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
  • Open Access

Rheologically Tuned Modes of Collective Transport in Active Viscoelastic Films

Henning Reinken* and Andreas M. Menzel

  • *Contact author: henning.reinken@ovgu.de
  • Contact author: a.menzel@ovgu.de

Phys. Rev. Lett. 135, 188301 – Published 29 October, 2025

DOI: https://doi.org/10.1103/gbm1-p9cg

Abstract

While many living biological media combine both viscous and elastic properties, most theoretical studies employ either purely fluid or solidlike descriptions. We here use a unified framework for active films on substrates capable of describing a range of viscoelastic behavior to explore the interplay between activity and rheology. The core of the study is a comprehensive state diagram showing a rich world of spatiotemporal dynamic states. Our results demonstrate the potential of tunable rheology to realize modes of controlled active transport on the microscale.

View figure in article

Physics Subject Headings (PhySH)

See Also

Unified description of viscous, viscoelastic, or elastic thin active films on substrates

Henning Reinken and Andreas M. Menzel
Phys. Rev. E 112, 045506 (2025)

Article Text

Supplemental Material

References (82)

  1. G. Li, E. Lauga, and A. M. Ardekani, Microswimming in viscoelastic fluids, J. Non-Newtonian Fluid Mech. 297, 104655 (2021).
  2. L. Hall-Stoodley, J. W. Costerton, and P. Stoodley, Bacterial biofilms: From the natural environment to infectious diseases, Nat. Rev. Microbiol. 2, 95 (2004).
  3. V. M. Worlitzer, A. Jose, I. Grinberg, M. Bär, S. Heidenreich, A. Eldar, G. Ariel, and A. Be’er, Biophysical aspects underlying the swarm to biofilm transition, Sci. Adv. 8, eabn8152 (2022).
  4. S. Jana, S. G. Charlton, L. E. Eland, J. G. Burgess, A. Wipat, T. P. Curtis, and J. Chen, Nonlinear rheological characteristics of single species bacterial biofilms, npj Biofilms Microbiomes 6, 19 (2020).
  5. 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).
  6. 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).
  7. E. Lauga and T. R. Powers, The hydrodynamics of swimming microorganisms, Rep. Prog. Phys. 72, 096601 (2009).
  8. J. Elgeti, R. G. Winkler, and G. Gompper, Physics of microswimmers—single particle motion and collective behavior: A review, Rep. Prog. Phys. 78, 056601 (2015).
  9. A. Doostmohammadi, J. Ignés-Mullol, J. M. Yeomans, and F. Sagués, Active nematics, Nat. Commun. 9, 3246 (2018).
  10. 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).
  11. J. Toner and Y. Tu, Flocks herds, and schools: A quantitative theory of flocking, Phys. Rev. E 58, 4828 (1998).
  12. J. Toner, Y. Tu, and S. Ramaswamy, Hydrodynamics and phases of flocks, Ann. Phys. (Amsterdam) 318, 170 (2005).
  13. H. Jeckel, E. Jelli, R. Hartmann, P. K. Singh, R. Mok, J. F. Totz, L. Vidakovic, B. Eckhardt, J. Dunkel, and K. Drescher, Learning the space-time phase diagram of bacterial swarm expansion, Proc. Natl. Acad. Sci. U.S.A. 116, 1489 (2019).
  14. A. Be’er, B. Ilkanaiv, R. Gross, D. B. Kearns, S. Heidenreich, M. Bär, and G. Ariel, A phase diagram for bacterial swarming, Commun. Phys. 3, 66 (2020).
  15. A. Be’er and G. Ariel, A statistical physics view of swarming bacteria, Mov. Ecol. 7, 1 (2019).
  16. D. Nishiguchi, I. S. Aranson, A. Snezhko, and A. Sokolov, Engineering bacterial vortex lattice via direct laser lithography, Nat. Commun. 9, 4486 (2018).
  17. I. S. Aranson, Bacterial active matter, Rep. Prog. Phys. 85, 076601 (2022).
  18. H. Reinken, S. Heidenreich, M. Bär, and S. H. L. Klapp, Pattern selection and the route to turbulence in incompressible polar active fluids, New J. Phys. 26, 063026 (2024).
  19. C. Dombrowski, L. Cisneros, S. Chatkaew, R. E. Goldstein, and J. O. Kessler, Self-concentration and large-scale coherence in bacterial dynamics, Phys. Rev. Lett. 93, 098103 (2004).
  20. 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. U.S.A. 109, 14308 (2012).
  21. H. Reinken, S. H. L. Klapp, M. Bär, and S. Heidenreich, Derivation of a hydrodynamic theory for mesoscale dynamics in microswimmer suspensions, Phys. Rev. E 97, 022613 (2018).
  22. R. Alert, J. Casademunt, and J.-F. Joanny, Active turbulence, Annu. Rev. Condens. Matter Phys. 13 (2022).
  23. H. Shen, P. Tan, and L. Xu, Probing the role of mobility in the collective motion of nonequilibrium systems, Phys. Rev. Lett. 116, 048302 (2016).
  24. E. Ferrante, A. E. Turgut, M. Dorigo, and C. Huepe, Elasticity-based mechanism for the collective motion of self-propelled particles with springlike interactions: A model system for natural and artificial swarms, Phys. Rev. Lett. 111, 268302 (2013).
  25. C. Hernández-López, P. Baconnier, C. Coulais, O. Dauchot, and G. Düring, Model of active solids: Rigid body motion and shape-changing mechanisms, Phys. Rev. Lett. 132, 238303 (2024).
  26. P. Baconnier, V. Démery, and O. Dauchot, Noise-induced collective actuation in active solids, Phys. Rev. E 109, 024606 (2024).
  27. E. Lång, A. Lång, P. Blicher, T. Rognes, P. G. Dommersnes, and S. O. Bøe, Topology-guided polar ordering of collective cell migration, Sci. Adv. 10, eadk4825 (2024).
  28. R. J. Hawkins and T. B. Liverpool, Stress reorganization and response in active solids, Phys. Rev. Lett. 113, 028102 (2014).
  29. A. Maitra and S. Ramaswamy, Oriented active solids, Phys. Rev. Lett. 123, 238001 (2019).
  30. D. Needleman and Z. Dogic, Active matter at the interface between materials science and cell biology, Nat. Rev. Mater. 2 (2017).
  31. P. Baconnier, D. Shohat, C. H. López, C. Coulais, V. Démery, G. Düring, and O. Dauchot, Selective and collective actuation in active solids, Nat. Phys. 18, 1234 (2022).
  32. L. Caprini, U. Marini Bettolo Marconi, A. Puglisi, and H. Löwen, Entropons as collective excitations in active solids, J. Chem. Phys. 159 (2023).
  33. C. Scheibner, A. Souslov, D. Banerjee, P. Surówka, W. T. Irvine, and V. Vitelli, Odd elasticity, Nat. Phys. 16, 475 (2020).
  34. M. Fruchart, C. Scheibner, and V. Vitelli, Odd viscosity and odd elasticity, Annu. Rev. Condens. Matter Phys. 14, 471 (2023).
  35. M. H. Köpf and L. M. Pismen, Non-equilibrium patterns in polarizable active layers, Physica (Amsterdam) 259D, 48 (2013).
  36. D. Saintillan and M. J. Shelley, Active suspensions and their nonlinear models, C. R. Phys. 14, 497 (2013).
  37. E. J. Hemingway, A. Maitra, S. Banerjee, M. C. Marchetti, S. Ramaswamy, S. M. Fielding, and M. E. Cates, Active viscoelastic matter: From bacterial drag reduction to turbulent solids, Phys. Rev. Lett. 114, 098302 (2015).
  38. A. J. T. M. Mathijssen, T. N. Shendruk, J. M. Yeomans, and A. Doostmohammadi, Upstream swimming in microbiological flows, Phys. Rev. Lett. 116, 028104 (2016).
  39. E. J. Hemingway, M. E. Cates, and S. M. Fielding, Viscoelastic and elastomeric active matter: Linear instability and nonlinear dynamics, Phys. Rev. E 93, 032702 (2016).
  40. E. L. C. VI M. Plan, J. M. Yeomans, and A. Doostmohammadi, Active matter in a viscoelastic environment, Phys. Rev. Fluids 5, 023102 (2020).
  41. A. Choudhary, S. Nambiar, and H. Stark, Orientational dynamics and rheology of active suspensions in weakly viscoelastic flows, Commun. Phys. 6, 163 (2023).
  42. H. Reinken and A. M. Menzel, Vortex pattern stabilization in thin films resulting from shear thickening of active suspensions, Phys. Rev. Lett. 132, 138301 (2024).
  43. H. Reinken and A. M. Menzel, Self-sustained patchy turbulence in shear-thinning active fluids, Commun. Phys. 8, 270 (2025).
  44. H. Reinken and A. M. Menzel, companion paper, Unified description of viscous, viscoelastic, or elastic thin active films on substrates, Phys. Rev. E 112, 045506 (2025).
  45. T. Brotto, J.-B. Caussin, E. Lauga, and D. Bartolo, Hydrodynamics of confined active fluids, Phys. Rev. Lett. 110, 038101 (2013).
  46. L. P. Dadhichi, A. Maitra, and S. Ramaswamy, Origins and diagnostics of the nonequilibrium character of active systems, J. Stat. Mech. (2018) 123201.
  47. A. Maitra, P. Srivastava, M. C. Marchetti, S. Ramaswamy, and M. Lenz, Swimmer suspensions on substrates: Anomalous stability and long-range order, Phys. Rev. Lett. 124, 028002 (2020).
  48. S. Liu, S. Shankar, M. C. Marchetti, and Y. Wu, Viscoelastic control of spatiotemporal order in bacterial active matter, Nature (London) 590, 80 (2021).
  49. B. Szabó, G. J. Szöllösi, B. Gönci, Z. Jurányi, D. Selmeczi, and T. Vicsek, Phase transition in the collective migration of tissue cells: Experiment and model, Phys. Rev. E 74, 061908 (2006).
  50. K.-D. N. T. Lam, M. Schindler, and O. Dauchot, Self-propelled hard disks: Implicit alignment and transition to collective motion, New J. Phys. 17, 113056 (2015).
  51. P. Baconnier, O. Dauchot, V. Démery, G. Düring, S. Henkes, C. Huepe, and A. Shee, Self-aligning polar active matter, Rev. Mod. Phys. 97, 015007 (2025).
  52. H. Temmen, H. Pleiner, M. Liu, and H. R. Brand, Convective nonlinearity in non-Newtonian fluids, Phys. Rev. Lett. 84, 3228 (2000).
  53. H. Pleiner, M. Liu, and H. R. Brand, Nonlinear fluid dynamics description of non-Newtonian fluids, Rheol. Acta 43, 502 (2004).
  54. A. M. Menzel, Linear theory of viscoelasticity in a generalized hydrodynamic framework, arXiv:2505.10032.
  55. P. C. Martin, O. Parodi, and P. S. Pershan, Unified hydrodynamic theory for crystals, liquid crystals, and normal fluids, Phys. Rev. A 6, 2401 (1972).
  56. M. Puljiz and A. M. Menzel, Memory-based mediated interactions between rigid particulate inclusions in viscoelastic environments, Phys. Rev. E 99, 012601 (2019).
  57. See Supplemental Material, which includes Refs. [58–60], at http://link.aps.org/supplemental/10.1103/gbm1-p9cg for details on the linear stability analysis of the isotropic and globally ordered polar states, for a list of the idealized explicit spatially uniform analytical solutions, for details on the numerical methods, for changes in the state diagram Fig. 1 upon parameter variations, for a description of the supplemental movies, for additional information on topological defects, and for details on the rheological switching function underlying Fig. 4(a).
  58. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Springer, Berlin, Heidelberg, 2007).
  59. D. R. Durran, Numerical Methods for Fluid Dynamics (Springer, New York, 2010).
  60. C. R. Harris, K. J. Millman, S. J. Van Der Walt, R. Gommers, P. Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith et al., Array programming with numpy, Nature (London) 585, 357 (2020).
  61. J.-B. Caussin, A. Solon, A. Peshkov, H. Chaté, T. Dauxois, J. Tailleur, V. Vitelli, and D. Bartolo, Emergent spatial structures in flocking models: A dynamical system insight, Phys. Rev. Lett. 112, 148102 (2014).
  62. H. Reinken, S. Heidenreich, M. Bär, and S. H. L. Klapp, Anisotropic mesoscale turbulence and pattern formation in microswimmer suspensions induced by orienting external fields, New J. Phys. 21, 013037 (2019).
  63. A. Patelli, I. Djafer-Cherif, I. S. Aranson, E. Bertin, and H. Chaté, Understanding dense active nematics from microscopic models, Phys. Rev. Lett. 123, 258001 (2019).
  64. L. Giomi, M. J. Bowick, X. Ma, and M. C. Marchetti, Defect annihilation and proliferation in active nematics, Phys. Rev. Lett. 110, 228101 (2013).
  65. N. Rana, R. Chatterjee, S. Ro, D. Levine, S. Ramaswamy, and P. Perlekar, Defect turbulence in a dense suspension of polar, active swimmers, Phys. Rev. E 109, 024603 (2024).
  66. H. Oh, A. M. Ketner, R. Heymann, E. Kesselman, D. Danino, D. E. Falvey, and S. R. Raghavan, A simple route to fluids with photo-switchable viscosities based on a reversible transition between vesicles and wormlike micelles, Soft Matter 9, 5025 (2013).
  67. R. Yang, S. Peng, and T. C. Hughes, Multistimuli responsive organogels based on a reactive azobenzene gelator, Soft Matter 10, 2188 (2014).
  68. I. Tomatsu, K. Peng, and A. Kros, Photoresponsive hydrogels for biomedical applications, Adv. Drug Delivery Rev. 63, 1257 (2011).
  69. N. Kuznetsov, V. Kovaleva, S. Belousov, and S. Chvalun, Electrorheological fluids: From historical retrospective to recent trends, Mater. Today Chem. 26, 101066 (2022).
  70. N. Darnton, L. Turner, K. Breuer, and H. C. Berg, Moving fluid with bacterial carpets, Biophys. J. 86, 1863 (2004).
  71. B. Kaehr and J. B. Shear, High-throughput design of microfluidics based on directed bacterial motility, Lab Chip 9, 2632 (2009).
  72. M. J. Kim and K. S. Breuer, Microfluidic pump powered by self-organizing bacteria, Small 4, 111 (2008).
  73. S. P. Thampi, A. Doostmohammadi, T. N. Shendruk, R. Golestanian, and J. M. Yeomans, Active micromachines: Microfluidics powered by mesoscale turbulence, Sci. Adv. 2, e1501854 (2016).
  74. F. Gu, B. Guiselin, N. Bain, I. Zuriguel, and D. Bartolo, Emergence of collective oscillations in massive human crowds, Nature (London) 638, 112 (2025).
  75. V. Yashunsky, D. J. G. Pearce, C. Blanch-Mercader, F. Ascione, P. Silberzan, and L. Giomi, Chiral edge current in nematic cell monolayers, Phys. Rev. X 12, 041017 (2022).
  76. H. Xu, Y. Huang, R. Zhang, and Y. Wu, Autonomous waves and global motion modes in living active solids, Nat. Phys. 19, 46 (2023).
  77. B. An, Y. Wang, Y. Huang, X. Wang, Y. Liu, D. Xun, G. M. Church, Z. Dai, X. Yi, T.-C. Tang et al., Engineered living materials for sustainability, Chem. Rev. 123, 2349 (2022).
  78. S. Kim, C. Laschi, and B. Trimmer, Soft robotics: A bioinspired evolution in robotics, Trends Biotechnol. 31, 287 (2013).
  79. Z. Wu, Y. Chen, D. Mukasa, O. S. Pak, and W. Gao, Medical micro/nanorobots in complex media, Chem. Soc. Rev. 49, 8088 (2020).
  80. Y. Kim and X. Zhao, Magnetic soft materials and robots, Chem. Rev. 122, 5317 (2022).
  81. M. Li, A. Pal, A. Aghakhani, A. Pena-Francesch, and M. Sitti, Soft actuators for real-world applications, Nat. Rev. Mater. 7, 235 (2022).
  82. H. Reinken and A. M. Menzel, Rheologically tuned modes of collective transport in active viscoelastic films (v1.1), Zenodo (2025), 10.5281/zenodo.17055518.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation