Active matter composed of self-propelled interacting units holds a major promise for the extraction of useful work from its seemingly chaotic dynamics. Streamlining active matter is especially important at the microscale, where the viscous forces prevail over inertia and transport requires a non-reciprocal motion. Here we report that microscopic active droplets representing aqueous dispersions of swimming bacteria Bacillus subtilis become unidirectionally motile when placed in an inactive nematic liquid-crystal medium. Random motion of bacteria inside the droplet is rectified into a directional self-locomotion of the droplet by the polar director structure that the droplet creates in the surrounding nematic through anisotropic molecular interactions at its surface. Droplets without active swimmers show no net displacement. The trajectory of the active droplet can be predesigned by patterning the molecular orientation of the nematic. The effect demonstrates that broken spatial symmetry of the medium can be the reason for and the means to control directional microscale transport.
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Joanny, J. F. & Ramaswamy, S. A drop of active matter. J. Fluid Mech. 705, 46–57 (2012).
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).
Vladescu, I. D. et al. Filling an emulsion drop with motile bacteria. Phys. Rev. Lett. 113, 268101 (2014).
Giomi, L. & DeSimone, A. Spontaneous division and motility in active nematic droplets. Phys. Rev. Lett. 112, 147802 (2014).
Khoromskaia, D. & Alexander, G. P. Motility of active fluid drops on surfaces. Phys. Rev. E 92, 062311 (2015).
Zwicker, D., Seyboldt, R., Weber, C. A., Hyman, A. A. & Julicher, F. Growth and division of active droplets provides a model for protocells. Nat. Phys. 13, 408–413 (2017).
Loisy, A., Eggers, J. & Liverpool, T. B. Tractionless self-propulsion of active drops. Phys. Rev. Lett. 123, 248006 (2019).
Weirich, K. L., Dasbiswas, K., Witten, T. A., Vaikuntanathan, S. & Gardel, M. L. Self-organizing motors divide active liquid droplets. Proc. Natl Acad. Sci. USA 116, 11125–11130 (2019).
Kruger, C., Klos, G., Bahr, C. & Maass, C. C. Curling liquid crystal microswimmers: a cascade of spontaneous symmetry breaking. Phys. Rev. Lett. 117, 048003 (2016).
Cates, M. E. & Tjhung, E. Theories of binary fluid mixtures: from phase-separation kinetics to active emulsions. J. Fluid Mech. 836, P1 (2017).
Gao, T. & Li, Z. R. Self-driven droplet powered by active nematics. Phys. Rev. Lett. 119, 108002 (2017).
Copar, S., Aplinc, J., Kos, Z., Zumer, S. & Ravnik, M. Topology of three-dimensional active nematic turbulence confined to droplets. Phys. Rev. X 9, 031051 (2019).
Morozov, M. & Michelin, S. Orientational instability and spontaneous rotation of active nematic droplets. Soft Matter 15, 7814–7822 (2019).
Ramos, G., Cordero, M. L. & Soto, R. Bacteria driving droplets. Soft Matter 16, 1359–1365 (2020).
Purcell, E. M. Life at low Reynolds-number. Am. J. Phys. 45, 3–11 (1977).
Howse, J. R. et al. Self-motile colloidal particles: from directed propulsion to random walk. Phys. Rev. Lett. 99, 048102 (2007).
Marchetti, M. C. Spontaneous flows and self-propelled drops. Nature 491, 340–341 (2012).
Sokolov, A., Apodaca, M. M., Grzybowski, B. A. & Aranson, I. S. Swimming bacteria power microscopic gears. Proc. Natl Acad. Sci. USA 107, 969–974 (2010).
Di Leonardo, R. et al. Bacterial ratchet motors. Proc. Natl Acad. Sci. USA 107, 9541–9545 (2010).
Kleman, M. & Lavrentovich, O. D. Soft Matter Physics: An Introduction (Springer, 2003).
Poulin, P., Stark, H., Lubensky, T. C. & Weitz, D. A. Novel colloidal interactions in anisotropic fluids. Science 275, 1770–1773 (1997).
Kuksenok, O. V., Ruhwandl, R. W., Shiyanovskii, S. V. & Terentjev, E. M. Director structure around a colloid particle suspended in a nematic liquid crystal. Phys. Rev. E 54, 5198–5203 (1996).
Gu, Y. D. & Abbott, N. L. Observation of Saturn-ring defects around solid microspheres in nematic liquid crystals. Phys. Rev. Lett. 85, 4719–4722 (2000).
Dombrowski, C., Cisneros, L., Chatkaew, S., Goldstein, R. E. & Kessler, J. O. Self-concentration and large-scale coherence in bacterial dynamics. Phys. Rev. Lett. 93, 098103 (2004).
Sokolov, A. & Aranson, I. S. Physical properties of collective motion in suspensions of bacteria. Phys. Rev. Lett. 109, 248109 (2012).
Zhou, S., Sokolov, A., Lavrentovich, O. D. & Aranson, I. S. Living liquid crystals. Proc. Natl Acad. Sci. USA 111, 1265–1270 (2014).
Pages, J. M., Ignes-Mullol, J. & Sagues, F. Anomalous diffusion of motile colloids dispersed in liquid crystals. Phys. Rev. Lett. 122, 198001 (2019).
Lubensky, T. C., Pettey, D., Currier, N. & Stark, H. Topological defects and interactions in nematic emulsions. Phys. Rev. E 57, 610–625 (1998).
Loudet, J. C., Hanusse, P. & Poulin, P. Stokes drag on a sphere in a nematic liquid crystal. Science 306, 1525–1525 (2004).
Turiv, T. et al. Effect of collective molecular reorientations on brownian motion of colloids in nematic liquid crystal. Science 342, 1351–1354 (2013).
Hardouin, J., Guillamat, P., Sagues, F. & Ignes-Mullol, J. Dynamics of ring disclinations driven by active nematic shells. Front. Phys. 7, 165 (2019).
Stark, H. & Ventzki, D. Non-linear Stokes drag of spherical particles in a nematic solvent. Europhys. Lett. 57, 60–66 (2002).
Lavrentovich, O. D. Active colloids in liquid crystals. Curr. Opin. Colloid 21, 97–109 (2016).
Khullar, S., Zhou, C. F. & Feng, J. J. Dynamic evolution of topological defects around drops and bubbles rising in a nematic liquid crystal. Phys. Rev. Lett. 99, 237802 (2007).
Fukuda, J., Stark, H., Yoneya, M. & Yokoyama, H. Dynamics of a nematic liquid crystal around a spherical particle. J. Phys. Condens. Mat. 16, S1957–S1968 (2004).
Zhou, C., Yue, P. & Feng, J. J. The rise of Newtonian drops in a nematic liquid crystal. J. Fluid Mech. 593, 385–404 (2007).
Guo, Y. et al. High-resolution and high-throughput plasmonic photopatterning of complex molecular orientations in liquid crystals. Adv. Mater. 28, 2353–2358 (2016).
Wioland, H., Woodhouse, F. G., Dunkel, J., Kessler, J. O. & Goldstein, R. E. Confinement stabilizes a bacterial suspension into a spiral vortex. Phys. Rev. Lett. 110, 268102 (2013).
Habibi, A., Blanc, C., Ben Mbarek, N. & Soltani, T. Passive and active microrheology of a lyotropic chromonic nematic liquid crystal disodium cromoglycate. J. Mol. Liq. 288, 111027 (2019).
Kim, Y. K., Noh, J., Nayani, K. & Abbott, N. L. Soft matter from liquid crystals. Soft Matter 15, 6913–6929 (2019).
Zhang, R., Roberts, T., Aranson, I. S. & de Pablo, J. J. Lattice Boltzmann simulation of asymmetric flow in nematic liquid crystals with finite anchoring. J. Chem. Phys. 144, 084905 (2016).
Marenduzzo, D., Orlandini, E. & Yeomans, J. M. Interplay between shear flow and elastic deformations in liquid crystals. J. Chem. Phys. 121, 582–591 (2004).
Sokolov, A., Zhou, S., Lavrentovich, O. D. & Aranson, I. S. Individual behavior and pairwise interactions between microswimmers in anisotropic liquid. Phys. Rev. E 91, 013009 (2015).
Najafi, A. & Golestanian, R. Simple swimmer at low Reynolds number: three linked spheres. Phys. Rev. E 69, 062901 (2004).
Avron, J. E., Kenneth, O. & Oaknin, D. H. Pushmepullyou: an efficient micro-swimmer. N. J. Phys. 7, 234 (2005).
Lavrentovich, O. D. Transport of particles in liquid crystals. Soft Matter 10, 1264–1283 (2014).
Sokolov, A., Mozaffari, A., Zhang, R., de Pablo, J. J. & Snezhko, A. Emergence of radial tree of bend stripes in active nematics. Phys. Rev. X 9, 031014 (2019).
Shi, J. & Powers, T. R. Swimming in an anisotropic fluid: how speed depends on alignment angle. Phys. Rev. Fluids 2, 123102 (2017).
Lintuvuori, J. S., Wurger, A. & Stratford, K. Hydrodynamics defines the stable swimming direction of spherical squirmers in a nematic liquid crystal. Phys. Rev. Lett. 119, 068001 (2017).
Daddi-Moussa-Ider, A. & Menzel, A. M. Dynamics of a simple model microswimmer in an anisotropic fluid: implications for alignment behavior and active transport in a nematic liquid crystal. Phys. Rev. Fluids 3, 094102 (2018).
Kos, Z. & Ravnik, M. Elementary flow field profiles of micro-swimmers in weakly anisotropic nematic fluids: Stokeslet, stresslet, rotlet and source flows. Fluids 3, 15 (2018).
Zhou, S. et al. Dynamic states of swimming bacteria in a nematic liquid crystal cell with homeotropic alignment. N. J. Phys. 19, 055006 (2017).
Woolverton, C. J., Gustely, E., Li, L. & Lavrentovich, O. D. Liquid crystal effects on bacterial viability. Liq. Cryst. 32, 417–423 (2005).
Dark, M. L., Moore, M. H., Shenoy, D. K. & Shashidhar, R. Rotational viscosity and molecular structure of nematic liquid crystals. Liq. Cryst. 33, 67–73 (2006).
Li, B. X., Borshch, V., Shiyanovskii, S. V., Liu, S. B. & Lavrentovich, O. D. Electro-optic switching of dielectrically negative nematic through nanosecond electric modification of order parameter. Appl Phys. Lett. 104, 201105 (2014).
Nayani, K., Cordova-Figueroa, U. M. & Abbott, N. L. Steering active emulsions with liquid crystals. Langmuir 36, 6948–6956 (2019).
Voloschenko, D., Pishnyak, O. P., Shiyanovskii, S. V. & Lavrentovich, O. D. Effect of director distortions on morphologies of phase separation in liquid crystals. Phys. Rev. E 65, 060701 (2002).
Smalyukh, I. I., Shiyanovskii, S. V. & Lavrentovich, O. D. Three-dimensional imaging of orientational order by fluorescence confocal polarizing microscopy. Chem. Phys. Lett. 336, 88–96 (2001).
Tinevez, J. Y. et al. TrackMate: an open and extensible platform for single-particle tracking. Methods 115, 80–90 (2017).
Thielicke, W. & Stamhuis, E. J. PIVlab—towards user-friendly, affordable and accurate digital particle image velocimetry in MATLAB. J. Open Res. Softw. 2, e30 (2014).
We thank B. Li, S. Shiyanovskii and participants of UC Santa Barbara Kavli Institute for Theoretical Physics (KITP) programme ‘Active 20: Symmetry, Thermodynamics, and Topology in Active Matter’ for fruitful discussions. The work is supported by NSF grants DMR-1905053 (analysis of dynamics), CMMI-1663394 (preparation of plasmonic metamasks for patterned cells), DMS-1729509 (preparation of bacterial dispersions), and by Office of Sciences, DOE, grant DE-SC0019105 (development of the alignment layers). This research was completed while M.R., H.B. and O.D.L. participated in KITP Active 20 programme, supported in part by the NSF grant PHY-1748958 and NIH grant R25GM067110.
The authors declare no competing interests.
Peer review information Nature Physics thanks Paulo Arratia, M Cristina and Uroš Tkalec for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary text and Fig. 1, and legends for Supplementary Videos 1–4.
Self-locomotion of an active droplet with bacteria B. subtilis of a diameter 2R = 90 μm in a thermotropic nematic liquid crystal. The droplet distorts the director field of the nematic and produces a point-defect hedgehog on the right-hand side. Asymmetry of the director field rectifies the flows outside the droplet and enables a directional propulsion of the active drop with the hedgehog leading the way.
Self-locomotion of an active droplet with bacteria B. subtilis of a diameter 2R = 130 μm in a thermotropic nematic. The active flows cause large fluctuations of the director field in the surrounding nematic, so that the equatorial ‘Saturn ring’ of a disclination shifts to the right and left. As a result, the quadrupolar symmetry of the nematic around the droplet is broken and the droplet moves in the direction in which the ring shifts. When the Saturn ring is temporarily located in the equatorial plane, the droplet shows no propulsion. At the end, the ring collapses into the point-defect hedgehog and the droplet gains the maximum speed.
Self-locomotion of four active droplets with bacteria B. subtilis in a thermotropic nematic. The droplets swim along the circular trajectories set by the photoalignment of the nematic medium.
Fluorescent microscopy of interior flows visualized by fluorescent tracers in a droplet of diameter 2R = 125 μm, c = 20c0. The hyperbolic hedgehog (invisible) is located on the right-hand side of the drop. Fluorescent Suncoast yellow spheres of diameter 200 nm, excitation wavelength 540 nm, emission wavelength 600 nm.
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Rajabi, M., Baza, H., Turiv, T. et al. Directional self-locomotion of active droplets enabled by nematic environment. Nat. Phys. (2020). https://doi.org/10.1038/s41567-020-01055-5