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Extensional flows with viscous heating

Published online by Cambridge University Press:  04 January 2007

JONATHAN J. WYLIE  and
HUAXIONG HUANG
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, CanadaM3J 1P3
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Abstract

In this paper we investigate the role played by viscous heating in extensional flows of viscous threads with temperature-dependent viscosity. We show that there exists an interesting interplay between the effects of viscous heating, which accelerates thinning, and inertia, which prevents pinch-off. We first consider steady drawing of a thread that is fed through a fixed aperture at given speed and pulled with a constant force at a fixed downstream location. For pulling forces above a critical value, we show that inertialess solutions cannot exist and inertia is crucial in controlling the dynamics. We also consider the unsteady stretching of a thread that is fixed at one end and pulled with a constant force at the other end. In contrast to the case in which inertia is neglected, the thread will always pinch at the end where the force is applied. Our results show that viscous heating can have a profound effect on the final shape and total extension at pinching.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 571 , 25 January 2007 , pp. 359 - 370
Copyright
Copyright © Cambridge University Press 2007

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