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

• Spider-capture fibers are very extensible. These fibers are decorated with liquid drops.
• We show that this is due to the presence of coils of fiber inside the drops.
• Capillary forces are responsible for the buckling and coiling of the fiber.
• We experimentally reproduce the coiling with synthetic fibers.
• We provide theoretical and numerical analysis of the experiments.

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.