(note that in the latter a [*gap*]{} rather that a [*loop*]{} is signalling the onset of the transition). A somewhat surprising feature is that, at fixed packing fraction $\eta$, the pressure decreases with increasing polydispersity [*less*]{} in the presence of adhesion rather than in its absence (i.e. for the HS case). An intuitive plausible interpretation of this feature can be found in Ref. [@Fantoni06].

The same perturbative approach allows the determination of the cloud and shadow curves for the various cases of size-dependence of $\ \tau _{ij}^{-1}$. This is reported in Figure \[fig4\] for cases II, IV (top panel) and I, V (bottom panel). In the first case the cloud and shadow lines collapse into a single curve, and this can be understood on the basis of the particular scaling properties of the free energy to this order in perturbation theory [@Fantoni06]. In all cases there is a breakdown of the perturbation theory on approaching the critical point, and this is a known general drawback of Evans’ perturbative scheme. Nevertheless, in all cases and to this order in perturbation theory, there is a tendency of the phase coexistence region to *increase* with polydispersity, in qualitative agreement with the intuitive picture 