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.

Furcated droplet motility on crystalline surfaces


Directed liquid motion has been conventionally mediated by functionalizing chemical inhomogeneity or texturing topological anisotropy on target surfaces. Here we show the self-propulsion of droplets that furcated in well-defined directions on piezoelectric single crystals in the absence of any apparent asymmetry or external force. By selecting the crystal plane to interface with the droplets, the thermoelastic–piezoelectric interplay yields intricate electric potential profiles, enabling various forms of self-propulsion including unidirectional, bifurcated and trifurcated. This effect originates from an anisotropic crystalline structure that generates contrasting macroscopic liquid behaviours and is observed with cold/hot and volatile droplets. Intrinsically oriented liquid motions have broad applicability in processes ranging from soft matter engineering, autonomous material delivery and thermal management to biochemical analysis.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Furcated droplets self-propulsion.
Fig. 2: Thermo-piezoelectric coupling.
Fig. 3: Dynamics of self-propulsion.
Fig. 4: Evaporation-driven self-propulsion.

Data availability

The data that support the findings reported in this study are available from the corresponding author upon reasonable request.


  1. Bouillant, A. et al. Leidenfrost wheels. Nat. Phys. 14, 1188–1192 (2018).

    CAS  Article  Google Scholar 

  2. Park, K.-C. et al. Condensation on slippery asymmetric bumps. Nature 531, 78–82 (2016).

    CAS  Article  Google Scholar 

  3. Ju, J. et al. A multi-structural and multi-functional integrated fog collection system in cactus. Nat. Commun. 3, 1247 (2012).

  4. Kim, H. et al. Water harvesting from air with metal-organic frameworks powered by natural sunlight. Science 356, 430–434 (2017).

    CAS  Article  Google Scholar 

  5. Abdelgawad, M. & Wheeler, A. R. The digital revolution: a new paradigm for microfluidics. Adv. Mater. 21, 920–925 (2009).

    CAS  Article  Google Scholar 

  6. Tang, X. et al. Mechano-regulated surface for manipulating liquid droplets. Nat. Commun. 8, 14831 (2017).

  7. Daniel, S., Chaudhury, M. K. & Chen, J. C. Fast drop movements resulting from the phase change on a gradient surface. Science 291, 633–636 (2001).

    CAS  Article  Google Scholar 

  8. Dung Luong, T. & Trung Nguyen, N. Surface acoustic wave driven microfluidics—a review. Micro Nanosyst. 2, 217–225 (2010).

    Article  Google Scholar 

  9. Lagubeau, G., Le Merrer, M., Clanet, C. & Quéré, D. Leidenfrost on a ratchet. Nat. Phys. 7, 395–398 (2011).

    CAS  Article  Google Scholar 

  10. Prakash, M., Quéré, D. & Bush, J. W. Surface tension transport of prey by feeding shorebirds: the capillary ratchet. Science 320, 931–934 (2008).

    CAS  Article  Google Scholar 

  11. Chen, H. et al. Continuous directional water transport on the peristome surface of Nepenthes alata. Nature 532, 85–89 (2016).

    CAS  Article  Google Scholar 

  12. Lv, J.-a et al. Photocontrol of fluid slugs in liquid crystal polymer microactuators. Nature 537, 179–184 (2016).

    CAS  Article  Google Scholar 

  13. Li, J. et al. Topological liquid diode. Sci. Adv. 3, eaao3530 (2017).

    Article  Google Scholar 

  14. Li, J. et al. Directional transport of high-temperature Janus droplets mediated by structural topography. Nat. Phys. 12, 606–612 (2016).

    CAS  Article  Google Scholar 

  15. De Jong, E., Wang, Y., Den Toonder, J. M. & Onck, P. R. Climbing droplets driven by mechanowetting on transverse waves. Sci. Adv. 5, eaaw0914 (2019).

    Article  Google Scholar 

  16. Chaudhury, M. K. & Whitesides, G. M. How to make water run uphill. Science 256, 1539–1541 (1992).

    CAS  Article  Google Scholar 

  17. Sun, Q. et al. Surface charge printing for programmed droplet transport. Nat. Mater. 18, 936–941 (2019).

    CAS  Article  Google Scholar 

  18. Ichimura, K., Oh, S.-K. & Nakagawa, M. Light-driven motion of liquids on a photoresponsive surface. Science 288, 1624–1626 (2000).

    CAS  Article  Google Scholar 

  19. Berna, J. et al. Macroscopic transport by synthetic molecular machines. Nat. Mater. 4, 704–710 (2005).

    CAS  Article  Google Scholar 

  20. Cho, S. K., Moon, H. & Kim, C.-J. Creating, transporting, cutting, and merging liquid droplets by electrowetting-based actuation for digital microfluidic circuits. J. Microelectromech. Syst. 12, 70–80 (2003).

    Article  Google Scholar 

  21. Kreder, M. J., Alvarenga, J., Kim, P. & Aizenberg, J. Design of anti-icing surfaces: smooth, textured or slippery? Nat. Rev. Mater. 1, 15003 (2016).

  22. Earle, M. J. et al. The distillation and volatility of ionic liquids. Nature 439, 831–834 (2006).

    CAS  Article  Google Scholar 

  23. Wong, T.-S. et al. Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity. Nature 477, 443–447 (2011).

    CAS  Article  Google Scholar 

  24. Furmidge, C. Studies at phase interfaces. I. The sliding of liquid drops on solid surfaces and a theory for spray retention. J. Colloid Sci. 17, 309–324 (1962).

    CAS  Article  Google Scholar 

  25. Wong, K.-K. Properties of Lithium Niobate (IET, 2002).

  26. Kreder, M. J. et al. Film dynamics and lubricant depletion by droplets moving on lubricated surfaces. Phys. Rev. 8, 031053 (2018).

    CAS  Article  Google Scholar 

  27. Shiri, S. & Bird, J. C. Heat exchange between a bouncing drop and a superhydrophobic substrate. Proc. Natl Acad. Sci. USA 114, 6930–6935 (2017).

    CAS  Article  Google Scholar 

  28. Nellis, G. & Klein, S. A. Heat Transfer (Cambridge Univ. Press, 2009).

  29. de Ruiter, J., Soto, D. & Varanasi, K. K. Self-peeling of impacting droplets. Nat. Phys. 14, 35–39 (2018).

    Article  Google Scholar 

  30. Lang, S. B. Pyroelectricity: from ancient curiosity to modern imaging tool. Phys. Today 58, 31 (2005).

    CAS  Article  Google Scholar 

  31. Berthier, J. Micro-Drops and Digital Microfluidics (Elsevier Science, 2012).

  32. Daniel, D., Timonen, J. V., Li, R., Velling, S. J. & Aizenberg, J. Oleoplaning droplets on lubricated surfaces. Nat. Phys. 13, 1020–1025 (2017).

    CAS  Article  Google Scholar 

  33. Tang, X. et al. Bioinspired nanostructured surfaces for on-demand bubble transportation. ACS Appl. Mater. Interfaces 10, 3029–3038 (2018).

    CAS  Article  Google Scholar 

  34. Darhuber, A. A., Davis, J. M., Troian, S. M. & Reisner, W. W. Thermocapillary actuation of liquid flow on chemically patterned surfaces. Phys. Fluids 15, 1295–1304 (2003).

    CAS  Article  Google Scholar 

  35. Tichý, J., Erhart, J., Kittinger, E. & Prívratská, J. Fundamentals of Piezoelectric Sensorics: Mechanical, Dielectric, and Thermodynamical Properties of Piezoelectric Materials (Springer, 2010).

  36. De Angelis, F. et al. Breaking the diffusion limit with super-hydrophobic delivery of molecules to plasmonic nanofocusing SERS structures. Nat. Photonics 5, 682 (2011).

    Article  Google Scholar 

  37. Soitu, C. et al. Raising fluid walls around living cells. Sci. Adv. 5, eaav8002 (2019).

    Article  Google Scholar 

  38. Gladman, A. S., Matsumoto, E. A., Nuzzo, R. G., Mahadevan, L. & Lewis, J. A. Biomimetic 4D printing. Nat. Mater. 15, 413–418 (2016).

    Article  Google Scholar 

  39. MacDonald, E. & Wicker, R. Multiprocess 3D printing for increasing component functionality. Science 353, aaf2093 (2016).

    CAS  Article  Google Scholar 

  40. Miljkovic, N. et al. Jumping-droplet-enhanced condensation on scalable superhydrophobic nanostructured surfaces. Nano Lett. 13, 179–187 (2013).

    CAS  Article  Google Scholar 

  41. Cooper, T. A. et al. Contactless steam generation and superheating under one sun illumination. Nat. Commun. 9, 5086 (2018).

    CAS  Article  Google Scholar 

Download references


We thank W.-D. Li and S.-P. Feng for equipment support, Y. Chen and H. Yu for valuable discussion and Z. Zhou for assistance in the experiment. L.W. acknowledges financial support from the Research Grants Council of Hong Kong (grant nos. GRF 17205421, 17204420, 17210319, 17204718 and CRF C1006-20WF, C1018-17G). X.T. acknowledges support from the Research Grants Council Postdoctoral Fellowship Scheme. This work was also supported in part by the Zhejiang Provincial, Hangzhou Municipal and Lin’an County governments.

Author information

Authors and Affiliations



X.T. and L.W. conceived and designed the project. X.T. performed the experiments to which W.L. also contributed. X.T. and L.W. analysed the data and wrote the paper.

Corresponding author

Correspondence to Liqiu Wang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Nanotechnology thanks Evelyn Wang 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. 1–18, Notes 1–4 and Tables 1 and 2.

Supplementary Video 1

Side view of droplet states on Si and LiNbO3 crystal surface.

Supplementary Video 2

Bottom view of unidirectional self-propulsion of droplets on \((01\bar 1\bar 1)\) LiNbO3.

Supplementary Video 3

Bottom view of bifurcated self-propulsion of droplets on \((10\bar 1\bar 1)\) LiNbO3.

Supplementary Video 4

Bottom view of trifurcated self-propulsion of droplets on (0001) LiNbO3.

Supplementary Video 5

Side view of spontaneous self-propulsion on different crystal planes.

Supplementary Video 6

Side view of droplet ascending uphill.

Supplementary Video 7

Side view of evaporation-driven continuous self-propulsion of organic solvents.

Supplementary Video 8

Bottom view of shape evolution of diethyl ether droplets on different crystal planes.

Supplementary Video 9

Bottom view of droplet self-navigation on LiNbO3 tiles.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tang, X., Li, W. & Wang, L. Furcated droplet motility on crystalline surfaces. Nat. Nanotechnol. 16, 1106–1112 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Find nanotechnology articles, nanomaterial data and patents all in one place. Visit Nano by Nature Research