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  • Open Access

Frost halo rings beneath freezing droplets on cryogenic surfaces

Xiong Wang1,*,†, Zhenyue Yuan1, and Ran Tao2,‡

  • *Present address: Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong 999077, People's Republic of China.
  • †Contact author: wangxion15@tsinghua.org.cn
  • ‡Contact author: taoran@uestc.edu.cn

Phys. Rev. Research 7, 043312 – Published 18 December, 2025

DOI: https://doi.org/10.1103/l61w-mj3p

Abstract

We experimentally investigate the frosting phenomena beneath freezing droplets on cryogenic surfaces and reveal the emergence of previously unreported dual frost halo rings. We report that droplets impacting from low heights produce dual frost halo rings beneath the freezing droplet, whereas higher impact heights result in a single halo ring. The formation of dual halos originates from the raised bimodal morphology of the freezing droplet, which is shaped by the interplay of hydrodynamic spreading, freezing kinetics, and mechanical peeling dynamics. The locally thicker region of the raised thickness profile cools more slowly than the surrounding edge, maintaining a higher temperature that promotes localized sublimation at the freezing droplet base and subsequent vapor desublimation onto the adjacent cryogenic substrate, thereby resulting in an internal frost halo ring. Through capillary wave propagation analysis, we identify the morphology transition of different frost halo rings characterized by a power-exponent relationship between the dimensionless droplet falling height and radius. These findings provide insights into the complex interplay between capillary hydrodynamics and freezing kinetics under cryogenic conditions.

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References (47)

  1. M. V. Gielen, R. de Ruiter, R. B. Koldeweij, D. Lohse, J. H. Snoeijer, and H. Gelderblom, Solidification of liquid metal drops during impact, J. Fluid Mech. 883, A32 (2020).
  2. B. Gorin, D. Bonn, and H. Kellay, Droplet impacts on cold surfaces, J. Fluid Mech. 944, A23 (2022).
  3. I. V. Roisman, Fast forced liquid film spreading on a substrate: Flow, heat transfer and phase transition, J. Fluid Mech. 656, 189 (2010).
  4. V. Thiévenaz, T. Séon, and C. Josserand, Solidification dynamics of an impacted drop, J. Fluid Mech. 874, 756 (2019).
  5. A. Huerre, C. Josserand, and T. Séon, Freezing and capillarity, Annu. Rev. Fluid Mech. 57, 257 (2024).
  6. R. De Ruiter, P. Colinet, P. Brunet, J. H. Snoeijer, and H. Gelderblom, Contact line arrest in solidifying spreading drops, Phys. Rev. Fluids 2, 043602 (2017).
  7. R. Grivet, A. Monier, A. Huerre, C. Josserand, and T. Séon, Contact line catch up by growing ice crystals, Phys. Rev. Lett. 128, 254501 (2022).
  8. V. Y. Lolla, S. F. Ahmadi, H. Park, A. P. Fugaro, and J. B. Boreyko, Arrested dynamics of droplet spreading on ice, Phys. Rev. Lett. 129, 074502 (2022).
  9. V. Thiévenaz, C. Josserand, and T. Séon, Retraction and freezing of a water film on ice, Phys. Rev. Fluids 5, 041601 (2020).
  10. W.-Z. Fang, F. Zhu, W.-Q. Tao, and C. Yang, How different freezing morphologies of impacting droplets form, J. Colloid Interface Sci. 584, 403 (2021).
  11. E. Ghabache, C. Josserand, and T. Séon, Frozen impacted drop: From fragmentation to hierarchical crack patterns, Phys. Rev. Lett. 117, 074501 (2016).
  12. R. Grivet, A. Huerre, T. Séon, and C. Josserand, Making superhydrophobic splashes by surface cooling, Phys. Rev. Fluids 8, 063603 (2023).
  13. P. Kant, H. Müller-Groeling, and D. Lohse, Pattern formation during the impact of a partially frozen binary droplet on a cold surface, Phys. Rev. Lett. 125, 184501 (2020).
  14. P. Kant, R. B. Koldeweij, K. Harth, M. A. van Limbeek, and D. Lohse, Fast-freezing kinetics inside a droplet impacting on a cold surface, Proc. Natl. Acad. Sci. USA 117, 2788 (2020).
  15. V. Kulkarni, S. Tamvada, N. Shirdade, N. Saneie, V. Y. Lolla, V. Batheyrameshbapu, and S. Anand, Increased solidification delays fragmentation and suppresses rebound of impacting drops, Phys. Rev. Fluids 9, 053604 (2024).
  16. P. Jin et al., Ultra-low ice-substrate adhesion and self-deicing during droplet impact freezing, Cell Rep. Phys. Sci. 3, 100894 (2022).
  17. W.-Z. Fang, F. Zhu, L. Zhu, W.-Q. Tao, and C. Yang, Self-peeling of frozen water droplets upon impacting a cold surface, Commun. Phys. 5, 51 (2022).
  18. T. Cebeci and F. Kafyeke, Aircraft icing, Annu. Rev. Fluid Mech. 35, 11 (2003).
  19. A. Dhyani, W. Choi, K. Golovin, and A. Tuteja, Surface design strategies for mitigating ice and snow accretion, Matter 5, 1423 (2022).
  20. M. J. Kreder, J. Alvarenga, P. Kim, and J. Aizenberg, Design of anti-icing surfaces: Smooth, textured or slippery? Nat. Rev. Mater. 1, 1 (2016).
  21. Y. Akiyama, M. Shinose, H. Watanabe, S. Yamada, and Y. Kanda, Cryoprotectant-free cryopreservation of mammalian cells by superflash freezing, Proc. Natl. Acad. Sci. USA 116, 7738 (2019).
  22. U. Demirci and G. Montesano, Cell encapsulating droplet vitrification, Lab Chip 7, 1428 (2007).
  23. R. Dou, R. E. Saunders, L. Mohamet, C. M. Ward, and B. Derby, High throughput cryopreservation of cells by rapid freezing of sub-μl drops using inkjet printing–Cryoprinting, Lab Chip 15, 3503 (2015).
  24. See Supplemental Material at http://link.aps.org/supplemental/10.1103/l61w-mj3p for additional details, which include the cold stage, image processing, spreading law, and Video S1.
  25. S. Zhen, H. Feng, S. Lin, Y. Jin, Z. Li, X. Deng, E. Bonaccurso, and L. Chen, Condensate halos in condensation frosting, Adv. Sci. 12, 2410657 (2025).
  26. Y. Zhao, F. Zhu, H. Zhang, T. H. New, L. Jin, and C. Yang, Triple condensate halo from a single water droplet impacting upon a cold surface, Appl. Phys. Lett. 114, 183703 (2019).
  27. S. Kavuri, G. Karapetsas, C. S. Sharma, and K. C. Sahu, Freezing of sessile droplet and frost halo formation, Phys. Rev. Fluids 8, 124003 (2023).
  28. S. Jung, M. K. Tiwari, and D. Poulikakos, Frost halos from supercooled water droplets, Proc. Natl. Acad. Sci. USA 109, 16073 (2012).
  29. J. de Ruiter, D. Soto, and K. K. Varanasi, Self-peeling of impacting droplets, Nat. Phys. 14, 35 (2017).
  30. A. Bejan, Convection Heat Transfer (John Wiley & Sons, New York, 2013).
  31. A. A. Griffith, VI. The phenomena of rupture and flow in solids, Philos. Trans. R. Soc. London, Ser. A 221, 163 (1921).
  32. T. L. Anderson and T. L. Anderson, Fracture Mechanics: Fundamentals and Applications (CRC Press, Boca Raton, Florida, 2005).
  33. J. W. Hutchinson and Z. Suo, Mixed mode cracking in layered materials, Adv. Appl. Mech. 29, 63 (1991).
  34. S. Sundaram, D. Lipkin, C. Johnson, and J. W. Hutchinson, The influence of transient thermal gradients and substrate constraint on delamination of thermal barrier coatings, J. Appl. Mech. 80, 011002 (2013).
  35. A. F. Bower, Applied Mechanics of Solids (CRC Press, 2009).
  36. P. Kékicheff et al., Condensation or desublimation: Nanolevel structural look on two frost formation pathways on surfaces with different wettabilities, ACS Nano 18, 15067 (2024).
  37. F. Wang, R. Tang, Z. Wang, and W. Yang, Frosting characteristics of superhydrophobic surface under desublimation frosting conditions, Int. J. Therm. Sci. 184, 108038 (2023).
  38. A. H. Persad and C. A. Ward, Expressions for the evaporation and condensation coefficients in the Hertz-Knudsen relation, Chem. Rev. 116, 7727 (2016).
  39. A. L. Buck, New equations for computing vapor pressure and enhancement factor, J. Appl. Meteorol. Climatol. 20, 1527 (1981).
  40. C. Walker, S. Lerch, M. Reininger, H. Eghlidi, A. Milionis, T. M. Schutzius, and D. Poulikakos, Desublimation frosting on nanoengineered surfaces, ACS Nano 12, 8288 (2018).
  41. Y. Renardy et al., Pyramidal and toroidal water drops after impact on a solid surface, J. Fluid Mech. 484, 69 (2003).
  42. X. Wang, X. Yan, J. Du, B. Ji, M. J. Inanlu, Q. Min, and N. Miljkovic, Spreading dynamics of microdroplets on nanostructured surfaces, J. Colloid Interface Sci. 635, 221 (2023).
  43. P. G. D. Gennes, Wetting: Statics and dynamics, Rev. Mod. Phys. 57, 827 (1985).
  44. M. Adamkiewicz and B. Rubinsky, Cryogenic 3D printing for tissue engineering, Cryobiology 71, 518 (2015).
  45. Z. Li, M. Xu, J. Wang, and F. Zhang, Recent advances in cryogenic 3D printing technologies, Adv. Eng. Mater. 24, 2200245 (2022).
  46. Y. Kakinuma, S. Kidani, and T. Aoyama, Ultra-precision cryogenic machining of viscoelastic polymers, CIRP Ann. 61, 79 (2012).
  47. M. Liu et al., Cryogenic minimum quantity lubrication machining: From mechanism to application, Front. Mech. Eng. 16, 649 (2022).

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