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

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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 languageEnglish
Pages (from-to)89-110
Number of pages22
JournalJournal of Engineering Mathematics
Issue number1
Early online date5 Feb 2020
Publication statusPublished - 22 Feb 2020


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


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