Packing of elastic wires in flexible shells

TL;DR

This study explores how elastic wires pack into flexible shells, revealing that friction and shell elasticity significantly influence packing patterns, leading to ordered or disordered structures depending on friction levels.

Contribution

It introduces the first analysis of elastic wire packing in flexible shells, highlighting the role of friction and elasticity in determining packing morphologies and phase transitions.

Findings

Low friction leads to ordered toroidal packing.

High friction results in disordered hierarchic structures.

A continuous phase transition separates the two packing regimes.

Abstract

The packing problem of long thin filaments that are injected into confined spaces is of fundamental interest for physicists and biologists alike. How linear threads pack and coil is well known only for the ideal case of rigid containers, though. Here, we force long elastic rods into flexible spatial confinement borne by an elastic shell to examine under which conditions recently acquired knowledge on wire packing in rigid spheres breaks down. We find that unlike in rigid cavities, friction plays a key role by giving rise to the emergence of two distinct packing patterns. At low friction, the wire densely coils into an ordered toroidal bundle with semi-ellipsoidal cross-section, while at high friction, it packs into a highly disordered, hierarchic structure. These two morphologies are shown to be separated by a continuous phase transition. Our findings demonstrate the dramatic impact of friction and confinement elasticity on filamentous packing and might drive future research on such systems in physics, biology and even medical technology toward including these mutually interacting effects.