  We study the effects of size polydispersity on the gas-liquid phase behaviour
of mixtures of sticky hard spheres. To achieve this, the system of coupled
quadratic equations for the contact values of the partial cavity functions of
the Percus-Yevick solution is solved within a perturbation expansion in the
polydispersity, i.e. the normalized width of the size distribution. This allows
us to make predictions for various thermodynamic quantities which can be tested
against numerical simulations and experiments. In particular, we determine the
leading-order effects of size polydispersity on the cloud curve delimiting the
region of two-phase coexistence and on the associated shadow curve; we also
study the extent of size fractionation between the coexisting phases. Different
choices for the size-dependence of the adhesion strengths are examined
carefully; the Asakura-Oosawa model of a mixture of polydisperse colloids and
small polymers is studied as a specific example.
