  This paper analytically explores a simplified model for the hydrodynamics of
nematic liquid crystal colloids. We integrate a Stokes equation for the
velocity field with a Ginzburg-Landau transported heat flow for the director
field. The study focuses on a bounded spatial domain containing periodically
distributed colloidal particles, which impose no-anchoring conditions on the
nematic liquid crystal. By progressively reducing the particle size to zero and
simultaneously increasing the number of particles, we delve into the associated
homogenisation problem. Our analysis uncovers a form of decoupling where the
velocity field asymptotically satisfies a Darcy equation, independent of the
director, while the director follows a gradient flow, unaffected by the
velocity field. One of the most intricate aspects of the homogenisation process
is the absence of an extension operator for the director field that preserves
the uniform estimates related to the system's energy. We address this challenge
with a novel variation of the Aubin-Lions lemma, specifically adapted for
homogenisation problems.
