  We propose a hybrid lattice Boltzmann algorithm to simulate the hydrodynamics
of colloidal particles inside a liquid crystalline host. To validate our
algorithm, we study the static and the microrheology of a colloid in a nematic,
with tangential anchoring of the director field at the particle surface, and we
confirm theories and experiments showing that the drag force in a nematic is
markedly anisotropic. We then apply our method to consider the case of a
colloid inside a cholesteric, and with normal anchoring at the surface. We show
that by tuning the ratio between particle size and cholesteric pitch it is
possible to control the defect configuration around the particle, and to
stabilise novel figure-of-eight or highly twisted loops close to the colloid
surface.
