Computer modeling of melt spinning from a crystallizing polymer.
Part I. The mathematical model
Polimery 2001, No 5, 335
SummaryThe 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 rheology (viscosity) of the polymer as also the momenturn balance equation and spinning dynamics. Maxwell's upper-convected model is used to allow for viscoelasticity. The effects obtained are comparad 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 als o multiple solutions of the model, consequent up on 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 moderato take-up speeds and to reduce appreciably the take-up stress.
Keywords: melt spinning, mathematical model of melt spinning, computer modeling, extensional flow, Newtonian fluid, Maxwell fluid, molecular orientation, nonisothermal crystallization, oriented crystallization, melt spinning from poly(ethylene terephthalate)