  Liquid crystalline media mediate interactions between suspended particles and
confining geometries, which not only has potential to guide patterning and
bottom-up colloidal assembly, but can also control colloidal migration in
microfluidic devices. However, simulating such dynamics is challenging because
nemato-elasticity, diffusivity and hydrodynamic interactions must all be
accounted for within complex boundaries. We model the advection of colloids
dispersed in flowing and fluctuating nematic fluids confined within 2D wavy
channels. A lock-key mechanism between colloids and troughs is found to be
stronger for planar anchoring compared to homeotropic anchoring due to the
relative location of the colloid-associated defects. Sufficiently large
amplitudes result in stick-slip trajectories and even permanent locking of
colloids in place. These results demonstrate that wavy walls not only have
potential to direct colloids to specific docking sites but also to control
site-specific resting duration and intermittent elution.
