Numerical analysis of Cosserat rod and string models for viscous jets in rotational spinning processes

  • The rotational spinning of viscous jets is of interest in many industrial applications, including pellet manufacturing [4, 14, 19, 20] and drawing, tapering and spinning of glass and polymer fibers [8, 12, 13], see also [15, 21] and references within. In [12] an asymptotic model for the dynamics of curved viscous inertial fiber jets emerging from a rotating orifice under surface tension and gravity was deduced from the three-dimensional free boundary value problem given by the incompressible Navier-Stokes equations for a Newtonian fluid. In the terminology of [1], it is a string model consisting of balance equations for mass and linear momentum. Accounting for inner viscous transport, surface tension and placing no restrictions on either the motion or the shape of the jet’s center-line, it generalizes the previously developed string models for straight [3, 5, 6] and curved center-lines [4, 13, 19]. Moreover, the numerical results investigating the effects of viscosity, surface tension, gravity and rotation on the jet behavior coincide well with the experiments of Wong [20].

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Author:W. Arne, N. Marheineke, A. Meister, R. Wegener
Serie (Series number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (167)
Document Type:Report
Language of publication:English
Year of Completion:2009
Year of Publication:2009
Publishing Institute:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Creating Corporation:Fraunhofer ITWM
Date of the Publication (Server):2009/10/16
GND-Keyword:Rotational spinning process; curved viscous fibers; asymptotic Cosserat models
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011