Numerical Simulation of Nematic Liquid Crystalline Flows Around a Circular Cylinder

Numerical solutions to the full set of partial differential equations for the Leslie-Ericksen theory are obtained for steady flows of non-tumbling nematic liquid crystals around a circular cylinder with an infinite axial length. The streamline pattern for fixed director orientation, which has been presented by Heuer et al., differs from our results, which are obtained without approximations. An upstream displacement of the streamlines is observed for small Ericksen numbers. This streamline displacement is shifted to the downstream region with increasing the Ericksen number because the effect of fluid inertia becomes large. The distinctive director orientation profile is predicted in the downstream region of a circular cylinder when the Ericksen number is large. Flow kinematics such as streamline pattern and director orientation profile change greatly between the Ericksen number of 10 and 50 for a planar anchoring configuration. For a homeotropic anchoring configuration, on the other hand, the effect of Ericksen number is suppressed in the present calculation. The orientation angle of the director relative to the streamline along the specific streamline explains successfully the relationship between director orientation and streamline patterns.