39,924 research outputs found
Critical phase behavior in multi-component fluid mixtures: Complete scaling analysis
We analyze the critical gas-liquid phase behavior of arbitrary fluid mixtures
in their coexistence region. We focus on the setting relevant for polydisperse
colloids, where the overall density and composition of the system are being
controlled, in addition to temperature. Our analysis uses the complete scaling
formalism and thus includes pressure mixing effects in the mapping from
thermodynamic fields to the effective fields of 3D Ising criticality. Because
of fractionation, where mixture components are distributed unevenly across
coexisting phases, the critical behavior is remarkably rich. We give scaling
laws for a number of important loci in the phase diagram. These include the
cloud and shadow curves, which characterise the onset of phase coexistence, a
more general set of curves defined by fixing the fractional volumes of the
coexisting phases to arbitrary values, and conventional coexistence curves of
the densities of coexisting phases for fixed overall density. We identify
suitable observables (distinct from the Yang-Yang anomalies discussed in the
literature) for detecting pressure mixing effects. Our analytical predictions
are checked against numerics using a set of mapping parameters fitted to
simulation data for a polydisperse Lennard-Jones fluid, allowing us to
highlight crossovers where pressure mixing becomes relevant close to the
critical point.Comment: 21 pages, 7 captioned figure
Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory
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.Comment: 20 pages; accepted for publication in Physical Chemistry Chemical
Physic
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