Elastocapillary self-folding: buckling, wrinkling and collapse of floating filaments

TL;DR

This paper investigates the self-buckling instability of floating flexible filaments caused by capillary forces, providing analytical models and exploring complex folding behaviors and long-term dynamics.

Contribution

It introduces an analytical framework for elastocapillary instability, linking capillary and bending stresses, and characterizes the resulting complex filament configurations.

Findings

Analytical formulas match numerical simulations.

Filament configurations include loops, needles, and racquets.

Long filaments undergo cascading self-folding events.

Abstract

When a flexible filament is confined to a fluid interface, the balance between capillary attraction, bending resistance, and tension from an external source can lead to a self-buckling instability. We perform an analysis of this instability and provide analytical formulae that compare favorably with the results of detailed numerical computations. The stability and long-time dynamics of the filament are governed by a single dimensionless elastocapillary number quantifying the ratio between capillary to bending stresses. Complex, folded filament configurations such as loops, needles, and racquet shapes may be reached at longer times, and long filaments can undergo a cascade of self-folding events.