Solitary Structures Sustained by Marangoni Flow

L.M. Pismen

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 6, Issue: 1, page 48-61
  • ISSN: 0973-5348

Abstract

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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. .

How to cite

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Pismen, L.M.. "Solitary Structures Sustained by Marangoni Flow." Mathematical Modelling of Natural Phenomena 6.1 (2010): 48-61. <http://eudml.org/doc/197650>.

@article{Pismen2010,
abstract = {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. .},
author = {Pismen, L.M.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {solitary structures; Marangoni convection; coalescence; nucleation},
language = {eng},
month = {6},
number = {1},
pages = {48-61},
publisher = {EDP Sciences},
title = {Solitary Structures Sustained by Marangoni Flow},
url = {http://eudml.org/doc/197650},
volume = {6},
year = {2010},
}

TY - JOUR
AU - Pismen, L.M.
TI - Solitary Structures Sustained by Marangoni Flow
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/6//
PB - EDP Sciences
VL - 6
IS - 1
SP - 48
EP - 61
AB - 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. .
LA - eng
KW - solitary structures; Marangoni convection; coalescence; nucleation
UR - http://eudml.org/doc/197650
ER -

References

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  1. A. A. Golovin and L. M. Pismen. Dynamic phase separation: From coarsening to turbulence via structure formation. Chaos, 14 No. 3, (2004) 845–854.  
  2. A. M. Turing. The chemical basis of morphogenesis. Philos. Trans. R. Soc. London B, 237 (1952), 37–72. 
  3. R. Kapral and K. Showalter (Eds.). Chemical waves and patterns. Kluwer Academic Publishers, New York, 1995.  
  4. L. M. Pismen. Patterns and Interfaces in dissipative dynamics. Springer Verlag, Berlin, 2006.  Zbl1098.37001
  5. Z. Dagan, L. M. Pismen. Marangoni waves induced by a multistable chemical reaction on thin liquid films. J. Coll. Interface Sci., 99 (1984), No. 1, 215–225. 
  6. L. M. Pismen. Composition and flow patterns due to chemo-Marangoni instability in liquid films. J. Coll. Interface Sci., 102 (1984), No. 1, 237–247. 
  7. A. Pereira, P. M. J. Trevelyan, U. Thiele, and S. Kalliadasis. Dynamics of a horizontal thin liquid film in the presence of reactive surfactants, Phys. Fluids, 19 (2007), No. 11, 112102.  Zbl1182.76595
  8. L. Rongy, A. De Wit. Solitary Marangoni-driven convective structures in bistable chemical systems. Phys. Rev. E, 77 (2008), No. 4, 046310. 
  9. L. M. Pismen. Interaction of reaction-diffusion fronts and Marangoni flow on the interface of deep fluid. Phys. Rev. Lett., 78 (1997), No. 2, 382–385. 
  10. L. M. Pismen, J. Rubinstein. Motion of vortex lines in the Ginzburg–Landau model. Physica (Amsterdam) D, 47 (1991), No. 3, 353–360. Zbl0728.35090
  11. R. L. Pego. Front migration in the nonlinear Cahn–Hilliard equation. Proc. Roy. Soc. Ln A, 422 No. 1863 (1989), 261–278.  Zbl0701.35159

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