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The eruptive regime of mass-transfer-driven Rayleigh–Marangoni convection

Published online by Cambridge University Press:  19 February 2016

Thomas Köllner ,
Karin Schwarzenberger ,
Kerstin Eckert  and
Thomas Boeck
Thomas Köllner*
Affiliation:
Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, P.O. Box 100565, D-98684 Ilmenau, Germany
Karin Schwarzenberger
Affiliation:
Institute of Fluid Mechanics, Chair of Magnetofluiddynamics, Measuring and Automation Technology, TU Dresden, D-01062 Dresden, Germany
Kerstin Eckert
Affiliation:
Institute of Fluid Mechanics, Chair of Magnetofluiddynamics, Measuring and Automation Technology, TU Dresden, D-01062 Dresden, Germany
Thomas Boeck
Affiliation:
Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, P.O. Box 100565, D-98684 Ilmenau, Germany
*
†Email address for correspondence: [email protected]
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Abstract

The transfer of an alcohol, 2-propanol, from an aqueous to an organic phase causes convection due to density differences (Rayleigh convection) and interfacial tension gradients (Marangoni convection). The coupling of the two types of convection leads to short-lived flow structures called eruptions, which were reported in several previous experimental studies. To unravel the mechanism underlying these patterns, three-dimensional direct numerical simulations and corresponding validation experiments were carried out and compared with each other. In the simulations, the Navier–Stokes–Boussinesq equations were solved with a plane interface that couples the two layers including solutal Marangoni effects. Our simulations show excellent agreement with the experimentally observed patterns. On this basis, the origin of the eruptions is explained by a two-step process in which Rayleigh convection continuously produces a concentration distribution that triggers an opposing Marangoni flow.

JFM classification

Convection: Buoyancy-driven instability Convection: Marangoni convection Nonlinear Dynamical Systems: Pattern formation
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 791 , 25 March 2016 , R4
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Copyright
© 2016 Cambridge University Press 

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References

Agble, D. & Mendes-Tatsis, M. A. 2000 The effect of surfactants on interfacial mass transfer in binary liquid–liquid systems. Intl J. Heat Mass Transfer 43 (6), 1025–1034.Google Scholar
Bakker, C. A. P., van Buytenen, P. M. & Beek, W. J. 1966 Interfacial phenomena and mass transfer. Chem. Engng Sci. 21, 1039–1046.Google Scholar
Berg, J. C. & Morig, C. R. 1969 Density effects in interfacial convection. Chem. Engng Sci. 24, 937–946.Google Scholar
Boeck, T., Nepomnyashchy, A., Simanovskii, I., Golovin, A., Braverman, L. & Thess, A. 2002 Three-dimensional convection in a two-layer system with anomalous thermocapillary effect. Phys. Fluids 14, 3899–3911.Google Scholar
Imaishi, N., Fujinawa, K. & Tadaki, T. 1980 Effect of oscillatory instability on stability of two-fluid layers. J. Chem. Engng Japan 13 (5), 360–365.CrossRefGoogle Scholar
Köllner, T., Schwarzenberger, K., Eckert, K. & Boeck, T. 2013 Multiscale structures in solutal Marangoni convection: Three-dimensional simulations and supporting experiments. Phys. Fluids 25, 092109.Google Scholar
Köllner, T., Schwarzenberger, K., Eckert, K. & Boeck, T. 2015 Solutal Marangoni convection in a Hele–Shaw geometry: impact of orientation and gap width. Eur. Phys. J. Special Topics 224 (2), 261–276.Google Scholar
Kostarev, K. G., Shmyrov, A. V., Zuev, A. L. & Viviani, A. 2011 Convective and diffusive surfactant transfer in multiphase liquid systems. Exp. Fluids 51 (2), 457–470.Google Scholar
Kroepelin, H. & Neumann, H. J. 1957 Eruptiver Stoffaustausch an ebenen Grenzflächen. Naturwissenschaften 44 (10), 304–304.Google Scholar
Lappa, M. & Piccolo, C. 2004 Higher modes of the mixed buoyant-Marangoni unstable convection originated from a droplet dissolving in a liquid/liquid system with miscibility gap. Phys. Fluids 16 (12), 4262–4272.CrossRefGoogle Scholar
Linde, H. & Schwarz, E. 1963 Untersuchungen zur Charakteristik der freien Grenzflächenkonvektion beim Stoffübergang an fluiden Grenzen. Z. Phys. Chem. 224, 331–352.CrossRefGoogle Scholar
Linde, H., Schwarzenberger, K. & Eckert, K. 2013 Pattern formation emerging from stationary solutal Marangoni instability: a roadmap through the underlying hierarchic structures. In Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics (ed. Rubio, R. G., Ryazantsev, Y. S., Starov, V. M., Huang, G.-X., Chetverikov, A. P., Arena, P., Nepomnyashchy, A. A., Ferrus, A. & Morozov, E. G.), Understanding Complex Systems, vol. 5, Springer.Google Scholar
Loodts, V., Thomas, C., Rongy, L. & De Wit, A. 2014 Control of convective dissolution by chemical reactions: general classification and application to $\text{CO}_{2}$ dissolution in reactive aqueous solutions. Phys. Rev. Lett. 113 (11), 114501.CrossRefGoogle Scholar
Merzkirch, W. 1987 Flow Visualization. Academic.Google Scholar
Orell, A. & Westwater, J. W. 1962 Spontaneous interfacial cellular convection accompanying mass transfer: Ethylene glycol–acetic acid–ethyl acetate. AIChE J. 8, 350–356.CrossRefGoogle Scholar
Rydberg, J. 2004 Solvent Extraction Principles and Practice, Revised and Expanded. CRC Press.Google Scholar
Schwarz, E.1968 Hydrodynamische Regime der Marangoni-Instabilität beim Stoffübergang über eine fluide Phasengrenze, PhD thesis, HU Berlin.Google Scholar
Schwarz, E. 1970 Zum Auftreten von Marangoni-Instabilität. Wärme- und Stoffübertragung 3, 131–133.Google Scholar
Schwarzenberger, K., Aland, S., Domnick, H., Odenbach, S. & Eckert, K. 2015a Relaxation oscillations of solutal Marangoni convection at curved interfaces. Colloids Surf. A 481, 633–643.CrossRefGoogle Scholar
Schwarzenberger, K., Köllner, T., Boeck, T., Odenbach, S. & Eckert, K. 2015b Hierarchical Marangoni roll cells: experiments and direct numerical simulations in three and two dimensions. In Computational Methods for Complex Liquid–Fluid Interfaces (ed. Rahni, M. T., Karbaschi, M. & Miller, R.), Progress in Colloid and Interface Science, vol. 5, CRC Press.Google Scholar
Schwarzenberger, K., Köllner, T., Linde, H., Boeck, T., Odenbach, S. & Eckert, K. 2014 Pattern formation and mass transfer under stationary solutal Marangoni instability. Adv. Colloid Interface Sci. 206, 344–371.Google Scholar
Sternling, C. V. & Scriven, L. E. 1959 Interfacial turbulence: hydrodynamic instability and the Marangoni effect. AIChE J. 5 (4), 514–523.Google Scholar
Trevelyan, P. M. J., Almarcha, C. & De Wit, A. 2011 Buoyancy-driven instabilities of miscible two-layer stratifications in porous media and Hele–Shaw cells. J. Fluid Mech. 670, 38–65.Google Scholar
Willert, C. 2013 Pivview 2c/3c user manual version 3.1.2. Göttingen, Germany.Google Scholar
Yiantsios, S. G., Serpetsi, S. K., Doumenc, F. & Guerrier, B. 2015 Surface deformation and film corrugation during drying of polymer solutions induced by Marangoni phenomena. Intl J. Heat Mass Transfer 89, 1083–1094.Google Scholar

Köllner et al. supplementary movie

Experimental (left) and numerical (right) shadowgraph images in a domain of 15 mm x 15 mm corresponding to figure 4. The experimental time is indicated in the movie. The numerical images are assigned to the experiments by adding an offset time of 73 s as described in the text.

Download Köllner et al. supplementary movie(Video)
Video 18.8 MB

Köllner et al. supplementary movie

Isosurface of 2-propanol concentration with c(1)=0.97 (orange) in the lower, aqueous phase and c(2)=0.2 (blue) in the upper, organic phase. The phases have a height of 20 mm and a horizontal area of 15 mm x 15 mm. Time is given in viscous units, i.e. in 333.3 s. The video corresponds to figure 4.

Download Köllner et al. supplementary movie(Video)
Video 20 MB