Evaporation and fluid dynamics of a sessile drop of capillary size

TL;DR

This paper presents a comprehensive theoretical and numerical study of the evaporation and fluid dynamics of a capillary-sized sessile drop, highlighting the stages of Marangoni convection and vortex evolution during evaporation.

Contribution

It develops a combined model accounting for hydrodynamics, thermal conduction, and vapor diffusion, and describes the dynamic vortex behavior during evaporation.

Findings

Simulation matches experimental evaporation rates for toluene drops.

Multiple stages of vortex formation and evolution are identified.

The number of vortices decreases over time, culminating in a single vortex.

Abstract

Theoretical description and numerical simulation of an evaporating sessile drop are developed. We jointly take into account the hydrodynamics of an evaporating sessile drop, effects of the thermal conduction in the drop and the diffusion of vapor in air. A shape of the rotationally symmetric drop is determined within the quasistationary approximation. Nonstationary effects in the diffusion of the vapor are also taken into account. Simulation results agree well with the data of evaporation rate measurements for the toluene drop. Marangoni forces associated with the temperature dependence of the surface tension, generate fluid convection in the sessile drop. Our results demonstrate several dynamical stages of the convection characterized by different number of vortices in the drop. During the early stage the street of vortices arises near a surface of the drop and induces a non-monotonic spatial distribution of the temperature over the drop surface. The initial number of near-surface vortices in the drop is controlled by the Marangoni cell size which is similar to that given by Pearson for flat fluid layers. This number quickly decreases with time, resulting in three bulk vortices in the intermediate stage. The vortices finally transform into the single convection vortex in the drop, existing during about 1/2 of the evaporation time.