Phase separation in complex mixtures with many components: analytical expressions for spinodal manifolds

TL;DR

This paper derives analytical expressions for spinodal and critical manifolds in complex mixtures with many components, facilitating the prediction of phase separation behavior in various scientific fields.

Contribution

It introduces a new analytical method to calculate spinodal and critical manifolds in high-dimensional component systems, simplifying complex stability analyses.

Findings

Derived explicit formulas for spinodal manifolds in N-dimensional systems.

Presented a numerical approach using linear programming for evaluation.

Provided insights into phase behavior relevant to polymers, food science, and cell biology.

Abstract

The phase behavior is investigated for systems composed of a large number of macromolecular components N, with N greater or equal to 2. Liquid-liquid phase separation is modelled using a virial expansion up to the second order of the concentrations of the components. Formal analytical expressions for the spinodal manifolds in N dimensions are derived that simplify their calculation (by transforming the original problem into inequalities that can be evaluated numerically using linear programming techniques). In addition, a new expression is obtained to calculate the critical manifold and the composition of the co-existing phases. The present analytical procedure complements previous attempts to handle spinodal decomposition for many components using a statistical approach based on Random Matrix Theory. The results are relevant for predicting effects of polydispersity on phase behavior in fields like polymer or food science, and to liquid-liquid phase separation in the cytosol of living cells.