TORSIONAL EFFECTS IN HIGH-ORDER VISCOELASTIC THIN-FILAMENT MODELS

The authors present an approximation theory for thin filaments, fibers or jets which yields families of transient 1-D models (time-dependent, one-dimensional, closed systems of PDEs). The spatial reduction from three dimensions to one is achieved by axisymmetry together with a local expansion in the radial jet coordinate; this reduction is in contrast to the predominant viscoelastic models in the literature which average out the radial dimension and thereby require moment equations for the computation of higher order corrections. The authors also allow torsional how effects, which are usually ignored, in a general Johnson-Segalman constitutive law. A formal perturbation theory, based on a slenderness parameter and a compatible velocity-pressure-stress ansatz, is then constructed for the full 3-D free surface boundary problem. This formalism contains all 1-D transient models that govern slender axisymmetric flows of inviscid, viscous, or viscoelastic fluids; specific models follow by positing the dominant balance of physical effects within this framework. The authors' previous applied papers based on this theory have analyzed various torsionless models. In this paper, they select a strongly elastic, torsional example in order to study the behavior of solutions through three orders in the perturbation expansion, illustrating passive as well as strongly destabilizing torsional coupling.