  Specialized Monte Carlo simulations and the moment free energy (MFE) method
are employed to study liquid-gas phase equilibria in size-disperse fluids. The
investigation is made subject to the constraint of fixed polydispersity, i.e.
the form of the `parent' density distribution $\rho^0(\sigma)$ of the particle
diameters $\sigma$, is prescribed. This is the experimentally realistic
scenario for e.g. colloidal dispersions. The simulations are used to obtain the
cloud and shadow curve properties of a Lennard-Jones fluid having diameters
distributed according to a Schulz form with a large (40%) degree of
polydispersity. Good qualitative accord is found with the results from a MFE
method study of a corresponding van der Waals model that incorporates
size-dispersity both in the hard core reference and the attractive parts of the
free energy. The results show that polydispersity engenders considerable
broadening of the coexistence region between the cloud curves. The principal
effect of fractionation in this region is a common overall scaling of the
particle sizes and typical inter-particle distances, and we discuss why this
effect is rather specific to systems with Schulz diameter distributions. Next,
by studying a family of such systems with distributions of various widths, we
estimate the dependence of the critical point parameters on $\delta$. In
contrast to a previous theoretical prediction, size-dispersity is found to
raise the critical temperature above its monodisperse value. Unusually for a
polydisperse system, the critical point is found to lie at or very close to the
extremum of the coexistence region in all cases. We outline an argument showing
that such behaviour will occur whenever size polydispersity affects only the
range, rather than the strength of the inter-particle interactions.
