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].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Orell, A., Westwater, J.W.: Spontaneous interfacial cellular convection accompanying mass transfer: ethylene glycol – acetic acid – ethyl acetate. AIChE J. 8, 350–356 (1962)
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)
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)
Linde, H., Schwarz, E.: Untersuchungen zur Charakteristik der freien Grenzflächenkonvektion beim Stoffübergang an fluiden Grenzen. Z. für Phys. Chem. 224, 331–352 (1963)
Linde, H., Schwarz, E.: Über grossräumige Rollzellen der freien Grenzflächenkonvektion. Monatsberichte Deutsche Akad. der Wiss. Berl. 7, 330–338 (1964)
Austin, L., Ying, W., Sawistowski, H.: Interfacial phenomena in binary liquid-liquid systems. Chem. Eng. Sci. 21, 1109–1110 (1966)
Bakker, C.A.P., van Buytenen, P.M., Beek, W.J.: Interfacial phenomena and mass transfer. Chem. Eng. Sci. 21, 1039–1046 (1966)
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)
Schwarz, E.: Zum Auftreten von Marangoni-Instabilität. Wärme Stoffübertrag. 3, 131–133 (1970)
Imaishi, N., Fujinawa, K.: An optical study of interfacial turbulence accompanying chemical absorption. Int. J. Chem. Eng. 20, 226–231 (1980)
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)
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)
Sternling, C.V., Scriven, L.E.: Interfacial turbulence: Hydrodynamic instability and the Marangoni effect. AIChE J. 5, 514–523 (1959)
Loeschcke, K., Schwarz, E., Linde, H.: Ein oszillatorisches Regime der Marangoni-Instabilität. Abhandlungen Dtsch. Akad. Wiss. Berl. 6b, 720–733 (1966)
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)
Linde, H., Schwarz, E., Gröger, K.: Zum Auftreten des oszillatorischen Regimes der Marangoni-Instabilität beim Stoffübergang. Chem. Eng. Sci. 22, 823–836 (1967)
Linde, H., Kunkel, M.: Einige neue qualitative Beobachtungen beim oszillatorischen Regime der Marangoni-Instabilität. Heat Mass Transf. 2, 60–64 (1969)
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)
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)
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)
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)
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)
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)
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)
Nepomnyashchy, A.A., Velarde, M.G., Colinet, P.: Interfacial phenomena and convection. Chapman & Hall/CRC, Pitman Series, Boca Raton (2002)
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)
Pearson, J.: On convection cells induced by surface tension. J. Fluid Mech. 4, 489–500 (1958)
Golovin, A.: Mass transfer under interfacial turbulence: Kinetic regulaties. Chem. Eng. Sci. 47, 2069–2080 (1992) (and references therein)
Berg, J.C., Morig, C.R.: Density effects in interfacial convection. Chem. Eng. Sci. 24, 937–946 (1969)
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)
Tanny, J., Chen, C.C., Chen, C.F.: Effects of interaction between Marangoni and double-diffusive instabilities. J. Fluid Mech. 303, 1–21 (1995)
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)
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)
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)
Linde, H.: Versuche zur Deutung des Einflusses der erzwungenen Konvektion auf die Grenzflächendynamik beim Stoffübergang. Abhandlungen Dtsch. Akad. Wiss. Berl. 6b, 710–719 (1966)
Schwarz, E.: Hydrodynamische Regime der Marangoni-Instabilität beim Stoffübergang über eine fluide Phasengrenze. Ph.D. thesis, HU Berlin (1967)
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)
Linde, H., Schwarz, E.: Divers photographic images. Recorded during the thesis of E. Schwarz
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)
Linde, H., Schwartz, P.: Zeitabhängiges Verhalten und Regelmässigkeit bei hydrodynamischen dissipativen Strukturen. Nova Acta Leopoldina NF 61, 105–125 (1989)
Keener, J.P., Tyson, J.J.: Spiral waves in the Belousov-Zhabotinskii reaction. Phys. D Nonlinear Phenom. 21, 307–324 (1986)
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)
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)
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-34070-3_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34069-7
Online ISBN: 978-3-642-34070-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)