Dynamics of Curved Viscous Fibers with Surface Tension

Technical Report, In: Berichte des Fraunhofer ITWM. Volume 115, Fraunhofer ITWM, 2007

Authors

• N. Marheineke
• Raimund Wegener

Abstract

In this paper we extend the slender body theory for the dynamics of a curved inertial viscous Newtonian fiber 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 flow 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 finite volume method with implicit flux discretization.

BibTeX

 
@TechReport{ Marheineke.Wegener07dynamics, 
   title = { Dynamics of Curved Viscous Fibers with Surface Tension }, 
   author = { N. Marheineke and Raimund Wegener },   
   booktitle = { Berichte des Fraunhofer ITWM },   
   volume = { 115 },  
   institution = { Fraunhofer ITWM },         
   year = 2007, 
} 

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This publication belongs to the project Fimod.