| The role of rheological constitutive assumptions in the numerical simulation of non-isothermal, high-speed melt spinning was investigated in the framework of a one-dimensional model. In addition to the Newtonian model, four non-Newtonian, viscoelastic constitutive models were considered: the Larson, Marrucci, Phan-Thien and upper-convected Maxwell models. Of the viscoelastic equations, the Phan-Thien model was the only one to admit realistic steady-state solutions for a range of process conditions and the agreement with limited experimental steady-state results for poly(ethylene terephthalate) spinning can be considered adequate.; Solutions to the linearized transient equations were obtained for the Newtonian, Maxwell, and Phan-Thien models in the Fourier domain. In particular, the role of heat transfer fluctuations on the level of final filament diameter irregularities was investigated via a transfer function approach. The simulated resonant frequencies are insensitive to constitutive assumptions although the magnitude of filament area gains is highly dependent on the choice of rheological model. The Phan-Thien model predicts that viscoelasticity can have destabilizing effect on the spinline, leading to area fluctuations in excess of Newtonian predictions. The viscoelastic simulations are in qualitative and rough quantitative agreement with experimental results for non-isothermal poly(ethylene terephthalate) spinning. However, the predictions are in gross disagreement with experimental results for poly(propylene), most likely due to crystallization effects which are not included in the mathematical model. |
