Singularities of Evaporating Droplets

Abstract

The evaporating-droplet problem of deposit-patterns and shrinking droplets has attracted a great deal of attention in the physics society. My Ph.D. dissertation studies some of these questions in the mathematical point of view. For the shrinking-droplet problem, it is proved that the singularity mechanism, that is the so-called “D-square law”, is stable under small perturbations and its shrinking surface near extinction is universally an ellipsoid. For the deposit-pattern problem, the pinning-unpinning mechanism of the contact line is studied with the introduction of suitable energies.