  We consider the interaction of two-dimensional colloids, in nematic liquid
crystals, with walls or geometrical boundaries. The interactions between
colloidal disks and flat walls, with homeotropic boundary conditions, are
always repulsive. The repulsions may be turned into strong attractions at
structured or sculpted walls with cavities, matching closely the shape and size
of the colloids. This key-lock type of interaction is analyzed in detail for
spherocylindrical cavities of various length to breath ratios, by minimizing
the Landau-de Gennes free energy functional of the orientational order
parameter. We find that the attractions occur only for walls with cavities
within a small range of the colloidal size and for a narrow range of
orientations around the wall's symmetry axis.
