Computer modeling of melt spinning from a crystallizing polymer. Part 1. The mathematical model

The model tries to allow for the essential effects occurring in the melt spinning process. The basic dynamic equations were reformulated to include heat production resulting from viscous dissipation of energy in the bulk and nonisochoric effects associated with temperature- and crystallinity-dependent variations in polymer density (eqns. 36a-36e). An additional first-order differential equation is introduced to allow for stress-induced crystallization. Crystallization affects the temperature profile and contributes a heat term in the energy balance equation. This influences significantly the theology (viscosity) of the polymer as also the momentum balance Equation and spinning dynamics. Maxwell's upper-convected model is used to allow for viscoelasticity. The effects obtained are compared with the model that assumes the occurrence of a purely Newtonian viscous fluid, The model allows for the occurrence of heating/cooling zones having various temperatures and for various air cross-blow rates. The effects discussed are illustrated with axial profiles of local velocity, temperature, tensile stress and crystallinity, all computed for melt spinning from poly(ethylene terephthalate) (PET) (Figs. 2-4, 7-9, Part II). Melt spinning from PET involving zone heating allowed to disclose a limited range of spinning speeds and zone temperatures, and also multiple solutions of the model, consequent upon coupling of stress-induced crystallization and crystallinity-controlled solidification. The range of admissible spinning speeds is governed by the temperature of the heating zone. Model computations showed zone heating to increase considerably amorphous orientation at moderate take-up speeds and to reduce appreciably the take-up stress.