Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Applied Mathematics

Supervisor(s)

Colin Denniston

Abstract

In this thesis, a new way of simulating a two-way coupling between a liquid crystal and an immersed object is proposed. It can be used for objects of various geometries and can be expanded to be used for an object of any geometry. Additionally, a simple yet effective model was suggested for calculations of transmitted light through a nematic liquid crystal sample. This model allowed us to clarify the behavior of a ferromagnetic disc in a nematic liquid crystal observed in experiments and incorrectly interpreted at that time.

Our simulations have demonstrated the following: in the absence of external forces and torques, discs with homeotropic (perpendicular) 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 between normal to the surface of the disc and director of the liquid crystal becomes greater than 90 degrees, the disc flips around the axis perpendicular to the rotation axis, thus resolving the distortion in the liquid crystal. An analysis of this behavior was performed in Chapter 3. In particular, we look at the impact of the disc thickness, and conditions on the edges of the object, on defect creation and the flipping transition. We also analyze the importance of backflow (i.e. coupling of tensor order parameter with velocity field). We also study the same system under the action of fast rotating weak magnetic fields, that demonstrates a different behavior: the disc avoids flipping via creation of two symmetric defects on the sides.

Some results on disc pairs are presented in Chapter 4. Interactions between discs, their motion and final position strongly depend on the distance between them, and the magnitude and angular velocity of the rotating magnetic field. Depending on the initial configuration of the system, different stable structures of discs result.