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Dynamic spreading and splashing of tin droplets: impact velocity effects and splashing boundary analysis

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Abstract

The spreading and splashing behavior of high-velocity metal liquid droplets upon impact with a substrate is a fundamental scientific concern in thermal spray and additive manufacturing for metal deposition. A thorough understanding of the spreading and splashing tendencies of individual liquid droplets, along with the factors influencing them, is crucial for improving the quality of sprayed coatings and additively manufactured components. In this research, high-speed photography was employed to document the propagation process, splashing events, and alterations in droplet structure following the impact of tin droplets onto stainless steel surfaces at varying velocities. The study unveiled that as the impact velocity rises, the droplet's dynamics undergo a series of transformations, encompassing retraction, spreading, and splashing, accompanied by dynamic fluctuations in the contact angle. Elevated impact velocities result in an augmentation of the droplet's maximum spreading diameter, coupled with a simultaneous reduction in spreading duration. Splashing occurs at relatively higher speeds and near the maximum forward contact angle. The paper verified a splashing prediction model based on the pressure balance of the liquid film and boundary conditions, successfully predicting the onset of droplet splashing. The results of the experiments can be applied to advanced technologies in thermal spray and additive manufacturing for metal deposition.

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References

  1. B. Wang, J. Wang, C. Yu, S. Luo, J. Peng, N. Li, T. Wang, L. Jiang, Z. Dong, Y. Wang, Sustained agricultural spraying: from leaf wettability to dynamic droplet impact behavior. Global Chall. 7(9), 2300007 (2023)

    Article  Google Scholar 

  2. D. Bolleddula, A. Berchielli, A. Aliseda, Impact of a heterogeneous liquid droplet on a dry surface: application to the pharmaceutical industry. Adv. Coll. Interface. Sci. 159(2), 144–159 (2010)

    Article  Google Scholar 

  3. C.-H. Wang, H.-L. Tsai, Y.-C. Wu, W.-S. Hwang, Investigation of molten metal droplet deposition and solidification for 3D printing techniques. J. Micromech. Microeng. 26(9), 095012 (2016)

    Article  ADS  Google Scholar 

  4. X. Zhang, Q. Wang, R. Zou, B. Song, C. Yan, Y. Shi, B. Su, 3D-printed superhydrophobic and magnetic device that can self-powered sense a tiny droplet impact. Engineering 15, 196–205 (2022)

    Article  Google Scholar 

  5. N. Gilani, N.T. Aboulkhair, M. Simonelli, M. East, I.A. Ashcroft, R.J. Hague, From impact to solidification in drop-on-demand metal additive manufacturing using MetalJet. Addit. Manuf. 55, 102827 (2022)

    Google Scholar 

  6. D. Smith, S. Askew, W. Morris, D. Shaw, M. Boyette, Droplet size and leaf morphology effects on pesticide spray deposition. Trans. ASAE 43(2), 255–259 (2000)

    Article  Google Scholar 

  7. D. Lohse, Fundamental fluid dynamics challenges in inkjet printing. Annu. Rev. Fluid Mech. 54, 349–382 (2022)

    Article  ADS  Google Scholar 

  8. H. Wijshoff, Drop dynamics in the inkjet printing process. Curr. Opin. Colloid Interface Sci. 36, 20–27 (2018)

    Article  Google Scholar 

  9. J. Lee, K.K. Subedi, G.W. Huang, J. Lee, S.-C. Kong, Numerical investigation of YSZ droplet impact on a heated wall for thermal spray application. J. Therm. Spray Technol. 31(7), 2039–2049 (2022)

    Article  ADS  Google Scholar 

  10. T. Colton, N.B. Crane, Influence of droplet velocity, spacing, and inter-arrival time on line formation and saturation in binder jet additive manufacturing. Addit. Manuf. 37, 101711 (2021)

    Google Scholar 

  11. A.M. Worthington, On impact with a liquid surface. Proc. R. Soc. Lond. 34(220–223), 217–230 (1883)

    Google Scholar 

  12. R. Rioboo, C. Tropea, M. Marengo, Outcomes from a drop impact on solid surfaces. Atomiz. Sprays 11(2), 155–165 (2001)

    Google Scholar 

  13. A.L. Yarin, Drop impact dynamics: splashing, spreading, receding, bouncing…. Annu. Rev. Fluid Mech. 38, 159–192 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  14. D. Khojasteh, M. Kazerooni, S. Salarian, R. Kamali, Droplet impact on superhydrophobic surfaces: a review of recent developments. J. Ind. Eng. Chem. 42, 1–14 (2016)

    Article  Google Scholar 

  15. A. Khan, K. Huang, M. Hu, X. Yu, D. Yang, Wetting behavior of metal-catalyzed chemical vapor deposition-grown one-dimensional cubic-SiC nanostructures. Langmuir 34(18), 5214–5224 (2018)

    Article  Google Scholar 

  16. A. Khan, S. Sohail, C. Jacob, The fabrication of stable superhydrophobic surfaces using a thin Au/Pd coating over a hydrophilic 3C-SiC nanorod network. Appl. Surf. Sci. 353, 964–972 (2015)

    Article  ADS  Google Scholar 

  17. S. Moghtadernejad, C. Lee, M. Jadidi, An introduction of droplet impact dynamics to engineering students. Fluids 5(3), 107 (2020)

    Article  ADS  Google Scholar 

  18. A. Asai, M. Shioya, S. Hirasawa, T. Okazaki, Impact of an ink drop on paper. J. Imaging Sci. Technol. 37, 205–205 (1993)

    Google Scholar 

  19. M. Pasandideh-Fard, Y. Qiao, S. Chandra, J. Mostaghimi, Capillary effects during droplet impact on a solid surface. Phys. Fluids 8(3), 650–659 (1996)

    Article  ADS  Google Scholar 

  20. T. Mao, D.C. Kuhn, H. Tran, Spread and rebound of liquid droplets upon impact on flat surfaces. AIChE J. 43(9), 2169–2179 (1997)

    Article  ADS  Google Scholar 

  21. C. Ukiwe, D.Y. Kwok, On the maximum spreading diameter of impacting droplets on well-prepared solid surfaces. Langmuir 21(2), 666–673 (2005)

    Article  Google Scholar 

  22. R. Rioboo, M. Marengo, C. Tropea, Time evolution of liquid drop impact onto solid, dry surfaces. Exp. Fluids 33(1), 112–124 (2002)

    Article  Google Scholar 

  23. S. Shakeri, S. Chandra, Splashing of molten tin droplets on a rough steel surface. Int. J. Heat Mass Transf. 45(23), 4561–4575 (2002)

    Article  Google Scholar 

  24. H. Almohammadi, A. Amirfazli, Droplet impact: Viscosity and wettability effects on splashing. J. Colloid Interface Sci. 553, 22–30 (2019)

    Article  ADS  Google Scholar 

  25. G. Riboux, J.M. Gordillo, Experiments of drops impacting a smooth solid surface: a model of the critical impact speed for drop splashing. Phys. Rev. Lett. 113(2), 024507 (2014)

    Article  ADS  Google Scholar 

  26. S. Lin, B. Zhao, S. Zou, J. Guo, Z. Wei, L. Chen, Impact of viscous droplets on different wettable surfaces: Impact phenomena, the maximum spreading factor, spreading time and post-impact oscillation. J. Colloid Interface Sci. 516, 86–97 (2018)

    Article  ADS  Google Scholar 

  27. C. Tang, M. Qin, X. Weng, X. Zhang, P. Zhang, J. Li, Z. Huang, Dynamics of droplet impact on solid surface with different roughness. Int. J. Multiph. Flow 96, 56–69 (2017)

    Article  Google Scholar 

  28. J. Du, Y. Zhang, Q. Min, Numerical investigations of the spreading and retraction dynamics of viscous droplets impact on solid surfaces. Colloids Surf. A 609, 125649 (2021)

    Article  Google Scholar 

  29. J. Du, X. Wang, Y. Li, Q. Min, X. Wu, Analytical consideration for the maximum spreading factor of liquid droplet impact on a smooth solid surface. Langmuir 37(24), 7582–7590 (2021)

    Article  Google Scholar 

  30. R. Dhiman, S. Chandra, Freezing-induced splashing during impact of molten metal droplets with high Weber numbers. Int. J. Heat Mass Transf. 48(25–26), 5625–5638 (2005)

    Article  Google Scholar 

  31. C.M. Megaridis, K. Boomsma, I.S. Bayer, Partial rebound of molten-metal droplets impacting on solid substrates. AIChE J. 50(7), 1356–1363 (2004)

    Article  ADS  Google Scholar 

  32. C. Li, G. Wu, M. Li, C. Hu, J. Wei, A heat transfer model for aluminum droplet/wall impact. Aerosp. Sci. Technol. 97, 105639 (2020)

    Article  Google Scholar 

  33. C. Zhang, L. Li, Z. Li, H. Chang, J. Liu, Investigation on the spreading and solidification of supercooled gallium droplets during impact. Int. J. Heat Mass Transf. 183, 122142 (2022)

    Article  Google Scholar 

  34. J. Huang, L. Qi, J. Luo, Q. Wang, A study on the solidification shapes of molten metal droplet impacting at low weber number. Phys. Fluids 35(9), 1–16 (2023)

    Article  Google Scholar 

  35. V. Mehdi-Nejad, J. Mostaghimi, S. Chandra, Air bubble entrapment under an impacting droplet. Phys. Fluids 15(1), 173–183 (2003)

    Article  ADS  Google Scholar 

  36. J. San Lee, B.M. Weon, J.H. Je, K. Fezzaa, How does an air film evolve into a bubble during drop impact? Phys. Rev. Lett. 109(20), 204501 (2012)

    Article  ADS  Google Scholar 

  37. M. Meda, V. Sukhotskiy, D. Cormier, Pinhole formation in printed electronic traces fabricated via molten metal droplet jetting. Electronics 10(13), 1568 (2021)

    Article  Google Scholar 

  38. X. Wang, H. Zhao, X. Luo, Z. Huang, Membrane-constrained acoustic metamaterials for low frequency sound insulation. Appl. Phys. Lett. 108(4), 1–5 (2016)

    Article  Google Scholar 

  39. J. Waldvogel, D. Poulikakos, Solidification phenomena in picoliter size solder droplet deposition on a composite substrate. Int. J. Heat Mass Transf. 40(2), 295–309 (1997)

    Article  Google Scholar 

  40. H. Yi, L. Qi, J. Luo, D. Zhang, H. Li, X. Hou, Effect of the surface morphology of solidified droplet on remelting between neighboring aluminum droplets. Int. J. Mach. Tools Manuf 130, 1–11 (2018)

    Article  Google Scholar 

  41. S.D. Aziz, S. Chandra, Impact, recoil and splashing of molten metal droplets. Int. J. Heat Mass Transf. 43(16), 2841–2857 (2000)

    Article  Google Scholar 

  42. X. Wang, W. Yu, M. Wang, F. Wang, B. Wu, Spreading behavior of Sn droplets impacting Cu and stainless steel substrates. Surfaces and Interfaces 29, 101790 (2022)

    Article  Google Scholar 

  43. W. Yu, M. Wang, F. Wang, X. Wang, B. Wu, Study of the dynamic wetting behavior of Sn droplet impacting Cu substrate. Appl. Phys. A 128(8), 646 (2022)

    Article  ADS  Google Scholar 

  44. M. Wang, W. Yu, X. Wang, F. Wang, B. Yang, Role of IMCs in the spreading-retracement process of Sn droplets impacting Cu and stainless steel substrates. JOM 75(1), 45–54 (2023)

    Article  ADS  Google Scholar 

  45. X. Wang, W. Yu, M. Wang, F. Wang, B. Yang, Spreading of high-speed tin droplets on copper substrate surfaces with ultrasonic vibration: Experiments and modeling. Mater. Chem. Phys. 308, 128295 (2023)

    Article  Google Scholar 

  46. K. Yokoi, Numerical studies of droplet splashing on a dry surface: triggering a splash with the dynamic contact angle. Soft Matter 7(11), 5120–5123 (2011)

    Article  ADS  Google Scholar 

  47. K. Yokoi, D. Vadillo, J. Hinch, I. Hutchings, Numerical studies of the influence of the dynamic contact angle on a droplet impacting on a dry surface. Phys. Fluids 21(7), 1–12 (2009)

    Article  Google Scholar 

  48. L. Tanner, The spreading of silicone oil drops on horizontal surfaces. J. Phys. D Appl. Phys. 12(9), 1473 (1979)

    Article  ADS  Google Scholar 

  49. Y. Yonemoto, K. Tashiro, K. Shimizu, T. Kunugi, Predicting the splash of a droplet impinging on solid substrates. Sci. Rep. 12(1), 5093 (2022)

    Article  ADS  Google Scholar 

  50. Y. Yonemoto, T. Kunugi, Analytical consideration of liquid droplet impingement on solid surfaces. Sci. Rep. 7(1), 2362 (2017)

    Article  ADS  Google Scholar 

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Acknowledgements

This work is financially supported by National Natural Science Foundation of China (Project No. 52061023)

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Authors and Affiliations

  1. School of Materials Science and Engineering, Lanzhou University of Technology, Lanzhou, 730050, Gansu, China

    Baoqing Yang, Weiyuan Yu, Xiwushan Wang, Mingkang Wang & Fengfeng Wang

  2. State Key Laboratory of Advanced Processing and Recycling of Non-Ferrous Metal, Lanzhou University of Technology, No. 287 Langongping Road, Lanzhou, 730050, People’s Republic of China

    Baoqing Yang, Weiyuan Yu, Xiwushan Wang, Mingkang Wang & Fengfeng Wang

  3. Institute of Modem Physics, Chinese Academy of Sciences, Nanchang Rd., Lanzhou, 730000, Gansu, China

    Fengfeng Wang

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  1. Baoqing Yang
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Contributions

Baoqing Yang: Investigation, Writing – original draft. Weiyuan Yu: Validation, Supervision, Funding acquisition, Writing – review & editing. Xiwushan Wang: Data curation, Formal analysis. Fengfeng Wang: Data curation. Mingkang Wang: Data curation.

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Correspondence to Weiyuan Yu.

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Yang, B., Yu, W., Wang, X. et al. Dynamic spreading and splashing of tin droplets: impact velocity effects and splashing boundary analysis. Appl. Phys. A 130, 424 (2024). https://doi.org/10.1007/s00339-024-07579-4

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