  Using a geometry-based fundamental measure density functional theory, we
calculate bulk fluid phase diagrams of colloidal mixtures of vanishingly thin
hard circular platelets and hard spheres. We find isotropic-nematic phase
separation with strong broadening of the biphasic region upon increasing the
pressure. In mixtures with large size ratio of platelet and sphere diameter,
there is also demixing between two nematic phases with differing platelet
concentrations. We formulate a fundamental-measure density functional for
mixtures of colloidal platelets and freely overlapping spheres, which represent
ideal polymers, and use it to obtain phase diagrams. We find that for low
platelet-polymer size ratio in addition to isotropic-nematic and
nematic-nematic phase coexistence, platelet-polymer mixtures also display
isotropic-isotropic demixing. In contrast, we do not find isotropic-isotropic
demixing in hard core platelet-sphere mixtures for the size ratios considered.
