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.

The evaporation of sessile droplets is analysed when the influence of the thermal properties of the system is strong. We obtain asymptotic solutions for the evolution, and hence explicit expressions for the lifetimes, of droplets when the substrate has a high thermal resistance relative to the droplet and when the saturation concentration of the vapour depends strongly on temperature. In both situations we find that the lifetimes of the droplets are significantly extended relative to those when thermal effects are weak.

The effect of the thermal properties of the system on the lifetime of an evaporating sessile droplet of water is analysed using a fully coupled model which involves determining the temperature of the droplet, the substrate and the atmosphere. The evolutions, and hence the lifetimes, of droplets of water evaporating in both of the extreme modes are calculated. In particular, it is shown how the lifetimes of droplets of water can be strongly influenced by thermal effects. Droplets with larger initial contact angles or on less conductive substrates generally have longer lifetimes than those with smaller initial contact angles or on more conductive substrates, and the physical mechanism by which the thermal properties of the system influence the evaporation can be understood in terms of the thermal anchoring between the droplet and the lower surface of the substrate.

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