Liquid ropes: a geometrical model for thin viscous jets instabilities

TL;DR

This paper introduces a geometrical model for thin viscous jets that explains complex stitch-like patterns formed when fluid threads fall onto a moving belt, without requiring inertia, using coupled ODEs to predict pattern formation.

Contribution

The paper presents a novel quasi-static geometrical model with coupled ODEs that accurately reproduces observed patterns in viscous jet instabilities, independent of inertia.

Findings

The model captures various stitch-like patterns observed experimentally.

Patterns depend on fall height and belt speed.

Inertia is not necessary for pattern formation.

Abstract

Thin viscous fluid threads falling onto a moving belt behave in a way reminiscent of a sewing machine, generating a rich variety of periodic stitch-like patterns including meanders, W-patterns, alternating loops, and translated coiling. These patterns form to accommodate the difference between the belt speed and the terminal velocity at which the falling thread strikes the belt. Using direct numerical simulations, we show that inertia is not required to produce the aforementioned patterns. We introduce a quasi-static geometrical model which captures the patterns, consisting of three coupled ODEs for the radial deflection, the orientation and the curvature of the path of the thread's contact point with the belt. The geometrical model reproduces well the observed patterns and the order in which they appear as a function of the fall height.