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Simulation of droplet impact dynamics on V-shaped walls

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Abstract

This paper presents the morphological evolution characteristics of a droplet impacting a V-shaped wall by using the lattice Boltzmann method (LBM). Four parameters are investigated comprehensively. The parameters vary over wide ranges: surface wettability (\(60^\circ \le \theta ^{eq} \le 120^\circ \)), Weber number (\(102.27 \le \text {We} \le 3681.82\)), bending angle of the V-shaped wall (90\(^\circ \le \theta \le 180^\circ \)), and eccentricity ratio (0 \(\le b \le \) 0.5). Two types of collision are observed: deposition and breakage. For breakage, the number of satellite droplets increases against the increment of We. The splashing occurs for a high We. And the lamella ejection is observed on the hydrophilic wall and the neutral wall. The lamella ejection will be slight against the increase of \(\theta ^{eq}\), while it will become obvious against the increment of \(\theta \). In addition, the nondimensional spreading length, width, and height are measured and analyzed. Regime maps are established based on We, Re, and \(\theta \).

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References

  1. Abolghasemibizaki, M., Dilmaghani, N., Mohammadi, R., Castano, C.E.: Viscous droplet impact on nonwettable textured surfaces. Langmuir 35(33), 10752–10761 (2019). https://doi.org/10.1021/acs.langmuir.9b01109

    Article  Google Scholar 

  2. Agrawal, S., Khurana, G., Dhar, P.: Droplet collision and jet evolution hydrodynamics in wetting modulated valley configurations. Phys. Fluids (2021). https://doi.org/10.1063/5.0048185

    Article  Google Scholar 

  3. Ahmed, G., Sellier, M., Jermy, M., Taylor, M.: Modeling the effects of contact angle hysteresis on the sliding of droplets down inclined surfaces. Eur. J. Mech. B Fluids 48, 218–230 (2014). https://doi.org/10.1016/j.euromechflu.2014.06.003

    Article  Google Scholar 

  4. Aidun, C.K., Clausen, J.R.: Lattice-boltzmann method for complex flows. Annu. Rev. Fluid Mech. 42, 439–472 (2010). https://doi.org/10.1146/annurev-fluid-121108-145519

    Article  MathSciNet  MATH  Google Scholar 

  5. Aksoy, Y.T., Eneren, P., Koos, E., Vetrano, M.R.: Spreading of a droplet impacting on a smooth flat surface: How liquid viscosity influences the maximum spreading time and spreading ratio. Phys. Fluids (2022). https://doi.org/10.1063/5.0086050

    Article  Google Scholar 

  6. Antonini, C., Amirfazli, A., Marengo, M.: Drop impact and wettability: from hydrophilic to superhydrophobic surfaces. Phys. Fluids (2012). https://doi.org/10.1063/1.4757122

    Article  Google Scholar 

  7. Benther, J.D., Pelaez-Restrepo, J.D., Stanley, C., Rosengarten, G.: Heat transfer during multiple droplet impingement and spray cooling: review and prospects for enhanced surfaces. Int. J. Heat Mass Transf. (2021). https://doi.org/10.1016/j.ijheatmasstransfer.2021.121587

    Article  Google Scholar 

  8. Cao, X.H., Ye, Y., Tang, Q., Chen, E.G., Jiang, Z.Z., Pan, J.H., Guo, T.L.: Numerical analysis of droplets from multinozzle inkjet printing. J. Phys. Chem. Lett. 11(19), 8442–8450 (2020). https://doi.org/10.1021/acs.jpclett.0c02250

    Article  Google Scholar 

  9. Chao, J.H., Mei, R.W., Singh, R., Shyy, W.: A filter-based, mass-conserving lattice Boltzmann method for immiscible multiphase flows. Int. J. Numer. Meth. Fluids 66(5), 622–647 (2011). https://doi.org/10.1002/fld.2276

    Article  MathSciNet  MATH  Google Scholar 

  10. Chen, G.Q., Huang, X., Zhang, A.M., Wang, S.P.: Simulation of three-dimensional bubble formation and interaction using the high-density-ratio lattice Boltzmann method. Phys. Fluids (2019). https://doi.org/10.1063/1.5082258

    Article  Google Scholar 

  11. Chen, M.J., Wu, D., Chen, D.Q., Deng, J., Liu, H.Z., Jiang, J.Z.: Experimental investigation on the movement of triple-phase contact line during a droplet impacting on horizontal and inclined surface. Chem. Eng. Sci. (2020). https://doi.org/10.1016/j.ces.2020.115864

    Article  Google Scholar 

  12. Chen, S.M., Bertola, V.: The impact of viscoplastic drops on a heated surface in the Leidenfrost regime. Soft Matter 12(36), 7624–7631 (2016). https://doi.org/10.1039/c6sm00893c

    Article  Google Scholar 

  13. De Rosis, A., Coreixas, C.: Multiphysics flow simulations using D3Q19 lattice Boltzmann methods based on central moments. Phys. Fluids (2020). https://doi.org/10.1063/5.0026316

    Article  Google Scholar 

  14. Ding, B., Wang, H., Zhu, X., Chen, R., Liao, Q.: Water droplet impact on superhydrophobic surfaces with various inclinations and supercooling degrees. Int. J. Heat Mass Transf. 138, 844–851 (2019). https://doi.org/10.1016/j.ijheatmasstransfer.2019.04.106

    Article  Google Scholar 

  15. Dong, H.M., Carr, W.W., Morris, J.F.: Visualization of drop-on-demand inkjet: Drop formation and deposition. Rev. Sci. Instrum. (2006). https://doi.org/10.1063/1.2234853

    Article  Google Scholar 

  16. Du, J.Y., Wang, X., Li, Y.Z., Min, Q., Wu, X.X.: Analytical consideration for the maximum spreading factor of liquid droplet impact on a smooth solid surface. Langmuir 37(24), 7582–7590 (2021). https://doi.org/10.1021/acs.langmuir.1c01076

    Article  Google Scholar 

  17. Ellis, A.S., Smith, F.T., White, A.H.: Droplet impact on to a rough surface. Q. J. Mech. Appl. Mech. 64(2), 107–139 (2011). https://doi.org/10.1093/qjmam/hbq026

    Article  MathSciNet  MATH  Google Scholar 

  18. Emdadi, M., Pournaderi, P.: Numerical simulation of conducting droplet impact on a surface under an electric field. Acta Mech. 231(3), 1083–1103 (2020). https://doi.org/10.1007/s00707-019-02574-w

    Article  MathSciNet  Google Scholar 

  19. Eral, H.B., ’t Mannetje, D.J.C.M., Oh, J.M.: Contact angle hysteresis: a review of fundamentals and applications. Colloid Polym. Sci. 291(2), 247–260 (2013). https://doi.org/10.1007/s00396-012-2796-6

    Article  Google Scholar 

  20. Fernandez-Toledano, J.C., Braeckeveldt, B., Marengo, M., De Coninck, J.: How wettability controls nanoprinting. Phys. Rev. Lett. (2020). https://doi.org/10.1103/PhysRevLett.124.224503

    Article  Google Scholar 

  21. Gong, S., Cheng, P.: Numerical investigation of droplet motion and coalescence by an improved lattice Boltzmann model for phase transitions and multiphase flows. Comput. Fluids 53, 93–104 (2012). https://doi.org/10.1016/j.compfluid.2011.09.013

    Article  MathSciNet  MATH  Google Scholar 

  22. Hassan, G., Yilbas, B.S., Al-Sharafi, A., Al-Qahtani, H., Al-Aqeeli, N.: Water droplet on inclined dusty hydrophobic surface: influence of droplet volume on environmental dust particles removal (vol 9, pg 3582, 2019). RSC Adv. 9(13), 7276–7276 (2019). https://doi.org/10.1039/c9ra90018g

    Article  Google Scholar 

  23. He, X., Chen, S., Zhang, R.: A lattice boltzmann scheme for incompressible multiphase flow and its application in simulation of rayleigh-taylor instability. J. Comput. Phys. 152(2), 642–663 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. He, X.Y., Doolen, G.D.: Thermodynamic foundations of kinetic theory and Lattice Boltzmann models for multiphase flows. J. Stat. Phys. 107(1–2), 309–328 (2002). https://doi.org/10.1023/A:1014527108336

    Article  MATH  Google Scholar 

  25. He, X.Y., Zhu, X., Wang, H., Tan, Y., Ding, B., Lv, Y.W., Liao, Q.: Dynamic behaviors and regime map of a molten blast furnace slag droplet impacting a solid surface. Fuel (2020). https://doi.org/10.1016/j.fuel.2020.118451

    Article  Google Scholar 

  26. Hu, Z.F., Chu, F.Q., Wu, X.M.: Double-peak characteristic of droplet impact force on superhydrophobic surfaces. Extreme Mech. Lett. (2022). https://doi.org/10.1016/j.eml.2022.101665

    Article  Google Scholar 

  27. Jadidbonab, H., Mitroglou, N., Karathanassis, I., Gavaises, M.: Experimental study of diesel-fuel droplet impact on a similarly sized polished spherical heated solid particle. Langmuir 34(1), 36–49 (2018). https://doi.org/10.1021/acs.langmuir.7b01658

    Article  Google Scholar 

  28. Kistovich, A.V., Chaplina, T.O.: Analytical and experimental modeling of the hydrocarbon slick form and its spreading on the water surface. Phys. Fluids (2021). https://doi.org/10.1063/5.0054709

    Article  Google Scholar 

  29. Lee, D., Fang, C.F., Ravan, A.S., Fuller, G.G., Shen, A.Q.: Temperature controlled tensiometry using droplet microfluidics. Lab. Chip. 17(4), 717–726 (2017). https://doi.org/10.1039/c6lc01384h

    Article  Google Scholar 

  30. Li, T., Wu, Y.: Impact dynamics of nanodroplets on V-Shaped substrates: asymmetrical behavior and fast-rebound dynamics. Langmuir 37(44), 13170–13178 (2021). https://doi.org/10.1021/acs.langmuir.1c02488

    Article  Google Scholar 

  31. Li, X.Y., Ma, X.H., Lan, Z.: Dynamic behavior of the water droplet impact on a textured hydrophobic/superhydrophobic surface: the effect of the remaining liquid film arising on the pillars’ tops on the contact time. Langmuir 26(7), 4831–4838 (2010). https://doi.org/10.1021/la903603z

    Article  Google Scholar 

  32. Li, Z., Kong, Q., Ma, X., Zang, D., Guan, X., Ren, X.: Dynamic effects and adhesion of water droplet impact on hydrophobic surfaces: bouncing or sticking. Nanoscale 9(24), 8249–8255 (2017). https://doi.org/10.1039/c7nr02906c

    Article  Google Scholar 

  33. Liu, D.D., Tran, T.: The ejecting lamella of impacting compound droplets. Appl. Phys. Lett. (2019). https://doi.org/10.1063/1.5097370

    Article  Google Scholar 

  34. Liu, H., Cai, C., Yan, Y.A., Jia, M., Yin, B.Z.: Numerical simulation and experimental investigation on spray cooling in the non-boiling region. Heat Mass Transf. 54(12), 3747–3760 (2018). https://doi.org/10.1007/s00231-018-2402-7

    Article  Google Scholar 

  35. Lunkad, S.F., Buwa, V.V., Nigam, K.D.P.: Numerical simulations of drop impact and spreading on horizontal and inclined surfaces. Chem. Eng. Sci. 62(24), 7214–7224 (2007). https://doi.org/10.1016/j.ces.2007.07.036

    Article  Google Scholar 

  36. Luo, X.M., Gong, H.Y., He, Z.L., Zhang, P., He, L.M.: Recent advances in applications of power ultrasound for petroleum industry. Ultrason. Sonochem. (2021). https://doi.org/10.1016/j.ultsonch.2020.105337

    Article  Google Scholar 

  37. Mehdi-Nejad, V., Mostaghimi, J., Chandra, S.: Air bubble entrapment under an impacting droplet. Phys. Fluids 15(1), 173–183 (2003). https://doi.org/10.1063/1.1527044

    Article  MATH  Google Scholar 

  38. Parizi, H.B., Rosenzweig, L., Mostaghimi, J., Chandra, S., Coyle, T., Salimi, H., Moreau, C.: 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  Google Scholar 

  39. Patil, N.D., Bhardwaj, R., Sharma, A.: Droplet impact dynamics on micropillared hydrophobic surfaces. Exp. Thermal Fluid Sci. 74, 195–206 (2016). https://doi.org/10.1016/j.expthermflusci.2015.12.006

    Article  Google Scholar 

  40. Qin, Y.Z., Guo, Q.Y., Chen, R.X., Zhuang, Y., Wang, Y.L.: Numerical investigation of water droplet impact on PEM fuel cell flow channel surface. Renew. Energy 168, 750–763 (2021). https://doi.org/10.1016/j.renene.2020.12.075

    Article  Google Scholar 

  41. Raya, S.A., Saaid, I.M., Ahmed, A.A., Umar, A.A.: A critical review of development and demulsification mechanisms of crude oil emulsion in the petroleum industry. J. Pet. Explor. Prod. Technol. 10(4), 1711–1728 (2020). https://doi.org/10.1007/s13202-020-00830-7

    Article  Google Scholar 

  42. Ruan, Y.X., Hou, Y., Xue, R., Luo, G.Q., Zhu, K.Z., Liu, X.F., Chen, L.: Effects of operational parameters on liquid nitrogen spray cooling. Appl. Therm. Eng. 146, 85–91 (2019). https://doi.org/10.1016/j.applthermaleng.2018.09.098

    Article  Google Scholar 

  43. Sikalo, S., Tropea, C., Ganic, E.N.: Impact of droplets onto inclined surfaces. J. Colloid Interface Sci. 286(2), 661–669 (2005). https://doi.org/10.1016/j.jcis.2005.01.050

    Article  Google Scholar 

  44. Srivastava, T., Jena, S.K., Kondaraju, S.: Droplet impact and spreading on inclined surfaces. Langmuir 37(46), 13737–13745 (2021). https://doi.org/10.1021/acs.langmuir.1c02457

    Article  Google Scholar 

  45. Swat, M.H., Thomas, G.L., Belmonte, J.M., Shirinifard, A., Hmeljak, D., Glazier, J.A.: Multi-scale modeling of tissues using compucell 3D. Comput. Methods Cell Biol. 110, 325–366 (2012). https://doi.org/10.1016/B978-0-12-388403-9.00013-8

    Article  Google Scholar 

  46. Tang, C.L., Qin, M.X., Weng, X.Y., Zhang, X.H., Zhang, P., Li, J.L., Huang, Z.H.: Dynamics of droplet impact on solid surface with different roughness. Int. J. Multiph. Flow 96, 56–69 (2017). https://doi.org/10.1016/j.ijmultiphaseflow.2017.07.002

    Article  Google Scholar 

  47. Verma, C., Alrefaee, S.H., Quraishi, M.A., Ebenso, E.E., Hussain, C.M.: Environmental, safety and economic risks of Covid-19 pandemic in petroleum industries: a prospective. J. Pet. Sci. Eng. (2021). https://doi.org/10.1016/j.petrol.2020.108161

    Article  Google Scholar 

  48. Wang, G., Fei, L.L., Luo, K.H.: Lattice Boltzmann simulation of water droplet impacting a hydrophobic plate with a cylindrical pore. Phys. Rev. Fluids (2020). https://doi.org/10.1103/PhysRevFluids.5.083602

    Article  Google Scholar 

  49. Washino, K., Tan, H.S., Salman, A.D., Hounslow, M.J.: Direct numerical simulation of solid-liquid-gas three-phase flow: Fluid-solid interaction. Powder Technol. 206(1–2), 161–169 (2011). https://doi.org/10.1016/j.powtec.2010.07.015

    Article  Google Scholar 

  50. Weisensee, P.B., Tian, J.J., Miljkovic, N., King, W.P.: Water droplet impact on elastic superhydrophobic surfaces. Sci. Rep. (2016). https://doi.org/10.1038/srep30328

    Article  Google Scholar 

  51. Wijshoff, H.: Drop dynamics in the inkjet printing process. Current Opin. Colloid Interface Sci. 36, 20–27 (2018). https://doi.org/10.1016/j.cocis.2017.11.004

    Article  Google Scholar 

  52. Wu, G.Q., Chen, S., Du, W.H., Zeng, S.B., Yu, Y., Zhai, S., Wang, Y.: On the collision of a droplet with a V-shaped wall. Int. Commun. Heat Mass Transf. (2022). https://doi.org/10.1016/j.icheatmasstransfer.2022.106269

    Article  Google Scholar 

  53. Xiong, W., Cheng, P.: Numerical investigation of air entrapment in a molten droplet impacting and solidifying on a cold smooth substrate by 3D lattice Boltzmann method. Int. J. Heat Mass Transf. 124, 1262–1274 (2018). https://doi.org/10.1016/j.ijheatmasstransfer.2018.04.056

    Article  Google Scholar 

  54. Xu, Y., Vincent, S., He, Q.C., Le-Quang, H.: Spread and recoil of liquid droplets impacting on solid surfaces with various wetting properties. Surf. Coat. Technol. 357, 140–152 (2019). https://doi.org/10.1016/j.surfcoat.2018.09.079

    Article  Google Scholar 

  55. Zhang, H.X., Zhang, X.W., Yi, X., He, F., Niu, F.L., Hao, P.F.: Effect of wettability on droplet impact: spreading and splashing. Exp. Thermal Fluid Sci. (2021). https://doi.org/10.1016/j.expthermflusci.2021.110369

    Article  Google Scholar 

  56. Zhang, J.F.: Lattice Boltzmann method for microfluidics: models and applications. Microfluid. Nanofluid. 10(1), 1–28 (2011). https://doi.org/10.1007/s10404-010-0624-1

    Article  Google Scholar 

  57. Zhang, L.H., Chen, S., Wang, X.Z., Wang, D., Li, Y., Ai, Q., Xu, B.M.: Ambient inkjet-printed high-efficiency perovskite solar cells: manipulating the spreading and crystallization behaviors of picoliter perovskite droplets. Solar Rrl (2021). https://doi.org/10.1002/solr.202100106

    Article  Google Scholar 

  58. Zhang, R.Y., He, X.Y., Chen, S.Y.: Interface and surface tension in incompressible lattice Boltzmann multiphase model. Comput. Phys. Commun. 129(1–3), 121–130 (2000). https://doi.org/10.1016/S0010-4655(00)00099-0

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Hubei Key Laboratory of Advanced Technology for Automotive Components, School of Automotive Engineering, Wuhan University of Technology, Wuhan, China

    Guoqiang Wu

  2. Hubei Collaborative Innovation Center for Automotive Components Technology, Wuhan, China

    Guoqiang Wu & Sheng Chen

  3. School of Computing, Engineering and Built Environment, Glasgow Caledonian University, Glasgow, UK

    Sheng Chen

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GW: Investigation, Writing–original draft. ML: Supervision and review. SC: Supervision, Writing–review & editing.

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Communicated by André Cavalieri.

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Wu, G., Chen, S. Simulation of droplet impact dynamics on V-shaped walls. Theor. Comput. Fluid Dyn. 37, 173–202 (2023). https://doi.org/10.1007/s00162-023-00652-3

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