Competing Marangoni and Rayleigh convection in evaporating binary droplets

TL;DR

This paper develops a quasi-stationary model to predict the interaction of Marangoni and Rayleigh convection in evaporating binary droplets, highlighting the role of gravity-driven natural convection even in small droplets.

Contribution

It introduces a validated phase diagram model that predicts flow regimes in binary droplets based on Rayleigh and Marangoni numbers, considering gravity effects.

Findings

Gravity can dominate convection in small droplets.

The model accurately predicts flow interactions.

Flow regimes depend on Rayleigh and Marangoni numbers.

Abstract

For a small sessile or pendant droplet it is generally assumed that gravity does not play any role once the Bond number is small. This is even assumed for evaporating binary sessile or pendant droplets, in which convective flows can be driven due to selective evaporation of one component and the resulting concentration and thus surface tension differences at the air-liquid interface. However, recent studies have shown that in such droplets gravity indeed can play a role and that natural convection can be the dominant driving mechanism for the flow inside evaporating binary droplets (Edwards et al., Phys. Rev. Lett. 121, 184501 (2018); Li et al., Phys. Rev. Lett. 122, 114501 (2019)). In this study, we derive and validate a quasi-stationary model for the flow inside evaporating binary sessile and pendant droplets, which successfully allows to predict the prevalence and the intriguing interaction of Rayleigh and/or Marangoni convection on the basis of a phase diagram for the flow field expressed in terms of the Rayleigh and Marangoni numbers.