Directional self-locomotion of active droplets enabled by nematic environment


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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Fig. 1: Self-propelled active HH droplets.
Fig. 2: Active droplet accompanied by an SR.
Fig. 3: Circular trajectories of active HH droplets in a nematic with a circular prepatterned director.
Fig. 4: Activity triggered flows inside and outside the HH droplet.

Data availability

Source data for Figs. 1d–i, 2c–f and 4c, f are available with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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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.

Author information




M.R. and H.B. performed the experiments, M.R., H.B., T.T. and O.D.L. analysed the data, O.D.L. conceived and supervised the project, M.R. and O.D.L. wrote the manuscript with the input from all co-authors.

Corresponding author

Correspondence to Oleg D. Lavrentovich.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Paulo Arratia, M Cristina and Uroš Tkalec for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary text and Fig. 1, and legends for Supplementary Videos 1–4.

Reporting Summary

Supplementary Video 1

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.

Supplementary Video 2

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.

Supplementary Video 3

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.

Supplementary Video 4

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.

Source data

Source Data Fig. 1

Source data for Fig. 1 d–i.

Source Data Fig. 2

Source data for Fig. 2 c–f.

Source Data Fig. 4

Source data for Fig.1 c,f.

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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).

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