Hostname: page-component-77f85d65b8-45ctf Total loading time: 0 Render date: 2026-04-19T16:35:36.481Z Has data issue: false hasContentIssue false
  • English
  • Français

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: pismen@technion.ac.il
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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