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Complex Patterns and Elementary Structures of Solutal Marangoni Convection: Experimental and Numerical Studies

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Transport Processes at Fluidic Interfaces

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

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Abstract

The transfer of a solute between two liquid layers is susceptible to convective instabilities of the time-dependent diffusive concentration profile that may be caused by the Marangoni effect or buoyancy. Marangoni instabilities depend on the change of interfacial tension and Rayleigh instabilities on the change of liquid densities with solute concentration. Such flows develop increasingly complex cellular or wavy patterns with very fine structures in the concentration field due to the low solute diffusivity. They are important in several applications such as extraction or coating processes. A detailed understanding of the patterns is lacking although a general phenomenological classification has been developed based on previous experiments. We use both highly resolved numerical simulations and controlled experiments to examine two exemplary systems. In the first case, a stationary Marangoni instability is counteracted by a stable density stratification producing a hierarchical cellular pattern. In the second case, Rayleigh instability is opposed by the Marangoni effect causing solutal plumes and eruptive events with short-lived Marangoni cells on the interface. A good qualitative and acceptable quantitative agreement between the experimental visualizations and measurements and the corresponding numerical results is achieved in simulations with a planar interface, and a simple linear model for the interface properties, i.e. no highly specific properties of the interface are required for the complex patterns. Simulation results are also used to characterize the mechanisms involved in the pattern formation.

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Notes

  1. 1.

    In this work, liquid/liquid layers will be considered exclusively. They usually have high Schmidt numbers Sc (i) = ν (i)∕D (i) > 1000. This is not the case for gas/liquid systems or for the thermal problem, which can give rise to oscillatory instabilities due to the additional time scales.

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Acknowledgements

Financial support by the Deutsche Forschungsgemeinschaft in the framework of the Priority Program 1506 (grants Ec201/2 and Bo1668/6) is gratefully acknowledged. Furthermore, we thank the computing center (UniRZ) of TU Ilmenau and FZ Jülich (NIC) for access to its parallel computing resources. We are also grateful to Prof. H. Linde for numerous fruitful discussions.

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Authors and Affiliations

  1. Institute of Process Engineering and Environmental Technology, Technische Universität Dresden, Dresden, Germany

    Kerstin Eckert & Karin Schwarzenberger

  2. Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany

    Kerstin Eckert

  3. Institute of Thermodynamics and Fluid Mechanics, TU Ilmenau, Helmholtzring 1, 98684, Ilmenau, Germany

    Thomas Köllner & Thomas Boeck

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  1. Kerstin Eckert
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  2. Thomas Köllner
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  3. Karin Schwarzenberger
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  4. Thomas Boeck
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Correspondence to Kerstin Eckert .

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  1. Fachbereich Mathematik, Technische Universität Darmstadt , Darmstadt, Germany

    Dieter Bothe

  2. Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Arnold Reusken

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Eckert, K., Köllner, T., Schwarzenberger, K., Boeck, T. (2017). Complex Patterns and Elementary Structures of Solutal Marangoni Convection: Experimental and Numerical Studies. In: Bothe, D., Reusken, A. (eds) Transport Processes at Fluidic Interfaces. Advances in Mathematical Fluid Mechanics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-56602-3_16

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