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From hydrodynamic lubrication to many-body interactions in dense suspensions of active swimmers

Research output: Contribution to journalArticle

Original languageEnglish
Article number76
Number of pages22
JournalEuropean Physical Journal E
Early online date14 Jun 2018
DateAccepted/In press - 25 May 2018
DateE-pub ahead of print - 14 Jun 2018
DatePublished (current) - Jun 2018


We study how hydrodynamic interactions affect the collective behaviour of active particles suspended in a fluid at high concentrations, with particular attention to lubrication forces which appear when the particles are very close to one another. We compute exactly the limiting behaviour of the hydrodynamic interactions between two spherical (circular) active swimmers in very close proximity to one another in the general setting in both three and (two) dimensions. Combining this with far-field interactions, we develop a novel numerical scheme which allows us to study the collective behaviour of large numbers of active particles with accurate hydrodynamic interactions when close to one another. We study active swimmers whose intrinsic flow fields are characterised by force dipoles and quadrupoles. Using this scheme, we are able to show that lubrication forces when the particles are very close to each other can play as important a role as long-range hydrodynamic interactions in determining their many-body behaviour. We find that when the swimmer force dipole is large, finite clusters and open gel-like clusters appear rather than complete phase separation. This suppression is due to near-field lubrication interactions. For swimmers with small force dipoles, we find surprisingly that a globally polar ordered phase appears because near-field lubrication rather than long-range hydrodnamics dominate the alignment mechanism. Polar order is present for very large system sizes and is stable to fluctuations with a finite noise amplitude. We explain the emergence of polar order using a minimal model in which only the leading rotational effect of the near-field interaction is included. These phenomena are also reproduced in two dimensions.

    Research areas

  • Pattern formation in cellular populations, hase separation and segregation in colloids, swimming of Microorganism, low-Reynolds number fluid flow, Synthetic biology

    Structured keywords

  • BrisSynBio
  • Bristol BioDesign Institute

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    Accepted author manuscript, 12 MB, PDF document


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