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Boundary accumulation of active rods in microchannels with elliptical cross-section

Chase Brown and Mykhailo Potomkin*

Shawn D. Ryan†

  • Department of Mathematics and Statistics and Center for Applied Data Analysis and Modeling, Cleveland State University, Cleveland, Ohio 44115, USA

  • *Contact author: mykhailp@ucr.edu
  • †http://academic.csuohio.edu/ryan-shawn/
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Phys. Rev. E 112, 045407 – Published 15 October, 2025

DOI: https://doi.org/10.1103/19cn-bn7m

Abstract

Many motile microorganisms and biomimetic microparticles have been successfully modeled as active rods—elongated bodies capable of self-propulsion. A hallmark of active rod dynamics under confinement is their tendency to accumulate at the walls. Unlike passive particles, which typically sediment and cease their motion at the wall, accumulated active rods continue to move along the wall, reorient, and may even escape from it. In addition to boundary accumulation, active rods also exhibit upstream swimming and a tendency to concentrate in regions of high boundary curvature. The dynamics of active rods at the wall and those away from it result in complex and nontrivial distributions. In this work, we examine how wall curvature and extruding fluid flow affect the distribution of active rods by studying elliptical perturbations of tubelike three-dimensional microchannels, that is, cylindrical confinements with circular cross-sections that are common in both natural systems and practical applications. We develop a computational model for individual active rods and, through both analytical methods and Monte Carlo simulations, investigate how their accumulation distribution depends on the background flow, rotational diffusion, and the cross-sectional aspect ratio. Additionally, we examined the role of wall torque on accumulated active rods. While it promotes escape by aligning rods tangentially along flat walls, we showed, both theoretically and numerically, that stable entrapment can occur at regions of high curvature despite this torque.

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References (54)

  1. I. S. Aranson, Bacterial active matter, Rep. Prog. Phys. 85, 076601 (2022).
  2. W. Paxton, A. Sen, and T. Mallouk, Motility of catalytic nanoparticles through self-generated forces, Chem. Eur. J. 11, 6462 (2005).
  3. W. Paxton, S. Sundararajan, T. Mallouk, and A. Sen, Chemical locomotion, Angew. Chem. Int. Ed. Engl. 45, 5420 (2006).
  4. W. Paxton, P. Baker, T. Kline, Y. Wang, T. Mallouk, and A. Sen, Catalytically induced electrokinetics for motors and micropumps, J. Am. Chem. Soc. 128, 14881 (2006).
  5. H. Wensink, J. Dunkel, S. Heidenreich, K. Drescher, R. Goldstein, H. Löwen, and J. M. Yeomans, Meso-scale turbulence in living fluids, Proc. Natl. Acad. Sci. USA 109, 14308 (2012).
  6. A. Sokolov and I. S. Aranson, Physical properties of collective motion in suspensions of bacteria, Phys. Rev. Lett. 109, 248109 (2012).
  7. A. Sokolov, R. E. Goldstein, F. I. Feldchtein, and I. S. Aranson, Enhanced mixing and spatial instability in concentrated bacterial suspensions, Phys. Rev. E 80, 031903 (2009).
  8. 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).
  9. M. Bär, R. Großmann, S. Heidenreich, and F. Peruani, Self-propelled rods: Insights and perspectives for active matter, Annu. Rev. Condens. Matter Phys. 11, 441 (2020).
  10. O. Hallatschek, S. S. Datta, K. Drescher, J. Dunkel, J. Elgeti, B. Waclaw, and N. S. Wingreen, Proliferating active matter, Nat. Rev. Phys. 5, 407 (2023).
  11. A. Sokolov and I. S. Aranson, Reduction of viscosity in suspension of swimming bacteria, Phys. Rev. Lett. 103, 148101 (2009).
  12. B. M. Haines, A. Sokolov, I. S. Aranson, L. Berlyand, and D. A. Karpeev, A three-dimensional model for the effective viscosity of bacterial suspensions, Phys. Rev. E 80, 041922 (2009).
  13. S. D. Ryan, B. M. Haines, L. Berlyand, F. Ziebert, and I. S. Aranson, Viscosity of bacterial suspensions: Hydrodynamic interactions and self-induced noise, Phys. Rev. E 83, 050904(R) (2011).
  14. M. Potomkin, S. Ryan, and L. Berlyand, Effective rheological properties in semi-dilute bacterial suspensions, Bull. Math. Biol. 78, 580 (2016).
  15. J. Hill, O. Kalkanci, J. L. McMurry, and H. Koser, Hydrodynamic surface interactions enable Escherichia coli to seek efficient routes to swim upstream, Phys. Rev. Lett. 98, 068101 (2007).
  16. H. C. Fu, T. R. Powers, and R. Stocker, Bacterial rheotaxis, Proc. Natl. Acad. Sci. USA 109, 4780 (2012).
  17. A. Costanzo, R. Di Leonardo, G. Ruocco, and L. Angelani, Transport of self-propelling bacteria in micro-channel flow, J. Phys.: Condens. Matter 24, 065101 (2012).
  18. 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).
  19. J. Palacci, S. Sacanna, A. Abramian, J. Barral, K. Hanson, A. Grosberg, D. Pine, and P. Chaikin, Artificial rheotaxis, Sci. Adv. 1, e1400214 (2015).
  20. J. Yuan, D. Raizen, and H. Bau, A hydrodynamic mechanism for attraction of undulatory microswimmers to surfaces (bordertaxis), J. R. Soc., Interface 12, 20150227 (2015).
  21. L. Ren, D. Zhou, Z. Mao, P. Xu, T. Huang, and T. Mallouk, Rheotaxis of bimetallic micromotors driven by chemical-acoustic hybrid power, ACS Nano 11, 10591 (2017).
  22. R. Baker, J. Kauffman, A. Laskar, O. Shklyaev, H. Shum, I. Aronson, A. Balazs, and A. Sen, Fight the flow: Collective rheotaxis of artificial swimmers in confined systems, Nanoscale 11, 10944 (2019).
  23. X.-L. Wu and A. Libchaber, Particle diffusion in a quasi-two-dimensional bacterial bath, Phys. Rev. Lett. 84, 3017 (2000).
  24. T. Vicsek and A. Zafeiris, Collective motion, Phys. Rep. 517, 71 (2012).
  25. S. D. Ryan, A. Sokolov, L. Berlyand, and I. Aranson, Correlation properties of collective motion in bacterial suspension, New J. Phys. 15, 105021 (2013).
  26. M. te Vrugt and R. Wittkowski, A review of active matter reviews, Eur. Phys. J. E 48, 12 (2025).
  27. M. Potomkin, A. Kaiser, L. Berlyand, and I. Aranson, Focusing of active particles in a converging flow, New J. Phys. 19, 115005 (2017).
  28. L. D. Rubio, M. Potomkin, R. D. Baker, A. Sen, L. Berlyand, and I. S. Aranson, Self-propulsion and shear flow align active particles in nozzles and channels, Adv. Intell. Syst. 3, 2000178 (2021).
  29. Y. Fily, A. Baskaran, and M. F. Hagan, Dynamics of self-propelled particles under strong confinement, Soft Matter 10, 5609 (2014).
  30. Y. Fily, A. Baskaran, and M. F. Hagan, Dynamics and density distribution of strongly confined noninteracting nonaligning self-propelled particles in a nonconvex boundary, Phys. Rev. E 91, 012125 (2015).
  31. N. Nikola, A. P. Solon, Y. Kafri, M. Kardar, J. Tailleur, and R. Voituriez, Active particles with soft and curved walls: Equation of state, ratchets, and instabilities, Phys. Rev. Lett. 117, 098001 (2016).
  32. A. C. Quillen, J. P. Smucker, and A. Peshkov, Boids in a loop: Self-propelled particles within a flexible boundary, Phys. Rev. E 101, 052618 (2020).
  33. K. Drescher, J. Dunkel, L. H. Cisneros, S. Ganguly, and R. E. Goldstein, Fluid dynamics and noise in bacterial cell–cell and cell–surface scattering, Proc. Natl. Acad. Sci. USA 108, 10940 (2011).
  34. B. Ezhilan and D. Saintillan, Transport of a dilute active suspension in pressure-driven channel flow, J. Fluid Mech. 777, 482 (2015).
  35. N. Figueroa-Morales, G. Mino, A. Rivera, R. Caballero, E. Clément, E. Altshuler, and A. Lindner, Living on the edge: Transfer and traffic of E. coli in a confined flow, Soft Matter 11, 6284 (2015).
  36. A. Bukatin, P. Denissenko, and V. Kantsler, Self-organization and multi-line transport of human spermatozoa in rectangular microchannels due to cell-cell interactions, Sci. Rep. 10, 9830 (2020).
  37. O. Sipos, K. Nagy, R. Di Leonardo, and P. Galajda, Hydrodynamic trapping of swimming bacteria by convex walls, Phys. Rev. Lett. 114, 258104 (2015).
  38. M. Paoluzzi, R. Di Leonardo, M. C. Marchetti, and L. Angelani, Shape and displacement fluctuations in soft vesicles filled by active particles, Sci. Rep. 6, 34146 (2016).
  39. L. Nicolle, Catheter associated urinary tract infections, Antimicrob. Resist. Infect. Control 3, 23 (2014).
  40. S. Park, P. Wolanin, E. Yuzbashyan, P. Silberzan, J. Stock, and R. Austin, Motion to form a quorum, Science 301, 188 (2003).
  41. N. Figueroa-Morales, A. Rivera, R. Soto, A. Lindner, E. Altshuler, and É. Clément, E. coli “super-contaminates” narrow ducts fostered by broad run-time distribution, Sci. Adv. 6, eaay0155 (2020).
  42. H. Brenner and R. Cox, The resistance to a particle of arbitrary shape in translational motion at small Reynolds numbers, J. Fluid Mech. 17, 561 (1963).
  43. M. Potomkin, V. Gyrya, I. Aranson, and L. Berlyand, Collision of microswimmers in a viscous fluid, Phys. Rev. E 87, 053005 (2013).
  44. M. Ramia, D. Tullock, and N. Phan-Thien, The role of hydrodynamic interaction in the locomotion of microorganisms, Biophys. J. 65, 755 (1993).
  45. W. DiLuzio, L. Turner, M. Mayer, P. Garstecki, D. Weibel, H. Berg, and G. Whitesides, Escherichia coli swim on the right-hand side, Nature (London) 435, 1271 (2005).
  46. See Supplemental Material at http://link.aps.org/supplemental/10.1103/19cn-bn7m for descriptions of supplementary videos, the derivation of the wall torque formula, and the justification of models describing angular dynamics in both lake and river problems in the absence of rotational diffusion.
  47. M. Potomkin, M. Tournus, L. Berlyand, and I. Aranson, Flagella bending affects macroscopic properties of bacterial suspensions, J. R. Soc., Interface 14, 20161031 (2017).
  48. X. Yang, M. L. Manning, and M. C. Marchetti, Aggregation and segregation of confined active particles, Soft Matter 10, 6477 (2014).
  49. E. Lushi, H. Wioland, and R. E. Goldstein, Fluid flows created by swimming bacteria drive self-organization in confined suspensions, Proc. Natl. Acad. Sci. USA 111, 9733 (2014).
  50. H. Zaki, E. Lushi, and K. E. Severi, Larval zebrafish exhibit collective circulation in confined spaces, Front. Phys. 9, 678600 (2021).
  51. M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
  52. J. O'Byrne, A. Solon, J. Tailleur, and Y. Zhao, An introduction to motility-induced phase separation, in Out-of-equilibrium Soft Matter (The Royal Society of Chemistry, London, UK, 2023).
  53. L. Berlyand, P. Jabin, M. Potomkin, and E. Ratajczyk, A kinetic approach to active rods dynamics in confined domains, Multiscale Model. Simul. 18, 1 (2020).
  54. L. Berlyand, S. Dang, P.-E. Jabin, and M. Potomkin, Multiscale analysis of a kinetic model of confined suspensions of self-propelled rods, arXiv:2508.16003.

Outline

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Phys. Rev. E 112, 045407– Published 15 October, 2025
  • Received 10 September 2024
  • Revised 26 August 2025
  • Accepted 9 September 2025
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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.

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