Measuring local volume fraction, long-wavelength correlations and fractionation in a phase-separating polydisperse fluid

TL;DR

This paper introduces a novel method to measure local volume fraction and correlations in a phase-separating polydisperse fluid, revealing early and intricate fractionation effects during spinodal decomposition.

Contribution

It presents a new coarse-grained Voronoi technique and correlation functions to analyze fractionation without phase distinction, applicable to various types of polydispersity.

Findings

Fractionation occurs early in phase separation.

Different interaction potentials lead to opposite fractionation directions.

The methods can be applied to experimental and simulated systems.

Abstract

We dynamically simulate fractionation (partitioning of particle species) during spinodal gas-liquid separation of a size-polydisperse colloid, using polydispersity up to ~40% and a skewed parent size distribution. We introduce a novel coarse-grained Voronoi method to minimise size bias in measuring local volume fraction, along with a variety of spatial correlation functions which detect fractionation without requiring a clear distinction between the phases. These can be applied whether or not a system is phase separated, to determine structural correlations in particle size, and generalise easily to other kinds of polydispersity (charge, shape, etc.). We measure fractionation in both mean size and polydispersity between the phases, its direction differing between model interaction potentials which are identical in the monodisperse case. These qualitative features are predicted by a perturbative theory requiring only a monodisperse reference as input. The results show that intricate fractionation takes place almost from the start of phase separation, so can play a role even in nonequilibrium arrested states. The methods for characterisation of inhomogeneous polydisperse systems could in principle be applied to experiment as well as modelling.