- 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
  • Open Access

Hydrodynamic stresses in a multi-species suspension of active Janus colloids

Gennaro Tucci1,*,†, Giulia Pisegna1,*,‡, Ramin Golestanian1,2,§, and Suropriya Saha1,∥

  • *These authors contributed equally to this work.
  • †Contact author: gennaro.tucci@ds.mpg.de
  • ‡Contact author: giulia.pisegna@ds.mpg.de
  • §Contact author: ramin.golestanian@ds.mpg.de
  • ∥Contact author: suropriya.saha@ds.mpg.de
PDF

Phys. Rev. Research 7, 033003 – Published 1 July, 2025

DOI: https://doi.org/10.1103/xrph-vgf3

Abstract

A realistic description of active particles should include interactions with the medium, commonly a momentum-conserving simple fluid, in which they are suspended. In this work, we consider a multispecies suspension of self-diffusiophoretic Janus colloids interacting via chemical and hydrodynamic fields. Through a systematic coarse-graining of the microscopic dynamics, we calculate the multicomponent contribution to the hydrodynamic stress tensor of the incompressible Stokesian fluid in which the particles are immersed. For a single species, we find that the strength of the stress produced by the gradients of the number density field is determined by the particles' self-propulsion and chemotactic alignment, and can be tuned to be either contractile or extensile. For a multispecies system, we unveil how different forms of activity modify the stress tensor and how it can acquire nonreciprocal couplings due to phoretic effects.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (71)

  1. G. Gompper, R. G. Winkler, T. Speck, A. Solon, C. Nardini, F. Peruani, H. Löwen, R. Golestanian, U. B. Kaupp, L. Alvarez et al., The 2020 motile active matter roadmap, J. Phys.: Condens. Matter 32, 193001 (2020).
  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. S. Ramaswamy, The mechanics and statistics of active matter, Annu. Rev. Condens. Matter Phys. 1, 323 (2010).
  4. R. Golestanian, Phoretic Active Matter, in Active Matter and Nonequilibrium Statistical Physics: Lecture Notes of the Les Houches Summer School: Volume 112, September 2018 (Oxford University Press, Oxford, UK, 2022).
  5. 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).
  6. H. Chaté, Dry aligning dilute active matter, Annu. Rev. Condens. Matter Phys. 11, 189 (2020).
  7. J. Toner and Y. Tu, Flocks, herds, and schools: A quantitative theory of flocking, Phys. Rev. E 58, 4828 (1998).
  8. Y. Hatwalne, S. Ramaswamy, M. Rao, and R. A. Simha, Rheology of active-particle suspensions, Phys. Rev. Lett. 92, 118101 (2004).
  9. D. Saintillan and M. J. Shelley, Theory of Active Suspensions, in Complex Fluids in Biological Systems: Experiment, Theory, and Computation, edited by S. E. Spagnolie (Springer, New York, NY, 2014/2015), pp. 319–355.
  10. R. Aditi Simha and S. Ramaswamy, Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles, Phys. Rev. Lett. 89, 058101 (2002).
  11. 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).
  12. C. W. Wolgemuth, Collective swimming and the dynamics of bacterial turbulence, Biophys. J. 95, 1564 (2008).
  13. N. Uchida and R. Golestanian, Synchronization and collective dynamics in a carpet of microfluidic rotors, Phys. Rev. Lett. 104, 178103 (2010).
  14. J. Dunkel, S. Heidenreich, K. Drescher, H. H. Wensink, M. Bär, and R. E. Goldstein, Fluid dynamics of bacterial turbulence, Phys. Rev. Lett. 110, 228102 (2013).
  15. A. Maitra, P. Srivastava, M. C. Marchetti, J. S. Lintuvuori, S. Ramaswamy, and M. Lenz, A nonequilibrium force can stabilize 2D active nematics, Proc. Natl. Acad. Sci. USA 115, 6934 (2018).
  16. R. Soto and R. Golestanian, Self-assembly of catalytically active colloidal molecules: Tailoring activity through surface chemistry, Phys. Rev. Lett. 112, 068301 (2014).
  17. A. V. Ivlev, J. Bartnick, M. Heinen, C.-R. Du, V. Nosenko, and H. Löwen, Statistical mechanics where Newton's third law is broken, Phys. Rev. X 5, 011035 (2015).
  18. J. Agudo-Canalejo and R. Golestanian, Active phase separation in mixtures of chemically interacting particles, Phys. Rev. Lett. 123, 018101 (2019).
  19. S. Saha, J. Agudo-Canalejo, and R. Golestanian, Scalar active mixtures: The nonreciprocal Cahn-Hilliard model, Phys. Rev. X 10, 041009 (2020).
  20. Z. You, A. Baskaran, and M. C. Marchetti, Nonreciprocity as a generic route to traveling states, Proc. Natl. Acad. Sci. USA 117, 19767 (2020).
  21. M. Fruchart, R. Hanai, P. B. Littlewood, and V. Vitelli, Non-reciprocal phase transitions, Nature (London) 592, 363 (2021).
  22. B. Nasouri and R. Golestanian, Exact phoretic interaction of two chemically active particles, Phys. Rev. Lett. 124, 168003 (2020).
  23. B. Nasouri and R. Golestanian, Exact axisymmetric interaction of phoretically active Janus particles, J. Fluid Mech. 905, A13 (2020).
  24. P. Illien, R. Golestanian, and A. Sen, ‘fuelled' motion: Phoretic motility and collective behaviour of active colloids, Chem. Soc. Rev. 46, 5508 (2017).
  25. H. C. Berg and E. M. Purcell, Physics of chemoreception, Biophys. J. 20, 193 (1977).
  26. A. Celani and M. Vergassola, Bacterial strategies for chemotaxis response, Proc. Natl. Acad. Sci. USA 107, 1391 (2010).
  27. R. Golestanian, T. B. Liverpool, and A. Ajdari, Propulsion of a molecular machine by asymmetric distribution of reaction products, Phys. Rev. Lett. 94, 220801 (2005).
  28. R. Golestanian, T. Liverpool, and A. Ajdari, Designing phoretic micro- and nano-swimmers, New J. Phys. 9, 126 (2007).
  29. J. R. Howse, R. A. Jones, A. J. Ryan, T. Gough, R. Vafabakhsh, and R. Golestanian, Self-motile colloidal particles: From directed propulsion to random walk, Phys. Rev. Lett. 99, 048102 (2007).
  30. S. Saha, R. Golestanian, and S. Ramaswamy, Clusters, asters, and collective oscillations in chemotactic colloids, Phys. Rev. E 89, 062316 (2014).
  31. S. Saha, S. Ramaswamy, and R. Golestanian, Pairing, waltzing and scattering of chemotactic active colloids, New J. Phys. 21, 063006 (2019).
  32. L. Baraban, S. M. Harazim, S. Sanchez, and O. G. Schmidt, Chemotactic behavior of catalytic motors in microfluidic channels, Angew. Chem. 52, 5662 (2013).
  33. S. Ebbens, R. A. Jones, A. J. Ryan, R. Golestanian, and J. R. Howse, Self-assembled autonomous runners and tumblers, Phys. Rev. E 82, 015304 (2010).
  34. S. Das, A. Garg, A. I. Campbell, J. Howse, A. Sen, D. Velegol, R. Golestanian, and S. J. Ebbens, Boundaries can steer active Janus spheres, Nat. Commun. 6, 8999 (2015).
  35. J. Simmchen, J. Katuri, W. E. Uspal, M. N. Popescu, M. Tasinkevych, and S. Sánchez, Topographical pathways guide chemical microswimmers, Nat. Commun. 7, 10598 (2016).
  36. P. Sharan, A. Daddi-Moussa-Ider, J. Agudo-Canalejo, R. Golestanian, and J. Simmchen, Pair interaction between two catalytically active colloids, Small 19, 2300817 (2023).
  37. A. I. Campbell, S. J. Ebbens, P. Illien, and R. Golestanian, Experimental observation of flow fields around active Janus spheres, Nat. Commun. 10, 3952 (2019).
  38. A. Joseph, C. Contini, D. Cecchin, S. Nyberg, L. Ruiz-Perez, J. Gaitzsch, G. Fullstone, X. Tian, J. Azizi, J. Preston, G. Volpe, and G. Battaglia, Chemotactic synthetic vesicles: Design and applications in blood-brain barrier crossing, Sci. Adv. 3, e1700362 (2017).
  39. F. Soto, D. Kupor, M. A. Lopez-Ramirez, F. Wei, E. Karshalev, S. Tang, F. Tehrani, and J. Wang, Onion-like multifunctional microtrap vehicles for attraction–trapping–destruction of biological threats, Angew. Chem. 132, 3508 (2020).
  40. R. Mundaca-Uribe, B. Esteban-Fernández de Ávila, M. Holay, P. L. Venugopalan, B. Nguyen, J. Zhou, A. Abbas, R. H. Fang, L. Zhang, and J. Wang, Zinc microrocket pills: Fabrication and characterization toward active oral delivery, Adv. Healthc. Mater. 9, 2000900 (2020).
  41. S. Tang, F. Zhang, H. Gong, F. Wei, J. Zhuang, E. Karshalev, B. Esteban-Fernández de Ávila, C. Huang, Z. Zhou, Z. Li et al., Enzyme-powered Janus platelet cell robots for active and targeted drug delivery, Sci. Robot. 5, eaba6137 (2020).
  42. P. L. Venugopalan, B. Esteban-Fernández deÁvila, M. Pal, A. Ghosh, and J. Wang, Fantastic voyage of nanomotors into the cell, ACS Nano 14, 9423 (2020).
  43. F. Soto, E. Karshalev, F. Zhang, B. Esteban Fernandez de Avila, A. Nourhani, and J. Wang, Smart materials for microrobots, Chem. Rev. 122, 5365 (2022).
  44. A. Ressnerova, F. Novotny, H. Michalkova, M. Pumera, V. Adam, and Z. Heger, Efficient protein transfection by swarms of chemically powered plasmonic virus-sized nanorobots, ACS Nano 15, 12899 (2021).
  45. C. C. Mayorga-Martinez, J. Zelenka, J. Grmela, H. Michalkova, T. Ruml, J. Mareš, and M. Pumera, Swarming aqua sperm micromotors for active bacterial biofilms removal in confined spaces, Adv. Sci. 8, 2101301 (2021).
  46. C. M. Oral, M. Ussia, and M. Pumera, Self-propelled activated carbon micromotors for “on-the-fly” capture of nitroaromatic explosives, J. Phys. Chem. C 125, 18040 (2021).
  47. M. Ussia, M. Urso, K. Dolezelikova, H. Michalkova, V. Adam, and M. Pumera, Active light-powered antibiofilm ZnO micromotors with chemically programmable properties, Adv. Funct. Mater. 31, 2101178 (2021).
  48. A. C. Hortelão, S. García-Jimeno, M. Cano-Sarabia, T. Patiño, D. Maspoch, and S. Sanchez, Lipobots: Using liposomal vesicles as protective shell of urease-based nanomotors, Adv. Funct. Mater. 30, 2002767 (2020).
  49. L. Wang, A. C. Hortelao, X. Huang, and S. Sánchez, Lipase-powered mesoporous silica nanomotors for triglyceride degradation, Angew. Chem. Int. Ed. 58, 7992 (2019).
  50. Z. Rahiminezhad, A. M. Tamaddon, S. Borandeh, and S. S. Abolmaali, Janus nanoparticles: New generation of multifunctional nanocarriers in drug delivery, bioimaging and theranostics, Appl. Mater. Today. 18, 100513 (2020).
  51. G. Tucci, R. Golestanian, and S. Saha, Nonreciprocal collective dynamics in a mixture of phoretic Janus colloids, New J. Phys. 26, 073006 (2024).
  52. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media (Martinus Nijhoff Publishers, The Hague, The Netherlands, 2012), Vol. 1.
  53. J. F. Brady and G. Bossis, Stokesian dynamics, Annu. Rev. Fluid Mech. 20, 111 (1988).
  54. G. B. Jeffery, The motion of ellipsoidal particles immersed in a viscous fluid, Proc. R. Soc. London A 102, 161 (1922).
  55. V. Ouazan-Reboul, J. Agudo-Canalejo, and R. Golestanian, Non-equilibrium phase separation in mixtures of catalytically active particles: Size dispersity and screening effects, Eur. Phys. J. E 44, 113 (2021).
  56. I. G. Currie and I. Currie, Fundamental Mechanics of Fluids (Taylor & Francis Group, Boca Raton, Florida, 2002).
  57. R. Golestanian, Collective behavior of thermally active colloids, Phys. Rev. Lett. 108, 038303 (2012).
  58. S. Mahdisoltani, R. B. A. Zinati, C. Duclut, A. Gambassi, and R. Golestanian, Nonequilibrium polarity-induced chemotaxis: Emergent galilean symmetry and exact scaling exponents, Phys. Rev. Res. 3, 013100 (2021).
  59. G. Pisegna, N. Rana, R. Golestanian, and S. Saha, Non-reciprocal mixtures in suspension: The role of hydrodynamic interactions, arXiv:2501.01330.
  60. A. Tiribocchi, R. Wittkowski, D. Marenduzzo, and M. E. Cates, Active model H: Scalar active matter in a momentum-conserving fluid, Phys. Rev. Lett. 115, 188302 (2015).
  61. S. Ghose and R. Adhikari, Irreducible representations of oscillatory and swirling flows in active soft matter, Phys. Rev. Lett. 112, 118102 (2014).
  62. S. Michelin and E. Lauga, Geometric tuning of self-propulsion for Janus catalytic particles, Sci. Rep. 7, 42264 (2017).
  63. G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic Press, Inc., San Diego, 1985).
  64. J. L. Anderson, Colloid transport by interfacial forces, Annu. Rev. Fluid Mech. 21, 61 (1989).
  65. M. E. Cates and E. Tjhung, Theories of binary fluid mixtures: from phase-separation kinetics to active emulsions, J. Fluid Mech. 836, P1 (2018).
  66. P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Rev. Mod. Phys. 49, 435 (1977).
  67. E. Lauga and S. Michelin, Stresslets induced by active swimmers, Phys. Rev. Lett. 117, 148001 (2016).
  68. L. Jibuti, L. Qi, C. Misbah, W. Zimmermann, S. Rafaï, and P. Peyla, Self-focusing and jet instability of a microswimmer suspension, Phys. Rev. E 90, 063019 (2014).
  69. X. Garcia, S. Rafaï, and P. Peyla, Light control of the flow of phototactic microswimmer suspensions, Phys. Rev. Lett. 110, 138106 (2013).
  70. M. Abramovitz and I. Stegun (eds.), in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series 55 (U.S. Department of Commerce, Washington, DC, 1964).
  71. E. Kanso and S. Michelin, Phoretic and hydrodynamic interactions of weakly confined autophoretic particles, J. Chem. Phys. 150, 044902 (2019).

Outline

Information

Phys. Rev. Research 7, 033003– Published 1 July, 2025
  • Received 12 February 2025
  • Accepted 30 May 2025
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. Open access publication funded by Max Planck Society.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation