The shielding effect extends the lifetimes of two-dimensional sessile droplets

Tools

Schofield, Feargus G. H. and Wray, Alexander W. and Pritchard, David and Wilson, Stephen K. (2020) The shielding effect extends the lifetimes of two-dimensional sessile droplets. Journal of Engineering Mathematics, 120 (1). pp. 89-110. ISSN 0022-0833 (https://doi.org/10.1007/s10665-019-10033-7)

[thumbnail of Schofield-etal-JEM2019-The-shielding-effect-extends-the-lifetimes-of-two-dimensional-sessile-droplets]
Preview
 Text. Filename: Schofield_etal_JEM2019_The_shielding_effect_extends_the_lifetimes_of_two_dimensional_sessile_droplets.pdf
Accepted Author Manuscript
Download (756kB)| Preview
[thumbnail of Schofield-etal-JEM2019-The-shielding-effect-extends-the-lifetimes-of-two-dimensional-sessile]
Preview
 Text. Filename: Schofield_etal_JEM2019_The_shielding_effect_extends_the_lifetimes_of_two_dimensional_sessile.pdf
Final Published Version
License: Creative Commons Attribution 4.0 logo
Download (901kB)| Preview

Abstract

We consider the diffusion-limited evaporation of thin two-dimensional sessile droplets either singly or in a pair. A conformal-mapping technique is used to calculate the vapour concentrations in the surrounding atmosphere, and thus to obtain closed-form solutions for the evolution and the lifetimes of the droplets in various modes of evaporation. These solutions demonstrate that, in contrast to in three dimensions, in large domains the lifetimes of the droplets depend logarithmically on the size of the domain, and more weakly on the mode of evaporation and the separation between the droplets. In particular, they allow us to quantify the shielding effect that the droplets have on each other, and how it extends the lifetimes of the droplets.

ORCID iDs

Schofield, Feargus G. H., Wray, Alexander W. ORCID logoORCID: https://orcid.org/0000-0002-3219-8272, Pritchard, David ORCID logoORCID: https://orcid.org/0000-0002-9235-7052 and Wilson, Stephen K. ORCID logoORCID: https://orcid.org/0000-0001-7841-9643;
CORE (COnnecting REpositories)