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.
Highlights
The evaporation of sessile droplets has been studied extensively in recent years [1]
As we did in the one-droplet problem, in order to validate the solution obtained in Section 3.1, we solved the two-droplet problem in the semi-circular domain using COMSOL Multiphysics [50]
We considered the diffusion-limited evaporation of thin twodimensional sessile droplets either singly or in a pair
Summary
The evaporation of sessile droplets has been studied extensively in recent years [1]. We present the governing equations (Section 2.1), show that the most apparently natural problem does not have a solution (Section 2.2), and show that by considering a suitably relaxed boundary condition we can obtain a physically acceptable solution via a conformal-mapping technique (Section 2.3). We validate this solution against numerical simulations (Section 2.4), and use it to obtain closed-form solutions for the evolution and lifetimes of the droplet in various modes of evaporation (Section 2.5). We develop asymptotic expressions for these lifetimes (Section 3.3.3), and use these expressions to compare the lifetimes of a single droplet and a pair of droplets in dimensional terms (Section 4)
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