Modeling of dry spinning of polymer fibers

A two-dimensional mathematical model has been developed for dry spinning of polymer fibers. Among the transport equations, a set of diffusion equations have been derived for ternary systems which explicitly express the solvent evaporation velocities for both components (acetone and water for acetate fiber spinning case). Phenomenological diffusion coefficients were estimated from empirical correlations for binary diffusion coefficients by fitting to residual solvent data. Mass and energy balances were also taken into consideration on the gas side. A novel viscoelastic constitutive model has been developed based on a simple entanglement network theory, which consists of a viscoelastic Giesekus component and a viscous Newtonian component in parallel mechanically. The two are linked through dependencies of the relaxation times on solvent evaporation. The Giesekus term is used to describe the rheological behaviors of the entanglement network segments as elastic dumbbells with modifications to consider their nonlinearity. The viscous term is employed to account for the rapid increase of stiffness of the entire entanglement network. The internal switch between these two terms is controlled by a relaxation time ratio beta which further depends on the solvent concentration changes. General simulation results of solvent concentrations, temperature, glass transition temperature, force distributions, stress contributions from Giesekus and viscous terms, and conformation tensor, as well as segment orientation, are discussed. Model predictions are in good agreement with the principal characteristics of dry spinning. A flash vaporization model for binary systems has also been proposed.;The developed two-dimensional dry spinning model together with a die swell subroutine supplied by an industrial company has been used to generate predictions, which were compared to experimental data. Based on the analysis of the predictions and comparisons, we learn that phase separation cannot occur during dry spinning because the solvent concentration path does not cross over the binodal curve; instead, it passes into the homogeneous glass transition region. Model predictions were compared with concentration data for different DPF (denier per fiber) fibers and fairly good agreement is acquired by tuning the prefactors in the phenomenological diffusion coefficients. It is also suggested that more systematic diffusion coefficient measurements are needed. (Abstract shortened by UMI.).