Multiparticle Collision Dynamics Modelling of Nematic Liquid Crystal with Variable Order Parameter

In this study we have generalized the particle-based multiparticle collision dynamics (MPC) method to model the hydrodynamics of nematic liquid crystals. We follow the tensorial formulation of nematodynamics given by the Qian-Sheng theory [Phys. Rev. E 58, 7475 (1998)]. A tensor assigned to each MPC particle represents the orientation of the nematic director, and whose average corresponds to the macroscopic tensor order parameter. The applicability of this new method is verified by performing several physical and numerical tests. We have tested: (a) the isotropic-nematic phase transition, (b) the annihilation dynamics of a pair of point defects, (c) the flow alignment of the nematic director in shear and Poiseuille flows, and (d) the velocity profile in shear and Poiseuille flows. We have found excellent agreement with existing literature. Additionally, we study the three-dimensional solutions of the Stokes equation. We describe the decay of stokeslets stresslet and rotlet flow fields in nematic liquid crystals. The present method can have far-reaching implications not only in modeling of nematic flows, but also to study the motion of colloids and microswimmers immersed in an anisotropic medium.