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Curvature-induced defect unbinding and dynamics in active nematic toroids

Nature Physics volume 14, pages 85–90 (2018)Cite this article

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Abstract

Nematic order on curved surfaces is often disrupted by the presence of topological defects, which are singular regions in which the orientational order is undefined. In the presence of force-generating active materials, these defects are able to migrate through space like swimming microorganisms. We use toroidal surfaces to show that despite their highly chaotic and non-equilibrium dynamics, pairs of defects unbind and segregate in regions of opposite Gaussian curvature. Using numerical simulations, we find that the degree of defect unbinding can be controlled by tuning the system activity, and even suppressed in strongly active systems. Furthermore, by using the defects as active microrheological tracers and quantitatively comparing our experimental and theoretical results, we are able to determine material properties of the active nematic. Our results illustrate how topology and geometry can be used to control the behaviour of active materials, and introduce a new avenue for the quantitative mechanical characterization of active fluids.

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Figure 1: Curvature-induced defect unbinding for a nematic on the surface of a torus.
Figure 2: Quantifying curvature-induced defect unbinding for an active nematic confined to the surface of a toroidal droplet.
Figure 3: Numerical simulations show that curvature-induced defect unbinding for active nematics is sensitive to defect velocity and defect density.
Figure 4: Defect number fluctuations depend on defect velocity.

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Acknowledgements

We thank the National Science Foundation for support (NSF 1609841). We also thank Z. Dogic and acknowledge use of Brandeis Biological Materials Facility, which is supported by NSF MRSEC DMR-1420382. We are thankful to S. DeCamp and K. Wu for their training and assistance with the active system, and P. Yunker for the use of his confocal microscope. P.W.E. is supported by FLAMEL under grant NSF 1258425. D.J.P. and L.G. are supported by The Netherlands Organization for Scientific Research (NWO/OCW) via the Frontiers of Nanoscience program and the Vidi scheme.

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Author notes

  1. Ya-Wen Chang

    Present address: Department of Chemical Engineering, Texas Tech University, Lubbock, Texas, 79409, USA

Authors and Affiliations

  1. School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

    Perry W. Ellis, Ya-Wen Chang & Alberto Fernandez-Nieves

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

    Daniel J. G. Pearce & Luca Giomi

  3. Instituut-Lorentz, Universiteit Leiden, 2300 RA Leiden, The Netherlands

    Guillermo Goldsztein

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Contributions

A.F.N. initially designed the experiment. P.W.E. and Y.W.C. performed the experiments. D.J.P. and L.G. performed the numerical simulations. P.W.E., D.J.P., G.G., L.G. and A.F.N. analysed and interpreted the data. P.W.E., D.J.P., L.G. and A.F.N. wrote the paper.

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Correspondence to Luca Giomi or Alberto Fernandez-Nieves.

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Ellis, P., Pearce, D., Chang, YW. et al. Curvature-induced defect unbinding and dynamics in active nematic toroids. Nature Phys 14, 85–90 (2018). https://doi.org/10.1038/nphys4276

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