Pressure and Phase Equilibria in Interacting Active Brownian Spheres

Abstract

We derive from first principles the mechanical pressure $P$, defined as the force per unit area on a bounding wall, in a system of spherical, overdamped, active Brownian particles at density $\rho$. Our exact result relates $P$, in closed form, to bulk correlators and shows that (i) $P(\rho )$ is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to $P$, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; (iii) $P(\rho )$ is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles, and show that the densities at coexistence do not satisfy a Maxwell construction on $P$.

arXiv comment6p (main text) + 4p (SI)

References in corpus (29)

• Self-motile colloidal particles: from directed propulsion to random walk
• Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles
• Athermal Phase Separation of Self-Propelled Particles with no Alignment
• Emergence of macroscopic directed motion in populations of motile colloids
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Long-lived Giant Number Fluctuations in a Swarming Granular Nematic
• Dynamic clustering in active colloidal suspensions with chemical signaling
• Collective Motion of Vibrated Polar Disks
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• Langevin Equation for the Density of a System of Interacting Langevin Processes
• Diffusive transport without detailed balance in motile bacteria: Does microbiology need statistical physics?
• A continuum theory of phase separation kinetics for active Brownian particles
• Phase behaviour of active Brownian particles: The role of dimensionality
• Scalar ${\varphi }^4$ field theory for active-particle phase separation
• Hydrodynamics determines collective motion and phase behavior of active colloids
• The effective temperature
• Pattern formation in self-propelled particles with density-dependent motility
• Effective Cahn-Hilliard equation for the phase separation of active Brownian particles
• Freezing and phase separation of self-propelled disks
• Towards a 'Thermodynamics' of Active Matter
• Cooperative Motion of Active Brownian Spheres in Three-Dimensional Dense Suspensions
• Spontaneous symmetry breaking in active droplets provides a generic route to motility
• Nonequilibrium equation of state in suspensions of active colloids
• Effects of Non-local Stress on the Determination of Shear Banding Flow
• Tunable long range forces mediated by self-propelled colloidal hard spheres
• Hydrodynamic suppression of phase separation in active suspensions
• Anomalous Thermomechanical Properties of a Self-propelled Colloidal Fluid
• Osmosis in a minimal model system
• Osmosis with active solutes

Cited by in corpus (215)

• Active Particles in Complex and Crowded Environments
• How far from equilibrium is active matter?
• Pressure is not a state function for generic active fluids
• The 2019 Motile Active Matter Roadmap
• Emergent behavior in active colloids
• Full phase diagram of active Brownian disks: from melting to motility-induced phase separation
• Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study
• Statistical Mechanics of Active Ornstein Uhlenbeck Particles
• The statistical physics of active matter: from self-catalytic colloids to living cells
• Inertial effects of self-propelled particles: from active Brownian to active Langevin motion
• Classical dynamical density functional theory: from fundamentals to applications
• Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
• Spontaneous velocity alignment in Motility-induced Phase Separation
• Multidimensional Stationary Probability Distribution for Interacting Active Particles
• Dynamics of a self-propelled particle in a harmonic trap
• Negative interfacial tension in phase-separated active suspensions
• Generalized Thermodynamics of Phase Equilibria in Scalar Active Matter
• Active particles with soft and curved walls: Equation of state, ratchets, and instabilities
• Minimal model of active colloids highlights the role of mechanical interactions in controlling the emergent behavior of active matter
• Generalized thermodynamics of Motility-Induced Phase Separation: Phase equilibria, Laplace pressure, and change of ensembles
• Virial pressure in systems of active Brownian particles
• An active approach to colloidal self-assembly
• Thermodynamic phases in two-dimensional active matter
• Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles
• Conformational properties of active semiflexible polymers
• Towards a statistical mechanical theory of active fluids
• Glassy dynamics of athermal self-propelled particles: Computer simulations and a nonequilibrium microscopic theory
• Stochastic thermodynamics for active matter
• Critical behavior of active Brownian particles
• The nonequilibrium glassy dynamics of self-propelled particles
• Non-reciprocity across scales in active mixtures
• Active Model H: Scalar Active Matter in a Momentum-Conserving Fluid
• Facilitation of polymer looping and giant polymer diffusivity in crowded solutions of active particles
• Active vs. Passive Hard Disks Against a Membrane : Mechanical Pressure and Instability
• A classical nucleation theory description of active colloid assembly
• Ideal bulk pressure of active Brownian particles
• Swim pressure on walls with curves and corners
• Self-Organized Critical Coexistence Phase in Repulsive Active Particles
• Shape and Displacement Fluctuations in Soft Vesicles Filled by Active Particles
• Freezing a Flock: Motility-Induced Phase Separation in Polar Active Liquids
• Generic long-range interactions between passive bodies in an active fluid
• On the distribution and swim pressure of run-and-tumble particles in confinement
• Nonequilibrium dynamics of mixtures of active and passive colloidal particles
• Chemical potential in active systems: predicting phase equilibrium from bulk equations of state?
• Mode-Coupling Theory for Active Brownian Particles
• Mechanical pressure and momentum conservation in dry active matter
• Microscopic Origins of the Swim Pressure and the Anomalous Surface Tension of Active Matter
• Phase co-existence in bidimensional passive and active dumbbell systems
• Confined run-and-tumble swimmers in one dimension
• Morphology of clusters of attractive dry and wet self-propelled spherical particle suspensions
• Steady-state distributions of ideal active Brownian particles under confinement and forcing
• Active colloids in the context of chemical kinetics
• Applicability of Effective Pair Potentials for Active Brownian Particles
• Destabilization of a flow focused suspension of magnetotactic bacteria
• Physics of muscle contraction
• Mechanical Theory of Nonequilibrium Coexistence and Motility-Induced Phase Separation
• Thermodynamic cycles with active matter
• Phase behavior of active Brownian disks, spheres, and dumbbells
• Linear response theory and Green-Kubo relations for active matter
• Non-Equilibrium Surface Tension of the Vapour-Liquid Interface of Active Lennard-Jones Particles
• Noether's Theorem in Statistical Mechanics
• Entropy production fluctuations encode collective behavior in active matter
• The Parental Active Model: a unifying stochastic description of self-propulsion
• Active Brownian particles at interfaces: An effective equilibrium approach
• Phase coexistence of active Brownian particles
• Sedimentation of self-propelled Janus colloids: polarization and pressure
• Pressure of a gas of underdamped active dumbbells
• Collective forces in scalar active matter
• Dissipation controls transport and phase transitions in active fluids: Mobility, diffusion and biased ensembles
• Kinetics of motility-induced phase separation and swim pressure
• Shape Transformations of Vesicles induced by Swim Pressure
• Interparticle torques suppress motility-induced phase separation for rodlike particles
• Thermodynamics of active field theories: Energetic cost of coupling to reservoirs
• Contact enhancement of locomotion in spreading cell colonies
• Resting and Traveling Localized States in an Active Phase-Field-Crystal Model
• Active phase separation: new phenomenology from non-equilibrium physics
• Time reversal symmetry breaking in two-dimensional non-equilibrium viscous fluids
• Interface stability, interface fluctuations, and the Gibbs-Thomson relation in motility-induced phase separations
• Active-Particle Polarization Without Alignment Forces
• Local stress and pressure in an inhomogeneous system of spherical active Brownian particles
• Collective motion in large deviations of active particles
• Disorder-Induced Long-Ranged Correlations in Scalar Active Matter
• Universal scaling in active single-file dynamics
• Thermodynamics of emergent structure in active matter
• Macroscopic Stochastic Thermodynamics
• Swimming to Stability: Structural and Dynamical Control via Active Doping
• Dynamics of active particles with space-dependent swim velocity
• Mesoscopic virial equation for nonequilibrium statistical mechanics
• Active hard-spheres in infinitely many dimensions
• Dynamics of active particles with translational and rotational inertia
• How irreversible are steady-state trajectories of a trapped active particle?
• Effective equilibrium states in the colored-noise model for active matter II. A unified framework for phase equilibria, structure and mechanical properties
• Predictive local field theory for interacting active Brownian spheres in two spatial dimensions
• Coexistence of active Brownian discs: Van der Waals theory and analytical results
• Chiral active matter in external potentials
• Disordered boundaries destroy bulk phase separation in scalar active matter
• Pressure in an exactly solvable model of active fluid
• Surface Tensions between Active Fluids and Solid Interfaces: bare vs dressed
• Irreversibility in active matter: General framework for active Ornstein-Uhlenbeck particles
• Collective dynamics of active Brownian particles in three spatial dimensions: a predictive field theory
• Microscopic derivation of the hydrodynamics of active-Brownian-particle suspensions
• Nonequilibrium phase behaviour from minimization of free power dissipation
• Van't Hoff's law for active suspensions: the role of the solvent chemical potential
• Collective effects in confined Active Brownian Particles
• Pressure, surface tension and curvature in active systems: A touch of equilibrium
• Green-Kubo approach to the average swim speed in active Brownian systems
• The stability phase diagram of active Brownian particles
• Critical behavior of active Brownian particles: Connection to field theories
• Liquid-gas transitions in steady heat conduction
• An Introduction to Motility-Induced Phase Separation
• Inclusions, Boundaries and Disorder in Scalar Active Matter
• Rheology of active fluids
• Effective Langevin equations for a polar tracer in an active bath
• Anomalous dynamics of an elastic membrane in an active fluid
• Polarization-Density Patterns of Active Particles in Motility Gradients
• Tuning Nonequilibrium Phase Transitions with Inertia
• Capillary action in scalar active matter
• Statistical Mechanics of Transport Processes in Active Fluids II: Equations of Hydrodynamics for Active Brownian Particles
• Active particles with polar alignment in ring-shaped confinement
• Activity-assisted self-assembly of colloidal particles
• Influence of interaction softness in phase separation of active particles
• Two-dimensional localized states in an active phase-field-crystal model
• Bodies in an Interacting Active Fluid: Far-Field Influence of a Single Body and Interaction Between Two Bodies
• Pair correlation of dilute Active Brownian Particles: from low activity dipolar correction to high activity algebraic depletion wings
• How statistical forces depend on thermodynamics and kinetics of driven media
• Hydrodynamics of polymers in an active bath
• Motility-Induced Clustering and Meso-Scale Turbulence in Active Polar Fluids
• Active Brownian Particles in Random and Porous Environments
• Generalized Archimedes' principle in active fluids
• Isotropic-nematic transition of self-propelled rods in three dimensions
• Hysteresis, reentrance, and glassy dynamics in systems of self-propelled rods
• Lack of an equation of state for the nonequilibrium chemical potential of gases of active particles in contact
• Phase separation of active Brownian particles in two dimensions: Anything for a quiet life
• Control of Active Brownian Particles: An exact solution
• Non-equilibrium forces following quenches in active and thermal matter
• Transition between globule and stretch states of a self-attracting chain in the repulsive active particle bath
• Active interface polarization is a state function
• Active fluids at circular boundaries: Swim pressure and anomalous droplet ripening
• Three-body correlations and conditional forces in suspensions of active hard disks
• Theory of Capillary Tension and Interfacial Dynamics of Motility-Induced Phases
• Vorticity Determines the Force on Bodies Immersed in Active Fluids
• Phototactic Supersmarticles
• Testing a thermodynamic approach to collective animal behavior in laboratory fish schools
• Pseudo energy wells in active systems
• Forces in inhomogeneous open active-particle systems
• Zeroth law of thermodynamics for nonequilibrium steady states in contact
• Statistical forces from close--to--equilibrium media
• Additivity, density fluctuations, and nonequilibrium thermodynamics for active Brownian particles
• Phase-field crystal description of active crystallites: elastic and inelastic collisions
• Sufficient conditions for the additivity of stall forces generated by multiple filaments or motors
• Statistical Field Theory and Effective Action Method for scalar Active Matter
• Capillary surfers: wave-driven particles at a vibrating fluid interface
• Large deviations and chemical potential in bulk-driven systems in contact
• Interacting particles in an activity landscape
• Derivation and analysis of a phase field crystal model for a mixture of active and passive particles
• Shear Induced Orientational Ordering in Active Glass
• Hyperuniformity and conservation laws in non-equilibrium systems
• Memory Effects in Active Particles with Exponentially Correlated Propulsion
• Collective behavior of squirmers in thin films
• Colloidal Brazil nut effect in microswimmer mixtures induced by motility contrast
• Kinetic temperature and pressure of an active Tonks gas
• Spontaneous assembly of colloidal vesicles driven by active swimmers
• The Mechanics of Nucleation and Growth and the Surface Tensions of Active Matter
• Mechanically-driven spreading of bacterial populations
• Statistical Mechanics and Hydrodynamics of Self-Propelled Hard Spheres
• Inhomogeneous entropy production in active crystals with point imperfections
• Breakdown of effective temperature, power law interactions and self-propulsion in a momentum conserving active fluid
• Dynamic Overlap Concentration Scale of Active Colloids
• Mean-field theory of active electrolytes: dynamic adsorption and overscreening
• From predicting to learning dissipation from pair correlations of active liquids
• Time-dependent properties of run-and-tumble particles: Density relaxation
• Nematic Torques in Scalar Active Matter: when Fluctuations Favor Polar Order and Persistence
• Phase Separation, Capillarity, and Odd Surface Flows in Chiral Active Matter
• Effect of reorientation statistics on torque response of self propelled particles
• An equation of state for active matter
• Dynamical phase transitions in one-dimensional hard-particle systems
• Passive objects in confined active fluids: a localization transition
• Active particles confined in deformable droplets
• Self-propulsion and self-navigation: Activity is a precursor to jamming
• Dynamical and structural properties of an absorbing phase transition: a case study from granular systems
• Wetting by active fluids
• Nonequilibrium chemical potentials of steady-state lattice gas models in contact: A large-deviations approach
• Active-passive mixtures with bulk loading: a minimal active engine in one dimension
• Nonequilibrium grand-canonical ensemble built from a physical particle reservoir
• Synthetic Quorum Sensing and Absorbing Phase Transitions in Colloidal Active Matter
• Velocity Distribution and Diffusion of an Athermal Inertial Run-and-Tumble Particle in a Shear-Thinning Medium
• Transmission of mobility via cooperative mechanisms in soft active matter
• Mean-field theory for the structure of strongly interacting active liquids
• Recovery of mechanical pressure in a gas of underdamped active dumbbells with Brownian noise
• Interplay of quenching temperature and drift in Brownian dynamics
• Emergent Gauge Symmetry in Active Brownian Matter
• Additivity and density fluctuations in Vicsek-like models of self-propelled particles
• Non-Stationary Critical Phenomena: Expanding The Critical Point
• Theory for the Anomalous Phase Behavior of Inertial Active Brownian Particles
• Propagating speed waves in flocks: a mathematical model
• Dynamic phase transition induced by active molecules simulating a facilitation mechanism in a supercooled liquid
• Thermodynamic nature of irreversibility in active matter
• Run-and-tumble particles in slit geometry as a splitting probability problem
• Controlling local order of athermal self-propelled particles
• Activity-driven emulsification of phase-separating binary mixtures
• Experimental Modeling of Chiral Active Robots and a Minimal Model of Non-Gaussian Displacements
• Active osmotic-like pressure on permeable inclusions
• Effective interactions in active Brownian particles
• Non-additive large deviations function for the particle densities of driven systems in contact
• An Infinite Set of Integral Formulae for Polar, Nematic, and Higher Order Structures at the Interface of Motility-Induced Phase Separation
• Memory effects, arches and polar defect ordering at the cross-over from wet to dry active nematics
• Correlated escape of active particles across a potential barrier
• Transverse Self-Propulsion Enhances the Aggregation of Active Dumbbells
• Hydrodynamics of simple active liquids: the emergence of velocity correlations
• Simulation of a flat folding nano-swimmer confined in a nanopore
• Active Cahn-Hilliard theory for nonequilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation
• A facilitation-induced fluidization transition in supercooled water triggered by a few active molecules
• Mechanistic insights into Z-ring formation and stability: A Langevin dynamics approach to FtsZ self-assembly
• Noncentral forces mediated between inclusions in a bath of active Brownian rods
• Oscillatory active microrheology of active suspensions