Inwon Kim (UCLA):

Title: Capillary Drops on Rough Surface

In the first lecture, we will discuss the problem of a liquid droplet resting on a solid surface, described with the interfacial free energy. We will discuss existing literature on both equilibrium drops and dynamic models. The main challenge arises due to possible singularities at the ``contact line", where the droplet boundary meets the surface.
 
In the second lecture, we will discuss the problem of determining the minimal energy shape of a liquid droplet resting on a rough solid surface. The shape of a liquid drop on a solid is strongly affected by the micro-structure of the surface on which it rests, where the surface inhomogeneity arises either by chemical composition or by roughness. Various physical models, the Cassie-Baxter or Wenzel Laws can be given rigorous sense via homogenization theory.  This is joint work with William Feldman.