Abstract

Abstract

Highlights

  • Evaporating droplets frequently occur in nature and applications, be it a rain droplet evaporating on a leaf, a droplet on a hot surface in spray cooling, a droplet of insecticides sprayed on a leaf or an inkjet-printed ink droplet on paper

  • Neglecting the small contribution of the Stefan flow, i.e. the convective transport of vapour governed by the sudden decrease of the mass density when molecules are entering the gas phase (Carle et al 2016), which is a minor effect at temperatures sufficiently below the boiling point, the evaporation rates jα are given by the diffusive fluxes at the liquid–gas interface, i.e

  • The transition into chaotic flow still remains to be investigated in detail, but the three-dimensional numerical results of Diddens et al (2017b) show that the route to chaos happens via a breaking of the axial symmetry, to what is seen in the case of intense thermal Marangoni flow in a pure droplet (Sefiane et al 2008)

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Summary

Introduction

Evaporating droplets frequently occur in nature and applications, be it a rain droplet evaporating on a leaf, a droplet on a hot surface in spray cooling, a droplet of insecticides sprayed on a leaf or an inkjet-printed ink droplet on paper. Marangoni and Rayleigh convection in binary droplets leading to a complicated scenario of initially chaotic flow driven by the solutal Marangoni effect and followed by either thermal Marangoni flow or the typical coffee-stain flow, when the droplet consists almost only of water at the end of the drying time (Diddens et al 2017b). This has been shown in recent studies by Edwards et al (2018) and Li et al (2019a), where it has been proven that, even in small droplets with small Bond numbers, the internal flow can be decisively determined by natural convection and not by Marangoni flow These findings give rise to the following question: How does the resulting flow type in an evaporating binary droplet depend on the parameters, i.e. when is the flow dominated by the Marangoni effect and when by natural convection?. The paper ends with a conclusion and a comparison with experimental data and a linearized investigation in appendix A and appendix B, respectively

Governing equations
Numerical solution of the dynamical equations as an instructive example
Quasi-stationary approximation of the dynamical equations
Evaporation numbers
Non-dimensionalized flow
Estimation of the outwards flow
Quasi-stationary limit
Procedure
Conclusion
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