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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
Article

Abstract

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.

Keywords

Active suspensions Collective motion Kinetic theory  Hydrodynamic stability 

Mathematics Subject Classification

92C05 92C17 76E99 76A05 

Notes

Acknowledgments

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

References

  1. Baskaran, A., Marchetti, M. C.: Nonequilibrium statistical mechanics of self-propelled hard rods. J. Stat. Mech.: Theor. Exp. P04019 (2010)Google Scholar
  2. Baskaran, A., Marchetti, M.C.: Statistical mechanics and hydrodynamics of bacterial suspensions. Proc. Natl. Acad. Sci. USA 106, 15567 (2009)CrossRefGoogle Scholar
  3. Bretherton, F.P.: The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 14, 284 (1962)MathSciNetCrossRefGoogle Scholar
  4. Bricard, A., Caussin, J.-B., Das, D., Savoie, C., Chikkadi, V., Shitara, K., Chepizhko, O., Peruani, F., Saintillan, D., Bartolo, D.: Emergent vortices in populations of colloidal rollers. Nature Comm. (2015, to appear)Google Scholar
  5. Bricard, A., Caussin, J.-B., Desreumaux, N., Dauchot, N., Bartolo, D.L.: Emergence of macroscopic directed motion in populations of motile colloids. Nature 503, 95 (2013)CrossRefGoogle Scholar
  6. Cisneros, L.H., Kessler, J.O., Ganguly, S., Goldstein, R.E.: Dynamics of swimming bacteria: transition to directional order at high concentration. Phys. Rev. E 83, 061907 (2011)CrossRefGoogle Scholar
  7. Deseigne, J., Dauchot, O., Chaté, H.: Collective motion of vibrated polar disks. Phys. Rev. Lett. 105, 098001 (2010)CrossRefGoogle Scholar
  8. Dombrowski, C., Cisneros, L., Chatkaew, S., Goldstein, R.E., Kessler, J.O.: Self-concentration and large-scale coherence in bacterial dynamics. Phys. Rev. Lett. 93, 098103 (2004)CrossRefGoogle Scholar
  9. Drescher, K., Goldstein, R.E., Michel, N., Polin, M., Tuval, I.: Direct measurement of the flow field around swimming microorganisms. Phys. Rev. Lett. 105, 168101 (2010)CrossRefGoogle Scholar
  10. Drescher, K., Dunkel, J., Cisneros, L.H., Ganguly, S., Goldstein, R.E.: Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering. Proc. Natl. Acad. Sci. USA 108, 10940 (2011)zbMATHCrossRefGoogle Scholar
  11. Dunkel, J., Heidenreich, S., Drescher, K., Wensink, H.H., Bär, M., Goldstein, R.E.: Fluid dynamics of bacterial turbulence. Phys. Rev. Lett. 110, 228102 (2013)CrossRefGoogle Scholar
  12. Ezhilan, B., Shelley, M.J., Saintillan, D.: Instabilities and nonlinear dynamics of concentrated active suspensions. Phys. Fluids 25, 070607 (2013)CrossRefGoogle Scholar
  13. Fürthauer, S., Ramaswamy, S.: Phase-synchronized state of oriented active fluids. Phys. Rev. Lett. 111, 238102 (2013)CrossRefGoogle Scholar
  14. Gachelin, J., Miño, G., Berthet, H., Lindner, A., Rousselet, A., Clément, E.: Non-Newtonian viscosity of Escherichia coli suspensions. Phys. Rev. Lett. 110, 268103 (2013)Google Scholar
  15. Gachelin, J., Rousselet, A., Lindner, A., Clément, E.: Collective motion in an active suspension of Escherichia coli bacteria. New J. Phys. 16, 025003 (2014)CrossRefGoogle Scholar
  16. Gao, T., Blackwell, R., Glaser, M.A., Betterton, M.D., Shelley, M.J.: Multiscale polar theory of microtubule and motor-protein assemblies. Phys. Rev. Lett. 114, 048101 (2015)CrossRefGoogle Scholar
  17. Goldstein, R.E.: Green algae as model organisms for biological fluid dynamics. Annu. Rev. Fluid Mech. 47, 353 (2015)zbMATHCrossRefGoogle Scholar
  18. Guasto, J.S., Johnson, K.A., Gollub, J.P.: Oscillatory flows induced by microorganisms swimming in two dimensions. Phys. Rev. Lett. 105, 168102 (2010)CrossRefGoogle Scholar
  19. Hatwalne, Y., Ramaswamy, S., Rao, M., Aditi Simha, R.: Rheology of active-particle suspensions. Phys. Rev. Lett. 92, 118101 (2004)CrossRefGoogle Scholar
  20. Hernandez-Ortiz, J.P., Underhill, P.T., Graham, M.D.: Dynamics of confined suspensions of swimming particles. J. Phys. Condens. Matt. 21, 204107 (2009)CrossRefGoogle Scholar
  21. Hohenegger, C., Shelley, M.J.: Stability of active suspensions. Phys. Rev. E 81, 046311 (2010)zbMATHMathSciNetCrossRefGoogle Scholar
  22. Keber, F.C., Loiseau, E., Sanchez, T., DeCamp, S.H., Giomi, L., Bowick, M.J., Marchetti, M.C., Dogic, Z., Bausch, A.R.: Topology and dynamics of active nematic vesicles. Science 345, 6201 (2014)CrossRefGoogle Scholar
  23. Koch, D.L., Subramanian, G.: Collective hydrodynamics of swimming microorganisms: living fluids. Annu. Rev. Fluid Mech. 43, 637 (2011)MathSciNetCrossRefGoogle Scholar
  24. Kumar, N., Soni, H., Ramaswamy, S., Sood, A.K.: Flocking at a distance in active granular matter. Nature Comm. 5, 4688 (2014)CrossRefGoogle Scholar
  25. Leoni, M., Liverpool, T.B.: Synchronization and liquid crystalline order in soft active fluids. Phys. Rev. Lett. 112, 148104 (2014)CrossRefGoogle Scholar
  26. Marchetti, M.C., Joanny, J.F., Ramaswamy, R., Liverpool, T.B., Prost, J., Rao, M., Aditi Simha, R.: Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143 (2013)CrossRefGoogle Scholar
  27. Mussler, M., Rafaï, S., Peyla, P., Wagner, C.: Effective viscosity of non-gravitactic Chlamydomonas reinhardtii microswimmer suspensions. EPL 101, 54004 (2013)CrossRefGoogle Scholar
  28. Rafaï, S., Jibuti, L., Peyla, P.: Effective viscosity of microswimmer suspensions. Phys. Rev. Lett. 104, 098102 (2010)zbMATHCrossRefGoogle Scholar
  29. Saintillan, D., Darve, E., Shaqfeh, E.S.G.: A smooth particle-mesh Ewald algorithm for Stokes suspension simulations: the sedimentation of rigid fibers. Phys. Fluids 17, 033301 (2005)CrossRefGoogle Scholar
  30. Saintillan, D.: The dilute rheology of swimming suspensions: a simple kinetic model. Exp. Mech. 50, 1275 (2010)CrossRefGoogle Scholar
  31. Saintillan, D., Shelley, M.J.: Orientational order and instabilities in suspensions of self-locomoting rods. Phys. Rev. Lett. 99, 058102 (2007)zbMATHCrossRefGoogle Scholar
  32. Saintillan, D., Shelley, M.J.: Instabilities and pattern formation in active particle suspensions: kinetic theory and continuum simulations. Phys. Rev. Lett. 100, 178103 (2008)CrossRefGoogle Scholar
  33. Saintillan, D., Shelley, M.J.: Instabilities, pattern formation, and mixing in active suspensions. Phys. Fluids 20, 123304 (2008)CrossRefGoogle Scholar
  34. Saintillan, D., Shelley, M.J.: Emergence of coherent structures and large-scale flows in motile suspensions. J. R. Soc. Interface 9, 571 (2012)CrossRefGoogle Scholar
  35. Saintillan, D., Shelley, M.J.: Active suspensions and their nonlinear models. C. R. Physique 14, 497 (2013)CrossRefGoogle Scholar
  36. Saintillan, D., Shelley, M.J.: Theory of active suspensions. In: Spagnolie, S.E. (ed.) Complex Fluids in Biological Systems: Experiment, Theory, and Computation, pp. 319–355. Springer, New York (2015)Google Scholar
  37. Sanchez, T., Chen, D.T., DeCamp, S.J., Heymann, M., Dogic, Z.: Spontaneous motion in hierarchically assembled active matter. Nature 491, 431 (2012)zbMATHCrossRefGoogle Scholar
  38. Schaller, V., Weber, C., Semmrich, C., Frey, E., Bausch, A.R.: Polar patterns of driven filaments. Nature 467, 73 (2010)CrossRefGoogle Scholar
  39. Sokolov, A., Aranson, I.S.: Reduction of viscosity in suspension of swimming bacteria. Phys. Rev. Lett. 103, 148101 (2009)CrossRefGoogle Scholar
  40. Subramanian, G., Koch, D.L.: Critical bacterial concentration for the onset of collective swimming. J. Fluid Mech. 632, 359 (2009)MathSciNetCrossRefGoogle Scholar

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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