Phase separation and nucleation in mixtures of particles with different temperatures

TL;DR

This paper develops a theoretical framework for phase separation in mixtures of particles at different temperatures, revealing effective equilibrium behavior in dilute limits and non-equilibrium effects at higher concentrations.

Contribution

It introduces a non-equilibrium model of particle mixtures with temperature differences and connects phase separation kinetics to classical thermodynamics and Cahn-Hilliard theory.

Findings

Effective equilibrium thermodynamics in dilute limit

Asymmetric phase diagrams due to activity differences

Scaling laws for interfacial properties and droplet dynamics

Abstract

Differences in activities in colloidal particles are sufficient to drive phase separation between active and passive (or less active) particles, even if they have only excluded volume interactions. In this paper, we study the phase separation kinetics and propose a theory of phase separation of colloidal mixtures in the diffusive limit. Our model considers a mixture of diffusing particles coupled to different thermostats, it thus has a non-equilibrium nature due to the temperature differences. However, we show that indeed the system recovers an effective equilibrium thermodynamics in the dilute limit. We obtain phase diagrams showing the asymmetry in concentrations due to activity differences. By using a more general approach, we show the equivalence of phase separation kinetics with the well known Cahn-Hilliard theory. On the other hand, higher order expansions in concentration indicate the emergence of non-equilibrium effects leading to a breakdown of the equilibrium analogy. We lay out the general theory in terms of accessible parameters which we demonstrate by several applications. In this simple formalism, we capture a positive surface tension for hard spheres}, and interesting scaling laws for interfacial properties, droplet growth dynamics, and phase segregation conditions. \rev{Several of our results are in agreement with existing numerical simulations while we also propose testable predictions.