Self-similar draining near a vertical edge

When a liquid film drains on a vertical plate, the film becomes nonuniform near the vertical edge. Here we experimentally report the three-dimensional (3D) self-similar shape of this film. Based on the well-known 2D self-similar solution of a draining film far from the edge, we identify a new 3D self-similar scaling, which converts the PDE for the film thickness with three independent variables into an ODE. Interferometry is performed to measure the film thickness as a function of position and time, and the results are in excellent agreement with the theoretical predictions.