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Rebounding dynamics of ceramic drops on hydrophobic substrates

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Abstract

In thermal spraying, molten YSZ (Yttria Stabilized Zirconia) drop impact is crucial to the understanding of formation of splats and hence coatings. However, existing studies hardly cast attention to the possible rebounding dynamics when successive molten YSZ drops impinge onto newly solidified splats whose temperature is still high so that freezing may be delayed. This work uses a newly developed numerical model based on the conservative level set method to probe into the rebounding dynamics of YSZ drops in practical thermal spraying conditions. The free-energy-based surface tension model in the phase field method was introduced to avoid the computing of curvature, which is however necessary in the continuum surface tension model. The projection method was invoked to solve the Navier–Stokes equations. The model was validated against an experiment of drop impact with rebounding, showing reasonable agreement. Moreover, the model was applied to both dense and hollow YSZ drop impact, with the details of fluid flow being analyzed. The maximum spread factor was found in agreement with existing scaling laws.

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

References

  1. P. Fauchais, A. Vardelle, B. Dussoubs, Quo vadis thermal spraying? J. Therm. Spray Technol. 10(1), 44–66 (2001). https://doi.org/10.1361/105996301770349510

    Article  ADS  Google Scholar 

  2. C. Li, X. Luo, S. Yao, G. Li, C. Li, C. Li, The bonding formation during thermal spraying of ceramic coatings: a review. J. Therm. Spray Technol. 31(4), 780–817 (2022). https://doi.org/10.1007/s11666-022-01379-z

    Article  ADS  Google Scholar 

  3. A. Lynam, A. Romero, F. Xu, R.G. Wellman, T. Hussain, Thermal spraying of ultra-high temperature ceramics: a review on processing routes and performance. J. Therm. Spray Technol. 31(4), 745–779 (2022). https://doi.org/10.1007/s11666-022-01381-5

    Article  ADS  Google Scholar 

  4. K. Zhang, Dissipative particle dynamics for anti-icing on solid surfaces. Chem. Phys. 568, 111824 (2023). https://doi.org/10.1016/j.chemphys.2023.111824‌

    Article  Google Scholar 

  5. C.-J. Lai, Y.-J. Chen, M.-X. Wu, C.-C. Wu, N.-T. Tang, T.-F. Hsu, S.-H. Lin, H.-F. Li, H. Yang, Self-cleaning and anti-fogging hierarchical structure arrays inspired by termite wing. Appl. Surf. Sci. 616, 156484 (2023). https://doi.org/10.1016/j.apsusc.2023.156484

    Article  Google Scholar 

  6. V. Pachchigar, M. Ranjan, K. Sooraj, S. Augustine, D. Kumawat, K. Tahiliani, S. Mukherjee, Self-cleaning and bouncing behaviour of ion irradiation produced nanostructured superhydrophobic PTFE surfaces. Surf. Coat. Technol. 420, 127331 (2021). https://doi.org/10.1016/j.surfcoat.2021.127331‌

    Article  Google Scholar 

  7. H.B. Parizi, L. Rosenzweig, J. Mostaghimi, S. Chandra, T.W. Coyle, H. Salimi, L. Pershin, A. McDonald, C. Moreau, Numerical simulation of droplet impact on patterned surfaces. J. Therm. Spray Technol. 16(5–6), 713–721 (2007). https://doi.org/10.1007/s11666-007-9122-8

    Article  ADS  Google Scholar 

  8. T.C. Wu, M. Bussmann, J. Mostaghimi, The impact of a partially molten YSZ particle. J. Therm. Spray Technol. 18(5–6), 957–964 (2009). https://doi.org/10.1007/s11666-009-9380-8

    Article  ADS  Google Scholar 

  9. M. Zhang, H.Y. Zhang, L.S. Zheng, Simulation of droplet spreading, splashing and solidification using smoothed particle hydrodynamics method. Int. J. Heat Mass Transf. 51(13–14), 3410–3419 (2008). https://doi.org/10.1016/j.ijheatmasstransfer.2007.11.009

    Article  Google Scholar 

  10. P. Wei, Z. Wei, L. Suli, F. Dong, J. Du, Splat formation during plasma spraying for 8mol% yttria-stabilized zirconia droplets impacting on stainless steel substrate. Appl. Surf. Sci. 321, 538–547 (2014). https://doi.org/10.1016/j.apsusc.2014.09.159

    Article  ADS  Google Scholar 

  11. M. Shen, B. Li, Q. Yang, Y. Bai, Y. Wang, S. Zhu, B. Zhao, T. Li, Y. Hu, A modified phase-field three-dimensional model for droplet impact with solidification. Int. J. Multiph. Flow 116, 51–66 (2019). https://doi.org/10.1016/j.ijmultiphaseflow.2019.04.004

    Article  MathSciNet  Google Scholar 

  12. J. Lee, K.K. Subedi, G.W. Huang, J. Lee, S. Kong, Numerical investigation of YSZ droplet impact on a heated wall for thermal spray application. J. Therm. Spray Technol. 31(7), 2039–2049 (2022). https://doi.org/10.1007/s11666-022-01437-6

    Article  ADS  Google Scholar 

  13. M. Shen, B. Li, Y. Bai, Numerical modeling of YSZ droplet impact/spreading with solidification microstructure formation in plasma spraying. Int. J. Heat Mass Transf. 150, 119267 (2020). https://doi.org/10.1016/j.ijheatmasstransfer.2019.119267

    Article  Google Scholar 

  14. M. Shen, B.Q. Li, Phase field modeling of air entrapment in binary droplet impact with solidification microstructure formation. Coatings 12(12), 1990 (2022). https://doi.org/10.3390/coatings12121990

    Article  Google Scholar 

  15. E. Olsson, G. Kreiss, S. Zahedi, A conservative level set method for two phase flow. J. Comput. Phys. 210(1), 225–246 (2005). https://doi.org/10.1016/j.jcp.2005.04.007

    Article  ADS  MathSciNet  Google Scholar 

  16. M. Shen, B.Q. Li, A 3D numerical study on impact-freezing of Nickel drops in thermal spraying conditions. Appl. Phys. A 129, 509 (2023). https://doi.org/10.1007/s00339-023-06781-0

    Article  ADS  Google Scholar 

  17. P.-H. Chiu, Y.-T. Lin, A conservative phase field method for solving incompressible two-phase flows. J. Comput. Phys. 230(1), 185–204 (2011). https://doi.org/10.1016/j.jcp.2010.09.021

    Article  ADS  MathSciNet  Google Scholar 

  18. W. Li, J. Wang, C. Zhu, L. Tian, N. Zhao, Numerical investigation of droplet impact on a solid superhydrophobic surface. Phys. Fluids 33(6), 1 (2021). https://doi.org/10.1063/5.0050378

    Article  Google Scholar 

  19. G. Li, C. Wang, Hierarchically porous YSZ hollow spheres with ultralow thermal conductivity. Mater. Res. Bull. (2014). https://doi.org/10.1016/j.materresbull.2014.05.029

    Article  Google Scholar 

  20. B.A. Dwiyantoro, Capillary effects during droplet formation on the solid surface. Adv. Mater. Res. 683, 889–893 (2013). https://doi.org/10.4028/www.scientific.net/amr.683.889

    Article  Google Scholar 

  21. J. Madejski, Solidification of droplets on a cold surface. Int. J. Heat Mass Transf. 19(9), 1009–1013 (1976). https://doi.org/10.1016/0017-9310(76)90183-6

    Article  ADS  Google Scholar 

  22. D. Richard, C. Clanet, D. Quéré, Contact time of a bouncing drop. Nature 417(6891), 811 (2002). https://doi.org/10.1038/417811a

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This research is supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 21KJB460034).

Funding

The funding has been received from Natural Science Foundation of the Jiangsu Higher Education Institutions of China with Grant no. 21KJB460034.

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Contributions

Mingguang Shen: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Ben Q. Li: Conceptualization (equal); Supervision (equal); Writing – review & editing (equal).

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Correspondence to Ben Q. Li.

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Shen, M., Li, B.Q. Rebounding dynamics of ceramic drops on hydrophobic substrates. Appl. Phys. A 130, 398 (2024). https://doi.org/10.1007/s00339-024-07532-5

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