Speaker: Will Feldman, University of Utah
Abstract: I will discuss some simplified models for the shape of liquid droplets on rough solid surfaces. These are elliptic free boundary problems with oscillatory coefficients. I will talk about the large-scale effects of small-scale surface roughness, e.g., contact line pinning, hysteresis, and formation of flat parts (facets) in the contact line, and how to understand these by homogenization theory. I will also mention a connection with the continuum scaling limit of an abelian sandpile-type model and some results in that setting.