  Colloidal particles suspended in liquid crystals can exhibit various
effective anisotropic interactions that can be tuned and utilized in
self-assembly processes. We simulate a two-dimensional system of hard disks
suspended in a solution of dense hard needles as a model system for colloids
suspended in a nematic lyotropic liquid crystal. The novel event-chain Monte
Carlo technique enables us to directly measure colloidal interactions in a
microscopic simulation with explicit liquid crystal particles in the dense
nematic phase. We find a directional short-range attraction for disks along the
director, which triggers chaining parallel to the director and seemingly
contradicts the standard liquid crystal field theory result of a quadrupolar
attraction with a preferred ${45^{\circ}}$ angle. Our results can be explained
by a short-range density-dependent depletion interaction, which has been
neglected so far. Directionality and strength of the depletion interaction are
caused by the weak planar anchoring of hard rods. The depletion attraction
robustly dominates over the quadrupolar elastic attraction if disks come close.
Self-assembly of many disks proceeds via intermediate chaining, which
demonstrates that in lyotropic liquid crystal colloids depletion interactions
play an important role in structure formation processes.
