Fractionation of polydisperse systems: multi-phase coexistence

TL;DR

This paper develops a theoretical framework using small-variable expansion to accurately predict phase coexistence and component partitioning in multi-phase polydisperse systems, with an explicit solution for hard spheres.

Contribution

It introduces a universal, controlled scheme for calculating phase equilibria in multi-component polydisperse mixtures, extending to many components and providing explicit solutions for specific cases.

Findings

Derived universal relations for component partitioning

Applicable to mixtures with many slightly-polydisperse components

Provided an explicit solution for hard sphere systems

Abstract

The width of the distribution of species in a polydisperse system is employed in a small-variable expansion, to obtain a well-controlled and compact scheme by which to calculate phase equilibria in multi-phase systems. General and universal relations are derived, which determine the partitioning of the fluid components among the phases. The analysis applies to mixtures of arbitrarily many slightly-polydisperse components. An explicit solution is approximated for hard spheres.