Modeling unsteady B\'enard-Marangoni instabilities in drying volatile droplets on a heated substrate

TL;DR

This paper presents three-dimensional numerical simulations of unsteady Bénard-Marangoni instabilities in evaporating volatile droplets on heated substrates, revealing complex flow patterns and instability behaviors.

Contribution

It introduces a comprehensive numerical model accounting for vapor diffusion, thermal conduction, and radiation, advancing understanding of internal flow instabilities in evaporating droplets.

Findings

Identification of nonstationary Bénard-Marangoni instability behavior.

Observation of flower-shaped BM cell structures near the triple line.

Dependence of cell growth and distribution on contact angle.

Abstract

We study unsteady internal flows in a sessile droplet of capillary size evaporating in constant contact line mode on a heated substrate. Three-dimensional simulations of internal flows in evaporating droplets of ethanol and silicone oil have been carried out. For describing the Marangoni flows we find it necessary to account for the diffusion of vapor in air, the thermal conduction in all three phases and thermal radiation. The equations have been solved numerically by finite element method using ANSYS Fluent. As a result of the simulations, the nonstationary behavior of B\'enard-Marangoni (BM) instabilities is obtained. At the first stage, a flower structure of BM cells near the triple line emerge. For smaller contact angles, the cells grow in size and occupy the central region of the droplet surface. Being closely connected with recent experimental and theoretical studies, the results obtained help to analyze and resolve the associated issues.