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Conjugated liquid layers driven by the short-wavelength Bénard–Marangoni instability: experiment and numerical simulation

Published online by Cambridge University Press:  13 October 2015

Iman Nejati ,
Mathias Dietzel  and
Steffen Hardt
Iman Nejati
Affiliation:
Institute for Nano- and Microfluidics, Center of Smart Interfaces, TU Darmstadt, Alarich-Weiss-Strasse 10, 64287 Darmstadt, Germany
Mathias Dietzel*
Affiliation:
Institute for Nano- and Microfluidics, Center of Smart Interfaces, TU Darmstadt, Alarich-Weiss-Strasse 10, 64287 Darmstadt, Germany
Steffen Hardt
Affiliation:
Institute for Nano- and Microfluidics, Center of Smart Interfaces, TU Darmstadt, Alarich-Weiss-Strasse 10, 64287 Darmstadt, Germany
*
†Email address for correspondence: [email protected]
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Abstract

The coupled dynamics of two conjugated liquid layers of disparate thicknesses, which coat a solid substrate and are subjected to a transverse temperature gradient, is investigated. The upper liquid layer evolves under the short-wavelength Bénard–Marangoni instability, whereas the lower, much thinner film undergoes a shear-driven long-wavelength deformation. Although the lubricating film should reduce the viscous stresses acting on the up to one hundred times thicker upper layer by only 10 %, it is found that the critical Marangoni number of marginal stability may be as low as if a stress-free boundary condition were applied at the bottom of the upper layer, i.e. much lower than the classical value of 79.6 known for a single film. Furthermore, it is experimentally verified that the deformation of the liquid–liquid interface, albeit small, has a non-negligible effect on the temperature distribution along the liquid–gas interface of the upper layer. This stabilizes the hexagonal pattern symmetry towards external disturbances and indicates a two-way coupling of the different layers. The experiments also demonstrate how convection patterns formed in a liquid film can be used to pattern a second conjugated film. The experimental findings are verified by a numerical model of the coupled layers.

JFM classification

Convection: Marangoni convection Nonlinear Dynamical Systems: Pattern formation Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 783 , 25 November 2015 , pp. 46 - 71
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Copyright
© 2015 Cambridge University Press 

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