  Quasi-two-dimensional (quasi-2D) colloidal hard-sphere suspensions confined
in a slit geometry are widely used as two dimensional (2D) model systems in
experiments that probe the glassy relaxation dynamics of 2D systems. However,
the question to what extent these quasi-2D systems indeed represent 2D systems
is rarely brought up. Here, we use computer simulations that take into account
hydrodynamic interactions to show that dense quasi-2D colloidal bi-disperse
hard-sphere suspensions exhibit much more rapid diffusion and relaxation than
their 2D counterparts at the same area fraction. This difference is induced by
the additional vertical space in the quasi-2D samples in which the small
colloids can move out of the 2D plane, therefore allowing overlap between
particles in the projected trajectories. Surprisingly, this difference in the
dynamics can be accounted for if, instead of using the surface density, one
characterizes the systems by means of a suitable structural quantity related to
the radial distribution function. This implies that in the two geometries the
relevant physics for glass-formation is essentially identical. Our results
provide not only practical implications on 2D colloidal experiments but also
interesting insights into the 3D-to-2D crossover in glass-forming systems.
