Cavity dynamics of water drop impact onto immiscible oil pool with different viscosity

Abstract

In this work, we numerically study the impact of a water droplet onto a deep oil pool. Two fluids are immiscible and the viscosity of the pool liquid is changed systematically. We focus on the cavity dynamics during the impact and especially the effects of the pool liquid viscosity and the impacting velocity. For the parameter range explored, we identify the regime where splashing occurs with corolla breaking into droplets, and the regime where no splashing is observed. Similarity is found for the time evolution of cavity depth for fixed impact velocity and different viscosity, if the cavity depth and time are nondimensionalized by the maximal depth and the time when the maximal depth is reached. Effective power-law scalings are also proposed to describe the dependence of the maximal cavity depth and the corresponding time on the impact velocity and pool liquid viscosity, in the term of Froude and Reynolds numbers.

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References

  1. 1.

    Martin, R.: Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res. 12, 61–93 (1993)

    Article  Google Scholar 

  2. 2.

    Prosperetti, A., Oguz, H.N.: The impact of drops on liquid surfaces and the underwater noise of rain. Annu. Rev. Fluid Mech. 25, 577–602 (1993)

    Article  Google Scholar 

  3. 3.

    Yarin, A.L.: Drop impact dynamics: Splashing, Spreading, Receding. Bouncing. Annu. Rev. Fluid Mech. 38, 159–192 (2006)

    MathSciNet  Article  Google Scholar 

  4. 4.

    Josserand, C., Thoroddsen, S.T.: Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48, 365–391 (2016)

    MathSciNet  Article  Google Scholar 

  5. 5.

    Arjan, B., Mark-Jan, M., Theo, D., et al.: Velocity profile inside piezoacoustic inkjet droplets in flight: comparison between experiment and numerical simulation. Phys. Rev. Appl. 1, 014004 (2014)

    Article  Google Scholar 

  6. 6.

    Shiraz, D.A., Sanjeev, C.: Impact, recoil and splashing of molten metal droplets. Int. J. Heat Mass Transf. 43, 2841–2857 (2000)

    Article  Google Scholar 

  7. 7.

    Gilet, T., Bourouiba, L.: Fluid fragmentation shapes rain-induced foliar disease transmission. J. R. Soc. Interface 12, 20141092 (2015)

    Article  Google Scholar 

  8. 8.

    Gart, S., Mates, J.E., Megaridis, C.M., et al.: Droplet impacting a cantilever: a leaf-raindrop system. Phys. Rev. Appl. 3, 044019 (2015)

    Article  Google Scholar 

  9. 9.

    Moreira, A.L.N., Moita, A.S., Panao, M.R.: Advances and challenges in explaining fuel spray impingement: how much of single droplet impact research is useful? Prog. Energy Combust. Sci. 36, 554–580 (2010)

    Article  Google Scholar 

  10. 10.

    Worthington, A.M.: The splash of a drop and allied phenomena. Proc. R. Soc. A 34, 217 (1882)

    Google Scholar 

  11. 11.

    Worthington, A.M., Cole, R.S.: Impact with a liquid surface, studied by aid of instantaneous photography. Philos. Trans. R. Soc. A 189, 137–148 (1897)

    MATH  Google Scholar 

  12. 12.

    Engel, O.G.: Crater depth in fluid impacts. J. Appl. Phys. 37, 1798–1808 (1966)

    Article  Google Scholar 

  13. 13.

    Engel, O.G.: Initial pressure, initial flow velocity, and the time dependence of crater depth in fluid impacts. J. Appl. Phys. 38, 3935–3940 (1967)

    Article  Google Scholar 

  14. 14.

    Zhang, L.V., Brunet, P., Eggers, J., et al.: Wavelength selection in the crown splash. Phys. Fluids 22, 122105 (2010)

    Article  Google Scholar 

  15. 15.

    Zhang, L.V., Toole, J., Fezzaa, K., et al.: Evolution of the ejecta sheet from the impact of a drop with a deep pool. J. Fluid Mech. 690, 5–15 (2012)

    Article  Google Scholar 

  16. 16.

    Esmailizadeh, L., Messler, R.: Bubble entrainment with drops. J. Colloid Interface Sci. 110, 561–574 (1986)

    Article  Google Scholar 

  17. 17.

    Pumphrey, H.C., Elmore, P.A.: The entrainment of bubbles by drop impacts. J. Fluid Mech. 220, 539–567 (1990)

    Article  Google Scholar 

  18. 18.

    Deng, Q., Anilkumar, A.V., Wang, T.G.: The role of viscosity and surface tension in bubble entrapment during drop impact onto a deep liquid pool. J. Fluid Mech. 578, 119–138 (2007)

    Article  Google Scholar 

  19. 19.

    Leng, L.J.: Splash formation by spherical drops. J. Fluid Mech. 427, 73–105 (2001)

    Article  Google Scholar 

  20. 20.

    Fedorchenko, A.I., Wang, A.B.: On some common features of drop impact on liquid surfaces. Phys. Fluids 16, 1349–1365 (2004)

    MathSciNet  Article  Google Scholar 

  21. 21.

    Satoshi, N., Zhi-Gang, Z., Ken-Ichiro, S., et al.: Transformation and fragmentation behavior of molten metal drop in sodium pool. Nucl. Eng. Des. 237, 2201–2209 (2007)

    Article  Google Scholar 

  22. 22.

    Bremond, N., Santanach-Carreras, E., Liang-Yin, C., et al.: Formation of liquid-core capsules having a thin hydrogel membrane: liquid pearls. Soft Matter 6, 2484–2488 (2010)

    Article  Google Scholar 

  23. 23.

    Murphy, D.W., Li, C., d’Albignac, V., et al.: Splash behaviour and oily marine aerosol production by raindrops impacting oil slicks. J. Fluid Mech. 780, 536–577 (2015)

    Article  Google Scholar 

  24. 24.

    Sharma, V., Szymusiak, M., Shen, H., et al.: Formation of polymeric toroidal–spiral particles. Langmuir 28, 729–735 (2012)

    Article  Google Scholar 

  25. 25.

    Walker, T.W., Logia, A.N., Fuller, G.: Multiphase flow of miscible liquids: jets and drops. Exp. Fluids 56, 106 (2015)

    Article  Google Scholar 

  26. 26.

    Che, Z., Matar, O.K.: Impact of droplets on immiscible liquid films. Soft Matter 14, 1540–1551 (2018)

    Article  Google Scholar 

  27. 27.

    Shaikh, S., Toyofuku, G., Hoang, R., et al.: Immiscible impact dynamics of droplets onto millimetric films. Exp. Fluids 59, 7 (2018)

    Article  Google Scholar 

  28. 28.

    Lhuissier, H., Sun, C., Prosperetti, A., et al.: Drop fragmentation at impact onto a bath of an immiscible liquid. Phys. Rev. Lett. 110, 264503 (2013)

    Article  Google Scholar 

  29. 29.

    Jain, U., Jalaal, M., Lohse, D., et al.: Deep pool water-impacts of viscous oil droplets. Soft Matter 15, 4629–4638 (2019)

    Article  Google Scholar 

  30. 30.

    Fujimatsu, T., Fujita, H., Hirota, M., et al.: Interfacial deformation between an impacting water drop and a silicone-oil surface. J. Colloid Interface Sci. 264, 212–220 (2003)

    Article  Google Scholar 

  31. 31.

    Ray, B., Biswas, G., Sharma, A.: Regimes during liquid drop impact on a liquid pool. J. Fluid Mech. 768, 492–523 (2015)

    Article  Google Scholar 

  32. 32.

    Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100, 335–354 (1992)

    MathSciNet  Article  Google Scholar 

  33. 33.

    Weller, H.G.: A New Approach to VOF-Based Interface Capturing Methods for Incompressible and Compressible Flow. Report TR/HGW/04. OpenCFD Ltd., Bracknell, Berkshire

  34. 34.

    Morton, D., Rudman, M., Liow, J.: An investigation of the flow regimes resulting from splashing drops. Phys. Fluids 12, 747–763 (2000)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants 91848201, 11988102, 11521202, 11872004, and 11802004). The authors also acknowledge the partial support from the Beijing Natural Science Foundation (Grants L172002). The numerical simulations were performed on Tianhe-1A, the National Super Computing Center in Tianjin, China. Muhammad Mohasan would like to thank Chinese Scholarship Council for providing Chinese Government Scholarship.

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Correspondence to Pengyu Lv or Yantao Yang.

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Executive Editor: Ke-Qing Xia.

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Mohasan, M., Aqeel, A.B., Lv, P. et al. Cavity dynamics of water drop impact onto immiscible oil pool with different viscosity. Acta Mech. Sin. (2021). https://doi.org/10.1007/s10409-020-01032-4

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Keywords

  • Drop impact
  • Immiscible fluids
  • Cavity dynamics