Coiling of an elastic beam inside a disk: A model for spider-capture silk

TL;DR

This paper models the buckling and spooling behavior of elastic fibers inside droplets, providing analytical and numerical insights that align well with experimental observations, relevant to spider silk and synthetic systems.

Contribution

It introduces a simplified 2D analytical model for fiber buckling in droplets and explores various equilibrium paths and their stability using numerical continuation.

Findings

Buckling threshold matches experimental data

Multiple equilibrium paths with different symmetries identified

Stability analysis of these paths conducted

Abstract

Motivated by recent experimental observations of capillary-induced spooling of fibers inside droplets both in spider capture silk and in synthetic systems, we investigate the behavior of a fiber packed in a drop. Using a simplified 2D model, we provide analytical predictions for the buckling threshold and the deep post-buckling asymptotic behavior. The threshold for spooling is found to be in particularly good agreement with experimental results. We further solve the Elastica equations for a fiber confined in a soft potential, and track the equilibrium paths using numerical continuation techniques. A wealth of different paths corresponding to different symmetries is uncovered, and their stability is finally discussed.