Dynamics of a disc in a nematic liquid crystal

We use lattice Boltzmann simulations to study the dynamics of a disc immersed in a nematic liquid crystal. In the absence of external torques, discs with homeotropic anchoring align with their surface normal parallel to the director of the nematic liquid crystal. In the presence of a weak magnetic field a ferromagnetic disc will rotate to equilibrate the elastic torque due to the distortion of the nematic director and the magnetic torque. When the magnetic field rotates the disc so that the angle theta between normal to the surface of the disc (a) over cap and director of the liquid crystal (n) over cap (n) over cap becomes greater than pi/2, the disc flips around the axis perpendicular to the rotation axis so that a (a) over cap sweeps through pi radians. An analysis of this behaviour was performed. In particular, we look at the impact of the disc thickness and edges on defect creation and the flipping transition. We also analyse the importance of backflow.