Evaporation of non-circular droplets

Wray, Alexander; Moore, Madeleine

Abstract

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.

Citation

Wray, A., & Moore, M. (2023). Evaporation of non-circular droplets. Journal of Fluid Mechanics, 961, Article A11. https://doi.org/10.1017/jfm.2023.229

• Journal Article Type: Article
• Acceptance Date: Mar 13, 2023
• Online Publication Date: Apr 17, 2023
• Publication Date: Apr 25, 2023
• Deposit Date: Apr 21, 2023
• Publicly Available Date: Apr 24, 2023
• Journal: Journal of Fluid Mechanics
• Print ISSN: 0022-1120
• Electronic ISSN: 1469-7645
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 961
• Article Number: A11
• DOI: https://doi.org/10.1017/jfm.2023.229
• Keywords: Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics; Applied Mathematics
• Public URL: https://hull-repository.worktribe.com/output/4267452