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

Feargus G. H. Schofield; Alexander W. Wray; David Pritchard; Stephen K. Wilson

doi:10.1007/s10665-019-10033-7

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

Feargus G. H. Schofield, Alexander W. Wray, David Pritchard, Stephen K. Wilson

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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.

Original language	English
Pages (from-to)	89-110
Number of pages	22
Journal	Journal of Engineering Mathematics
Volume	120
Issue number	1
Early online date	5 Feb 2020
DOIs	https://doi.org/10.1007/s10665-019-10033-7
Publication status	Published - 22 Feb 2020

Keywords

evaporation
two dimensional
sessile droplets
conformal mapping
finite domain
shielding effect
lifetimes

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10.1007/s10665-019-10033-7Licence: CC BY 4.0

Schofield-etal-JEM2019-The-shielding-effect-extends-the-lifetimes-of-two-dimensional-sessile-dropletsAccepted author manuscript, 739 KB
Schofield-etal-JEM2019-The-shielding-effect-extends-the-lifetimes-of-two-dimensional-sessile
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title = "The shielding effect extends the lifetimes of two-dimensional sessile droplets",

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.",

keywords = "evaporation, two dimensional, sessile droplets, conformal mapping, finite domain, shielding effect, lifetimes",

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AU - Schofield, Feargus G. H.

AU - Wray, Alexander W.

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AU - Wilson, Stephen K.

PY - 2020/2/22

Y1 - 2020/2/22

N2 - 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.

AB - 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.

KW - evaporation

KW - two dimensional

KW - sessile droplets

KW - conformal mapping

KW - finite domain

KW - shielding effect

KW - lifetimes

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JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

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