In this paper we present a theory describing the diffusion limited evaporation of sessilewater droplets in presence of contact angle hysteresis. Theory describes two stages ofevaporation process: (I) evaporation with a constant radius of the droplet base; and (II)evaporation with constant contact angle. During stage (I) the contact angle decreases fromstatic advancing contact angle to static receding contact angle, during stage (II) thecontact angle remains equal to the static receding contact angle. Universal dependencesare deduced for both evaporation stages. Obtained universal curves are validated againstavailable in the literature experimental data.

We present a phase field approach to wetting problems, related tothe minimization of capillary energy. We discuss in detail boththe Γ-convergence results on which our numerical algorithmare based, and numerical implementation. Two possible choices ofboundary conditions, needed to recover Young's law for the contactangle, are presented. We also consider an extension of theclassical theory of capillarity, in which the introduction of adissipation mechanism can explain and predict the hysteresis ofthe contact angle. We illustrate the performance of the model byreproducing numerically a broad spectrum of experimental results:advancing and receding drops, drops on inclined planes andsuperhydrophobic surfaces.