## Slender Body Theory for the Dynamics of Curved Viscous Fibers

### Slender Body Theory for the Dynamics of Curved Viscous Fibers

• The paper at hand presents a slender body theory for the dynamics of a curved inertial viscous Newtonian ber. Neglecting surface tension and temperature dependence, the ber ow is modeled as a three-dimensional free boundary value problem via instationary incompressible Navier-Stokes equations. From regular asymptotic expansions in powers of the slenderness parameter leading-order balance laws for mass (cross-section) and momentum are derived that combine the unrestricted motion of the ber center-line with the inner viscous transport. The physically reasonable form of the one-dimensional ber model results thereby from the introduction of the intrinsic velocity that characterizes the convective terms.
• The paper at hand presents a slender body theory for the dynamics of a curved inertial viscous Newtonian ber. Neglecting surface tension and temperature dependence, the ber ow is modeled as a three-dimensional free boundary value problem via instationary incompressible Navier-Stokes equations. From regular asymptotic expansions in powers of the slenderness parameter leading-order balance laws for mass (cross-section) and momentum are derived that combine the unrestricted motion of the ber center-line with the inner viscous transport. The physically reasonable form of the one-dimensional ber model results thereby from the introduction of the intrinsic velocity that characterizes the convective terms.

Author: S. Panda, R. Wegener, N. Marheineke urn:nbn:de:hbz:386-kluedo-14153 Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (86) Report German 2006 2006 Fraunhofer-Institut für Techno- und Wirtschaftsmathematik 2006/03/08 Asymptotic expansions; Curved viscous fibers; Fluid dynamics; Free boundary value problem; Navier-Stokes equations; Slender body theory Fraunhofer (ITWM) 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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