title: Liquid ropes: a geometrical model for thin viscous jet instabilities.
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 stitchlike 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 quasistatic geometrical model which captures the patterns, consisting of three coupled ordinary differential equations 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 belt speed.
authors.affiliation: CNRS and UPMC Université Paris 06, UMR 7190, Institut Jean le Rond d'Alembert, Paris 75005, France.|Laboratoire FAST, Université Paris-Sud, CNRS, Bâtiment 502, Campus Universitaire, Orsay 91405, France.|Laboratory of Fluid Mechanics and Instabilities, EPFL, CH1015 Lausanne, Switzerland.|Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: P-T
authors.initials: PT
authors.lastname: Brun
authors.affiliation: CNRS and UPMC Université Paris 06, UMR 7190, Institut Jean le Rond d'Alembert, Paris 75005, France.
authors.forename: Basile
authors.initials: B
authors.lastname: Audoly
authors.affiliation: Laboratoire FAST, Université Paris-Sud, CNRS, Bâtiment 502, Campus Universitaire, Orsay 91405, France.
authors.forename: Neil M
authors.initials: NM
authors.lastname: Ribe
authors.affiliation: Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
authors.forename: T S
authors.initials: TS
authors.lastname: Eaves
authors.affiliation: Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
authors.forename: John R
authors.initials: JR
authors.lastname: Lister