Evaporation of non-circular droplets

The dynamics of thin, non-circular droplets evaporating in the diffusion-limited regime is 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. As our solution for the flux fundamentally represents a novel result in potential theory, the applications are numerous, as the mixed boundary value problem arises in fields as diverse as electrostatics and contact mechanics. Here, we demonstrate the practicality of our result by considering the analytically tractable case of deposition of solute from large droplets in detail, including a matched asymptotic analysis to resolve the pressure, streamlines and deposition up to second order.

Automated summary

This study examines the dynamics of thin, non-circular droplets evaporating in the diffusion-limited regime. A novel asymptotic approach is used to solve the challenging non-rectilinear mixed boundary problem, and an asymptotic expansion for the evaporative flux from the free surface of the droplet is obtained. Despite its theoretical validity only for nearly circular droplets, it is demonstrated that this methodology can be successfully applied to droplets with various footprint shapes, including polygons and highly non-convex domains. The practicality of the solution is demonstrated by considering the analytically tractable case of solute deposition from large droplets, including a matched asymptotic analysis up to second order.