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Abstract

An asymptotic model is derived for the competitive diffusion-limited evaporation of multiple thin sessile droplets under the assumption that the droplets are well separated. Exact solutions of the model are obtained for a pair of and for a polygonal array of identical droplets, and the model is found to perform well even outside its formal range of validity, up to and including the limit of touching droplets. The shielding effect of droplets on each other is demonstrated, and the model is used to investigate the effect of this shielding on droplet evolutions and lifetimes, as well as on the coffee-ring effect. The theoretical predictions of the model are found to be in good agreement with recent experimental results for seven relatively closely-spaced droplets, suggesting that the model could be a useful tool for studying a wide range of other droplet configurations.
Original languageEnglish
Article numberA45
Number of pages19
JournalJournal of Fluid Mechanics
Volume884
Early online date17 Dec 2019
DOIs
Publication statusE-pub ahead of print - 17 Dec 2019

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Evaporation
evaporation
shielding
Shielding
coffee
Coffee
life (durability)
rings
configurations
predictions

Keywords

  • drops and bubbles
  • capillary flows
  • interfacial flows (free surface)
  • condensation/evaporation
  • phase change

Cite this

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title = "Competitive evaporation of multiple sessile droplets",
abstract = "An asymptotic model is derived for the competitive diffusion-limited evaporation of multiple thin sessile droplets under the assumption that the droplets are well separated. Exact solutions of the model are obtained for a pair of and for a polygonal array of identical droplets, and the model is found to perform well even outside its formal range of validity, up to and including the limit of touching droplets. The shielding effect of droplets on each other is demonstrated, and the model is used to investigate the effect of this shielding on droplet evolutions and lifetimes, as well as on the coffee-ring effect. The theoretical predictions of the model are found to be in good agreement with recent experimental results for seven relatively closely-spaced droplets, suggesting that the model could be a useful tool for studying a wide range of other droplet configurations.",
keywords = "drops and bubbles, capillary flows, interfacial flows (free surface), condensation/evaporation, phase change",
author = "Wray, {Alexander W.} and Duffy, {Brian R.} and Wilson, {Stephen K.}",
year = "2019",
month = "12",
day = "17",
doi = "10.1017/jfm.2019.919",
language = "English",
volume = "884",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

TY - JOUR

T1 - Competitive evaporation of multiple sessile droplets

AU - Wray, Alexander W.

AU - Duffy, Brian R.

AU - Wilson, Stephen K.

PY - 2019/12/17

Y1 - 2019/12/17

N2 - An asymptotic model is derived for the competitive diffusion-limited evaporation of multiple thin sessile droplets under the assumption that the droplets are well separated. Exact solutions of the model are obtained for a pair of and for a polygonal array of identical droplets, and the model is found to perform well even outside its formal range of validity, up to and including the limit of touching droplets. The shielding effect of droplets on each other is demonstrated, and the model is used to investigate the effect of this shielding on droplet evolutions and lifetimes, as well as on the coffee-ring effect. The theoretical predictions of the model are found to be in good agreement with recent experimental results for seven relatively closely-spaced droplets, suggesting that the model could be a useful tool for studying a wide range of other droplet configurations.

AB - An asymptotic model is derived for the competitive diffusion-limited evaporation of multiple thin sessile droplets under the assumption that the droplets are well separated. Exact solutions of the model are obtained for a pair of and for a polygonal array of identical droplets, and the model is found to perform well even outside its formal range of validity, up to and including the limit of touching droplets. The shielding effect of droplets on each other is demonstrated, and the model is used to investigate the effect of this shielding on droplet evolutions and lifetimes, as well as on the coffee-ring effect. The theoretical predictions of the model are found to be in good agreement with recent experimental results for seven relatively closely-spaced droplets, suggesting that the model could be a useful tool for studying a wide range of other droplet configurations.

KW - drops and bubbles

KW - capillary flows

KW - interfacial flows (free surface)

KW - condensation/evaporation

KW - phase change

UR - https://www.cambridge.org/core/journals/journal-of-fluid-mechanics

U2 - 10.1017/jfm.2019.919

DO - 10.1017/jfm.2019.919

M3 - Article

VL - 884

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

M1 - A45

ER -