Phase behaviour of active Brownian particles: the role of dimensionality.

Recently, there has been much interest in activity-induced phase separations in concentrated suspensions of "active Brownian particles" (ABPs), self-propelled spherical particles whose direction of motion relaxes through thermal rotational diffusion. To date, almost all these studies have been restricted to 2 dimensions. In this work we study activity-induced phase separation in 3D and compare the results with previous and new 2D simulations. To this end, we performed state-of-the-art Brownian dynamics simulations of up to 40 million ABPs - such very large system sizes are unavoidable to evade finite size effects in 3D. Our results confirm the picture established for 2D systems in which an activity-induced phase separation occurs, with strong analogies to equilibrium gas-liquid spinodal decomposition, in spite of the purely non-equilibrium nature of the driving force behind the phase separation. However, we also find important differences between the 2D and 3D cases. Firstly, the shape and position of the phase boundaries is markedly different for the two cases. Secondly, for the 3D coarsening kinetics we find that the domain size grows in time according to the classical diffusive t(1/3) law, in contrast to the nonstandard subdiffusive exponent observed in 2D.

[1]  M. Cates,et al.  Scalar φ4 field theory for active-particle phase separation , 2013, Nature Communications.

[2]  Alexander Panchenko,et al.  Particle-based simulations of self-motile suspensions , 2013, Comput. Phys. Commun..

[3]  Holger Stark,et al.  Hydrodynamics determines collective motion and phase behavior of active colloids in quasi-two-dimensional confinement. , 2013, Physical review letters.

[4]  Silke Henkes,et al.  Freezing and phase separation of self-propelled disks. , 2013, Soft matter.

[5]  G. Gompper,et al.  Collective behavior of penetrable self-propelled rods in two dimensions. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  R. Winkler,et al.  Cooperative motion of active Brownian spheres in three-dimensional dense suspensions , 2013, 1308.6423.

[7]  S. Ramaswamy,et al.  Hydrodynamics of soft active matter , 2013 .

[8]  T. Speck,et al.  Microscopic theory for the phase separation of self-propelled repulsive disks , 2013, 1307.4908.

[9]  Adriano Tiribocchi,et al.  Continuum theory of phase separation kinetics for active Brownian particles. , 2013, Physical review letters.

[10]  Thomas Speck,et al.  Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles. , 2013, Physical review letters.

[11]  Michael F Hagan,et al.  Reentrant phase behavior in active colloids with attraction. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  David J. Pine,et al.  Living Crystals of Light-Activated Colloidal Surfers , 2013, Science.

[13]  H. Stark,et al.  Rectification of self-propelled particles by symmetric barriers. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  R. Golestanian,et al.  Hydrodynamic suppression of phase separation in active suspensions. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  J. Tailleur,et al.  When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation , 2012, 1206.1805.

[16]  H. H. Wensink,et al.  Emergent states in dense systems of active rods: from swarming to turbulence , 2012, Journal of physics. Condensed matter : an Institute of Physics journal.

[17]  M E Cates,et al.  Diffusive transport without detailed balance in motile bacteria: does microbiology need statistical physics? , 2012, Reports on progress in physics. Physical Society.

[18]  C. Ybert,et al.  Dynamic clustering in active colloidal suspensions with chemical signaling. , 2012, Physical review letters.

[19]  W. Ebeling,et al.  Active Brownian particles , 2012, The European Physical Journal Special Topics.

[20]  J. Tailleur,et al.  Pattern formation in self-propelled particles with density-dependent motility. , 2012, Physical review letters.

[21]  M Cristina Marchetti,et al.  Athermal phase separation of self-propelled particles with no alignment. , 2012, Physical review letters.

[22]  Sam McCandlish,et al.  Spontaneous segregation of self-propelled particles with different motilities , 2011, 1110.2479.

[23]  S. Das,et al.  Universality in fluid domain coarsening: The case of vapor-liquid transition , 2011, 1104.3740.

[24]  Robert H. Austin,et al.  Collective escape of chemotactic swimmers through microscopic ratchets. , 2010, Physical review letters.

[25]  Hugues Chaté,et al.  Collective motion of vibrated polar disks. , 2010, Physical review letters.

[26]  H. Swinney,et al.  Collective motion and density fluctuations in bacterial colonies , 2010, Proceedings of the National Academy of Sciences.

[27]  Stephen J. Ebbens,et al.  In pursuit of propulsion at the nanoscale , 2010 .

[28]  M E Cates,et al.  Arrested phase separation in reproducing bacteria creates a generic route to pattern formation , 2010, Proceedings of the National Academy of Sciences.

[29]  R Di Leonardo,et al.  Bacterial ratchet motors , 2009, Proceedings of the National Academy of Sciences.

[30]  R. Di Leonardo,et al.  Self-starting micromotors in a bacterial bath. , 2008, Physical review letters.

[31]  M E Cates,et al.  Statistical mechanics of interacting run-and-tumble bacteria. , 2008, Physical review letters.

[32]  Robert Austin,et al.  A Wall of Funnels Concentrates Swimming Bacteria , 2007, Journal of bacteriology.

[33]  M E Cates,et al.  Binary fluids under steady shear in three dimensions. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Ramin Golestanian,et al.  Self-motile colloidal particles: from directed propulsion to random walk. , 2007, Physical review letters.

[35]  S. Ramaswamy,et al.  Long-Lived Giant Number Fluctuations in a Swarming Granular Nematic , 2006, Science.

[36]  M. Cates,et al.  Nonequilibrium steady states in sheared binary fluids. , 2005, Physical review letters.

[37]  Sanjay Puri,et al.  Kinetics of Phase Transitions , 2004 .

[38]  T. Lubensky,et al.  Principles of condensed matter physics , 1995 .

[39]  M. Cates,et al.  Inertial effects in three-dimensional spinodal decomposition of a symmetric binary fluid mixture: a lattice Boltzmann study , 2000, Journal of Fluid Mechanics.

[40]  A. Wagner,et al.  Phase Separation under Shear in Two-dimensional Binary Fluids , 1999, cond-mat/9904033.

[41]  A. Wagner,et al.  Breakdown of Scale Invariance in the Coarsening of Phase-Separating Binary Fluids , 1997, cond-mat/9710039.

[42]  M. Schnitzer,et al.  Theory of continuum random walks and application to chemotaxis. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[43]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[44]  R. Yamamoto,et al.  Computer Simulation of Vapor-Liquid Phase Separation , 1996 .