Systematic Derivation of an Asymptotic Model for the Dynamics of Curved Viscous Fibers

In: Mathematical Methods in the Applied Sciences. 2007

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. For the numerical investigation of the viscous, gravitational and rotational effects on the fiber dynamics, a finite volume approach on a staggered grid with implicit upwind flux discretization is applied.

BibTeX

 
@Article{ Panda.Marheineke.EA07systematic, 
   title = { Systematic Derivation of an Asymptotic Model for the Dynamics of Curved Viscous Fibers }, 
   author = { S. Panda and N. Marheineke and Raimund Wegener },    
   journal = { Mathematical Methods in the Applied Sciences },             
   year = 2007, 
} 

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This publication belongs to the project Fimod.