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Abstract

Liquid crystals establish a nearly unique combination of thermodynamic, hydrodynamic, and topological
behavior. This poses a challenge to their theoretical understanding and modeling. The arena where these effects
come together is the mesoscopic (micron) scale. It is then important to develop models aimed at capturing this
variety of dynamics.We have generalized the particle-based multiparticle collision dynamics (MPCD) method to
model the dynamics of nematic liquid crystals. Following the Qian-Sheng theory [Phys. Rev. E 58, 7475 (1998)]
of nematics, the spatial and temporal variations of the nematic director field and order parameter are described
by a tensor order parameter. The key idea is to assign tensorial degrees of freedom to each MPCD particle,
whose mesoscopic average is the tensor order parameter. This nematic MPCD method includes backflow effect,
velocity-orientation coupling, and thermal fluctuations. We validate the applicability of this method by testing
(i) the nematic-isotropic phase transition, (ii) the flow alignment of the director in shear and Poiseuille flows, and
(iii) the annihilation dynamics of a pair of line defects. We find excellent agreement with existing literature. We
also investigate the flow field around a force dipole in a nematic liquid crystal, which represents the leading-order
flow field around a force-free microswimmer. The anisotropy of the medium not only affects the magnitude of
velocity field around the force dipole, but can also induce hydrodynamic torques depending on the orientation
of dipole axis relative to director field. A force dipole experiences a hydrodynamic torque when the dipole axis
is tilted with respect to the far-field director. The direction of hydrodynamic torque is such that the pusher-
(or puller-) type force dipole tends to orient along (or perpendicular to) the director field. Our nematic MPCD
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.