  We study the theoretical phase behavior of an asymmetric binary mixture of
hard spheres, of which the smaller component is monodisperse and the larger
component is polydisperse. The interactions are modelled in terms of the second
virial coefficient and are assumed to be additive hard sphere interactions. The
polydisperse component is subdivided into sub-components and has an average
size ten times the size of the monodisperse component. We give the set of
equations that defines the phase diagram for mixtures with more than two
components in a solvent. We calculate the theoretical liquid-liquid phase
separation boundary (the binodal), the critical point and the spinodal. We vary
the distribution of the polydisperse component in skewness, modality,
polydispersity and number of sub-components. We compare the phase behavior of
the polydisperse mixtures with binary monodisperse mixtures for the same
average size and binary monodisperse mixtures for the same effective
interaction. We find that the largest species in the larger (polydisperse)
component causes the largest shift in the position of the phase boundary,
critical point and spinodal compared to the binary monodisperse binary
mixtures. The polydisperse component also shows fractionation. The smaller
species of the polydisperse component favor the phase enriched in the smaller
component. This phase also has a higher volume fraction compared to the
monodisperse mixture.
