Modelling Elastically-Mediated Liquid-Liquid Phase Separation

TL;DR

This paper develops a continuum model for liquid-liquid phase separation in elastic networks, revealing how droplet size and density depend on the network's shear modulus, with implications for biological and synthetic systems.

Contribution

It introduces a novel continuum theory linking elastic network properties to phase separation behavior, supported by experimental validation.

Findings

Droplet size decreases as shear modulus increases, following a ~[modulus]^{-1/3} relation.

Droplet number density increases linearly with shear modulus.

Phase diagrams are provided to guide understanding and fabrication of phase-separated systems.

Abstract

We propose a continuum theory of the liquid-liquid phase separation in an elastic network where phase-separated microscopic droplets rich in one fluid component can form as an interplay of fluids mixing, droplet nucleation, network deformation, thermodynamic fluctuation, \emph{etc}. We find that the size of the phase separated droplets decreases with the shear modulus of the elastic network in the form of $\sim[\mathrm{modulus}]^{-1/3}$ and the number density of the droplet increases almost linearly with the shear modulus $\sim[\mathrm{modulus}]$, which are verified by the experimental observations. Phase diagrams in the space of (fluid constitution, mixture interaction, network modulus) are provided, which can help to understand similar phase separations in biological cells and also to guide fabrications of synthetic cells with desired phase properties.