Shapes of a filament on the surface of a bubble

TL;DR

This study investigates how elastic filaments adopt various shapes on spherical bubbles, influenced by geometry, elasticity, and gravity, revealing a bifurcation from geodesic to latitudinal configurations and coiling behavior.

Contribution

It combines experiments, theoretical analysis, and numerical modeling to characterize the morphological phase-space of filaments on spherical surfaces, highlighting the transition mechanisms.

Findings

Filaments transition from geodesic to latitudinal shapes as gravity increases.

A simple arc-based model captures the shape transition effectively.

Numerical energy minimization aligns well with experimental observations.

Abstract

The shape assumed by a slender elastic structure is a function both of the geometry of the space in which it exists and the forces it experiences. We explore by experiments and theoretical analysis, the morphological phase-space of a filament confined to the surface of a spherical bubble. The morphology is controlled by varying bending stiffness and weight of the filament, and its length relative to the bubble radius. When the dominant considerations are geometry of confinement and elastic energy, the filament lies along a geodesic and when gravitational energy becomes significant, a bifurcation occurs, with a part of the filament occupying a longitude and the rest along a curve approximated by a latitude. Far beyond the transition, when the filament is much longer than the diameter, it coils around the selected latitudinal region. A simple model with filament shape as a composite of two arcs captures the transition well and for better quantitative agreement with the subcritical nature of bifurcation, we study the morphology by numerical energy minimization. Our analysis of filament's morphological space spanned by a geometric parameter, and one that compares elastic energy with body forces, may provide guidance for packing slender structures on complex surfaces.