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Stretching of viscous threads at low Reynolds numbers

Published online by Cambridge University Press:  19 August 2011

Jonathan J. Wylie ,
Huaxiong Huang  and
Robert M. Miura
Jonathan J. Wylie*
Affiliation:
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
Huaxiong Huang
Affiliation:
Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA Department Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3
Robert M. Miura
Affiliation:
Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA
*
†Email address for correspondence: mawylie@cityu.edu.hk
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Abstract

We investigate the classical problem of the extension of an axisymmetric viscous thread by a fixed applied force with small initial inertia and small initial surface tension forces. We show that inertia is fundamental in controlling the dynamics of the stretching process. Under a long-wavelength approximation, we derive leading-order asymptotic expressions for the solution of the full initial-boundary value problem for arbitrary initial shape. If inertia is completely neglected, the total extension of the thread tends to infinity as the time of pinching is approached. On the other hand, the solution exhibits pinching with finite extension for any non-zero Reynolds number. The solution also has the property that inertia eventually must become important, and pinching must occur at the pulled end. In particular, pinching cannot occur in the interior as can happen when inertia is neglected. Moreover, we derive an asymptotic expression for the extension.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface)

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 683 , 25 September 2011 , pp. 212 - 234
Copyright
Copyright © Cambridge University Press 2011

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