- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Diversity of phase transitions and phase separations in active fluids

Thibault Bertrand1,* and Chiu Fan Lee2,†

  • 1Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
  • 2Department of Bioengineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom

  • *t.bertrand@imperial.ac.uk
  • †c.lee@imperial.ac.uk
PDF

Phys. Rev. Research 4, L022046 – Published 25 May, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L022046

Abstract

Active matter is not only indispensable to our understanding of diverse biological processes, but also provides a fertile ground for discovering novel physics. Many emergent properties impossible for equilibrium systems have been demonstrated in active systems. These emergent features include motility-induced phase separation, a long-ranged ordered (collective motion) phase in two dimensions, and order-disorder phase coexistences (banding and reverse-banding regimes). Here, we unify these diverse phase transitions and phase coexistences into a single formulation based on generic hydrodynamic equations for active fluids. We also reveal a novel comoving coexistence phase and a multicritical point.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (59)

  1. S. Ramaswamy, The mechanics and statistics of active matter, Annu. Rev. Condens. Matter Phys. 1, 323 (2010).
  2. M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Hydrodynamics of soft active matter, Rev. Mod. Phys. 85, 1143 (2013).
  3. C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys. 88, 045006 (2016).
  4. P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, UK, 1995).
  5. J. Toner and Y. Tu, Long-Range Order in a Two-Dimensional Dynamical XY Model: How Birds Fly Together, Phys. Rev. Lett. 75, 4326 (1995).
  6. J. Toner and Y. Tu, Flocks, herds, and schools: A quantitative theory of flocking, Phys. Rev. E 58, 4828 (1998).
  7. J. Toner, Y. Tu, and S. Ramaswamy, Hydrodynamics and phases of flocks, Ann. Phys. 318, 170 (2005).
  8. J. Toner, Reanalysis of the hydrodynamic theory of fluid, polar-ordered flocks, Phys. Rev. E 86, 031918 (2012).
  9. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet, Novel Type of Phase Transition in a System of Self-Driven Particles, Phys. Rev. Lett. 75, 1226 (1995).
  10. H. Chaté, F. Ginelli, G. Grégoire, and F. Raynaud, Collective motion of self-propelled particles interacting without cohesion, Phys. Rev. E 77, 046113 (2008).
  11. G. Grégoire and H. Chaté, Onset of Collective and Cohesive Motion, Phys. Rev. Lett. 92, 025702 (2004).
  12. F. Thüroff, C. A. Weber, and E. Frey, Numerical Treatment of the Boltzmann Equation for Self-Propelled Particle Systems, Phys. Rev. X 4, 041030 (2014).
  13. A. P. Solon and J. Tailleur, Revisiting the Flocking Transition Using Active Spins, Phys. Rev. Lett. 111, 078101 (2013).
  14. A. P. Solon and J. Tailleur, Flocking with discrete symmetry: The two-dimensional active ising model, Phys. Rev. E 92, 042119 (2015).
  15. A. Gopinath, M. F. Hagan, M. C. Marchetti, and A. Baskaran, Dynamical self-regulation in self-propelled particle flows, Phys. Rev. E 85, 061903 (2012).
  16. A. Baskaran and M. C. Marchetti, Hydrodynamics of self-propelled hard rods, Phys. Rev. E 77, 011920 (2008).
  17. A. Baskaran and M. C. Marchetti, Enhanced Diffusion and Ordering of Self-Propelled Rods, Phys. Rev. Lett. 101, 268101 (2008).
  18. E. Bertin, M. Droz, and G. Grégoire, Boltzmann and hydrodynamic description for self-propelled particles, Phys. Rev. E 74, 022101 (2006).
  19. E. Bertin, M. Droz, and G. Grégoire, Hydrodynamic equations for self-propelled particles: Microscopic derivation and stability analysis, J. Phys. A: Math. Theor. 42, 445001 (2009).
  20. A. Peshkov, I. S. Aranson, E. Bertin, H. Chaté, and F. Ginelli, Nonlinear Field Equations for Aligning Self-Propelled Rods, Phys. Rev. Lett. 109, 268701 (2012).
  21. A. Peshkov, E. Bertin, F. Ginelli, and H. Chaté, Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models, Eur. Phys. J.: Spec. Top. 223, 1315 (2014).
  22. E. Bertin, A. Baskaran, H. Chaté, and M. C. Marchetti, Comparison between Smoluchowski and Boltzmann approaches for self-propelled rods, Phys. Rev. E 92, 042141 (2015).
  23. M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
  24. J. Tailleur and M. E. Cates, Statistical Mechanics of Interacting Run-and-Tumble Bacteria, Phys. Rev. Lett. 100, 218103 (2008).
  25. Y. Fily and M. C. Marchetti, Athermal Phase Separation of Self-Propelled Particles with No Alignment, Phys. Rev. Lett. 108, 235702 (2012).
  26. G. S. Redner, M. F. Hagan, and A. Baskaran, Structure and Dynamics of a Phase-Separating Active Colloidal Fluid, Phys. Rev. Lett. 110, 055701 (2013).
  27. J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, Living crystals of light-activated colloidal surfers, Science 339, 936 (2013).
  28. I. Buttinoni, J. Bialké, F. Kümmel, H. Löwen, C. Bechinger, and T. Speck, Dynamical Clustering and Phase Separation in Suspensions of Self-Propelled Colloidal Particles, Phys. Rev. Lett. 110, 238301 (2013).
  29. R. Wittkowski, A. Tiribocchi, J. Stenhammar, R. J. Allen, D. Marenduzzo, and M. E. Cates, Scalar ϕ4 field theory for active-particle phase separation, Nat. Commun. 5, 4351 (2014).
  30. E. Tjhung, C. Nardini, and M. E. Cates, Cluster Phases and Bubbly Phase Separation in Active Fluids: Reversal of the Ostwald Process, Phys. Rev. X 8, 031080 (2018).
  31. M. N. van der Linden, L. C. Alexander, D. G. A. L. Aarts, and O. Dauchot, Interrupted Motility Induced Phase Separation in Aligning Active Colloids, Phys. Rev. Lett. 123, 098001 (2019).
  32. F. Peruani, T. Klauss, A. Deutsch, and A. Voss-Boehme, Traffic Jams, Gliders, and Bands in the Quest for Collective Motion of Self-Propelled Particles, Phys. Rev. Lett. 106, 128101 (2011).
  33. F. D. C. Farrell, M. C. Marchetti, D. Marenduzzo, and J. Tailleur, Pattern Formation in Self-Propelled Particles with Density-Dependent Motility, Phys. Rev. Lett. 108, 248101 (2012).
  34. A. Martín-Gómez, D. Levis, A. Díaz-Guilera, and I. Pagonabarraga, Collective motion of active Brownian particles with polar alignment, Soft Matter 14, 2610 (2018).
  35. E. Sesé-Sansa, I. Pagonabarraga, and D. Levis, Velocity alignment promotes motility-induced phase separation, Europhys. Lett. 124, 30004 (2018).
  36. L. Caprini, U. Marini Bettolo Marconi, and A. Puglisi, Spontaneous Velocity Alignment in Motility-Induced Phase Separation, Phys. Rev. Lett. 124, 078001 (2020).
  37. A. Jayaram, A. Fischer, and T. Speck, From scalar to polar active matter: Connecting simulations with mean-field theory, Phys. Rev. E 101, 022602 (2020).
  38. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L022046 for further analytical and simulation details as well as movies of each of the phase coexistences described in this paper.
  39. J. Dunkel, S. Heidenreich, M. Bär, and R. E. Goldstein, Minimal continuum theories of structure formation in dense active fluids, New J. Phys. 15, 045016 (2013).
  40. V. M. Worlitzer, G. Ariel, A. Be'er, H. Stark, M. Bär, and S. Heidenreich, Motility-induced clustering and meso-scale turbulence in active polar fluids, New J. Phys. 23, 033012 (2021).
  41. S. K. Schnyder, J. J. Molina, Y. Tanaka, and R. Yamamoto, Collective motion of cells crawling on a substrate: Roles of cell shape and contact inhibition, Sci. Rep. 7, 5163 (2017).
  42. D. Nesbitt, G. Pruessner, and C. F. Lee, Uncovering novel phase transitions in dense dry polar active fluids using a lattice Boltzmann method, New J. Phys. 23, 043047 (2021).
  43. D. Geyer, D. Martin, J. Tailleur, and D. Bartolo, Freezing a Flock: Motility-Induced Phase Separation in Polar Active Liquids, Phys. Rev. X 9, 031043 (2019).
  44. C. A. Weber, D. Zwicker, F. Jülicher, and C. F. Lee, Physics of active emulsions, Rep. Prog. Phys. 82, 064601 (2019).
  45. J.-L. Barrat and J.-P. Hansen, Basic Concepts for Simple and Complex Liquids (Cambridge University Press, Cambridge, UK, 2003).
  46. A. P. Solon, H. Chaté, and J. Tailleur, From Phase to Microphase Separation in Flocking Models: The Essential Role of Nonequilibrium Fluctuations, Phys. Rev. Lett. 114, 068101 (2015).
  47. A. P. Solon, J.-B. Caussin, D. Bartolo, H. Chaté, and J. Tailleur, Pattern formation in flocking models: A hydrodynamic description, Phys. Rev. E 92, 062111 (2015).
  48. B. Partridge and C. F. Lee, Critical Motility-Induced Phase Separation Belongs to the Ising Universality Class, Phys. Rev. Lett. 123, 068002 (2019).
  49. J. T. Siebert, F. Dittrich, F. Schmid, K. Binder, T. Speck, and P. Virnau, Critical behavior of active Brownian particles, Phys. Rev. E 98, 030601(R) (2018).
  50. F. Caballero, C. Nardini, and M. E. Cates, From bulk to microphase separation in scalar active matter: A perturbative renormalization group analysis, J. Stat. Mech. (2018) 123208.
  51. F. Ginelli and H. Chaté, Relevance of Metric-Free Interactions in Flocking Phenomena, Phys. Rev. Lett. 105, 168103 (2010).
  52. A. Peshkov, S. Ngo, E. Bertin, H. Chaté, and F. Ginelli, Continuous Theory of Active Matter Systems with Metric-Free Interactions, Phys. Rev. Lett. 109, 098101 (2012).
  53. L. Chen, J. Toner, and C. F. Lee, Critical phenomenon of the order-disorder transition in incompressible active fluids, New J. Phys. 17, 042002 (2015).
  54. R. Großmann, F. Peruani, and M. Bär, Superdiffusion, large-scale synchronization, and topological defects, Phys. Rev. E 93, 040102(R) (2016).
  55. B. Mahault, X.-C. Jiang, E. Bertin, Y.-Q. Ma, A. Patelli, X.-Q. Shi, and H. Chaté, Self-Propelled Particles with Velocity Reversals and Ferromagnetic Alignment: Active Matter Class with Second-Order Transition to Quasi-Long-Range Polar Order, Phys. Rev. Lett. 120, 258002 (2018).
  56. A. Cairoli and C. F. Lee, Hydrodynamics of active Lévy matter, arXiv:1903.07565.
  57. A. Cairoli and C. F. Lee, Active Lévy matter: Anomalous diffusion, hydrodynamics and linear stability, arXiv:1904.08326.
  58. H. H. Wensink, J. Dunkel, S. Heidenreich, K. Drescher, R. E. Goldstein, H. Löwen, and J. M. Yeomans, Meso-scale turbulence in living fluids, Proc. Natl. Acad. Sci. USA 109, 14308 (2012).
  59. P. Jentsch and C. F. Lee, Novel critical phenomena in compressible polar active fluids: A functional renormalization group approach, arXiv:2205.01610.

Outline

Information

Phys. Rev. Research 4, L022046– Published 25 May, 2022
  • Received 10 December 2020
  • Accepted 10 May 2022
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation