Journal of Nonlinear Science

, Volume 25, Issue 5, pp 1125–1139 | Cite as

Spontaneous Flows in Suspensions of Active Cyclic Swimmers

  • Tommaso Brotto
  • Denis Bartolo
  • David SaintillanEmail author


Many swimming cells rely on periodic deformations to achieve locomotion. We introduce in this work a theoretical model and numerical simulations in order to elucidate the impact of these cyclic strokes on the emergence of mesoscale structures and collective motion in swimmer suspensions. The model extends previous kinetic theories for populations of identical swimmers to the case of self-propelled particles undergoing transitions between pusher and puller states, and is applied to quantify how the unsteadiness of the hydrodynamic velocity field, to which each swimmer population contributes, affects the onset and characteristics of spontaneous flows. A linear stability analysis reveals that the sign of the population-averaged dipole determines the stability of the uniform isotropic state, with suspensions dominated by pushers being subject to growing nematic bend fluctuations. Stochastic transitions, however, are also seen to provide an additional damping mechanism. To investigate the population dynamics above the instability threshold, we also perform direct particle simulations based on a slender-body model, where the growth or decay of the active power generated by the swimmers is found to be a robust measure of the structural and dynamical instability.


Active suspensions Collective motion Kinetic theory  Hydrodynamic stability 

Mathematics Subject Classification

92C05 92C17 76E99 76A05 



D.S. gratefully acknowledges partial support from a Total-ESPCI ParisTech Chair.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Tommaso Brotto
    • 1
  • Denis Bartolo
    • 2
  • David Saintillan
    • 3
    Email author
  1. 1.Laboratoire de Physique StatistiqueÉcole Normale Supérieure de ParisParisFrance
  2. 2.Laboratoire de PhysiqueÉcole Normale Supérieure de LyonLyonFrance
  3. 3.Department of Mechanical and Aerospace EngineeringUniversity of California San DiegoLa JollaUSA

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