A simplified two-dimensional model of the melt spinning of semi-crystalline hollow compound fibers

Abstract

A two-dimensional model of the melt spinning of semi-crystalline hollow compound fibers is presented. The model accounts for the orientation of the polymer molecules by means of a Doi–Edwards formulation for the molecular orientation tensor, and for the crystallization of the polymer by means of the Avrami–Kolmogorov kinetics with a modification for the flow-induced crystallization, and uses a Newtonian rheology where the dynamic viscosity is a function of the temperature, molecular orientation and degree of crystallization. The model is based on the leading-order one-dimensional equations for the fiber's geometry and axial and radial velocity components determined from an asymptotic analysis of slender fibers at low Reynolds numbers, and two-dimensional equations for the temperature, molecular orientation tensor and crystallization. It is shown that almost complete molecular orientation is achieved close to the maximum swell cross-section due to the large contraction of the fiber there, whereas, for the conditions considered here, the ultimate degree of crystallization is not achieved at the take-up cross-section. It is also shown that there are non-uniformities in the temperature and crystallinity profiles at the take-up cross-section which may have an effect on the fiber's properties.