- 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

Hydroelastic scattering and trapping of microswimmers

Sagnik Garai1, Ursy Makanga1, Akhil Varma1, and Christina Kurzthaler1,2,3,*

  • *Contact author: ckurzthaler@pks.mpg.de
PDF

Phys. Rev. Research 7, L042005 – Published 3 October, 2025

DOI: https://doi.org/10.1103/rcdx-gftq

Abstract

Deformable boundaries are omnipresent in the habitats of swimming microorganisms, leading to intricate hydroelastic couplings. Employing a perturbation theory, valid for small deformations, we study the swimming dynamics of pushers and pullers near instantaneously deforming boundaries, endowed with a bending rigidity and surface tension. Our results reveal that pushers can either reorient away from the boundary, leading to overall hydroelastic scattering, or become trapped by the boundary, akin to the enhanced trapping found for pullers. These findings demonstrate that the complex hydroelastic interactions can generate behaviors that are in striking contrast to swimming near planar walls.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (76)

  1. E. Lauga and T. R. Powers, The hydrodynamics of swimming microorganisms, Rep. Prog. Phys. 72, 096601 (2009).
  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. E. Lauga, The Fluid Dynamics of Cell Motility, 1st ed. (Cambridge University Press, Cambridge, 2020).
  5. G. Gompper et al., The 2020 motile active matter roadmap, J. Phys.: Condens. Matter 32, 193001 (2020).
  6. C. Kurzthaler, L. Gentile, and H. A. Stone, Out-of-Equilibrium Soft Matter (The Royal Society of Chemistry, 2023).
  7. E. M. Purcell, Life at low Reynolds number, Am. J. Phys. 45, 3 (1977).
  8. R. Hartmann, P. K. Singh, P. Pearce, R. Mok, B. Song, F. Díaz-Pascual, J. Dunkel, and K. Drescher, Emergence of three-dimensional order and structure in growing biofilms, Nat. Phys. 15, 251 (2019).
  9. 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).
  10. S. Otte, E. P. Ipiña, R. Pontier-Bres, D. Czerucka, and F. Peruani, Statistics of pathogenic bacteria in the search of host cells, Nat. Commun. 12, 1990 (2021).
  11. S. S. Suarez and A. A. Pacey, Sperm transport in the female reproductive tract, Hum. Reprod. Update 12, 23 (2006).
  12. R. Golestanian, Phoretic active matter, arXiv:1909.03747 [cond-mat.soft].
  13. G. Volpe et al., Roadmap for animate matter, J. Phys.: Condens. Matter 37, 333501 (2025).
  14. Z. Wu, Y. Chen, D. Mukasa, O. S. Pak, and W. Gao, Medical micro/nanorobots in complex media, Chem. Soc. Rev. 49, 8088 (2020).
  15. B. J. Nelson, I. K. Kaliakatsos, and J. J. Abbott, Microrobots for minimally invasive medicine, Annu. Rev. Biomed. Eng. 12, 55 (2010).
  16. E. Lauga, W. R. DiLuzio, G. M. Whitesides, and H. A. Stone, Swimming in circles: Motion of bacteria near solid boundaries, Biophys. J. 90, 400 (2006).
  17. R. Di Leonardo, D. Dell'Arciprete, L. Angelani, and V. Iebba, Swimming with an image, Phys. Rev. Lett. 106, 038101 (2011).
  18. K. Ishimoto and E. A. Gaffney, Squirmer dynamics near a boundary, Phys. Rev. E 88, 062702 (2013).
  19. G.-J. Li and A. M. Ardekani, Hydrodynamic interaction of microswimmers near a wall, Phys. Rev. E 90, 013010 (2014).
  20. W. E. Uspal, M. N. Popescu, S. Dietrich, and M. Tasinkevych, Self-propulsion of a catalytically active particle near a planar wall: from reflection to sliding and hovering, Soft Matter 11, 434 (2015).
  21. M. Kuron, P. Stärk, C. Holm, and J. de Graaf, Hydrodynamic mobility reversal of squirmers near flat and curved surfaces, Soft Matter 15, 5908 (2019).
  22. N. Desai and S. Michelin, Instability and self-propulsion of active droplets along a wall, Phys. Rev. Fluids 6, 114103 (2021).
  23. A. Poddar, A. Bandopadhyay, and S. Chakraborty, Near-wall hydrodynamic slip triggers swimming state transition of micro-organisms, J. Fluid Mech. 894, A11 (2020).
  24. C. Kurzthaler and H. A. Stone, Microswimmers near corrugated, periodic surfaces, Soft Matter 17, 3322 (2021).
  25. K. Ishimoto, E. A. Gaffney, and D. J. Smith, Squirmer hydrodynamics near a periodic surface topography, Front. Cell Dev. Biol. 11, 1123446 (2023).
  26. W. Helfrich, Elastic properties of lipid bilayers: Theory and possible experiments, Z. Naturforsch. C 28, 693 (1973).
  27. F. L. H. Brown, Elastic modeling of biomembranes and lipid bilayers, Annu. Rev. Phys. Chem. 59, 685 (2008).
  28. H. R. Vutukuri, M. Hoore, C. Abaurrea-Velasco, L. van Buren, A. Dutto, T. Auth, D. A. Fedosov, G. Gompper, and J. Vermant, Active particles induce large shape deformations in giant lipid vesicles, Nature (London) 586, 52 (2020).
  29. S. C. Takatori and A. Sahu, Active contact forces drive nonequilibrium fluctuations in membrane vesicles, Phys. Rev. Lett. 124, 158102 (2020).
  30. F. Fessler, M. Wittmann, J. Simmchen, and A. Stocco, Autonomous engulfment of active colloids by giant lipid vesicles, Soft Matter 20, 5904 (2024).
  31. A. Azadbakht, T. R. Weikl, and D. J. Kraft, Nonadditivity in many-body interactions between membrane-deforming spheres increases disorder, ACS Nano 18, 23067 (2024).
  32. R. Trouilloud, T. S. Yu, A. E. Hosoi, and E. Lauga, Soft swimming: Exploiting deformable interfaces for low Reynolds number locomotion, Phys. Rev. Lett. 101, 048102 (2008).
  33. V. A. Shaik and A. M. Ardekani, Motion of a model swimmer near a weakly deforming interface, J. Fluid Mech. 824, 42 (2017).
  34. R. Ledesma-Aguilar and J. M. Yeomans, Enhanced motility of a microswimmer in rigid and elastic confinement, Phys. Rev. Lett. 111, 138101 (2013).
  35. J. M. Skotheim and L. Mahadevan, Soft lubrication, Phys. Rev. Lett. 92, 245509 (2004).
  36. L. Bureau, G. Coupier, and T. Salez, Lift at low Reynolds number, Eur. Phys. J. E 46, 111 (2023).
  37. B. Rallabandi, Fluid-elastic interactions near contact at low Reynolds number, Annu. Rev. Fluid Mech. 56, 491 (2024).
  38. H. S. Davies, D. Débarre, N. El Amri, C. Verdier, R. P. Richter, and L. Bureau, Elastohydrodynamic lift at a soft wall, Phys. Rev. Lett. 120, 198001 (2018).
  39. H. Lorentz, A general theorem concerning the motion of a viscous fluid and a few consequences derived from it, Versl. Kon. Acad. Wet. Amst. 5, 168 (1897).
  40. S. H. Lee, R. S. Chadwick, and L. G. Leal, Motion of a sphere in the presence of a plane interface. Part 1. An approximate solution by generalization of the method of Lorentz, J. Fluid Mech. 93, 705 (1979).
  41. C. Berdan II and L. G. Leal, Motion of a sphere in the presence of a deformable interface: I. Perturbation of the interface from flat: the effects on drag and torque, J. Colloid. Interface Sci. 87, 62 (1982).
  42. B. Rallabandi, N. Oppenheimer, M. Y. B. Zion, and H. A. Stone, Membrane-induced hydroelastic migration of a particle surfing its own wave, Nat. Phys. 14, 1211 (2018).
  43. K. Drescher, R. E. Goldstein, N. Michel, M. Polin, and I. Tuval, Direct measurement of the flow field around swimming microorganisms, Phys. Rev. Lett. 105, 168101 (2010).
  44. 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).
  45. A. Daddi-Moussa-Ider, B. Rallabandi, S. Gekle, and H. A. Stone, Reciprocal theorem for the prediction of the normal force induced on a particle translating parallel to an elastic membrane, Phys. Rev. Fluids 3, 084101 (2018).
  46. S. Nambiar and J. S. Wettlaufer, Hydrodynamics of slender swimmers near deformable interfaces, Phys. Rev. Fluids 7, 054001 (2022).
  47. A. P. Berke, L. Turner, H. C. Berg, and E. Lauga, Hydrodynamic attraction of swimming microorganisms by surfaces, Phys. Rev. Lett. 101, 038102 (2008).
  48. P. Prakash, M. Vona, and R. E. Goldstein, Feeders and expellers, two types of animalcules with outboard cilia, have distinct surface interactions, Phys. Rev. Fluids 9, 103101 (2024).
  49. S. Kim and S. Karrila, Microhydrodynamics: Principles and Selected Applications, Butterworth-Heinemann Series in Chemical Engineering (Dover Publications, Mineola, New York, 2005).
  50. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media, Mechanics of Fluids and Transport Processes (Springer Netherlands, Dordrecht, 1983), Vol. 1.
  51. L. G. Leal, Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes (Cambridge University Press, Cambridge, 2007), Vol. 7.
  52. See Supplemental Material at http://link.aps.org/supplemental/10.1103/rcdx-gftq, for details on the theory and simulations, which includes Refs. [67, 68, 69, 70, 71, 72, 73, 74, 75, 76].
  53. J. F. Faucon, M. D. Mitov, P. Méléard, I. Bivas, and P. Bothorel, Bending elasticity and thermal fluctuations of lipid membranes. Theoretical and experimental requirements, J. Phys. 50, 2389 (1989).
  54. F. Brochard and J. F. Lennon, Frequency spectrum of the flicker phenomenon in erythrocytes, J. Phys. 36, 1035 (1975).
  55. H. Masoud and H. A. Stone, The reciprocal theorem in fluid dynamics and transport phenomena, J. Fluid Mech. 879, P1 (2019).
  56. G. J. Elfring, A note on the reciprocal theorem for the swimming of simple bodies, Phys. Fluids 27, 023101 (2015).
  57. S. E. Spagnolie and E. Lauga, Hydrodynamics of self-propulsion near a boundary: predictions and accuracy of far-field approximations, J. Fluid Mech. 700, 105 (2012).
  58. J. Hu, M. Yang, G. Gompper, and R. G. Winkler, Modelling the mechanics and hydrodynamics of swimming E. coli, Soft Matter 11, 7867 (2015).
  59. 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).
  60. Y. Li and P. R. ten Wolde, Shape transformations of vesicles induced by swim pressure, Phys. Rev. Lett. 123, 148003 (2019).
  61. C. Wang, Y.-k. Guo, W.-d. Tian, and K. Chen, Shape transformation and manipulation of a vesicle by active particles, J. Chem. Phys. 150, 044907 (2019).
  62. V. Kantsler, J. Dunkel, M. Polin, and R. E. Goldstein, Ciliary contact interactions dominate surface scattering of swimming eukaryotes, Proc. Natl. Acad. Sci. USA 110, 1187 (2013).
  63. N. Fares, M. Lavaud, Z. Zhang, A. Jha, Y. Amarouchene, and T. Salez, Observation of Brownian elastohydrodynamic forces acting on confined soft colloids, Proc. Natl. Acad. Sci. USA 121, e2411956121 (2024).
  64. M. Molaei, M. Barry, R. Stocker, and J. Sheng, Failed escape: Solid surfaces prevent tumbling of Escherichia coli, Phys. Rev. Lett. 113, 068103 (2014).
  65. G. Junot, T. Darnige, A. Lindner, V. A. Martinez, J. Arlt, A. Dawson, W. C. Poon, H. Auradou, and E. Clément, Run-to-tumble variability controls the surface residence times of E. coli bacteria, Phys. Rev. Lett. 128, 248101 (2022).
  66. C. Kurzthaler, Y. Zhao, N. Zhou, J. Schwarz-Linek, C. Devailly, J. Arlt, J.-D. Huang, W. C. K. Poon, T. Franosch, J. Tailleur, and V. A. Martinez, Characterization and control of the run-and-tumble dynamics of Escherichia coli, Phys. Rev. Lett. 132, 038302 (2024).
  67. M. J. Lighthill, On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers, Commun. Pure Appl. Math. 5, 109 (1952).
  68. 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).
  69. M. N. Popescu, W. E. Uspal, and S. Dietrich, Self-diffusiophoresis of chemically active colloids, Eur. Phys. J.: Spec. Top. 225, 2189 (2016).
  70. S. Michelin, Self-propulsion of chemically active droplets, Annu. Rev. Fluid Mech. 55, 77 (2023).
  71. M. Deserno, Fluid lipid membranes: From differential geometry to curvature stresses, Chem. Phys. Lipids 185, 11 (2015).
  72. K. Kamrin, M. Z. Bazant, and H. A. Stone, Effective slip boundary conditions for arbitrary periodic surfaces: The surface mobility tensor, J. Fluid Mech. 658, 409 (2010).
  73. A. T. Chwang and T. Y.-T. Wu, Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows, J. Fluid Mech. 67, 787 (1975).
  74. H. Bateman and B. M. Project, Tables of Integral Transforms (McGraw-Hill Book Company, New York, 1954).
  75. K. Aderogba and J. R. Blake, Action of a force near the planar surface between two semi-infinite immiscible liquids at very low Reynolds numbers, Bull. Aust. Math. Soc. 18, 345 (1978).
  76. M. Abramowitz, Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables (Dover Publications, Inc., Mineola, New York, 1974).

Outline

Information

Phys. Rev. Research 7, L042005– Published 3 October, 2025
  • Received 4 February 2025
  • Accepted 1 September 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