| Cholesteric liquid crystals(CLC) are mesophases, where the average direction of molecular orientation exhibits a chiral (twisted) pattern along its normal direction. In the past, the rheological and flow properties of CLC have been studied scarcely. This is due to the natural tendency of a cholesteric to favor its characteric, twisted configuration, which naturally leads to more complex arrangements of the optic axis than in pure nematics and complicated spatial structures. In this dissertation, we address the issues related to rheology and flow induced structures in CLC and nematic polymers, with emphasis on the role of the anisotropic elasticities.; In the first part of this dissertation, we study the permeation flow problem using a mesoscopic theory obtained from the kinetic theory for Cholesteric liquid crystal polymers and resolve the inconsistency issue in the literature. Then we give a systematic study on steady structures and transient behavior in flows of nematic polymers.; In the second part of this dissertation, we develop a hydrodynamic theory for flows of CLCPs following the continuum mechanics formulation of McMillan's second order tensor theory for liquid crystals and study phase transition in chiral nematic liquid crystals as well as the rheological behaviors and the flow properties of CLCPs. |