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Pattern Formation Emerging from Stationary Solutal Marangoni Instability: A Roadmap Through the Underlying Hierarchic Structures

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Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

The complexity of interfacial convection has long exerted a pull and, at the same time, is the reason why this type of flow still belongs to the class of problems in chemical engineering and non-linear physics which are not fully resolved. This flow arises from the Marangoni instability which typically occurs when surface-active solutes, or heat, undergo a mass or heat transfer across an interface. During these processes various types of both quasi-steady and time-dependent flow structures have been observed [1–12].

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References

  1. Orell, A., Westwater, J.W.: Spontaneous interfacial cellular convection accompanying mass transfer: ethylene glycol – acetic acid – ethyl acetate. AIChE J. 8, 350–356 (1962)

    Article  Google Scholar 

  2. Sawistowski, H., Goltz, G.: The effect of interface phenomena on mass-transfer rates in liquid-liquid extraction. Chem. Eng. Res. Des. 41, 174–181 (1963)

    Google Scholar 

  3. Linde, H., Pfaff, S., Zirkel, C.: Strömunguntersuchungen zur hydrodynamischen Instabilität flüssig-gasförmiger Phasengrenzen mit Hilfe der Kapillarspaltmethode. Z. für Phys. Chemie 225, 72–100 (1964)

    Google Scholar 

  4. Linde, H., Schwarz, E.: Untersuchungen zur Charakteristik der freien Grenzflächenkonvektion beim Stoffübergang an fluiden Grenzen. Z. für Phys. Chem. 224, 331–352 (1963)

    Google Scholar 

  5. Linde, H., Schwarz, E.: Über grossräumige Rollzellen der freien Grenzflächenkonvektion. Monatsberichte Deutsche Akad. der Wiss. Berl. 7, 330–338 (1964)

    Google Scholar 

  6. Austin, L., Ying, W., Sawistowski, H.: Interfacial phenomena in binary liquid-liquid systems. Chem. Eng. Sci. 21, 1109–1110 (1966)

    Article  Google Scholar 

  7. Bakker, C.A.P., van Buytenen, P.M., Beek, W.J.: Interfacial phenomena and mass transfer. Chem. Eng. Sci. 21, 1039–1046 (1966)

    Article  Google Scholar 

  8. Thomas, W., Nicholl, E. McK.: An optical study of interfacial turbulence occurring during the absorption of CO2 into monoethanolamine. Chem. Eng. Sci. 22, 1877–1878 (1967)

    Google Scholar 

  9. Schwarz, E.: Zum Auftreten von Marangoni-Instabilität. Wärme Stoffübertrag. 3, 131–133 (1970)

    Article  Google Scholar 

  10. Imaishi, N., Fujinawa, K.: An optical study of interfacial turbulence accompanying chemical absorption. Int. J. Chem. Eng. 20, 226–231 (1980)

    Google Scholar 

  11. Agble, D., Mendes-Tatsis, M.: The effect of surfactants on interfacial mass transfer in binary liquid-liquid systems. Int. J. Heat Mass Transf. 43, 1025–1034 (2000)

    Article  MATH  Google Scholar 

  12. Sun, Z.F., Yu, K.T., Wang, S.Y., Miao, Y.Z.: Absorption and desorption of carbon dioxide into and from organic solvents: Effects of Rayleigh and Marangoni instability. Ind. Eng. Chem. Res. 41, 1905–1913 (2002)

    Article  Google Scholar 

  13. Sternling, C.V., Scriven, L.E.: Interfacial turbulence: Hydrodynamic instability and the Marangoni effect. AIChE J. 5, 514–523 (1959)

    Article  Google Scholar 

  14. Loeschcke, K., Schwarz, E., Linde, H.: Ein oszillatorisches Regime der Marangoni-Instabilität. Abhandlungen Dtsch. Akad. Wiss. Berl. 6b, 720–733 (1966)

    Google Scholar 

  15. Linde, H., Loeschcke, K.: Rollzellen und Oszillation beim Wärmeübergang zwischen Gas und Flüssigkeit. Zellgrössen und Frequenzen im Vergleich mit der Theorie der Marangoni Instabilität von Sterling und Scriven. Chem. Ing. Tech. 39, 65–74 (1967)

    Google Scholar 

  16. Linde, H., Schwarz, E., Gröger, K.: Zum Auftreten des oszillatorischen Regimes der Marangoni-Instabilität beim Stoffübergang. Chem. Eng. Sci. 22, 823–836 (1967)

    Article  Google Scholar 

  17. Linde, H., Kunkel, M.: Einige neue qualitative Beobachtungen beim oszillatorischen Regime der Marangoni-Instabilität. Heat Mass Transf. 2, 60–64 (1969)

    Google Scholar 

  18. Linde, H., Velarde, M.G., Wierschem, A., Waldhelm, W., Loeschcke, K., Rednikov, A.Y.: Interfacial wave motions due to Marangoni instability. J. Colloid Interface Sci. 188, 16–26 (1997)

    Article  Google Scholar 

  19. Linde, H., Velarde, M.G., Waldhelm, W., Loeschcke, K., Wierschem, A.: On the various wave motions observed at a liquid interface due to Marangoni stresses and instability. Ind. Eng. Chem. Res. 44, 1396–1412 (2005)

    Article  Google Scholar 

  20. Reichenbach, J., Linde, H.: Linear perturbation analysis of surface-tension-driven convection at a plane interface (Marangoni instability). J. Colloid Interface Sci. 84, 433–443 (1981)

    Article  Google Scholar 

  21. Hennenberg, M., Bisch, P., Vignes-Adler, M., Sanfeld, A.: Mass transfer, Marangoni effect, and instability of interfacial longitudinal waves: I. Diffusional exchanges. J. Colloid Interface Sci. 69, 128–137 (1979)

    Article  Google Scholar 

  22. Hennenberg, M., Bisch, P., Vignes-Adler, M., Sanfeld, A.: Mass transfer, Marangoni effect, and instability of interfacial longitudinal waves. II. Diffusional exchanges and adsorption-desorption processes. J. Colloid Interface Sci. 74, 495–508 (1980)

    Google Scholar 

  23. Mendes-Tatsis, M.A., Perez De Ortiz, E.S.: Marangoni instabilities in systems with an interfacial chemical reaction. Chem. Eng. Sci. 51, 3755–3761 (1996)

    Google Scholar 

  24. Slavtchev, S., Hennenberg, M., Legros, J.-C., Lebon, G.: Stationary solutal Marangoni instability in a two-layer system. J. Colloid Interface Sci. 203, 354–368 (1998)

    Article  Google Scholar 

  25. Nepomnyashchy, A.A., Velarde, M.G., Colinet, P.: Interfacial phenomena and convection. Chapman & Hall/CRC, Pitman Series, Boca Raton (2002)

    MATH  Google Scholar 

  26. Slavtchev, S., Kalitzova-Kurteva, P., Mendes, M.: Marangoni instability of liquid-liquid systems with a surface-active solute. Colloids Surf. A Physicochem. Eng. Asp. 282–283, 37–49 (2006)

    Article  Google Scholar 

  27. Pearson, J.: On convection cells induced by surface tension. J. Fluid Mech. 4, 489–500 (1958)

    Article  ADS  MATH  Google Scholar 

  28. Golovin, A.: Mass transfer under interfacial turbulence: Kinetic regulaties. Chem. Eng. Sci. 47, 2069–2080 (1992) (and references therein)

    Google Scholar 

  29. Berg, J.C., Morig, C.R.: Density effects in interfacial convection. Chem. Eng. Sci. 24, 937–946 (1969)

    Article  Google Scholar 

  30. Gumerman, R.J., Homsy, G.M.: Convective instabilities in concurrent two phase flow: Part I. Linear stability. AIChE J. 20, 981–988 (1974) (and the subsequent articles in this series)

    Google Scholar 

  31. Tanny, J., Chen, C.C., Chen, C.F.: Effects of interaction between Marangoni and double-diffusive instabilities. J. Fluid Mech. 303, 1–21 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  32. Grahn, A.: Two-dimensional numerical simulations of Marangoni-Bénard instabilities during liquid-liquid mass transfer in a vertical gap. Chem. Eng. Sci. 61, 3586–3592 (2006)

    Article  Google Scholar 

  33. Sczech, R., Eckert, K., Acker, M.: Convective instability in a liquid-liquid system due to complexation with a crown ether. J. Phys. Chem. A 112, 7357–7364 (2008)

    Article  Google Scholar 

  34. Schwarzenberger, K., Eckert, K., Odenbach, S.: Relaxation oscillations between Marangoni cells and double diffusive fingers in a reactive liquid-liquid system. Chem. Eng. Sci. 68, 530–540 (2012)

    Article  Google Scholar 

  35. Linde, H.: Versuche zur Deutung des Einflusses der erzwungenen Konvektion auf die Grenzflächendynamik beim Stoffübergang. Abhandlungen Dtsch. Akad. Wiss. Berl. 6b, 710–719 (1966)

    Google Scholar 

  36. Schwarz, E.: Hydrodynamische Regime der Marangoni-Instabilität beim Stoffübergang über eine fluide Phasengrenze. Ph.D. thesis, HU Berlin (1967)

    Google Scholar 

  37. Linde, H., Schwartz, P., Wilke, H.: Dissipative structures and nonlinear kinetics of the Marangoni-instability. In: Dynamics and Instability of Fluid Interfaces. Springer, Berlin (1979)

    Google Scholar 

  38. Linde, H., Schwarz, E.: Divers photographic images. Recorded during the thesis of E. Schwarz

    Google Scholar 

  39. Shi, Y., Eckert, K.: A novel Hele-Shaw cell design for the analysis of hydrodynamic instabilities in liquid-liquid systems. Chem. Eng. Sci. 63, 3560–3563 (2008)

    Article  Google Scholar 

  40. Linde, H., Schwartz, P.: Zeitabhängiges Verhalten und Regelmässigkeit bei hydrodynamischen dissipativen Strukturen. Nova Acta Leopoldina NF 61, 105–125 (1989)

    Google Scholar 

  41. Keener, J.P., Tyson, J.J.: Spiral waves in the Belousov-Zhabotinskii reaction. Phys. D Nonlinear Phenom. 21, 307–324 (1986)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  42. Linde, H.: Topological similarities in dissipative structures of Marangoni-instability and Belousov-Zhabotinsky-reaction. In: Self-Organization: Autowaves and Structures Far from Equilibrium, Springer, Berlin (1984)

    Google Scholar 

  43. Schwarzenberger, K., Köllner, T., Linde, H., Odenbach, S., Boeck, T., Eckert, K.: On the transition from cellular to wave-like patterns during solutal Marangoni convection. Eur. Phys. J. Special Topics 219, 121–130 (2013)

    Article  ADS  Google Scholar 

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Acknowledgement

The financial support for two of us (K.S. and K.E.) by the Deutsche Forschungsgemeinschaft in the form of the Priority Programme 1506 and by Deutsches Zentrum für Luft- und Raumfahrt (Grants no. 50WM0638 and 50WM1144) is gratefully acknowledged.

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Authors and Affiliations

  1. Str. 201, Nr. 6, 13156, Berlin, Germany

    H. Linde

  2. Institute of Fluid Mechanics, Technische Universität Dresden, 01062, Dresden, Germany

    K. Schwarzenberger & K. Eckert

Authors
  1. H. Linde
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  2. K. Schwarzenberger
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  3. K. Eckert
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Correspondence to K. Eckert .

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Editors and Affiliations

  1. , Dpt. Quimica-Fisica-I, UCM, Madrid, 28040, Spain

    Ramon G. Rubio

  2. Instituto Pluridisciplinar, UCM, Paseo Juan XXIII 1, Madrid, 28040, Spain

    Yuri S. Ryazantsev

  3. , Dpt. of Chemical Engineering, Loughborough University, Loughborough, LE11 3TU, United Kingdom

    Victor M Starov

  4. , Physics Dpt., East China Normal University, Zhongshan Northern Road 3663, Shanghai, 200062, China, People's Republic

    Guo-Xiang Huang

  5. , Faculty of Physics, Saratov State University, Astrakhanskaya Str. 83, Saratov, 410012, Russia

    Alexander P Chetverikov

  6. , Dpt. di Ingegneria Elettrica Elettronica, Università di Catania, V. le A. Doria 6, Catania, 95125, Italy

    Paolo Arena

  7. , Dept. of Mathematics, Technion, Haifa, 32000, Israel

    Alex A. Nepomnyashchy

  8. , Instituto Cajal, CSIC, Av. Dr. Arce 37, Madrid, 28002, Spain

    Alberto Ferrus

  9. Shirshov Institute of Oceanology, Nakhimovsky prospekt 36, Moscow, 117851, Russia

    Eugene G. Morozov

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Linde, H., Schwarzenberger, K., Eckert, K. (2013). Pattern Formation Emerging from Stationary Solutal Marangoni Instability: A Roadmap Through the Underlying Hierarchic Structures. In: Rubio, R., et al. Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34070-3_16

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  • DOI: https://doi.org/10.1007/978-3-642-34070-3_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34069-7

  • Online ISBN: 978-3-642-34070-3

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