  We provide an exact mapping between the density functional of a binary
mixture and that of the effective one-component fluid in the limit of infinite
asymmetry. The fluid of parallel hard cubes is thus mapped onto that of
parallel adhesive hard cubes. Its phase behaviour reveals that demixing of a
very asymmetric mixture can only occur between a solvent-rich fluid and a
permeated large particle solid or between two large particle solids with
different packing fractions. Comparing with hard spheres mixtures we conclude
that the phase behaviour of very asymmetric hard-particle mixtures can be
determined from that of the large component interacting via an adhesive-like
potential.
