ABSTRACT:A comparison is made of the predictions of one-dimensional mathematical model simulations of dry spinning based on Newtonian and viscoelastic constitutive equations for the spin dope. The viscoelastic model is based upon a modified Giesekus constitutive equation with a temperature and composition-dependent relaxation time. The simulation algorithm includes the effects of the glass transition on the expected solution viscosity and relaxation time behavior along the spinline. Predictions of axial velocity, tensile stress, and composition profiles for the two cases suggest the role of viscoelasticity in the locking-in behavior associated with fiber solidification along the spinline. The effects of model parameters and processing conditions are also discussed.
Part I: Model Development and PredictionsThis paper addresses the development and application of a two-dimensional, three component model for the dry spinning process of polymer fibers. The model presented is an expansion of a previously developed two-component dry spinning model [1] that incorporated both viscous and viscoelastic effects in the constitutive equation for the spin fluid, along with two-dimensional effects to account for radial variations in the fiber temperature and composition profiles along the spin line. The model presented in this paper includes the effects of water in the spin dope through incorporation of the diffusion equations for ternary mass transfer. Mass and energy balances on the gas side are also taken into account so that the effects of ambient conditions can be investigated. Calculations are based on the system: cellulose acetate-acetone-water. Results are presented for profiles of solvent concentration, temperature, and glass transition temperature profiles for typical industrial operating conditions. Force and stress distributions in the fiber at various points along the spinline, analyzed in terms of contributions from the viscoelastic and viscous terms in the constitutive equation, illustrate the role of these stresses in the freezing in of structure along the spinline. Model predictions are shown to be in good agreement with the principal characteristics of dry spinning.
In this work, predictions based on the 2D dry spinning model developed in Part I of this work [2] along with a die swell subroutine supplied by an industrial company, are used to compare with fiber concentration and elongation to break data from an industrial spinline. Die swell ratio predictions agree well with measured values and solidification along the spinline is shown to be due to homogeneous glass transition in the absence of phase separation. Concentration profiles along the spinline are well fit by the model using previously determined prefactors for the diffusion coefficients. A good correlation of elongation at break data is found to occur with a characteristic variable r GTP , the ratio of the rheological force of the viscoelastic Giesekus contribution to the total rheological force (Giesekus + viscous) at the glass transition point. Moreover, the regression obtained from this fit can be further used to make predictions for elongation at break under different operating conditions. Finally, the effects of spinning conditions and model parameters on fiber mechanical properties were investigated.
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