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.
Subscribe to Journal
Get full journal access for 1 year
only $15.58 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
The data that support the plots within this paper and other findings of this study are available from the corresponding author on request.
Giomi, L. Geometry and topology of turbulence in active nematics. Phys. Rev. X 5, 031003 (2015).
Wensink, H. H. et al. Meso-scale turbulence in living fluids. Proc. Natl Acad. Sci. USA 109, 14308–14313 (2012).
Blanch-Mercader, C. et al. Turbulent dynamics of epithelial cell cultures. Phys. Rev. Lett. 120, 208101 (2018).
Guillamat, P., Ignés-Mullol, J. & Sagués, F. Taming active turbulence with patterned soft interfaces. Nat. Commun. 8, 564 (2017).
Sanchez, T., Chen, D. T. N., DeCamp, S. J., Heymann, M. & Dogic, Z. Spontaneous motion in hierarchically assembled active matter. Nature 491, 431–434 (2012).
Cross, M. C. & Hohenberg, P. C. Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112 (1993).
Ramaswamy, S. The mechanics and statistics of active matter. Annu. Rev. Condens. Matter Phys. 1, 323–345 (2010).
Marchetti, M. C. et al. Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189 (2013).
Menzel, A. M. Tuned, driven and active soft matter. Phys. Rep. 554, 1–45 (2015).
Bratanov, V., Jenko, F. & Frey, E. New class of turbulence in active fluids. Proc. Natl Acad. Sci. USA 112, 15048–15053 (2015).
Urzay, J., Doostmohammadi, A. & Yeomans, J. M. Multi-scale statistics of turbulence motorized by active matter. J. Fluid Mech. 822, 762–773 (2017).
Slomka, J. & Dunkel, J. Symmetry breaking and turbulence in active fluids. Proc. Natl Acad. Sci. USA 114, 15048–15053 (2017).
Thampi, S. P., Golestanian, R. & Yeomans, J. M. Instabilities and topological defects in active nematics. Europhys. Lett. 105, 18001 (2014).
Giomi, L., Bowick, M. J., Mishra, P., Sknepnek, R. & Marchetti, M. C. Defect dynamics in active nematics. Phil. Trans. R. Soc. A 372, 20130365 (2014).
Aditi Simha, R. & Ramaswamy, S. Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles. Phys. Rev. Lett. 89, 058101 (2002).
Edwards, S. A. & Yeomans, J. M. Spontaneous flow states in active nematics: a unified picture. Europhys. Lett. 85, 18008 (2009).
Zhou, S., Sokolov, A., Lavrentovich, O. D. & Aranson, I. S. Living liquid crystals. Proc. Natl Acad. Sci. USA 111, 1265–1270 (2014).
Duclos, G. et al. Spontaneous shear flow in confined cellular nematics. Nat. Phys. 14, 728–732 (2018).
Guillamat, P., Ignés-Mullol, J. & Sagués, F. Control of active liquid crystals with a magnetic field. Proc. Natl Acad. Sci. USA 113, 5498–5502 (2016).
Giomi, L., Bowick, M. J., Ma, X. & Marchetti, M. C. Defect annihilation and proliferation in active nematics. Phys. Rev. Lett. 110, 228101 (2013).
Thampi, S. P., Golestanian, R. & Yeomans, J. M. Velocity correlations in an active nematic. Phys. Rev. Lett. 111, 118101 (2013).
Pismen, L. M. & Sagués, F. Viscous dissipation and dynamics of defects in an active nematic interface. Eur. Phys. J. E 40, 92 (2017).
Jülicher, F., Kruse, K., Prost, J. & Joanny, J. F. Active behavior of the cytoskeleton. Phys. Rep. 449, 3–28 (2007).
Prost, J., Jülicher, F. & Joanny, J. F. Active gel physics. Nat. Phys. 11, 111–117 (2015).
Voituriez, R., Joanny, J. F. & Prost, J. Spontaneous flow transition in active polar gels. Europhys. Lett. 70, 404–410 (2005).
Guillamat, P., Ignés-Mullol, J., Shankar, S., Marchetti, M. C. & Sagues, F. Probing the shear viscosity of an active nematic film. Phys. Rev. E 94, 060602(R) (2016).
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).
Gao, T., Betterton, M. D., Jhang, A.-S. & Shelley, M. J. Analytical structure, dynamics, and coarse graining of a kinetic model of an active fluid. Phys. Rev. Fluids 2, 093302 (2017).
Henkin, G., DeCamp, S. J., Chen, D. T. N., Sanchez, T. & Dogic, Z. Tunable dynamics of microtubule-based active isotropic gels. Phil. Trans. R. Soc. A 372, 20140142 (2014).
Hemingway, E. J., Mishra, P., Marchetti, M. C. & Fielding, S. M. Correlation lengths in hydrodynamic models of active nematics. Soft Matter 12, 7943–7952 (2016).
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.
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Figures 1–3, Supplementary Discussion, Supplementary References 1–3.
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%.
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).
About this article
Cite this article
Martínez-Prat, B., Ignés-Mullol, J., Casademunt, J. et al. Selection mechanism at the onset of active turbulence. Nat. Phys. 15, 362–366 (2019) doi:10.1038/s41567-018-0411-6
Physical Review X (2019)
Physical Review X (2019)
Proceedings of the National Academy of Sciences (2019)
Physical Review X (2019)
Nature Physics (2019)