A finite-element model for computing fluid flow inside a sessile evaporating droplet on a solid surface

TL;DR

This paper presents a finite element model to accurately simulate fluid flow within a sessile evaporating droplet on a solid surface, aligning well with analytical solutions and revealing characteristic flow patterns.

Contribution

A novel finite element approach with quadratic elements for modeling axisymmetric fluid flow in evaporating droplets, validated against analytical solutions.

Findings

Radial velocity profiles match analytical models.

Velocity contours show characteristic outward flow.

Model accurately captures flow dynamics inside droplets.

Abstract

A finite element model was developed to compute the fluid flow inside a sessile evaporating droplet on hydrophilic substrate in ambient conditions. The evaporation is assumed as quasi-steady and the flow is considered as axisymmetric with a pinned contact line. The Navier-Stokes equations in cylindrical coordinates were solved inside the droplet. Galerkin weight residual approach and velocity pressure formulation was used to discretise the governing equations. Six node triangular mesh and quadratic shape functions were used to obtain higher accuracy solutions. Radial velocity profiles in axial directions calculated by the FEM solver were compared with a existing analytical model and were found in excellent agreement. The contours of velocity magnitude and streamlines show the characteristic flow i.e. radially outward inside the evaporating droplet.