Computer simulation of flow and molecular orientation in liquid crystal polymers

The Ericksen-Leslie equations of motion for nematic liquid crystals are used to study the flow behaviour of nematic liquid crystal polymers. It is recogized that liquid crystal polymers are very viscous, and therefore the terms in governing equations which account for the director elasticity are neglected in comparison with the viscous terms. The resulting Ericksen anisotropic fluid equations are identical to those of Doi in the weak velocity gradient limit. The equations are solved using an ADI finite-difference technique, in geometries chosen to model the gross features of polymer processing equipment. The orthogonal mapping technique is used to map the irregularly shaped physical domains on a unit square computational domain. The results show that the molecular orientation is a strong function of the flow geometry. In particular, it is found that even a smal divergence in the channel profile causes the molecules to orient nearly perpendicular to the flow direction. Also, no stable orientation may exist in a channel of strongly varying shape, even a converging one.