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Forms and Patterns of Viscous and Elastic Threads

Presented by: 
Neil Ribe CNRS (Centre national de la recherche scientifique), Université Paris-Sud 11, CNRS (Centre national de la recherche scientifique)
Date: 
Tuesday 26th September 2017 - 11:00 to 12:00
Venue: 
INI Seminar Room 2
Abstract: 
Some of the most beautiful and easy-to-produce instabilities in fluid mechanics
are those that occur when a thin stream of viscous fluid like honey falls steadily
from a certain height onto a solid surface. In addition to the familiar 'liquid rope
coiling' effect, one can observe periodic folding with or without rotation of the
folding plane; periodic collapse and rebuilding of the hollow cylinder formed by a
primary coiling instability; and 'liquid supercoiling', in which the cylinder as a
whole undergoes steady secondary folding and rotation. Using a combination of
laboratory experiments, analytical theory, and numerical simulation, I and my
colleagues have determined a phase diagram for these states in the space of
dimensionless fall height and flow rate, and have identified the dimensionless
parameter that controls which state or states are observed under given
conditions. We have also studied pattern formation in the closely related 'fluid
mechanical sewing machine’ (FMSM), wherein a viscous thread falling onto a
moving belt generates a wealth of complicated 'stitch' patterns including
meanders, alternating loops, and doubly periodic patterns. We have determined
experimentally and numerically the phase diagram for these patterns in the
space of dimensionless fall height and belt speed, and have formulated a simple
reduced (three degrees of freedom) model that successfully predicts the patterns
in the limit of negligible inertia. In closing, I shall compare the observed FMSM
patterns with those of the ‘elastic sewing machine’ in which a normal elastic
thread falls onto a moving belt.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons