Theory of Capillary Tension and Interfacial Dynamics of Motility-Induced Phases

Abstract

The statistical mechanics of equilibrium interfaces has been well-established for over a half century. In the last decade, a wealth of observations have made increasingly clear that a new perspective is required to describe interfaces arbitrarily far from equilibrium. In this work, beginning from microscopic particle dynamics that break time-reversal symmetry, we systematically derive the interfacial dynamics of coexisting motility-induced phases. Doing so allows us to identify the athermal energy scale that excites interfacial fluctuations and the nonequilibrium surface tension that resists these excitations. Our theory identifies that, in contrast to equilibrium fluids, this active surface tension contains contributions arising from nonconservative forces which act to suppress interfacial fluctuations and, crucially, is distinct from the mechanical surface tension of Kirkwood and Buff. We find that the interfacial stiffness scales linearly with the intrinsic persistence length of the constituent active particle trajectories, in agreement with simulation data. We demonstrate that at wavelengths much larger than the persistence length, the interface obeys surface area minimizing Boltzmann statistics with our derived nonequilibrium interfacial stiffness playing an identical role to that of equilibrium systems.

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Cited by in corpus (15)

• Active phase separation: new phenomenology from non-equilibrium physics
• Hyperuniform interfaces in non-equilibrium phase coexistence
• The Mechanics of Nucleation and Growth and the Surface Tensions of Active Matter
• Phase Separation, Capillarity, and Odd Surface Flows in Chiral Active Matter
• Theory of Nonequilibrium Multicomponent Coexistence
• Interfacial and density fluctuations in a lattice model of motility-induced phase separation
• Wetting by active fluids
• Hydrodynamics of a hard-core active lattice gas
• Theory for the Anomalous Phase Behavior of Inertial Active Brownian Particles
• Conservation laws and slow dynamics determine the universality class of interfaces in active matter
• What is active wetting?
• Chemotaxis-induced phase separation
• Non-equilibrium pathways between cluster morphologies in active phase separation: necking, rupture and cavitation
• Critical Motility-Induced Phase Separation in Three Dimensions is Consistent with Ising Universality
• Active Cahn-Hilliard theory for nonequilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation