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Thermal instability in drawing viscous threads

Published online by Cambridge University Press:  14 October 2021

Jonathan J. Wylie ,
Huaxiong Huang  and
Robert M. Miura
Jonathan J. Wylie
Affiliation:
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
Huaxiong Huang
Affiliation:
Department Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3
Robert M. Miura
Affiliation:
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA
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Abstract

We consider the stretching of a thin viscous thread, whose viscosity depends on temperature, that is heated by a radiative heat source. The thread is fed into an apparatus at a fixed speed and stretched by imposing a higher pulling speed at a fixed downstream location. We show that thermal effects lead to the surprising result that steady states exist for which the force required to stretch the thread can decrease when the pulling speed is increased. By considering the nature of the solutions, we show that a simple physical mechanism underlies this counterintuitive behaviour. We study the stability of steady-state solutions and show that a complicated sequence of bifurcations can arise. In particular, both oscillatory and non-oscillatory instabilities can occur in small isolated windows of the imposed pulling speed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 570 , 10 January 2007 , pp. 1 - 16
Copyright
Copyright © Cambridge University Press 2007

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