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

Abstract

SUMMARYThis 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.

Asymptotic Transition From Cosserat Rod to String Models for Curved Viscous Inertial Jets

“…Accounting for inner viscous transport, surface tension and placing no restrictions on either the motion or the shape of the jet's center-line, it generalizes the previously developed string models for straight [4,7,8] and curved [5,17,23] center-lines. However, the applicability of the string model is restricted to certain parameter ranges.…”

On Modeling of Curved Jets of Viscous Fluid Hitting a Moving Surface

“…The system is defined by the three dimensionless quantities and the nozzle orientation. Similar problems of the curved jets under the influence of gravity, or centrifugal and Coriolis forces but no moving surface, are described in [5,16,[18][19][20]. Various aspects of the problem addressed here have been studied in [2,12,13,17,21].…”

“…Growing interest in modeling of industrial processes (such as production of glass wool [19], high-temperature thermal isolation [1], and rotor spinning process [6], [14], [12]) requires development and study of models of a fluid jet hitting a moving surface under influence of external forces. These models are used to predict the jet shape, study jet stability, and describe the influence of the process parameters.…”

Discrete viscous threads

“…Ribe [2004] solves the non-linear boundary value problem for viscous coiling in the corotating frame, where the shape becomes stationary. Panda et al [2008] present dynamic simulations of stretched viscous filaments in a geometry where bending and twist can be neglected.…”