### Abstract

The emergence of coherent structures, large-scale flows and correlated dynamics in suspensions of motile particles such as swimming micro-organisms or artificial microswimmers is studied using direct particle simulations. A detailed model is proposed for a slender rod-like particle that propels itself in a viscous fluid by exerting a prescribed tangential stress on its surface, and a method is devised for the efficient calculation of hydrodynamic interactions in large-scale suspensions of such particles using slender-body theory and a smooth particle-mesh Ewald algorithm. Simulations are performed with periodic boundary conditions for various system sizes and suspension volume fractions, and demonstrate a transition to large-scale correlated motions in suspensions of rear-actuated swimmers, or Pushers, above a critical volume fraction or system size. This transition, which is not observed in suspensions of head-actuated swimmers, or Pullers, is seen most clearly in particle velocity and passive tracer statistics. These observations are consistent with predictions from our previous mean-field kinetic theory, one of which states that instabilities will arise in uniform isotropic suspensions of Pushers when the product of the linear system size with the suspension volume fraction exceeds a given threshold. We also find that the collective dynamics of Pushers result in giant number fluctuations, local alignment of swimmers and strongly mixing flows. Suspensions of Pullers, which evince no large-scale dynamics, nonetheless display interesting deviations from the random isotropic state.

Original language | English (US) |
---|---|

Pages (from-to) | 571-585 |

Number of pages | 15 |

Journal | Journal of the Royal Society Interface |

Volume | 9 |

Issue number | 68 |

DOIs | |

State | Published - Mar 7 2012 |

### Fingerprint

### Keywords

- Collective dynamics
- Suspensions
- Swimming micro-organisms

### ASJC Scopus subject areas

- Biophysics
- Biotechnology
- Bioengineering
- Biomedical Engineering
- Biomaterials
- Biochemistry

### Cite this

*Journal of the Royal Society Interface*,

*9*(68), 571-585. https://doi.org/10.1098/rsif.2011.0355

**Emergence of coherent structures and large-scale flows in motile suspensions.** / Saintillan, David; Shelley, Michael.

Research output: Contribution to journal › Article

*Journal of the Royal Society Interface*, vol. 9, no. 68, pp. 571-585. https://doi.org/10.1098/rsif.2011.0355

}

TY - JOUR

T1 - Emergence of coherent structures and large-scale flows in motile suspensions

AU - Saintillan, David

AU - Shelley, Michael

PY - 2012/3/7

Y1 - 2012/3/7

N2 - The emergence of coherent structures, large-scale flows and correlated dynamics in suspensions of motile particles such as swimming micro-organisms or artificial microswimmers is studied using direct particle simulations. A detailed model is proposed for a slender rod-like particle that propels itself in a viscous fluid by exerting a prescribed tangential stress on its surface, and a method is devised for the efficient calculation of hydrodynamic interactions in large-scale suspensions of such particles using slender-body theory and a smooth particle-mesh Ewald algorithm. Simulations are performed with periodic boundary conditions for various system sizes and suspension volume fractions, and demonstrate a transition to large-scale correlated motions in suspensions of rear-actuated swimmers, or Pushers, above a critical volume fraction or system size. This transition, which is not observed in suspensions of head-actuated swimmers, or Pullers, is seen most clearly in particle velocity and passive tracer statistics. These observations are consistent with predictions from our previous mean-field kinetic theory, one of which states that instabilities will arise in uniform isotropic suspensions of Pushers when the product of the linear system size with the suspension volume fraction exceeds a given threshold. We also find that the collective dynamics of Pushers result in giant number fluctuations, local alignment of swimmers and strongly mixing flows. Suspensions of Pullers, which evince no large-scale dynamics, nonetheless display interesting deviations from the random isotropic state.

AB - The emergence of coherent structures, large-scale flows and correlated dynamics in suspensions of motile particles such as swimming micro-organisms or artificial microswimmers is studied using direct particle simulations. A detailed model is proposed for a slender rod-like particle that propels itself in a viscous fluid by exerting a prescribed tangential stress on its surface, and a method is devised for the efficient calculation of hydrodynamic interactions in large-scale suspensions of such particles using slender-body theory and a smooth particle-mesh Ewald algorithm. Simulations are performed with periodic boundary conditions for various system sizes and suspension volume fractions, and demonstrate a transition to large-scale correlated motions in suspensions of rear-actuated swimmers, or Pushers, above a critical volume fraction or system size. This transition, which is not observed in suspensions of head-actuated swimmers, or Pullers, is seen most clearly in particle velocity and passive tracer statistics. These observations are consistent with predictions from our previous mean-field kinetic theory, one of which states that instabilities will arise in uniform isotropic suspensions of Pushers when the product of the linear system size with the suspension volume fraction exceeds a given threshold. We also find that the collective dynamics of Pushers result in giant number fluctuations, local alignment of swimmers and strongly mixing flows. Suspensions of Pullers, which evince no large-scale dynamics, nonetheless display interesting deviations from the random isotropic state.

KW - Collective dynamics

KW - Suspensions

KW - Swimming micro-organisms

UR - http://www.scopus.com/inward/record.url?scp=84856900404&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856900404&partnerID=8YFLogxK

U2 - 10.1098/rsif.2011.0355

DO - 10.1098/rsif.2011.0355

M3 - Article

VL - 9

SP - 571

EP - 585

JO - Journal of the Royal Society Interface

JF - Journal of the Royal Society Interface

SN - 1742-5689

IS - 68

ER -