  We analyse a binary mixture of colloidal parallel hard cylindrical particles
with identical diameters but dissimilar lengths $L_1$ and $L_2$, with
$s=L_2/L_1=3$, confined by two parallel hard walls in a planar slit-pore
geometry, using a fundamental--measure density functional theory. This model
presents nematic (N) and two types of smectic (S) phases, with first- and
second-order N-S bulk transitions and S-S demixing, and surface behaviour at a
single hard wall which includes complete wetting by the S phase mediated (or
not) by an infinite number of surface-induced layering (SIL) transitions. In
the present paper the effects of confinement on this model colloidal fluid
mixture are studied. Confinement brings about profound changes in the phase
diagram, resulting from competition between the three relevant length scales:
pore width $h$, smectic period $d$ and length ratio $s$. Four main effects are
identified: (i) Second-order bulk N-S transitions are suppressed. (ii) Demixing
transitions are weakly affected, with small shifts in the $\mu_1-\mu_2$
(chemical potentials) plane. (iii) Confinement-induced layering (CIL)
transitions occurring in the two confined one-component fluids in some cases
merge with the demixing transition. (iv) Surface-induced layering (SIL)
transitions occurring at a single surface as coexistence conditions are
approached are also shifted in the confined fluid. Trends with pore size are
analysed by means of complete $\mu_1-\mu_2$ and $p-\bar{x}$ (pressure-mean pore
composition) phase diagrams for particular values of pore size. This work,
which is the first one to address the behaviour of liquid-crystalline mixtures
under confinement, could be relevant as a first step to understand
self-assembling properties of mixtures of metallic nanoparticles under external
fields in restricted geometry.
