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 stress singularity at the contact line is regularized using slip and we perform a matched-asymptotic analysis in the limit of small slip. A generalization of Tanner's law to account for the effect of mass transfer is derived and the behaviour of the drop close to extinction is analysed. 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 `$d^{13/7}$-law' should be more appropriate. Our asymptotic results are validated by comparison with numerical simulations.