Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Rechargeable self-assembled droplet microswimmers driven by surface phase transitions


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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

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.


  1. 1.

    Elgeti, J., Winkler, R. G. & Gompper, G. Physics of microswimmers—single particle motion and collective behavior: a review. Rep. Prog. Phys. 78, 056601 (2015).

    ADS  MathSciNet  Article  Google Scholar 

  2. 2.

    Lauga, E. & Powers, T. R. The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601 (2009).

  3. 3.

    Balzani, V., Credi, A., Raymo, F. M. & Stoddart, J. F. Artificial molecular machines. Angew. Chem. Int. Ed. 39, 3348–3391 (2000).

    Article  Google Scholar 

  4. 4.

    Schwarz-Linek, J. et al. Phase separation and rotor self-assembly in active particle suspensions. Proc. Natl Acad. Sci. USA 109, 4052–4057 (2012).

    ADS  Article  Google Scholar 

  5. 5.

    Paxton, W. F. et al. Catalytic nanomotors: autonomous movement of striped nanorods. J. Am. Chem. Soc. 126, 13424–13431 (2004).

    Article  Google Scholar 

  6. 6.

    Michelin, S. & Lauga, E. Efficiency optimization and symmetry-breaking in a model of ciliary locomotion. Phys. Fluids 22, 111901 (2013).

  7. 7.

    Kassem, S. et al. Artificial molecular motors. Chem. Soc. Rev. 46, 2592–2621 (2017).

    Article  Google Scholar 

  8. 8.

    Fischer, P. Vision statement: interactive materials—drivers of future robotic systems. Adv. Mater. 32, 1–4 (2020).

    Article  Google Scholar 

  9. 9.

    Khaldi, A., Elliott, J. A. & Smoukov, S. K. Electro-mechanical actuator with muscle memory. J. Mater. Chem. C 2, 8029–8034 (2014).

    Article  Google Scholar 

  10. 10.

    Marshall, J. E., Gallagher, S., Terentjev, E. M. & Smoukov, S. K. Anisotropic colloidal micromuscles from liquid crystal elastomers. J. Am. Chem. Soc. 136, 474–479 (2014).

    Article  Google Scholar 

  11. 11.

    Khaldi, A., Plesse, C., Vidal, F. & Smoukov, S. K. Smarter actuator design with complementary and synergetic functions. Adv. Mater. 27, 4418–4422 (2015).

    Article  Google Scholar 

  12. 12.

    Wang, T. et al. Electroactive polymers for sensing. Interface Focus 6, 20160026 (2016).

    Article  Google Scholar 

  13. 13.

    Lesov, I. et al. Bottom-up synthesis of polymeric micro- and nanoparticles with regular anisotropic shapes. Macromolecules 51, 7456–7462 (2018).

    ADS  Article  Google Scholar 

  14. 14.

    Sanchez, S., Soler, L. & Katuri, J. Chemically powered micro- and nanomotors. Angew. Chem. Int. Ed. 54, 1414–1444 (2015).

    Article  Google Scholar 

  15. 15.

    Soh, S., Bishop, K. J. M. & Grzybowski, B. A. Dynamic self-assembly in ensembles of camphor boats. J. Phys. Chem. B 112, 10848–10853 (2008).

    Article  Google Scholar 

  16. 16.

    Jiang, H. R., Yoshinaga, N. & Sano, M. Active motion of a Janus particle by self-thermophoresis in a defocused laser beam. Phys. Rev. Lett. 105, 1–4 (2010).

    Google Scholar 

  17. 17.

    Ren, L. et al. 3D steerable, acoustically powered microswimmers for single-particle manipulation. Sci. Adv. 5, eaax3084 (2019).

  18. 18.

    Ghosh, A. & Fischer, P. Controlled propulsion of artificial magnetic nanostructured propellers. Nano Lett. 9, 2243–2245 (2009).

    ADS  Article  Google Scholar 

  19. 19.

    Chang, S. T., Paunov, V. N., Petsev, D. N. & Velev, O. D. Remotely powered self-propelling particles and micropumps based on miniature diodes. Nat. Mater. 6, 235–240 (2007).

    ADS  Article  Google Scholar 

  20. 20.

    Takatori, S. C. & Brady, J. F. Towards a thermodynamics of active matter. Phys. Rev. E 91, 032117 (2015).

    ADS  Article  Google Scholar 

  21. 21.

    Buttinoni, I., Volpe, G., Kümmel, F., Volpe, G. & Bechinger, C. Active Brownian motion tunable by light. J. Phys. Condens. Matter 24, 284129 (2012).

    Article  Google Scholar 

  22. 22.

    Xuan, M. et al. Near infrared light-powered Janus mesoporous silica nanoparticle motors. J. Am. Chem. Soc. 138, 6492–6497 (2016).

    Article  Google Scholar 

  23. 23.

    Lv, H., Xing, Y., Du, X., Xu, T. & Zhang, X. Construction of dendritic Janus nanomotors with H2O2 and NIR light dual-propulsion via a Pickering emulsion. Soft Matter 16, 4961–4968 (2020).

    ADS  Article  Google Scholar 

  24. 24.

    Shao, J. et al. Erythrocyte membrane modified Janus polymeric motors for thrombus therapy. ACS Nano 12, 4877–4885 (2018).

    Article  Google Scholar 

  25. 25.

    Peyer, K. E., Tottori, S., Qiu, F., Zhang, L. & Nelson, B. J. Magnetic helical micromachines. Chem. Eur. J. 19, 28–38 (2013).

    Article  Google Scholar 

  26. 26.

    Lee, S. et al. A capsule-type microrobot with pick-and-drop motion for targeted drug and cell delivery. Adv. Healthcare Mater. 7, 1–6 (2018).

    Google Scholar 

  27. 27.

    Medina-Sánchez, M., Schwarz, L., Meyer, A. K., Hebenstreit, F. & Schmidt, O. G. Cellular cargo delivery: toward assisted fertilization by sperm-carrying micromotors. Nano Lett. 16, 555–561 (2016).

    ADS  Article  Google Scholar 

  28. 28.

    Cates, M. E. Diffusive transport without detailed balance in motile bacteria: does microbiology need statistical physics? Rep. Prog. Phys. 75, 042601 (2012).

    ADS  Article  Google Scholar 

  29. 29.

    Robinson, D. G., Hoppenrath, M., Oberbeck, K., Luykx, P. & Ratajczak, R. Localization of pyrophosphatase and V-ATPase in Chlamydomonas reinhardtii. Bot. Acta 111, 108–122 (1998).

    Article  Google Scholar 

  30. 30.

    Goldstein, R. E. Green algae as model organisms for biological fluid dynamics. Annu. Rev. Fluid Mech. 47, 343–375 (2015).

    ADS  MathSciNet  Article  Google Scholar 

  31. 31.

    Denkov, N., Tcholakova, S., Lesov, I., Cholakova, D. & Smoukov, S. K. Self-shaping of oil droplets via the formation of intermediate rotator phases upon cooling. Nature 528, 392–395 (2015).

    ADS  Article  Google Scholar 

  32. 32.

    Cholakova, D. & Denkov, N. Rotator phases in alkane systems: in bulk, surface layers and micro/nano-confinements. Adv. Colloid Interface Sci. 269, 7–42 (2019).

    Article  Google Scholar 

  33. 33.

    Cholakova, D., Denkov, N., Tcholakova, S., Lesov, I. & Smoukov, S. K. Control of drop shape transformations in cooled emulsions. Adv. Colloid Interface Sci. 235, 90–107 (2016).

    Article  Google Scholar 

  34. 34.

    Denkov, N., Cholakova, D., Tcholakova, S. & Smoukov, S. K. On the mechanism of drop self-shaping in cooled emulsions. Langmuir 32, 7985–7991 (2016).

    Article  Google Scholar 

  35. 35.

    Burrows, S. A., Korotkin, I., Smoukov, S. K., Boek, E. & Karabasov, S. Benchmarking of molecular dynamics force fields for solid–liquid and solid–solid phase transitions in alkanes. J. Phys. Chem. B 125, 5145–5159 (2021).

    Article  Google Scholar 

  36. 36.

    Haas, P. A., Goldstein, R. E., Smoukov, S. K., Cholakova, D. & Denkov, N. Theory of shape-shifting droplets. Phys. Rev. Lett. 118, 1–5 (2017).

    Article  Google Scholar 

  37. 37.

    Haas, P. A., Cholakova, D., Denkov, N., Goldstein, R. E. & Smoukov, S. K. Shape-shifting polyhedral droplets. Phys. Rev. Res. 1, 023017 (2019).

    Article  Google Scholar 

  38. 38.

    Gordon, R., Hanczyc, M. M., Denkov, N. D., Tiffany, M. A. & Smoukov, S. K. in Habitability of the Universe before Earth: Astrobiology: Exploring Life on Earth and Beyond (eds Gordon, R. & Sharov, A.) 427–490 (Academic Press, 2018).

  39. 39.

    Fuller, R. B. & Applewhite, E. J. Synergetics 2: Further Explorations in the Geometry of Thinking (MacMillan 1979).

  40. 40.

    Gosselin, F. P., Neetzow, P. & Paak, M. Buckling of a beam extruded into highly viscous fluid. Phys. Rev. E 90, 052718 (2014).

    ADS  Article  Google Scholar 

  41. 41.

    De Canio, G., Lauga, E. & Goldstein, R. E. Spontaneous oscillations of elastic filaments induced by molecular motors. J. R. Soc. Interface 14, 20170491 (2017).

    Article  Google Scholar 

  42. 42.

    Ui, T. J., Hussey, R. G. & Roger, R. P. Stokes drag on a cylinder in axial motion. Phys. Fluids 27, 787–795 (1984).

    ADS  Article  Google Scholar 

  43. 43.

    Gueron, S. & Levit-Gurevich, K. Energetic considerations of ciliary beating and the advantage of metachronal coordination. Proc. Natl Acad. Sci. USA 96, 12240–12245 (1999).

    ADS  MATH  Article  Google Scholar 

  44. 44.

    Kotar, J., Leoni, M., Bassetti, B., Cosentino, M. & Cicuta, P. Hydrodynamic synchronization of colloidal oscillators. Proc. Natl Acad. Sci. USA 107, 7669–7673 (2010).

  45. 45.

    Brumley, D. R., Wan, K. Y., Polin, M. & Goldstein, R. E. Flagellar synchronization through direct hydrodynamic interactions. eLife 3, 1–15 (2014).

    Article  Google Scholar 

  46. 46.

    Wan, K. Y. & Goldstein, R. E. Coordinated beating of algal flagella is mediated by basal coupling. Proc. Natl Acad. Sci. USA 113, E2784–E2793 (2016).

    ADS  Article  Google Scholar 

  47. 47.

    Geyer, V. F., Jülicher, F., Howard, J. & Friedrich, B. M. Cell-body rocking is a dominant mechanism for flagellar synchronization in a swimming alga. Proc. Natl Acad. Sci. USA 110, 18058–18063 (2013).

    ADS  Article  Google Scholar 

  48. 48.

    Small, D. M. The Physical Chemistry of Lipids: From Alkanes to Phospholipids (Plenum Press, 1986).

  49. 49.

    May, G. J., Davidson, A. & Monahov, B. Lead batteries for utility energy storage: a review. J. Energy Storage 15, 145–157 (2018).

    Article  Google Scholar 

  50. 50.

    Yang, X., Xiang, L., Dong, Y., Cao, Y. & Wang, C. Effect of nonionic surfactant Brij 35 on morphology, cloud point, and pigment stability in Monascus extractive fermentation. J. Sci. Food Agric. 100, 4521–4530 (2020).

    Article  Google Scholar 

  51. 51.

    Yang, X. et al. Effects of nonionic surfactants on pigment excretion and cell morphology in extractive fermentation of Monascus sp. NJ1. J. Sci. Food Agric. 100, 1832–1832 (2020).

    Article  Google Scholar 

  52. 52.

    Yang, X. et al. Effects of nonionic surfactants on pigment excretion and cell morphology in extractive fermentation of Monascus sp. NJ1. J. Sci. Food Agric. 99, 1233–1239 (2019).

    Article  Google Scholar 

  53. 53.

    Tang, J. et al. Solid lipid nanoparticles with TPGS and Brij 78: a co-delivery vehicle of curcumin and piperine for reversing P-glycoprotein-mediated multidrug resistance in vitro. Oncol. Lett. 13, 389–395 (2017).

    Article  Google Scholar 

  54. 54.

    Tomasi, R. F.-X., Sart, S., Champetier, T. & Baroud, C. N. Individual control and quantification of 3D spheroids in a high-density microfluidic droplet array. Cell Rep. 31, 107670 (2020).

    Article  Google Scholar 

Download references


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




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.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks Marisol Ripoll and the other, anonymous, reviewer(s) 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 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.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Cholakova, D., Lisicki, M., Smoukov, S.K. et al. Rechargeable self-assembled droplet microswimmers driven by surface phase transitions. Nat. Phys. 17, 1050–1055 (2021).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing