Equivalent variational approaches to biaxial liquid crystal dynamics

Abstract

Within the framework of liquid crystal flows, the Qian and Sheng (QS) model (Qian and Sheng 1998 Phys. Rev. E. 58, 7475. (doi:10.1103/PhysRevE.58.7475)) for Q-tensor dynamics is compared with the Volovik and Kats (VK) theory (Volovik and Kats 1981 Sov. Phys. 54, 122-126) of biaxial nematics by using Hamilton's variational principle. Under the assumption of rotational dynamics for the Q-tensor, the variational principles underling the two theories are equivalent and the conservative VK theory emerges as a specialization of the QS model. Also, after presenting amicropolar variant of the VK model, Rayleigh dissipation is included in the treatment. Finally, the treatment is extended to account for nontrivial eigenvalue dynamics in the VK model and this is done by considering the effect of scaling factors in the evolution of the Q-tensor.