| Fiber spinning is an industrial process by which polymer fibers are manufactured for composites, textiles, and structural reinforcing. Economical operation of fiber spinlines demands techniques for maximizing production rate while controlling the properties of the final product, techniques that have historically been developed through experiments. However, modern analyses have yielded process models that augment empirical studies and allow accurate process design. This dissertation develops and extends analytical and computational models for non-isothermal fiber spinning.; The essential problem of process modeling is to predict properties of the spun fiber, given process conditions and characteristics of the polymer melt. Since many important properties depend on molecular orientation, and since orientation is in turn a strong function of stress at solidification, the problem becomes one of predicting stress in the fiber during manufacture, especially near solidification.; It is shown that the variation of temperature across the filament radius is a leading-order effect in fiber spinning, and that the temperature in a rigid fiber is approximately quadratic across the radius. Consequently, an assumed quadratic form for temperature with coefficients that depend on local heat transfer conditions matches the exact solution well for a rigid fiber. The assumed form is used to develop a thermomechanical model for a filament, consisting of integro-differential equations containing integrals of nonlinear functions involving temperature. Numerical solutions of the model show strong thermomechanical coupling, with the finite thermal conductivity of the polymer resulting in significant radial dependence of temperature and stress. The new model is then extended to accommodate a solidification surface that, as a result of the radial variation in temperature, is not flat across the fiber radius. The dependence of solidification temperature on stress is accounted for, and parameter studies are conducted.; Finally, the temperature dependence of viscosity is investigated and the Williams-Landel-Ferry (WLF) formula is used in place of the customary Arrhenius equation to model viscosity at temperatures near glass transition. Conditions for joining the Arrhenius and WLF equations are suggested, and the effects on the spinline of parameters in the combination Arrhenius-WLF viscosity model are studied. |
