The stability of slowly evaporating thin liquid films of binary mixtures

TL;DR

This paper investigates the stability of thin binary liquid films during evaporation, considering thermocapillarity, solutocapillarity, and van der Waals forces, revealing two primary instability modes through analysis and simulations.

Contribution

It derives coupled evolution equations for binary film stability and identifies two distinct instability modes influenced by volatility and Marangoni effects.

Findings

Identifies monotonic and oscillatory instability modes.

Shows how volatility and Marangoni effects influence instability.

Provides nonlinear dynamics insights through simulations.

Abstract

We consider the evaporation of a thin liquid layer which consists of a binary mixture of volatile liquids. The mixture is on top of a heated substrate and in contact with the gas phase that consists of the same vapour as the binary mixture. The effect of thermocapillarity, solutocapillarity and the van der Waals interactions are considered. We derive the long-wave evolution equations for the free interface and the volume fraction that govern the two-dimensional stability of the layer subject to the above coupled mechanisms and perform a linear stability analysis. Our results demonstrate two modes of instabilities, a monotonic instability mode and an oscillatory instability mode. We supplement our results from stability analysis with transient simulations to examine the dynamics in the nonlinear regime and analyse how these instabilities evolve with time. More precisely we discuss how the effect of relative volatility along with the competition between thermal and solutal Marangoni effect defines the mode of instability that develops during the evaporation of the liquid layer due to preferential evaporation of one of the components.