Dynamics of curved viscous fibers with surface tension

  • In this paper we extend the slender body theory for the dynamics of a curved inertial viscous Newtonian fiber [23] by the inclusion of surface tension in the systematic asymptotic framework and the deduction of boundary conditions for the free fiber end, as it occurs in rotational spinning processes of glass fibers. The fiber ow is described by a three-dimensional free boundary value problem in terms of instationary incompressible Navier-Stokes equations under the neglect of temperature dependence. From standard regular expansion techniques in powers of the slenderness parameter we derive asymptotically leading-order balance laws for mass and momentum combining the inner viscous transport with unrestricted motion and shape of the fiber center-line which becomes important in the practical application. For the numerical investigation of the effects due to surface tension, viscosity, gravity and rotation on the fiber behavior we apply a fnite volume method with implicit flux discretization.

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Metadaten
Author:N. Marheineke, R. Wegener
URN (permanent link):urn:nbn:de:hbz:386-kluedo-15370
Serie (Series number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (115)
Document Type:Report
Language of publication:English
Year of Completion:2007
Year of Publication:2007
Publishing Institute:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Tag:Slender body theory ; curved viscous fibers with surface tension ; free boundary value problem
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:510 Mathematik

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