On thin evaporating drops: when is the d$^2$-law valid?

We study the evolution of a thin, axisymmetric, partially wetting drop as it evaporates. The effects of viscous dissipation, capillarity, slip, and diffusion-dominated vapour transport are taken into account. A matched-asymptotic analysis in the limit of small slip is used to derive a generalization of Tanner’s law that takes account of the effect of mass transfer. We find a criterion for when the contact-set radius close to extinction evolves as the square-root of the time remaining until extinction — the famous d 2 -law. However, for a sufficiently large rate of evaporation, our analysis predicts that a (slightly different) ‘d 13/7 -law’ is more appropriate. Our asymptotic results are validated by comparison with numerical simulations