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Thin viscous fluid threads falling onto a moving belt behave in a wayreminiscent of a sewing machine, generating a rich variety of periodicstitch-like patterns including meanders, W-patterns, alternating loops, andtranslated coiling. These patterns form to accommodate the difference betweenthe belt speed and the terminal velocity at which the falling thread strikesthe belt. Using direct numerical simulations, we show that inertia is notrequired to produce the aforementioned patterns. We introduce a quasi-staticgeometrical model which captures the patterns, consisting of three coupled ODEsfor the radial deflection, the orientation and the curvature of the path of thethread's contact point with the belt. The geometrical model reproduces well theobserved patterns and the order in which they appear as a function of the fallheight.

Liquid ropes: a geometrical model for thin viscous jets instabilities