellconstruction, but multiple spots attract and coalesce. In a conservative system, there isa range of stable spot sizes, but solitary spots may exist only in a limited parametricrange, beyond which multiple spots nucleate. Repeated coalescence and nucleation leads tochaotic dynamics of spots observed computationally in Ref. [1].

Keywords

solitary structuresMarangoni convectioncoalescencenucleation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 1: Instability and patterns. Issue dedicated to the memory of A.Golovin , 2011 , pp. 48 - 61
Copyright
© EDP Sciences, 2010

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References

Golovin, A. A. and Pismen, L. M.. Dynamic phase separation: From coarsening to turbulence via structure formation . Chaos, 14 No. 3, (2004) 845–854. CrossRefGoogle Scholar
Turing, A. M.. The chemical basis of morphogenesis . Philos. Trans. R. Soc. London B, 237 (1952), 37–72.CrossRefGoogle Scholar
R. Kapral and K. Showalter (Eds.). Chemical waves and patterns. Kluwer Academic Publishers, New York, 1995.
L. M. Pismen. Patterns and Interfaces in dissipative dynamics. Springer Verlag, Berlin, 2006.
Dagan, Z., Pismen, L. M.. Marangoni waves induced by a multistable chemical reaction on thin liquid films . J. Coll. Interface Sci., 99 (1984), No. 1, 215–225.CrossRefGoogle Scholar
Pismen, L. M.. Composition and flow patterns due to chemo-Marangoni instability in liquid films . J. Coll. Interface Sci., 102 (1984), No. 1, 237–247.CrossRefGoogle Scholar
Pereira, A., Trevelyan, P. M. J., Thiele, U., and Kalliadasis, S.. Dynamics of a horizontal thin liquid film in the presence of reactive surfactants, Phys. Fluids, 19 (2007), No. 11, 112102. CrossRefGoogle Scholar
Rongy, L., De Wit, A.. Solitary Marangoni-driven convective structures in bistable chemical systems . Phys. Rev. E, 77 (2008), No. 4, 046310.CrossRefGoogle ScholarPubMed
Pismen, L. M.. Interaction of reaction-diffusion fronts and Marangoni flow on the interface of deep fluid . Phys. Rev. Lett., 78 (1997), No. 2, 382–385.CrossRefGoogle Scholar
Pismen, L. M., Rubinstein, J.. Motion of vortex lines in the Ginzburg–Landau model . Physica (Amsterdam) D, 47 (1991), No. 3, 353–360.CrossRefGoogle Scholar
Pego, R. L.. Front migration in the nonlinear Cahn–Hilliard equation . Proc. Roy. Soc. Ln A, 422 No. 1863 (1989), 261–278. CrossRefGoogle Scholar