Slender Body Theory for the Dynamics of Curved Viscous Fibers

Technical Report, Berichte des Fraunhofer ITWM, Nr. 86, 2006

Authors

• S. Panda
• N. Marheineke
• Raimund Wegener

Abstract

The paper presents a slender body theory for the dynamics of a curved inertial viscous Newtonian fiber. Neglecting surface tension and temperature dependence, the fiber flow 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 fiber center-line with the inner viscous transport. The physically reasonable form of the one-dimensional fiber model results thereby from the introduction of the intrinsic velocity that characterizes the convective terms.This work deals with the modeling and simulation of the dynamics of a curved inertial viscous Newtonian fiber. Neglecting surface tension and temperature dependence, the fiber flow is modeled as a 3D free boundary value problem (BVP) via instationary incompressible Navier-Stokes equations (NSE). From regular asymptotic expansions in powers of the slenderness parameter leading-order balance laws for mass and momentum are derived that combine the unrestricted motion of the fiber center-line with the inner viscous transport. The form of the 1D fiber model results from the introduction of the intrinsic velocity characterizing the convective terms. For the numerical simulations of the fiber evolution a finite volume approach is applied.

BibTeX

 
@TechReport{ Panda.Marheineke.EA06slender, 
   title = { Slender Body Theory for the Dynamics of Curved Viscous Fibers }, 
   author = { S. Panda and N. Marheineke and Raimund Wegener },     
   series = { Berichte des Fraunhofer ITWM, Nr. 86 },            
   year = 2006, 
} 

---

This publication belongs to the project Fimod.