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Rechargeable self-assembled droplet microswimmers driven by surface phase transitions

Abstract

The design of artificial microswimmers is often inspired by the strategies of natural microorganisms. Many of these creatures exploit the fact that elasticity breaks the time-reversal symmetry of motion at low Reynolds numbers, but this principle has been notably absent from model systems of active, self-propelled microswimmers. Here we introduce a class of microswimmers that spontaneously self-assembles and swims without using external forces, driven instead by surface phase transitions induced by temperature variations. The swimmers are made from alkane droplets dispersed in an aqueous surfactant solution, which start to self-propel on cooling, pushed by rapidly growing thin elastic tails. When heated, the same droplets recharge by retracting their tails, swimming for up to tens of minutes in each cycle. Thermal oscillations of approximately 5 °C induce the swimmers to harness heat from the environment and recharge multiple times. We develop a detailed elasto-hydrodynamic model of these processes and highlight the molecular mechanisms involved. The system offers a convenient platform for examining symmetry breaking in the motion of swimmers exploiting flagellar elasticity. The mild conditions and biocompatible media render these microswimmers potential probes for studying biological propulsion and interactions between artificial and biological swimmers.

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Fig. 1: Emulsion droplets deform on cooling and eventually form dynamic swimmers with one or two fibre-extruding nozzles.
Fig. 2: Main parameters describing the swimmers shape and motion.
Fig. 3: Droplet swimming speed.
Fig. 4: Kinematics of swimming.

Data availability

Source data are provided with this paper. The data that support the findings of this study are available from the corresponding authors upon reasonable request.

Code availability

The code used in this study is available from the corresponding authors upon reasonable request.

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Acknowledgements

This study was funded by the European Research Council (ERC) EMATTER (no. 280078) and the Engineering and Physical Sciences Research Council Fellowship no. EP/R028915/1 to S.K.S. This project has received funding from the ERC under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 682754 to E.L.). The study received financial support from project no. KP-06-DV-4/2019 with the Bulgarian Ministry of Education and Science, under the National Research Program ‘VIHREN’ to N.D. The work has been supported by the National Science Center of Poland SONATA grant no. 2018/31/D/ST3/02408 to M.L. The study falls under the umbrella of European network COST CA17120 Chemobrionics. We are grateful to M. Paraskova (Sofia University) for her help with part of the image analysis and for the preparation of some figures.

Author information

Affiliations

Authors

Contributions

D.C. discovered the phenomenon and clarified the experimental conditions under which this new type of swimmer is obtained and can be controlled. D.C., S.T. and N.D. suggested studying the process in more detail. D.C. and S.T. designed the experimental part of the study. S.K.S. designed the part of the study about filament retraction. D.C. performed most of the experiments with respect to fibre extrusion, summarized the obtained results and analysed them (with inputs from S.T., N.D. and S.K.S.), while E.E.L., D.C. and J.C. performed most of experiments for fibre retraction (with input from S.K.S.). E.E.L. clarified the experimental conditions for controlled retraction of the tails. S.K.S. made the first analytical model for swimming by using the estimates of sphere and cylinder drag forces. M.L. and E.L. developed the theoretical description for the extrusion of fibre and motion of droplets. S.K.S., D.C. and M.L. analysed movies and developed insights into relating the dynamic features to the material properties of fibres. M.L. and G.D.C. developed the computer code used in the numerical simulations. S.K.S. and N.D. prepared the initial manuscript draft. D.C. edited the manuscript and prepared the figures and movies. M.L. prepared the theoretical part of the Supporting Information. M.L. and E.L. edited the manuscript. All the authors critically read the manuscript and approved it.

Corresponding authors

Correspondence to Maciej Lisicki or Stoyan K. Smoukov or Eric Lauga or Nikolai Denkov.

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Competing interests

The authors declare no competing interests.

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Peer review information Nature Physics thanks Marisol Ripoll and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–11, Tables 1 and 2, experimental results and theoretical modelling description.

Reporting Summary

Supplementary Video 1

Extrusion of a single fibre from tetradecane swimmers in 1.5 wt% Brij 58 surfactant solution at 0.4 °C min–1 cooling rate. Extrusion rate UF ≈ 14.0 μm s–1 and swimming speed US ≈ 0.7 μm s–1.

Supplementary Video 2

Extrusion of two in-phase fibres from a pentadecane swimmer in 1.5 wt% Brij 58 surfactant solution at 0.25 °C min–1 cooling rate. Extrusion rate UF ≈ 2.70 μm s–1 and swimming speed US ≈ 0.23 μm s–1.

Supplementary Video 3

Extrusion of two out-of-phase fibres for a pentadecane swimmer in 1.5 wt% Brij 58 surfactant solution at 0.25 °C min–1 cooling rate. Extrusion rate UF ≈ 3.10 μm s–1 and swimming speed US ≈ 0.25 μm s–1.

Supplementary Video 4

Simulation results, presented in dimensionless scales, for an extruded filament pushed straight into a fluid at a constant speed, UF, which sets the velocity scale. The length scale is set by the buckling length of the filament, l. The dimensionless time shown at the bottom is set by the ratio l/UF. Changing the material or the dynamic parameters of the process affects the dimensional time at which the buckling occurs and the dimensional distance at which the beam becomes unstable. After a short period of straight motion, the fluid-drag-induced tension in the beam increases beyond the buckling threshold and the beam deflects. As a result, a meander-type pattern is created, which closely resembles the experimentally observed fibre deformations.

Supplementary Video 5

Simulation results for a filament retracted from the fluid at a constant speed, shown in a dimensionless form (as shown in the caption of Supplementary Video 4). Starting from a deformed shape of the beam, the dynamics is quite different compared with extrusion. The beam initially straightens and then it is dragged into the nozzle without buckling. The final stage of the process is a linear decrease in the extruded length. The slight tilt with respect to the horizontal is a result of the initial asymmetry of the configuration.

Supplementary Video 6

Fibre retraction on the heating of a pentadecane swimmer in 1.5 wt% Brij 58 surfactant solution at ~3 °C min–1 heating rate. Although each of the pre-extruded fibres is >2,500 µm long, they completely retract on heating back into the initial droplet and recharge the swimmer.

Supplementary Video 7

One full cycle of fibre extrusion on cooling at 0.3 °C min–1 and fibre retraction on heating at 0.2 °C min–1 for several pentadecane swimmers in 1.5 wt% Brij 58 surfactant solution (one fibre per swimmer).

Supplementary Video 8

Three full, consecutive cycles of fibre extrusion on cooling and retraction on heating at 0.23 °C min–1 for a pentadecane swimmer with two fibres in 1.5 wt% Brij 58 surfactant solution.

Supplementary Video 9

Video of pentadecane swimmers in 1.5 wt% Brij 58 solution extruding two fibres. Different colour curves show the tracking of individual droplets performed with MTrackJ plugin in the ImageJ program. For estimating the swimming speed, US, we used the tracks of the ‘white dots’ in the centre of the swimmers, numbered as 1, 5 and 9 in the video.

Supplementary Video 10

Video of an extruding filament (tail) on cooling a typical swimmer droplet of pentadecane in a 0.5 wt% Brij S20 solution. Cooling rate, 0.9 °C min–1; extrusion rate, 2.50 μm s–1; swimmer speed, 0.34 μm s–1. Scale bar, 20 μm. The video is played at four times speed.

Supplementary Video 11

Video of an extruding filament (tail) on cooling a typical swimmer droplet of pentadecane in a 0.5 wt% Brij S20 solution. Cooling rate, 2.8 °C min–1; extrusion rate, 12.40 μm s–1; swimmer speed, 0.68 μm s–1. Scale bar, 20 μm. The video is played at four times speed.

Supplementary Video 12

Video of a retracting filament on heating a typical swimmer droplet of pentadecane in a 0.5 wt% Brij S20 solution. Heating rate, 1.5 °C min–1; retraction rate, 4.8 µm s–1. Scale bar, 20 µm.

Supplementary Table 1

Data included in Figs. 1 and 3.

Source data

Source Data Fig. 3

Data included in Fig. 3.

Source Data Fig. 4

Data included in Fig. 4.

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Cholakova, D., Lisicki, M., Smoukov, S.K. et al. Rechargeable self-assembled droplet microswimmers driven by surface phase transitions. Nat. Phys. (2021). https://doi.org/10.1038/s41567-021-01291-3

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