Marangoni convection in an evaporating droplet: Analytical and numerical descriptions

TL;DR

This paper presents an analytical and numerical study of Marangoni convection in evaporating droplets, highlighting the importance of boundary conditions in modeling fluid flow within sessile drops.

Contribution

It develops an analytical approach for describing Marangoni convection that aligns well with numerical simulations, without solving Navier-Stokes equations explicitly.

Findings

Analytical model agrees with numerical results for single-vortex flows.

Boundary conditions significantly influence Marangoni convection patterns.

The approach covers a wide range of contact angles.

Abstract

The stationary single vortex Marangoni convection in an axially symmetrical sessile drop of capillary size is considered. The detailed description of the fluid flows is presented for a wide range of contact angles, which takes into account the boundary conditions and the mass balance equation, without explicitly solving the Navier--Stokes equations. The analytical approach developed is compared with the results of numerical simulations and demonstrated to describe reasonably well the single-vortex Marangoni flows. This indicates the substantial role of the boundary conditions in the problem.