  We develop the scaled particle theory to describe the thermodynamic
properties and orientation ordering of a binary mixture of hard spheres (HS)
and hard spherocylinders (HSC) confined in a disordered porous medium. Using
this theory the analytical expressions of the free energy, the pressure and the
chemical potentials of HS and HSC have been derived. The improvement of
obtained results is considered by introducing the Carnahan-Starling-like and
Parsons-Lee-like corrections. Phase diagrams for the isotropic-nematic
transition are calculated from the bifurcation analysis of the integral
equation for the orientation singlet distribution function and from the
conditions of thermodynamic equilibrium. Both the approaches correctly predict
the isotropic-nematic transition at low concentrations of hard spheres.
However, the thermodynamic approach provides more accurate results and is able
to describe the demixing phenomena in the isotropic and nematic phases. The
effects of porous medium on the isotropic-nematic phase transition and demixing
behaviour in a binary HS/HSC mixture are discussed.
