Two types of thin film flows: (1) Similarity solutions near corners and (2) Soap films with surfactant gradients

I will discuss two types of problems involving thin films, one for a film on a planar impermeable substrate and the other for situations involving soap films. First, I will illustrate an experimentally motivated solution of the thin-film equations that involves three independent variables. In particular, we consider a thin film draining along an edge of a vertical plate and report the three-dimensional film shape. Then, we construct an analytical solution of the PDEs involve three independent variables and show it can be reduced to a nonlinear ordinary differential equation, which can be compared with the experimental measurements. Second, for situations such as soap films we consider the thin-film equations with Marangoni effects (surface tension varies along the surface) but allowing for asymmetry, e.g., top to bottom differences. We discuss some aspects of the dynamics and show the coupling to deformation of the centerline (the film bends).