Computational analytical approach to shear-extensional flow in fiber spinning of liquid crystalline polymer melt

A continuum theory of constitutive equation of co-rotational derivative type was developed for anisotropic viscoelastic fluid—liquid crystalline(LC) polymer. The theory was specialized to a constitutive equation of co-rotational type LCP-H model and LCP-Qs model. Using the constitutive equation of LCP-Qs model, the shear-extensional flow was studied for the extrusion process near the die exit of the fiber spinning of liquid crystalline polymer melt. Bifurcation of extensional viscosity was observed in the case without orientation and the two cases when the directors were parallel to flow and vertical to flow for the LC polymer melts. The extensional viscosity increases when the director rotates from the flow direction to that vertical to flow. Based on the LCP-Qs model a computational analytical theory was developed for extrusion process of LC polymer melt, contraction of the extrudate was predicted by the theory. The computational symbolic manipulation such as computer software Maple was used for the problem solution. An important conclusion can be drawn that the director tumbling has remarkable influence on extensional viscosity but no principal one on LC polymer melt extrusion.