Numerical Simulation of Smectic C Liquid Crystalline Flow between Parallel Plates

Numerical simulation of smectic C liquid crystalline flows between parallel plates has been performed using the continuum theory proposed by Leslie et al. We have evaluated a set of viscous and elastic coefficients in the theory with resort to equations proposed by Osipov et al. and Carlsson et al. and to a director tilt angle of a smectic liquid crystal (TBBA). Two possible cases of smectic layer arrangements are considered in this simulation. When the layer normal vector is parallel to the velocity gradient direction, the c-director orients to the shear flow direction, and orientation boundary layers are formed close to the walls at high Ericksen numbers. The velocity profile between parallel plates is almost linear. When the layer normal vector is parallel to the vorticity direction, the c-director takes aligning or tumbling behaviors, depending on the ratio of magnitude of two viscosities, A2 and A5. For the tumbling situation, the c-director orientation angle at the middle plane is a step-like discontinuous function of Er, that is similar to the tumbling behavior of nematic liquid crystals.