  We study theoretically the effect of a gravitational field on the equilibrium
behaviour of a colloidal suspension of rods with different length-to-width
aspect ratios. The bulk phases of the system are described with analytical
equations of state. The gravitational field is then incorporated via
sedimentation path theory, which assumes a local equilibrium condition at each
altitude of the sample. The bulk phenomenology is significantly enriched by the
presence of the gravitational field. In a suspension of elongated rods with
five stable phases in bulk, the gravitational field stabilizes up to fifteen
different stacking sequences. The sample height has a non-trivial effect on the
stable stacking sequence. New layers of distinct bulk phases appear either at
the top, at the bottom, or simultaneously at the top and the bottom when
increasing the sample height at constant colloidal concentration. We also study
sedimentation in a mass-polydisperse suspension in which all rods have the same
shape but different buoyant masses.
