1{D Isothermal Spinning Models for Liquid Crystalline Polymer Fibers

A slender 1{D model for laments of liquid crystalline polymers (LCPs) is applied to simulate isothermal ber spinning of materials with internal orientation. The model and predictions focus on the hydrodynamic{orientation interactions in spinning ows, isolated from other signi cant spinline e ects of temperature, crystallization and phase changes. An important practical feature of the model is that spun ber orientation (in particular, birefringence) is deduced from rst principles along with ber diameter and velocity. A nonlinear stress{optical relation is provided by a constitutive law, which gives the ber axial stress in terms of viscous Newtonian, orientational, and capillary contributions to stress. One result of our modeling and simulations is that, in isothermal spinning, the microstructure (orientation tensor) is weakly radially dependent and can be calculated along with the free surface ber ow from 1{D models. Families of numerical steady state solutions are presented which predict the steady ber diameter, velocity and LCP orientation pro les from upstream to the take{up location in isothermal spinning. Linearized stability of these LCP spinning states is computed to reveal upper bounds on throughput in terms of the critical draw ratio, above which the process is unstable. Interestingly, enhancement of the e ects of LCP kinetic energy or relaxation can either stabilize or destabilize steady spinning solutions, depending on the relative balance of other physical e ects. Enhanced anisotropic drag (i.e., increasing the ratio of frictional resistance encountered orthogonal versus parallel to the LCP molecular axis) destabilizes spinning states: the critical draw ratio is lowered on the order of a couple percent to as much as twenty percent in cases reported here which compare isotropic to highly anisotropic friction tensors. Evidence is given for a preferred degree of upstream LCP alignment at which the critical draw ratio achieves a maximum, indicating an important role played by near-spinneret conditions in increasing throughput. 2