Couette Flows of Liquid Crystal Polymers

Abstract

Abstract Using the BMAB theory with the Doi closure approximation and a biaxial representation of the orientation tensor, we demonstrate that the steady states of liquid crystal polymeric Couette flows between two concentric, circular cylinders in relative rotation exhibit biaxial symmetries. Therefore, two order parameters and a triad of directors must be employed to model average molecular orientation in the flow. With two directors confined to the plane orthogonal to the axis of rotation, stable steady states may exhibit flow-aligning, log-rolling and mixed flow-aligning and log-rolling behavior depending on the initial orientation between the two cylinders. The orientational pattern and the degree of orientation is sensitive to the value of the polymer concentration, the anisotropic drag coefficient and the ratio of the radius of the two cylinders. Molecules achieve higher degree of orientation at the wall of the inner cylinder than at that of the outer cylinder in the flow-aligning regime, and vice versa in the log-rolling regime.