Numerical Study through Finite Differences of the Ill-Posed-Initial Conditions in the Classical Melt Spinning Model

Abstract

The non isothermal melt spinning process at low take up velocities is composed of three distinctive zones of major interest for research. One is associated with the 1-D flow in the extrusion capillary. The second one starting at the capillary end is designated swelling zone, and presents a 2-D flow where the filament relaxes before entering the 2-D spinning flow (the third zone). Here, elongational deformations predominate before the solidified filament is taken at the spinneret end. The purpose of the present work is to analyze numerically within the structure of the classical melt spinning model the relevance of the unknown axial position after the swelling zone, where initial conditions of the non isothermal spinning flow are imposed. This aspect constitutes an ill-posed problem that must be analyzed carefully in relation to the useful numerical results obtained along the
spinning length relatively far from the swelling zone. In this context of analysis, our results provide a new insight of this problem and also show that an additional physical constraint may lead one to place appropriate initial conditions for computational purposes. This constraint is based on the consideration of the rheometric and process elongational viscosity curves. The Phan-Thien and Tanner viscoelastic
constitutive equation is used here to illustrate main results and conclusions of the present work.