A smooth cascade of wrinkles at the edge of a floating elastic film

TL;DR

This paper investigates how a patterned elastic sheet floating on fluid surface transitions from bulk wrinkles to edge structures, revealing a smooth cascade of multiscale morphologies controlled by a key dimensionless parameter.

Contribution

It introduces the concept of a smooth cascade of wrinkles at the edge of a floating elastic film, contrasting with previous sharp or branched patterns, and identifies the controlling parameter.

Findings

Discovered a smooth multiscale wrinkle cascade at the sheet edge.

Identified a dimensionless parameter governing edge morphology.

Demonstrated continuous mode transition from bulk to edge structures.

Abstract

The mechanism by which a patterned state accommodates the breaking of translational symmetry by a phase boundary or a sample wall has been addressed in the context of Landau branching in type-I superconductors, refinement of magnetic domains, and compressed elastic sheets. We explore this issue by studying an ultrathin polymer sheet floating on the surface of a fluid, decorated with a pattern of parallel wrinkles. At the edge of the sheet, this corrugated profile meets the fluid meniscus. Rather than branching of wrinkles into generations of ever-smaller sharp folds, we discover a smooth cascade in which the coarse pattern in the bulk is matched to fine structure at the edge by the continuous introduction of discrete, higher wavenumber Fourier modes. The observed multiscale morphology is controlled by a dimensionless parameter that quantifies the relative strength of the edge forces and the rigidity of the bulk pattern.