Hydrodynamics in Motile Active Matter

Reference work entry


Hydrodynamic interactions determine the individual and collective behavior of nano- to micrometer size active objects such as swimming bacteria, sperm, algae, and synthetic colloidal microswimmers. Based on the Navier-Stokes equations of hydrodynamics, the major contributions to the flow field of a swimmer in a Newtonian fluid are presented. The propulsion of beating and rotating filaments is shown to emerge as consequence of the distinct friction coefficients for parallel and perpendicular motion of the filament. Hydrodynamic interactions with a wall lead to a preferred alignment of a swimmer adjacent to a wall. Moreover, the rotational motion of a flagellar bundle of swimming bacteria combined with the counterrotation of the cell body leads to circular trajectories on a surface, where the handedness depends on the wall slip. Even more, the collective behavior of active matter is determined by hydrodynamic interactions, which is illustrated by cilia synchronization and the squirmer model for microswimmers.


  1. Abkenar M, Marx K, Auth T, Gompper G (2013) Collective behavior of penetrable self-propelled rods in two dimensions. Phys Rev E 88:062314CrossRefADSGoogle Scholar
  2. Afzelius B (1976) A human syndrome caused by immotile cilia. Science 193:317CrossRefADSGoogle Scholar
  3. Alarcón F, Valeriani C, Pagonabarraga I (2017) Morphology of clusters of attractive dry and wet self-propelled spherical particle suspensions. Soft Matter 13:814CrossRefADSGoogle Scholar
  4. Bechinger C, Di Leonardo R, Löwen H, Reichhardt C, Volpe G, Volpe G (2016) Active particles in complex and crowded environments. Rev Mod Phys 88:045006CrossRefADSMathSciNetGoogle Scholar
  5. Berg HC (2003) The rotary motor of bacterial flagella. Annu Rev Biochem 72:19CrossRefGoogle Scholar
  6. Berke AP, Turner L, Berg HC, Lauga E (2008) Hydrodynamic attraction of swimming microorganisms by surfaces. Phys Rev Lett 101:038102CrossRefADSGoogle Scholar
  7. Bialké J, Speck T, Löwen H (2012) Crystallization in a dense suspension of self-propelled particles. Phys Rev Lett 108:168301CrossRefADSGoogle Scholar
  8. Blake JR (1971) A spherical envelope approach to ciliary propulsion. J Fluid Mech 46:199CrossRefADSzbMATHGoogle Scholar
  9. Brumley DR, Polin M, Pedley TJ, Goldstein RE (2012) Hydrodynamic synchronization and metachronal waves on the surface of the colonial alga Volvox carteri. Phys Rev Lett 109:268102CrossRefADSGoogle Scholar
  10. Buttinoni I, Bialké J, Kümmel F, Löwen H, Bechinger C, Speck T (2013) Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles. Phys Rev Lett 110:238301CrossRefADSGoogle Scholar
  11. Calladine CR (1975) Construction of bacterial flagella. Nature 255:121CrossRefADSGoogle Scholar
  12. Cartwright JHE, Piro O, Tuval I (2004) Fluid-dynamical basis of the embryonic development of left-right asymmetry in vertebrates. Proc Natl Acad Sci USA 101:7234CrossRefADSGoogle Scholar
  13. Cates ME, Tailleur J (2015) Motility-induced phase separation. Annu Rev Condens Matter Phys 6:219CrossRefADSGoogle Scholar
  14. Copeland MF, Weibel DB (2009) Bacterial swarming: a model system for studying dynamic self-assembly. Soft Matter 5:1174CrossRefADSGoogle Scholar
  15. Dhont JKG (1996) An introduction to dynamics of colloids. Elsevier, AmsterdamGoogle Scholar
  16. Di Leonardo R, Dell’Arciprete D, Angelani L, Iebba V (2011) Swimming with an image. Phys Rev Lett 106:038101CrossRefADSGoogle Scholar
  17. Drescher K, Goldstein RE, Tuval I (2010) Fidelity of adaptive phototaxis. Proc Natl Acad Sci USA 107:11171CrossRefADSGoogle Scholar
  18. Drescher K, Dunkel J, Cisneros LH, Ganguly S, Goldstein RE (2011) Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering. Proc Natl Acad Sci USA 10940:108Google Scholar
  19. Elgeti J, Gompper G (2013) Emergence of metachronal waves in cilia arrays. Proc Natl Acad Sci USA 110:4470CrossRefADSGoogle Scholar
  20. Elgeti J, Gompper G (2016) Microswimmers near surfaces. Eur Phys J Spec Top 225:2333CrossRefGoogle Scholar
  21. Elgeti J, Winkler RG, Gompper G (2015) Physics of microswimmers—single particle motion and collective behavior: a review. Rep Prog Phys 78:056601CrossRefADSMathSciNetGoogle Scholar
  22. Ginelli F, Peruani F, Bär M, Chaté H (2010) Large-scale collective properties of self-propelled rods. Phys Rev Lett 104:184502CrossRefADSGoogle Scholar
  23. Götze IO, Gompper G (2010) Mesoscale simulations of hydrodynamic squirmer interactions. Phys Rev E 82:041921CrossRefADSGoogle Scholar
  24. Gray J, Hancock GJ (1955) The propulsion of sea-urchin spermatozoa. J Exp Biol 32:802Google Scholar
  25. Heinrichsen J (1978) Bacterial surface translocation: a survey and a classification. Bacteriol Rev 36:478CrossRefGoogle Scholar
  26. Hu J, Wysocki A, Winkler RG, Gompper G (2015a) Physical sensing of surface properties by microswimmers – directing bacterial motion via wall slip. Sci Rep 5:9586CrossRefADSGoogle Scholar
  27. Hu J, Yang M, Gompper G, Winkler RG (2015b) Modelling the mechanics and hydrodynamics of swimming E. coli. Soft Matter 11:7843Google Scholar
  28. Ishikawa T (2009) Suspension biomechanics of swimming microbes. J R Soc Interface 6:815CrossRefGoogle Scholar
  29. Ishikawa T, Simmonds MP, Pedley TJ (2006) Hydrodynamic interaction of two swimming model micro-organisms. J Fluid Mech 568:119CrossRefADSMathSciNetzbMATHGoogle Scholar
  30. Kearns DB (2010) A field guide to bacterial swarming motility. Nat Rev Microbiol 8:634CrossRefGoogle Scholar
  31. Keller SR, Wu TY (1977) A porous prolate-spheroidal model for ciliated micro-organisms. J Fluid Mech 80:259CrossRefADSzbMATHGoogle Scholar
  32. Kim S, Karrila SJ (1991) Microhydrodynamics: principles and selected applications. Butterworth-Heinemann, BostonGoogle Scholar
  33. Kyoya K, Matsunaga D, Imai Y, Omori T, Ishikawa T (2015) Shape matters: near-field fluid mechanics dominate the collective motions of ellipsoidal squirmers. Phys Rev E 92:063027CrossRefADSGoogle Scholar
  34. Lauga E, Powers TR (2009) The hydrodynamics of swimming microorganisms. Rep Prog Phys 72:096601CrossRefADSMathSciNetGoogle Scholar
  35. Lauga E, DiLuzio WR, Whitesides GM, Stone HA (2006) Swimming in circles: motion of bacteria near solid boundaries. Biophys J 90:400CrossRefGoogle Scholar
  36. Lighthill MJ (1952) On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers. Comm Pure Appl Math 5:109CrossRefMathSciNetzbMATHGoogle Scholar
  37. Llopis I, Pagonabarraga I (2010) Hydrodynamic interactions in squirmer motion: swimming with a neighbour and close to a wall. J Non-Newtonian Fluid Mech 165:946CrossRefzbMATHGoogle Scholar
  38. López HM, Gachelin J, Douarche C, Auradou H, Clément E (2015) Turning bacteria suspensions into superfluids. Phys Rev Lett 115:028301CrossRefADSGoogle Scholar
  39. Macnab RM (1977) Bacterial flagella rotating in bundles: a study in helical geometry. Proc Natl Acad Sci USA 74:221CrossRefADSGoogle Scholar
  40. Marchetti MC, Fily Y, Henkes S, Patch A, Yllanes D (2016) Minimal model of active colloids highlights the role of mechanical interactions in controlling the emergent behavior of active matter. Curr Opin Colloid Interface Sci 21:34CrossRefGoogle Scholar
  41. Moore HDM, Taggart DA (1995) Sperm pairing in the opossum increases the efficiency of sperm movement in a viscous environment. Biol Reprod 52:947CrossRefGoogle Scholar
  42. Palacci J, Sacanna S, Steinberg AP, Pine DJ, Chaikin PM (2013) Living crystals of light-activated colloidal surfers. Science 339:936CrossRefADSGoogle Scholar
  43. Platzer J, Sterr W, Hausmann M, Schmitt R (1997) Three genes of a motility operon and their role in flagellar rotary speed variation in Rhizobium meliloti. J Bacteriol 179:6391CrossRefGoogle Scholar
  44. Popkin G (2016) The physics of life. Nature 529:16CrossRefADSGoogle Scholar
  45. Pozrikidis C (1992) Boundary integral and singularity methods for linearized viscous flow. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  46. Purcell EM (1977) Life at low Reynolds number. Am J Phys 45:3CrossRefADSGoogle Scholar
  47. Qian B, Jiang H, Gagnon DA, Breuer KS, Powers TR (2009) Minimal model for synchronization induced by hydrodynamic interactions. Phys Rev E 80:061919CrossRefADSGoogle Scholar
  48. Redner GS, Hagan MF, Baskaran A (2013) Structure and dynamics of a phase-separating active colloidal fluid. Phys Rev Lett 110:055701CrossRefADSGoogle Scholar
  49. Reichert M, Stark H (2005) Synchronization of rotating helices by hydrodynamic interactions. Eur Phys J E 17:493CrossRefGoogle Scholar
  50. Reigh SY, Winkler RG, Gompper G (2012) Synchronization and bundling of anchored bacterial flagella. Soft Matter 8:4363CrossRefADSGoogle Scholar
  51. Saintillan D (2010) The dilute rheology of swimming suspensions: a simple kinetic model. Exp Mech 50:1275CrossRefGoogle Scholar
  52. Sivinski J (1984) Sperm in competition. In: Smith RL (ed) Sperm competition and the evolution of animal mating systems. Academic, Orlando, p 174Google Scholar
  53. Sleigh MA (1962) The Biology of Cilia and Flagella. Pergamon Press, OxfordGoogle Scholar
  54. Spagnolie SE, Lauga E (2012) Hydrodynamics of self-propulsion near a boundary: predictions and accuracy of far-field approximations. J Fluid Mech 700:105CrossRefADSMathSciNetzbMATHGoogle Scholar
  55. Theers M, Westphal E, Gompper G, Winkler RG (2016) Modeling a spheroidal microswimmer and cooperative swimming in a narrow slit. Soft Matter 12:7372CrossRefADSGoogle Scholar
  56. Theers M, Westphal E, Qi K, Winkler RG, Gompper G (2018) Clustering of microswimmers: interplay of shape and hydrodynamics. Soft Matter 14:8590–8603CrossRefADSGoogle Scholar
  57. Tirado MM, Martínez CL, de la Torre JG (1984) Comparison of theories for the translational and rotational diffusion coefficients of rod-like macromolecules. Application to short DNA fragments. J Chem Phys 81:2047Google Scholar
  58. Vicsek T, Zafeiris A (2012) Collective motion. Phys Rep 517:71CrossRefADSGoogle Scholar
  59. Wang Q, Pan J, Snell WJ (2006) Intraflagellar transport particles participate directly in cilium-generated signaling in Chlamydomonas. Cell 125:549CrossRefGoogle Scholar
  60. Wensink HH, Dunkel J, Heidenreich S, Drescher K, Goldstein RE, Löwen H, Yeomans JM (2012) Meso-scale turbulence in living fluids. Proc Natl Acad Sci USA 109:14308CrossRefADSzbMATHGoogle Scholar
  61. Winkler RG (2016) Low Reynolds number hydrodynamics and mesoscale simulations. Eur Phys J Spec Top 225:2079CrossRefGoogle Scholar
  62. Wysocki A, Winkler RG, Gompper G (2014) Cooperative motion of active Brownian spheres in three-dimensional dense suspensions. EPL 105:48004CrossRefADSGoogle Scholar
  63. Yeomans JM, Pushkin DO, Shum H (2014) An introduction to the hydrodynamics of swimming microorganisms. Eur Phys J Spec Top 223:1771CrossRefGoogle Scholar
  64. Yoshinaga N, Liverpool TB (2017) Hydrodynamic interactions in dense active suspensions: from polar order to dynamical clusters. Phys Rev E 96:020603CrossRefADSGoogle Scholar
  65. Zöttl A, Stark H (2014) Hydrodynamics determines collective motion and phase behavior of active colloids in quasi-two-dimensional confinement. Phys Rev Lett 112:118101CrossRefADSGoogle Scholar
  66. Zöttl A, Stark H (2016) Emergent behavior in active colloids. J Phys Condens Matter 28:253CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute for Advanced Simulation and Institute for Complex SystemsForschungszentrum JülichJülichGermany

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