Phase separation in liquids with many interacting components



Immiscible liquids can be found everywhere – examples include vinaigrette and ouzo in the kitchen, multi-phase hydrocarbon-water mixtures common in oil production, and in virtually all living things. Within the living cell, thousands of biomolecules organize themselves into several coexisting liquid-like phases that enable various functions. Despite their ubiquity in nature and industry, it is still little understood how numerous interactions between components encode their macroscopic multiphase behavior. We use statistical physics approaches to show the resulting dynamic, compositional and stationary properties of coexisting phases in fluid mixtures with many randomly interacting components. Building on these findings, we demonstrate design strategies for coding linear or non-monotonic scaling relationships between the number of phases and components and propose active routes to tunably modify the multiphase coexistence.


Fluids in natural systems, such as the cytoplasm of a cell, often contain thousands of molecular species organized into several coexisting phases that enable different and specific functions. How interactions between numerous molecular species code for different emergent phases is not well understood. Here we use approaches from random matrix theory and statistical physics to describe the emergent phase behavior of fluid mixtures with many species whose interactions are randomly drawn from an underlying distribution. Through numerical simulations and stability analyzes, we show that these mixtures have step-by-step phase separation kinetics and are characterized by several coexisting phases in the steady state with different compositions. The random matrix theory predicts the number of coexisting phases, validated by simulations with different numbers of components and interaction parameters. Surprisingly, this model predicts an upper limit on the number of phases derived from dynamic considerations that is much lower than the limit from Gibbs’ phase rule obtained from thermodynamic equilibrium constraints. We design ensembles that encode either linear or non-monotonic scaling relationships between the number of components and coexisting phases, which we validate through simulation and theory. Inspired by parallels in biological systems, we finally show that the inclusion of the non-equilibrium conversion of components through chemical reactions can make the total number of coexisting phases in the steady state controllable without changing the liquid composition. Together, our study provides a model framework that describes the dynamic and stationary phase behavior of liquid-like mixtures with many interacting components.


    • Accepted October 3, 2021.
  • Authors’ contributions: KS and MPB designed research; KS did research; KS analyzed data; and KS and MPB wrote the paper.

  • The authors do not declare any competing interests.

  • This article is a PNAS direct submission. AK is a guest editor invited by the Editorial Board.

  • This article provides supporting information online at


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