- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

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

Nonmonotonic Diffusion in Sheared Active Suspensions of Squirmers

Zhouyang Ge1,2,*,†, John F. Brady3, and Gwynn J. Elfring1,‡

  • *Contact author: zhoge@nju.edu.cn
  • †Present address: School of Materials Science and Intelligent Engineering, Nanjing University, Suzhou 215163, China.
  • ‡Contact author: gelfring@mech.ubc.ca
PDF

Phys. Rev. Lett. 135, 238302 – Published 4 December, 2025

DOI: https://doi.org/10.1103/54qq-1s51

Abstract

We investigate how shear influences the dynamics of active particles in dilute to concentrated suspensions. Using apolar active suspensions of squirmers as model systems, we show how their longtime diffusive dynamics can surprisingly slow down and vary nonmonotonically with the shear rate arising from an interplay between the activity-induced persistent motion and shear-induced reorientation and diffusion. Further simulations of self-propelled particles with tunable persistence exhibit richer dynamics and confirm the observed coupling, suggesting that nonmonotonic diffusion may be a general feature of fluids endowed with an underlying microstructure and large persistence. Our results reveal a nonlinear effect of shear on diffusion in active suspensions, elucidate how internal and external forcing interact, and provide new possibilities to modulate transport in active fluids.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (58)

  1. M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Rev. Mod. Phys. 85, 1143 (2013).
  2. G. Gompper, R. G. Winkler, T. Speck, A. Solon, C. Nardini, F. Peruani, H. Löwen, R. Golestanian, U. B. Kaupp, L. Alvarez et al., J. Phys. Condens. Matter 32, 193001 (2020).
  3. X. L. Wu and A. Libchaber, Phys. Rev. Lett. 84, 3017 (2000).
  4. M. J. Kim and K. S. Breuer, Phys. Fluids 16, L78 (2004).
  5. D. T. N. Chen, A. W. C. Lau, L. A. Hough, M. F. Islam, M. Goulian, T. C. Lubensky, and A. G. Yodh, Phys. Rev. Lett. 99, 148302 (2007).
  6. G. Miño, T. E. Mallouk, T. Darnige, M. Hoyos, J. Dauchet, J. Dunstan, R. Soto, Y. Wang, A. Rousselet, and E. Clement, Phys. Rev. Lett. 106, 048102 (2011).
  7. A. E. Patteson, A. Gopinath, P. K. Purohit, and P. E. Arratia, Soft Matter 12, 2365 (2016).
  8. Y. Peng, L. Lai, Y. S. Tai, K. Zhang, X. Xu, and X. Cheng, Phys. Rev. Lett. 116, 068303 (2016).
  9. C. Dombrowski, L. Cisneros, S. Chatkaew, R. E. Goldstein, and J. O. Kessler, Phys. Rev. Lett. 93, 098103 (2004).
  10. A. Sokolov, I. S. Aranson, J. O. Kessler, and R. E. Goldstein, Phys. Rev. Lett. 98, 158102 (2007).
  11. H. H. Wensink, J. Dunkel, S. Heidenreich, K. Drescher, R. E. Goldstein, H. Löwen, and J. M. Yeomans, Proc. Natl. Acad. Sci. U.S.A. 109, 14308 (2012).
  12. J. Dunkel, S. Heidenreich, K. Drescher, H. H. Wensink, M. Bär, and R. E. Goldstein, Phys. Rev. Lett. 110, 228102 (2013).
  13. Y. Peng, Z. Liu, and X. Cheng, Sci. Adv. 7, eabd1240 (2021).
  14. J. Hill, O. Kalkanci, J. L. McMurry, and H. Koser, Phys. Rev. Lett. 98, 068101 (2007).
  15. T. Kaya and H. Koser, Phys. Rev. Lett. 103, 138103 (2009).
  16. T. Kaya and H. Koser, Biophys. J. 102, 1514 (2012).
  17. H. M. López, J. Gachelin, C. Douarche, H. Auradou, and E. Clément, Phys. Rev. Lett. 115, 028301 (2015).
  18. D. Saintillan, Annu. Rev. Fluid Mech. 50, 563 (2018).
  19. J. Y. Chui, C. Douarche, H. Auradou, and R. Juanes, Soft Matter 17, 7004 (2021).
  20. E. C. Eckstein, D. G. Bailey, and A. H. Shapiro, J. Fluid Mech. 79, 191 (1977).
  21. D. Leighton and A. Acrivos, J. Fluid Mech. 177, 109 (1987).
  22. V. Breedveld, D. van den Ende, A. Tripathi, and A. Acrivos, J. Fluid Mech. 375, 297 (1998).
  23. A. Sierou and J. F. Brady, J. Fluid Mech. 506, 285 (2004).
  24. A. Acrivos, J. Rheol. 39, 813 (1995).
  25. F. da Cunha and E. Hinch, J. Fluid Mech. 309, 211 (1996).
  26. G. Drazer, J. Koplik, B. Khusid, and A. Acrivos, J. Fluid Mech. 460, 307 (2002).
  27. H. Zhang, P. Pham, B. Metzger, D. I. Kopelevich, and J. E. Butler, Phys. Rev. Fluids 8, 064303 (2023).
  28. H. Zhang, D. I. Kopelevich, and J. E. Butler, J. Fluid Mech. 1001, A42 (2024).
  29. S. Athani, B. Metzger, R. Mari, Y. Forterre, and P. Rognon, J. Fluid Mech. 998, A55 (2024).
  30. A. M. Fiore and J. W. Swan, J. Fluid Mech. 878, 544 (2019).
  31. Z. Ge and G. J. Elfring, J. Fluid Mech. 1003, A17 (2025).
  32. M. J. Lighthill, Commun. Pure Appl. Math. 5, 109 (1952).
  33. J. R. Blake, J. Fluid Mech. 46, 199 (1971).
  34. T. J. Pedley, IMA J. Appl. Math. 81, 488 (2016).
  35. G. J. Elfring and J. F. Brady, J. Fluid Mech. 952, A19 (2022).
  36. T. Ishikawa, M. Simmonds, and T. J. Pedley, J. Fluid Mech. 568, 119 (2006).
  37. T. Ishikawa, J. T. Locsei, and T. J. Pedley, Phys. Rev. E 82, 021408 (2010).
  38. B. Delmotte, E. E. Keaveny, E. Climent, and F. Plouraboué, IMA J. Appl. Math. 83, 680 (2018).
  39. See Supplemental Material at http://link.aps.org/supplemental/10.1103/54qq-1s51 for a detailed description of our simulation method, setup, and verification, which also includes Refs. [40–46].
  40. Z. Ge and G. J. Elfring, Phys. Rev. E 106, 054616 (2022).
  41. J. Israelachvili, Intermolecular and Surface Forces (Academic Press, New York, 2011).
  42. A. W. Lees and S. F. Edwards, J. Phys. C 5, 1921 (1972).
  43. R. Mari, R. Seto, J. F. Morris, and M. M. Denn, J. Rheol. 58, 1693 (2014).
  44. C. Beenakker and P. Mazur, Physica (Amsterdam) 126A, 349 (1984).
  45. A. J. Ladd, J. Chem. Phys. 93, 3484 (1990).
  46. F. Guzmán-Lastra and R. Soto, Phys. Rev. E 87, 042311 (2013).
  47. G. Batchelor and J.-T. Green, J. Fluid Mech. 56, 375 (1972).
  48. P. Romanczuk, M. Bär, W. Ebeling, B. Lindner, and L. Schimansky-Geier, Eur. Phys. J. Special Topics 202, 1 (2012).
  49. R. Golestanian, Phys. Rev. Lett. 102, 188305 (2009).
  50. Y. Fily and M. C. Marchetti, Phys. Rev. Lett. 108, 235702 (2012).
  51. M. Sandoval, N. K. Marath, G. Subramanian, and E. Lauga, J. Fluid Mech. 742, 50 (2014).
  52. S. C. Takatori and J. F. Brady, Phys. Rev. Lett. 118, 018003 (2017).
  53. S. M. Fielding, D. Marenduzzo, and M. E. Cates, Phys. Rev. E 83, 041910 (2011).
  54. S. Guo, D. Samanta, Y. Peng, X. Xu, and X. Cheng, Proc. Natl. Acad. Sci. U.S.A. 115, 7212 (2018).
  55. V. A. Martinez, E. Clément, J. Arlt, C. Douarche, A. Dawson, J. Schwarz-Linek, A. K. Creppy, V. Škultéty, A. N. Morozov, H. Auradou, and W. C. K. Poon, Proc. Natl. Acad. Sci. U.S.A. 117, 2326 (2020).
  56. J. John, A. Panahi, D. Pu, and G. Natale, Curr. Opin. Colloid Interface Sci. 75, 101886 (2025).
  57. J. Martín-Roca, C. Valeriani, K. Thijssen, T. Shendruk, and A. Cacciuto, Phys. Rev. Lett., 10.1103/13q9-xp1q.
  58. The source code to generate all data reported in this article is publicly available at https://github.com/GeZhouyang/FSD.

Outline

Information

Phys. Rev. Lett. 135, 238302– Published 4 December, 2025
  • Received 13 May 2025
  • Revised 13 August 2025
  • Accepted 12 November 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. Funded by Bibsam.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation