Pattern formation in coiling of falling viscous threads: Revisiting the geometric model

TL;DR

This study revisits the geometric model of viscous fluid coiling, experimentally exploring pattern formation, discovering new patterns, and identifying deviations from the model that suggest additional dynamics.

Contribution

The paper provides new experimental data on pattern formation in viscous thread coiling and compares it with the geometric model, revealing previously unreported patterns and deviations.

Findings

Explicitly shows the W pattern in the regime diagram.

Reports the first observation of a period-doubled W pattern.

Identifies deviations between the model predictions and experimental results.

Abstract

The "Fluid Mechanic Sewing Machine" creates periodic patterns through the coiling nature of a viscous fluid falling onto a moving surface. At relatively moderate heights, the reported patterns are translating coiling, alternating loops, W pattern, and meander. A simplified theoretical model based on the geometry and local bending of the contact point can predict these patterns. We experimentally explore the patterns in this region by collecting new data to compare with the model. Our review of the model's bifurcation diagram reveals additional patterns beyond the ones reported, although current experiments have not shown their existence. The W pattern, previously omitted in a regime diagram because of its small region, is now shown explicitly. We report on the consistent appearance of a period-doubled version of the W pattern, as well as rare appearances of resonant patterns, both reported for the first time. Comparing the theoretical model to experimental data, we find that the predicted phase diagram and the meander variation deviate from observations. These deviations hint at an unaccounted dynamics that merits further study.