Systematic derivation of an asymptotic model for the dynamics of curved viscous fibers

This 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 in terms of 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 centerline 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.