  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 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 new 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 toque is such that the
pusher- (or puller-) type force dipole tends to orient along (or perpendicular
to) the director field.
