Evaporation of non-circular droplets

TL;DR

This paper develops a novel asymptotic method to analyze the evaporation dynamics of non-circular droplets, providing analytical insights into flux, pressure, and solute deposition for complex shapes.

Contribution

It introduces a new asymptotic approach for non-rectilinear evaporation problems, applicable to various droplet shapes including polygons and non-convex domains.

Findings

Validated the method for a wide range of shapes.

Derived analytical expressions for evaporative flux and solute deposition.

Extended the analysis to second-order accuracy for pressure and flow fields.

Abstract

The dynamics of thin, non-circular droplets evaporating in the diffusion-limited regime are examined. The challenging non-rectilinear mixed-boundary problem this poses is solved using a novel asymptotic approach and an asymptotic expansion for the evaporative flux from the free surface of the droplet is found. While theoretically valid only for droplets that are close to circular, it is demonstrated that the methodology can successfully be applied to droplets with a wide variety of footprint shapes, including polygons and highly non-convex domains. While the applications of this are numerous, the analytically-tractable case of deposition of solute from large droplets is examined in detail, including a matched asymptotic analysis to resolve the pressure, streamlines and deposition up to second order.