Sliding uphill: Using Surface Evolver to study the curvature-driven propulsion of floating films.*

Whereas a solid object will roll down an incline, capillary forces can create situations in which solids appear to move uphill. We study an initially-planar ultrathin elastic film, which propels itself up a curved meniscus into a flat interfacial region. This behavior is driven by the ability of the sheet to readily wrinkle, thereby approximating different surface topographies. In particular, previous work showed that a thin film and droplet will deform together into a three-dimensional shape that minimizes the exposed liquid surface area [1]. In our problem, gravity and surface tension must both be taken into account in an analogous geometric optimization. To understand the energies driving this propulsion, we use Surface Evolver simulations to measure the equilibrium energy when the sheet this pinned at different radial positions along the liquid bath. We investigate how these energy gradients depend on the liquid volume and sheet radius. These measurements can be linked back to the experimentally-measured velocities by estimating the drag on the sheet due to the fluid.

[1] Paulsen et al., Nat. Mater. 14 (2015).