Curvature-driven propulsion of floating films: Part 2

The remaining pieces of breakfast cereal spontaneously clump together in a cereal bowl due to the interactions of the menisci around each particle. A highly-bendable elastic sheet participates in a very different interaction with the liquid around it. In the previous talk, experimental results were given where a polymer film spontaneously propels itself to a region that more closely matches its intrinsic curvature. These results were interpreted as falling within a geometric framework, where the sheet bends and wrinkles in such a way as to minimize the exposed liquid surface area [1]. Implementing this model is a nontrivial optimization problem, due to the wide variety of configurations available to the sheet and interface. We use Surface Evolver simulations and analytic calculations to study the energetic cost of placing an ultrathin elastic disc on a local topography of arbitrary curvature. We establish scaling laws that relate the total energy to the principal radii of curvature. By estimating the fluid drag forces, we develop theoretical predictions for sheet velocity, which we compare with our experiments. (This is part 2 of a 2-talk series).
[1] Paulsen et al., Nat. Mater. 14 (2015).