  We use Onsager theory and the local density approximation to study
sedimentation-diffusion equilibrium density profiles of binary mixtures of
thick and thin hard rods. We construct stacking diagrams for three diameter
ratios, and find that even a simple spindle-shaped phase diagram with only
isotropic-nematic demixing can lead to counter-intuitive stacking sequences
such as an isotropic phase sandwiched between two nematic phases. For the most
complex phase diagram considered here, we find sixteen distinct stacking
sequences, including several with five sedimented layers. By adding
sedimentation paths to composition-pressure and density-density phase diagrams
and calculating density and composition profiles, we show that conclusions
about bulk phase diagrams of binary mixtures on the basis of
sedimentation-diffusion equilibria should be drawn warily.
