Document Type : Research Note

**Authors**

Faculty of New Technologies and Aerospace Engineering, Shahid Beheshti University, Tehran, Iran

**Abstract**

The present work aims to investigate the effect of surface topology and wettability on the impacting droplet dynamics at different flow conditions. A multiphase lattice Boltzmann method (LBM) is employed for the simulation of interfacial dynamics. Firstly, the results obtained based on the present method for some benchmark two-phase flow problems are validated. Then, three surface topologies, including a flat substrate, semicircular cavity, and semicircular bump, are considered to get insight into the physical treatment of the impacting droplet. The present study shows that although the surface topology affects the spreading and rebounding processes of the impacting droplet, the hydrophilicity plays a significant role in the final form of the liquid phase and dictates a similar treatment for all the studied topologies. Considering different sizes for the bump, it is found that the shape of the droplet deforms almost the same immediately after the impaction for all the bump sizes and the spreading process is not affected by the wettability. However, the receding dynamics is significantly affected by the bump size and the wetting condition of the bump surface. It is found that the contact time is minimized by increment the bump size and hydrophobicity of the surface.

**Keywords**

- Impacting droplet
- surface topology
- wettability effect
- multiphase lattice Boltzmann method
- Allen-Cahn equation

**Main Subjects**

References:

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25. Wang, X., Xu, B., Wang, Y., et al. "Directional migration of single droplet on multi-wetting gradient surface by 3D lattice Boltzmann method", Computers and Fluids, 198, 104392 (2020). DOI: 10.1016/j.comp fluid.2019.104392.

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28. Ezzatneshan, E. "Implementation of a curved walland an absorbing open-boundary condition for the D3Q19 lattice Boltzmann method for simulation of incompressible fluid flows", Scientia Iranica, 26, pp. 2329-2341 (2018). DOI: 10.24200/SCI.2018.20608.

29. Ezzatneshan, E. and Goharimehr, R. "A pseudopotential lattice Boltzmann method for simulation of twophase flow transport in porous medium at high-density and high-viscosity ratios", Geo fluids, 2021, pp. 1-18 (2021). DOI: 10.1155/2021/5668743.

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31. Ezzatneshan, E. and Vaseghnia, H. "Dynamics of an acoustically driven cavitation bubble cluster in the vicinity of a solid surface", Physics of Fluids, 33, 123311 (2021). DOI: 10.1063/5.0075290.

32. Fakhari, A., Mitchell, T., Leonardi, C., et al. "Improved locality of the phase-"eld lattice-Boltzmann model for immiscible fluids at high density ratios", Phys Rev E., 96, 053301 (2017). DOI: 10.1103/PhysRevE.96.053301.

33. Lallemand, P. and Luo, L.S. "Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, galilean invariance, and stability", Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics, 61, pp. 6546-62 (2000). DOI: 10.1103/physreve.61.6546.

34. Gupta, A. and Kumar, R. "Two-dimensional lattice boltzmann model for droplet impingement and breakup in low density ratio liquids", Communications in Computational Physics, 10, pp. 767-784 (2015). DOI: 10.4208/cicp.221209.160910a.

35. Cherdantsev, A.V., Hann, D.B., Hewakandamby, H.B.N., et al. "Study of the impacts of droplets deposited from the gas core onto a gas-sheared liquid "lm", International Journal of Multiphase Flow, 88, pp. 69-86 (2017). DOI: 10.1016/j.ijmultiphase

ow.2022.104033.

36. Liu, Y., Tan, P., and Xu, L. "Compressible air entrapment in high-speed drop impacts on solid surfaces", Journal of Fluid Mechanics, 716 (2013).DOI: 10.1017/jfm.2012.583.

37. Xiong, W. and Cheng, P. "Numerical investigation of air entrapment in a molten droplet impacting and solidifying on a cold smooth substrate by 3D lattice Boltzmann method", International Journal of Heat and Mass Transfer, 124, pp. 1262-1274 (2018). DOI: 10.1016/j.ijheatmasstransfer.2018.04.056.

38. Yarin, A.L. "Drop impact dynamics: Splashing, spreading, receding, bouncing", Annual Review of Fluid Mechanics, 38, pp. 159-192 (2006).DOI: 10.1146/annurev. fluid.38.050304.092144.

39. Antonini, C., Villa, F., Bernagozzi, I., et al. "Drop rebound after impact: The role of the receding contact angle", Langmuir, 29, pp. 16045-16050 (2013). DOI: 10.1021/la4012372.

2. Breitenbach, J., Roisman, I.V., and Tropea, C. "From drop impact physics to spray cooling models: a critical review", Experiments in Fluids, 59 (2018). DOI: 10.1007/s00348-018-2514-3.

3. Quetzeri-Santiago, M., Castrejon-Pita, A.J.R., and Castrejon-Pita, A.A. "On the analysis of the contact angle for impacting droplets using a polynomial "tting approach", Experiments in Fluids, 61 (2020). DOI: 10.1007/s00348-020-02971-1.

4. Wei, Y. and Thoraval, M.-J. "Maximum spreading of an impacting air-in-liquid compound drop", Physics of Fluids, 33, 061703 (2021). DOI: 10.1063/5.0053384.

5. Ezzatneshan, E. and Khosroabadi, A. "Droplet spreading dynamics on hydrophobic textured surfaces: A Lattice Boltzmann study", Computers and Fluids, 105063 (2021). DOI: 10.1016/j.comp fluid.2021.105063.

6. Dalgamoni, H.N. and Yong, X. "Numerical and theoretical modeling of droplet impact on spherical surfaces", Physics of Fluids, 33, 052112 (2021). DOI: 10.1063/5.0047024.

7. Garcia Perez, J., Leclaire, S., Ammar, S., et al. "Investigations of water droplet impact and freezing on a cold substrate with the Lattice Boltzmann method", International Journal of Thermo fluids, 12, 100109 (2021). DOI: 10.1016/j.ijft.2021.100109.

8. Xu, W., Lan, Z., Peng, B., et al. "Directional movement of droplets in grooves: Suspended or immersed?", Scienti"c Reports, 6 (2016). DOI: 10.1038/srep18836.

9. Han, T., Noh, H., Park, H.S., et al. "Effects of wettability on droplet movement in a V-shaped groove", Scienti"c Reports, 8 (2018). DOI: 10.1038/s41598-018-34407-6.

10. Bakshi, S., Roisman, I.V., and Tropea, C. "Investigations on the impact of a drop onto a small spherical target", Physics of Fluids, 19, 032102 (2007). DOI: 10.1063/1.2716065.

11. Charalampous, G., and Hardalupas, Y. "Collisions of droplets on spherical particles", Physics of Fluids, 29, 103305 (2017). DOI: 10.1063/1.5005124.

12. Banitabaei, S.A. and Amirfazli, A. "Droplet impact onto a solid sphere: Effect of wettability and impact velocity", Physics of Fluids, 29, 062111 (2017). DOI: 10.1063/1.4990088.

13. Mitra, S., Sathe, M.J., Doroodchi, E., et al. "Droplet impact dynamics on a spherical particle", Chemical Engineering Science, 100, pp. 105-119 (2013). DOI: 10.1016/j.ces.2013.01.037.

14. Zhu, Y., Liu, H.-R., Mu, K., et al. "Dynamics of drop impact onto a solid sphere: spreading and retraction", Journal of Fluid Mechanics, 824 (2017). DOI: 10.1017/jfm.2017.388.

15. Bordbar, A., Taassob, A., Khojasteh, D., et al. "Maximum spreading and rebound of a droplet impacting onto a spherical surface at low Weber Numbers", Langmuir, 34, pp. 5149-5158 (2018). DOI: 10.1021/acs.langmuir.8b00625.

16. Milacic, E., Baltussen, M.W., and Kuipers, J.A.M. "Direct numerical simulation study of droplet spreading on spherical particles", Powder Technology, 354, pp. 11-18 (2019). DOI: 10.1016/j.powtec.2019.05.064.

17. Min, X.L. X.Z.J. "Maximum spreading of droplets impacting spherical surfaces", Physics of Fluids, 31, 092102 (2019). DOI: 10.1063/1.5117278.

18. Hu, Z., Zhang, X., Gao, S., et al. "Axial spreading of droplet impact on ridged superhydrophobic surfaces", Journal of Colloid and Interface Science, 599, pp. 130- 139 (2021). DOI: 10.1016/j.jcis.2021.04.078.

19. Huang, J., Wang, L., and He, K. "Three-dimensional study of double droplets impact on a wettabilitypatterned surface", Computers and Fluids, 248, 105669 (2022). DOI: 10.1016/j.comp fluid.2022.105669.

20. Gu, Z., Shang, Y., Li, D., et al. "Lattice Boltzmann simulation of droplet impacting on the super hydrophobic surface with a suspended octagonal prism", Physics of Fluids, 34, 012015 (2022). DOI: 10.1063/5.0073258.

21. Radhakrishnan, J., Diaz, M., Cordovilla, F., et al. "Water droplets impact dynamics on laser engineered superhydrophobic ceramic surface", Optics and Laser Technology, 158, 108887 (2023). DOI: 10.1016/j.optlastec.2022.108887.

22. Ezzatneshan, E. "Study of surface wettability effect on cavitation inception by implementation of the lattice Boltzmann method", Physics of Fluids, 29, 113304 (2017). DOI: 10.1063/1.4990876.

23. Fakhari, A. and Bolster, D. "Diffuse interface modeling of three-phase contact line dynamics on curved boundaries: A lattice Boltzmann model for large density and viscosity ratios", Journal of Computational Physics, 334, pp. 620-638 (2017). DOI: 10.1016/j.jcp.2017.01.025.

24. Ezzatneshan, E. and Goharimehr, R. "Study of spontaneous mobility and imbibition of a liquid droplet in contact with "brous porous media considering wettability effects", Physics of Fluids, 32, 113303 (2020). DOI: 10.1063/5.0027960.

25. Wang, X., Xu, B., Wang, Y., et al. "Directional migration of single droplet on multi-wetting gradient surface by 3D lattice Boltzmann method", Computers and Fluids, 198, 104392 (2020). DOI: 10.1016/j.comp fluid.2019.104392.

26. Shen, S., Bi, F., and Guo, Y. "Simulation of droplets impact on curved surfaces with lattice Boltzmann method", International Journal of Heat and Mass Transfer, 55, pp. 6938-6943 (2012). DOI: 10.1016/j.ijheatmasstransfer.2012.07.007.

27. Ezzatneshan, E. "Implementation of D3Q19 lattice Boltzmann Method with a curved wall boundary condition for simulation of practical flow problems", International Journal of Engineering, 30 (2017). DOI: 10.5829/idosi.ije.2017.30.09c.11.

28. Ezzatneshan, E. "Implementation of a curved walland an absorbing open-boundary condition for the D3Q19 lattice Boltzmann method for simulation of incompressible fluid flows", Scientia Iranica, 26, pp. 2329-2341 (2018). DOI: 10.24200/SCI.2018.20608.

29. Ezzatneshan, E. and Goharimehr, R. "A pseudopotential lattice Boltzmann method for simulation of twophase flow transport in porous medium at high-density and high-viscosity ratios", Geo fluids, 2021, pp. 1-18 (2021). DOI: 10.1155/2021/5668743.

30. Li, Q.-Z., Lu, Z.-L., Zhou, D., et al. "Uni"ed simpli"ed multiphase lattice Boltzmann method for ferrofluid flows and its application", Physics of Fluids, 32, 093302 (2020). DOI: 10.1063/5.0021463.

31. Ezzatneshan, E. and Vaseghnia, H. "Dynamics of an acoustically driven cavitation bubble cluster in the vicinity of a solid surface", Physics of Fluids, 33, 123311 (2021). DOI: 10.1063/5.0075290.

32. Fakhari, A., Mitchell, T., Leonardi, C., et al. "Improved locality of the phase-"eld lattice-Boltzmann model for immiscible fluids at high density ratios", Phys Rev E., 96, 053301 (2017). DOI: 10.1103/PhysRevE.96.053301.

33. Lallemand, P. and Luo, L.S. "Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, galilean invariance, and stability", Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics, 61, pp. 6546-62 (2000). DOI: 10.1103/physreve.61.6546.

34. Gupta, A. and Kumar, R. "Two-dimensional lattice boltzmann model for droplet impingement and breakup in low density ratio liquids", Communications in Computational Physics, 10, pp. 767-784 (2015). DOI: 10.4208/cicp.221209.160910a.

35. Cherdantsev, A.V., Hann, D.B., Hewakandamby, H.B.N., et al. "Study of the impacts of droplets deposited from the gas core onto a gas-sheared liquid "lm", International Journal of Multiphase Flow, 88, pp. 69-86 (2017). DOI: 10.1016/j.ijmultiphase

ow.2022.104033.

36. Liu, Y., Tan, P., and Xu, L. "Compressible air entrapment in high-speed drop impacts on solid surfaces", Journal of Fluid Mechanics, 716 (2013).DOI: 10.1017/jfm.2012.583.

37. Xiong, W. and Cheng, P. "Numerical investigation of air entrapment in a molten droplet impacting and solidifying on a cold smooth substrate by 3D lattice Boltzmann method", International Journal of Heat and Mass Transfer, 124, pp. 1262-1274 (2018). DOI: 10.1016/j.ijheatmasstransfer.2018.04.056.

38. Yarin, A.L. "Drop impact dynamics: Splashing, spreading, receding, bouncing", Annual Review of Fluid Mechanics, 38, pp. 159-192 (2006).DOI: 10.1146/annurev. fluid.38.050304.092144.

39. Antonini, C., Villa, F., Bernagozzi, I., et al. "Drop rebound after impact: The role of the receding contact angle", Langmuir, 29, pp. 16045-16050 (2013). DOI: 10.1021/la4012372.

Transactions on Mechanical Engineering (B)

May and June 2024Pages 667-680