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Selection mechanism at the onset of active turbulence

Nature Physics volume 15, pages 362–366 (2019)Cite this article

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Abstract

Active turbulence describes a flow regime that is erratic, and yet endowed with a characteristic length scale1. It arises in animate soft-matter systems as diverse as bacterial baths2, cell tissues3 and reconstituted cytoskeletal preparations4. However, the way that these turbulent dynamics emerge in active systems has so far evaded experimental scrutiny. Here, we unveil a direct route to active nematic turbulence by demonstrating that, for radially aligned unconfined textures, the characteristic length scale emerges at the early stages of the instability. We resolve two-dimensional distortions of a microtubule-based extensile system5 in space and time, and show that they can be characterized in terms of a growth rate that exhibits quadratic dependence on a dominant wavenumber. This wavelength selection mechanism is justified on the basis of a continuum model for an active nematic including viscous coupling to the adjacent fluid phase. Our findings are in line with the classical pattern-formation studies in non-active systems6, bettering our understanding of the principles of active self-organization, and providing potential perspectives for the control of biological fluids.

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Fig. 1: Route to active turbulence.
Fig. 2: Sequential instabilities.
Fig. 3: Dependence of k* and Ω* on material parameters and scaling Ω*(k*).

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author on request.

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Acknowledgements

The authors thank R. Alert and M. Shelley for fruitful discussions. B.M.-P. thanks S. Marco for advice regarding image analysis. The authors are indebted to the Brandeis University MRSEC Biosynthesis facility for providing the tubulin. The authors thank M. Pons, A. LeRoux and G. Iruela (Universitat de Barcelona) for their assistance in the expression of motor proteins. B.M.-P., J.I.-M. and F.S. acknowledge funding from MINECO (project FIS2016-78507-C2-1-P, AEI/FEDER, EU). J.C. acknowledges support from MINECO (project FIS2016-78507-C2-2-P, AEI/FEDER, EU) and the Generalitat de Catalunya under project 2014-SGR-878. B.M.-P. acknowledges funding from UAM under the IFIMAC Master Grant, and from Generalitat de Catalunya through a FI-2018 PhD Fellowship. Brandeis University MRSEC Biosynthesis facility is supported by NSF MRSEC DMR-1420382.

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Authors and Affiliations

  1. Departament de Ciència dels Materials i Química Física, Universitat de Barcelona, Barcelona, Catalonia, Spain

    Berta Martínez-Prat, Jordi Ignés-Mullol & Francesc Sagués

  2. Institute of Nanoscience and Nanotechnology, Universitat de Barcelona, Barcelona, Catalonia, Spain

    Berta Martínez-Prat, Jordi Ignés-Mullol & Francesc Sagués

  3. Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona, Catalonia, Spain

    Jaume Casademunt

  4. Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona, Catalonia, Spain

    Jaume Casademunt

Authors
  1. Berta Martínez-Prat
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  4. Francesc Sagués
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Contributions

F.S., J.I.-M. and B.M.-P. conceived the experiments. J.I.-M. and B.M.-P. designed the experimental set-up. B.M.-P. performed the experiments. F.S., J.I.-M. and B.M.-P. analysed and interpreted the data. J.C. performed the theoretical analysis. F.S. wrote the manuscript in collaboration with all the authors.

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Correspondence to Jordi Ignés-Mullol.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Supplementary Figures 1–3, Supplementary Discussion, Supplementary References 1–3.

Reporting Summary

Supplementary Video 1

Route to active turbulence. The capillary tube is introduced into the open sample, inducing the radial alignment of the material, which rapidly buckles to display a concentric pattern. Proliferation of ±1/2 defects prompts the breaking of the structure. Experimental conditions are: [ATP] = 1.5 mM, [streptavidin] = 8.2 µg ml–1, [MTs] = 1.3 mg ml–1 and [PEG] = 1.7%.

Supplementary Video 2

Sequential instabilities. At low concentration of motors (that is, low concentration of streptavidin), it was possible to observe sequential patterns with orthogonal directions formed because of repeated bend instabilities. Experimental conditions are: [ATP] = 1.5 mM, [streptavidin] = 7.5 µg ml–1, [MTs] = 1.3 mg ml–1 and [PEG] = 1.7%(w/w).

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Martínez-Prat, B., Ignés-Mullol, J., Casademunt, J. et al. Selection mechanism at the onset of active turbulence. Nat. Phys. 15, 362–366 (2019). https://doi.org/10.1038/s41567-018-0411-6

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