Selection mechanism at the onset of active turbulence

Jaume Casademunt

doi:10.1038/S41567-018-0411-6

Outline

Selection mechanism at the onset of active turbulence

Jaume Casademunt

2019, Nature Physics

https://doi.org/10.1038/S41567-018-0411-6

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20 pages

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Abstract

Active turbulence describes a flow regime that is erratic, and yet endowed with a characteristic length scale 1 . It arises in animate soft-matter systems as diverse as bacterial baths 2 , cell

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Acknowledgements The authors thank R. Alert and M. Shelley for fruitful discussions, and the two anonymous reviewers for their useful comments that helped improve the theoretical analysis. B.M.-P. thanks S. Marco for advising in the image analysis. The authors are indebted to the Brandeis University MRSEC Biosynthesis facility for providing the tubulin. We 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. acknowl- edge funding from MINECO (project FIS2016-78507-C2-1-P, AEI/FEDER, EU). J.C. acknowledges sup- port from MINECO (project FIS2016-78507-C2-2-P, AEI/FEDER, EU) and Generalitat de Catalunya under project 2014-SGR-878. B.M. 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 role of boundary layers in conventional liquid crystals is commonly related to the mesogen anchoring on confining walls. In the classical view, anchoring enslaves the orientational field of the passive material under equilibrium conditions. In this work, we show that an active nematic can develop active boundary layers that topologically polarize the confining walls. We find that negatively-charged defects accumulate in the boundary layer, regardless of the wall curvature, and they influence the overall dynamics of the system to the point of fully controlling the behavior of the active nematic in situations of strong confinement. Further, we show that wall defects exhibit behaviors that are essentially different from those of their bulk counterparts, such as high motility or the ability to recombine with another defect of like-sign topological charge. These exotic behaviors result from a change of symmetry induced by the wall in the director field around the defect. Finally, we suggest that the collective dynamics of wall defects might be described in terms of a model equation for one-dimensional spatio-temporal chaos. In fluid dynamics and soft materials science, boundary layers refer to the part of the flow that is close to a boundary, featuring built-up slip velocities associated to localized profiles of scalar fields, like pressure, temperature, solute concentration or ionic charge density 1,2. Although the length scale spanned by such boundary layers is much smaller than any macroscopic length, the details of the interfacial transport processes entirely control the distant fluid dynamics. Here, we reveal the existence of a new type of boundary layer in a confined Active Nematic (AN) 3 , which we call active boundary layer (ABL). Defects, i. e. regions of undefined local order, is similarly a transversal concept in condensed, both hard and soft, materials. Although normally transitory for systems near equilibrium, defects play a significant role in many contexts, from phase transitions, mediated by defect proliferation 4,5 , to colloid assembly, via defect entanglement in liquid crystal (LC)-based dispersions 6-8. In this latter context, defects refer to singularities in the orientational field that are endowed with topological indices that bear characteristics similar to electric charges. Stressing this resemblance, and expanding the conventional notion of electrified interfaces, we demonstrate that active LCs 3,9,10 engender ABLs that become polarized by accumulating equal-sign topological defects. We experimentally realize two-dimensional ANs by the selfassembly of filamentous bundles of microtubules and kinesin molecular motors at the water/oil interface 11-13 , which form an active ordered film populated by motile topological defects characterized by semi-integer topological indices, or charges 3. Trefoil-like-1/2 defects are passively advected by the flow while comet-like +1/2 defects actively drive the system. Experiments 11,12,14-17 and theoretical models 18-22 show that ANs feature a balanced population of positive and negative semi-integer defects that continuously unbind and recombine, resulting in a turbulent mixing regime 16,23-25. Different from this traditional view, we show here that, under lateral confinement, ANs can feature ABLs that are exclusively populated by negative defects. When analyzed individually, these boundary defects display differences with respect to their bulk counterparts, both in terms of their motility, symmetries, and built-up stresses. Remarkably, we identify recombination events between equal-sign defects residing at the boundary.

Selection mechanism at the onset of active turbulence

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