Conjugated liquid layers driven by the short-wavelength B\'enard-Marangoni instability: experiment and numerical simulation

TL;DR

This study investigates the coupled dynamics of two liquid layers under a temperature gradient, revealing how their interaction influences stability, pattern formation, and potential applications in surface patterning through combined experimental and numerical methods.

Contribution

It provides new insights into the stability and pattern formation of conjugated liquid layers driven by short-wavelength Bénard-Marangoni instability, supported by experimental verification and numerical modeling.

Findings

Lower critical Marangoni number due to layer coupling

Interface deformation affects temperature distribution and stability

Convection patterns can be used for surface patterning

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 (SW) B\'enard-Marangoni (BM) 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.