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Asymptotic model for the dynamics of curved viscous fibres with surface tension

Published online by Cambridge University Press:  10 March 2009

NICOLE MARHEINEKE  and
RAIMUND WEGENER
NICOLE MARHEINEKE*
Affiliation:
Technische Universität Kaiserslautern, Fachbereich Mathematik, Germany
RAIMUND WEGENER
Affiliation:
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik, Kaiserslautern, Germany
*
†Email address for correspondence: nicole@mathematik.uni-kl.de
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Abstract

In this paper, we derive and investigate an asymptotic model for the dynamics of curved viscous inertial Newtonian fibres subjected to surface tension, as they occur in rotational spinning processes. Accordingly, we extend the slender body theory of Panda, Marheineke & Wegener (Math. Meth. Appl. Sci., vol. 31, 2008, p. 1153) by including surface tension and deducing boundary conditions for the free end of the fibre. The asymptotic model accounts for the inner viscous transport and places no restrictions on either the motion or the shape of the fibre centreline. Depending on the capillary number, the boundary conditions yield an explicit description for the temporal evolution of the fibre end. We study numerically the behaviour of the fibre as a function of the effects of viscosity, gravity, rotation and surface tension.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 622 , 10 March 2009 , pp. 345 - 369
Copyright
Copyright © Cambridge University Press 2009

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