Marangoni instability triggered by selective evaporation of a binary liquid inside a Hele-Shaw cell

TL;DR

This study investigates Marangoni instability caused by selective evaporation of ethanol-water in a Hele-Shaw cell, combining experiments, simulations, and stability analysis to understand the onset and evolution of surface-tension-driven convection.

Contribution

It provides a comprehensive analysis of Marangoni instability due to selective evaporation, integrating experimental observations, numerical simulations, and stability theory.

Findings

Experimental visualization of convective cell growth.

Numerical simulations align with experimental data.

Identification of a critical Marangoni number for stability.

Abstract

Interfacial stability is important for many processes involving heat and mass transfer across two immiscible phases. When this transfer takes place in the form of evaporation of a binary solution with one component being more volatile than the other, gradients in surface tension can arise. These gradients can ultimately destabilise the liquid-gas interface. In the present work, we study the evaporation of an ethanol-water solution, for which ethanol has a larger volatility. The solution is contained in a horizontal Hele-Shaw cell which is open from one end to allow for evaporation into air. A Marangoni instability is then triggered at the liquid-air interface. We study the temporal evolution of this instability by observing the effects that it has on the bulk of the liquid. More specifically, the growth of convective cells is visualized with confocal microscopy and the velocity field close to the interface is measured with micro-particle-image-velocimetry. The results of numerical simulations based on quasi 2D equations satisfactorily compare with the experimental observations, even without consideration of evaporative cooling, although this cooling can play an extra role in experiments. Furthermore, a linear stability analysis applied to a simplified version of the quasi 2D equations showed reasonably good agreement with the results from simulations at early times, when the instability has just been triggered and no coarsening has taken place. In particular, we find a critical Marangoni number below which a regime of stability is predicted.