  New insights into phase separation in colloidal suspensions are provided via
a new dynamical theory based on the Polydisperse Lattice-Gas model. The model
gives a simplified description of polydisperse colloids, incorporating a
hard-core repulsion combined with polydispersity in the strength of the
attraction between neighbouring particles. Our mean-field equations describe
the local concentration evolution for each of an arbitrary number of species,
and for an arbitrary overall composition of the system. We focus on the
predictions for the dynamics of colloidal gas-liquid phase separation after a
quench into the coexistence region. The critical point and the relevant
spinodal curves are determined analytically, with the latter depending only on
three moments of the overall composition. The results for the early-time
spinodal dynamics show qualitative changes as one crosses a 'quenched' spinodal
that excludes fractionation and so allows only density fluctuations at fixed
composition. This effect occurs for dense systems, in agreement with a
conjecture by Warren that, at high density, fractionation should be generically
slow because it requires inter-diffusion of particles. We verify this
conclusion by showing that the observed qualitative changes disappear when
direct particle-particle swaps are allowed in the dynamics. Finally, the rich
behaviour beyond the spinodal regime is examined, where we find that the
evaporation of gas bubbles with strongly fractionated interfaces causes
long-lived composition heterogeneities in the liquid phase; we introduce a
two-dimensional density histogram method that allows such effects to be easily
visualized for an arbitrary number of particle species.
