Phase separation and nucleation in mixtures of particles with different temperatures

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.

arXiv commentPublished version, 19 pages (main text+appendix), 4 figures

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• Nonideal Reaction-Diffusion Systems: Multiple Routes to Instability
• Inclusions, Boundaries and Disorder in Scalar Active Matter
• Non-reciprocal alignment induces asymmetric clustering in active mixtures
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• Spontaneous Demixing of Binary Colloidal Flocks
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• Rectification in a mixture of active and passive particles subject to a ratchet potential
• Dynamics and steady states of a tracer particle in a confined critical fluid
• Spontaneous propulsion of an isotropic colloid in a phase-separating environment
• Towards a liquid-state theory for active matter
• Stability of flocking in the reciprocal two-species Vicsek model: Effects of relative population, motility, and noise
• Nanorheology of active-passive polymer mixtures is topology-sensitive
• Algebraic depletion interactions in two-temperature mixtures
• Species interconversion of deformable particles yields transient phase separation
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• Active Cahn-Hilliard theory for nonequilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation