Analytical solution for inviscid flow inside an evaporating sessile drop

TL;DR

This paper derives an exact analytical solution for the inviscid flow inside an evaporating sessile drop, accounting for various contact angles, flux distributions, and boundary conditions, enhancing understanding of evaporation dynamics.

Contribution

It provides the first exact analytical solution for inviscid flow in evaporating drops with arbitrary contact angles and flux distributions, including pinned and free contact lines.

Findings

Analytical solutions for uniform and diffusive flux cases.

Flow patterns vary with contact angle and wetting conditions.

Behavior analyzed for small and hemispherical droplets.

Abstract

Inviscid flow within an evaporating sessile drop is analyzed. The field equation, E^2(Psi)=0, is solved for the stream function. The exact analytical solution is obtained for arbitrary contact angle and distribution of evaporative flux along the free boundary. Specific results and computations are presented for evaporation corresponding to both uniform flux and purely diffusive gas phase transport into an infinite ambient. Wetting and non-wetting contact angles are considered with flow patterns in each case being illustrated. The limiting behaviors of small contact angle and droplets of hemispherical shape are treated. All of the above categories are considered for the cases of droplets whose contact lines are either pinned or free to move during evaporation.