Abstract
The oscillation characteristics of a single droplet after normal collision with smooth surfaces are numerically investigated by using volume of fluid (VOF) method. An adaptive mesh refinement technique is used to guarantee the high computational accuracy of the interaction between the falling liquid droplet and the solid surface. The results of VOF simulations are consonant with the previously reported experiments. The effects of seven key issues on the oscillation characteristics of a liquid droplet advancing/recoiling onto both hydrophilic and hydrophobic surfaces are studied quantitatively with the help of dimensionless wetting length, average amplitude ratio and average oscillation period. These issues include impact velocity, contact angle, slip length, surface tension, droplet density, liquid viscosity and droplet diameter. Especially, surface and interface effects gradually become a primary factor that controls the droplet behavior as droplet size is reduced, and therefore the oscillation concerning micrometer-size droplet may be damped more rapidly. The presented study can contribute to provide more insight into the wetting kinetics of droplet collision, the interface interaction between the liquid droplet and the solid surface, and the oscillation features of the droplet spreading/receding after droplet impact.
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Adapted from the work of Li and Zhang (see Li and Zhang 2019); (b) Dynamic depiction of droplet rebounding using dynamic adaptive local grid refinement; (c) Time evolution of the droplet's wetting diameter
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References
Antonini, C., Amirfazli, A., Marengo, M.: Drop impact and wettability: From hydrophilic to superhydrophobic surfaces. Phys. Fluids 24(10), 102104 (2012). https://doi.org/10.1063/1.4757122
Alabuzhev, A.A.: Forced Axisymmetric Oscillations of a Drop, which is Clamped Between Different Surfaces. Microgravity Sci. Technol. 32, 545–553 (2020). https://doi.org/10.1007/s12217-020-09783-2
Blake, T.D., De Coninck, C.: The influence of solid-liquid interactions on dynamic wetting. Adv. Colloid Interfac. 96(1), 21–36 (2002). https://doi.org/10.1016/s0001-8686(01)00073-2
Bai, F., He, X., Yang, X., et al.: Three dimensional phase-field investigation of droplet formation in microfluidic flow focusing devices with experimental validation. Int. J. Multiphas. Flow 93, 130–141 (2008). https://doi.org/10.1016/j.ijmultiphaseflow.2017.04.008
Bird, J.C., Dhiman, R., Kwon, H.M., et al.: Reducing the contact time of a bouncing drop. Nature 503(7476), 385–388 (2013). https://doi.org/10.1038/nature12740
Blake, T.D.: The physics of moving wetting lines. J. Colloid Interf. Sci. 299(1), 1–13 (2006). https://doi.org/10.1016/j.jcis.2006.03.051
Banitabaei, S.A., Amirfazli, A.: Droplet impact onto a solid particle: effect of wettability and impact velocity. Phys. Fluids 29(6), 062111 (2017). https://doi.org/10.1063/1.4990088
Brandenbourger, M., Caps, H., Vitry, Y., et al.: Electrically Charged Droplets in Microgravity. Microgravity Sci. Technol. 29, 229–239 (2017). https://doi.org/10.1007/s12217-017-9542-0
Cox, R.G.: The Dynamics of the Spreading of Liquids on a Solid Surface. Part 1. Viscous Flow, J. Fluid Mech. 168(-1), 169–194 (1986). https://doi.org/10.1017/s0022112086000332
Chen, S., Phan-Thien, N., Fan, X.J., et al.: Dissipative particle dynamics simulation of polymer drops in a periodic shear flow. J. Non-Newtonian Fluid 118(1), 65–81 (2004). https://doi.org/10.1016/j.jnnfm.2004.02.005
Dupont, J.B., Legendre, D.: Numerical simulation of static and sliding drop with contact angle hysteresis. J. Comput. Phys. 229(7), 2453–2478 (2010). https://doi.org/10.1016/j.jcp.2009.07.034
Deepu, P., Chowdhuri, S., Basu, S.: Oscillation dynamics of sessile droplets subjected to substrate vibration. Chem. Eng. Sci. 118, 9–19 (2014). https://doi.org/10.1016/j.ces.2014.07.028
Gilet, T., Bush, J.W.M.: Droplets bouncing on a wet, inclined surface. Phys. Fluids 24(12), 122103 (2012). https://doi.org/10.1063/1.4771605
Guo, Y., Wei, L., Liang, G., et al.: Simulation of droplet impact on liquid film with CLSVOF. Int. J. Heat Mass Tran. 53, 26–33 (2014). https://doi.org/10.1016/j.icheatmasstransfer.2014.02.00
Gong, S., Cheng, P.: Numerical simulation of pool boiling heat transfer on smooth surfaces with mixed wettability by lattice Boltzmann method. Int. J. Heat Mass Tran. 80, 206–216 (2015). https://doi.org/10.1016/j.ijheatmasstransfer.2014.08.09
Gauthier, A., Symon, S., Clanet, C., et al.: Water impacting on superhydrophobic macrotextures. Nat. Commun. 6(1), 8001 (2015). https://doi.org/10.1038/ncomms9001
Gunjal, P.R., Ranade, V.V., Chaudhari, R.V.: Dynamics of drop impact on solid surface: Experiments and VOF simulations. AIChE J. 51(1), 59–78 (2005). https://doi.org/10.1002/aic.10300
Huh, C., Scriven, L.E.: Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interf. Sci. 35(1), 85–101 (1971). https://doi.org/10.1016/0021-9797(71)90188-3
Herbert, S., Fischer, S., Gambaryan-Roisman, T., et al.: Local heat transfer and phase change phenomena during single drop impingement on a hot surface. Int. J. Heat Mass Tran. 61, 605–614 (2013). https://doi.org/10.1016/j.ijheatmasstransfer.2013.01.08
Hasan, M.N., Chandy, A., Choi, J.W.: Numerical analysis of post-impact droplet deformation for direct-print. Eng. Appl. Comp. Fluid 9(1), 543–555 (2015). https://doi.org/10.1080/19942060.2015.1071526
Josserand, C., Thoroddsen, S.T.: Drop Impact on a Solid Surface. Annu. Rev. Fluid Mech. 48, 365–391 (2016). https://doi.org/10.1146/annurev-fluid-122414-034401
Koplik, J., Zhang, R.: Nanodrop impact on solid surfaces. Phys. Fluids 25(2), 022003 (2012). https://doi.org/10.1063/1.4790807
Kordilla, J., Tartakovsky, A.M., Geyer, T.: A smoothed particle hydrodynamics model for droplet and film flow on smooth and rough fracture surfaces. Adv. Water Resour. 59, 1–14 (2013). https://doi.org/10.1016/j.advwatres.2013.04.009
Karimdoost-Yasuri, A., Passandideh-Fard, M.: On the microscopic parameters at a moving contact line during wetting process. Int. J. Surf. Sci. Eng. 7(3), 197–216 (2013). https://doi.org/10.1504/ijsurfse.2013.056423
Lagrée, P.Y., Staron, L., Popinet, S.: The granular column collapse as a continuum: validity of a two-dimensional Navier-Stokes model with a μ(I)-rheology. J. Fluid Mech. 686, 378–408 (2011). https://doi.org/10.1017/jfm.2011.335
Li, Z., Hu, G.H., Wang, Z.L., et al.: Three dimensional flow structures in a moving droplet on substrate: A dissipative particle dynamics study. Phys. Fluids 25(7), 072103 (2013). https://doi.org/10.1063/1.4812366
Liu, Y., Andrew, M., Li, J., et al.: Symmetry-breaking in drop bouncing on curved surfaces. Nat. Commun. 6(1), 10034 (2015). https://doi.org/10.1038/ncomms10034
Li, X.H., Zhang, X.X., Chen, M.: Estimation of viscous dissipation in nanodroplet impact and spreading. Phys. Fluids 27(5), 052007 (2015). https://doi.org/10.1063/1.4921141
Liang, G., Mudawar, I.: Review of mass and momentum interactions during drop impact on a liquid film. Int. J. Heat Mass Tran. 101, 577–599 (2016). https://doi.org/10.1016/j.ijheatmasstransfer.2016.05.062
Liang, G., Mudawar, I.: Review of drop impact on heated walls. Int. J. Heat Mass Tran. 106, 103–126 (2017). https://doi.org/10.1016/j.ijheatmasstransfer.2016.10.03
Li, B.X., Li, X.H., Chen. M.: Spreading and breakup of nanodroplet impinging on surface. Phys. Fluids 29(1), 012003 (2017). https://doi.org/10.1063/1.4974053
Li, D., Duan, X.: Numerical analysis of droplet impact and heat transfer on an inclined wet surface. Int. J. Heat Mass Tran. 128, 459–468 (2019). https://doi.org/10.1016/j.ijheatmasstransfer.2018.09.02
Liang, G., Zhang, T., Chen, Y., et al.: Two-phase heat transfer of multi-droplet impact on liquid film. Int. J. Heat Mass Tran. 139, 832–847 (2019a). https://doi.org/10.1016/j.ijheatmasstransfer.2019.05.055
Liang, G., Zhang, T., Chen, L., et al.: Single-phase heat transfer of multi-droplet impact on liquid film. Int. J. Heat Mass Tran. 132, 288–292 (2019b). https://doi.org/10.1016/j.ijheatmasstransfer.2018.11.145
Li, H., Zhang, K.: Dynamic behavior of water droplets impacting on the superhydrophobic surface: Both experimental study and molecular dynamics simulation study. Appl. Surf. Sci. 498, 143793 (2019). https://doi.org/10.1016/j.apsusc.2019.143793
Mukherjee, S., Abraham, J.: Crown behavior in drop impact on wet walls. Phys. Fluids 19(5), 052103 (2007). https://doi.org/10.1063/1.2736085
Malgarinos, I., Nikolopoulos, N., Marengo, M., et al.: VOF simulations of the contact angle dynamics during the drop spreading: Standard models and a new wetting force model. Adv. Colloid Interfac. 212(3), 1–20 (2014). https://doi.org/10.1016/j.cis.2014.07.004
Meng, S., Yang, R., Wu, J.S., et al.: Simulation of droplet spreading on porous substrates using smoothed particle hydrodynamics. Int. J. Heat Mass Tran. 77, 828–833 (2014). https://doi.org/10.1016/j.ijheatmasstransfer.2014.05.056
Ma, T.Y., Zhang, F., Liu, H.F., et al.: Modeling of droplet/wall interaction based on SPH method. Int. J. Heat Mass Tran. 105, 296–304 (2017). https://doi.org/10.1016/j.ijheatmasstransfer.2016.09.10
Pomeau, Y.: Recent progress in the moving contact line problem: a review. CR. Mecanique 330(3), 207–222 (2002). https://doi.org/10.1016/s1631-0721(02)01445-6
Popinet, S.: Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 190(2), 572–600 (2003). https://doi.org/10.1016/S0021-9991(03)00298-5
Popinet, S.: An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228(16), 5838–5866 (2009). https://doi.org/10.1016/j.jcp.2009.04.042
Rein, M.: Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res. 12(2), 61–93 (1993). https://doi.org/10.1016/0169-5983(93)90106-k
Rioboo, R., Marengo, M., Tropea, C.: Time evolution of liquid drop impact onto solid, dry surfaces. Exp. Fluids 33(1), 112–124 (2002). https://doi.org/10.1007/s00348-002-0431-x
Ren, W., Weinan, E.: Boundary conditions for the moving contact line problem. Phys. Fluids 19(2), 022101 (2007). https://doi.org/10.1063/1.2646754
Roisman, I.V., Opfer, L., Tropea, C., et al.: Drop impact onto a dry surface: Role of the dynamic contact angle. Colloids Surfaces A 322(1–3), 183–191 (2008). https://doi.org/10.1016/j.colsurfa.2008.03.005
Šikalo, Š, Wilhelm, H.D., Roisman, I.V., et al.: Dynamic contact angle of spreading droplets: Experiments and simulations. Phys. Fluids 17(6), 062103 (2005). https://doi.org/10.1063/1.1928828
Shen, S., Bi, F., Guo, Y.: Simulation of droplets impact on curved surfaces with lattice Boltzmann method. Int. J. Heat Mass Tran. 55(23–24), 6938–6943 (2012). https://doi.org/10.1016/j.ijheatmasstransfer.2012.07.00
Sprittles, J.E., Shikhmurzaev, Y.D.: The dynamics of liquid drops and their interaction with solids of varying wettabilities. Phys. Fluids 24(8), 082001 (2012). https://doi.org/10.1063/1.4739933
Sibley, D.N., Nold, A., Savva, N., et al.: A comparison of slip, disjoining pressure, and interface formation models for contact line motion through asymptotic analysis of thin two-dimensional droplet spreading. J. Eng. Math. 94(1), 19–41 (2015). https://doi.org/10.1007/s10665-014-9702-9
Song, M., Liu, Z., Ma, Y., et al.: Reducing the contact time using macro anisotropic superhydrophobic surfaces: effect of parallel wire spacing on the drop impact. NPG Asia Mater. 9(8), e415 (2017). https://doi.org/10.1038/am.2017.122
Worthington, A.M.: A Second Paper on the Forms Assumed by Drops of Liquids Falling Vertically on a Horizontal Plate. Proc. R. Soc. London 25(171–178), 498–503 (1876). https://doi.org/10.1098/rspl.1876.0073
Wang, Y.B., Wang, X.D., Wang, T.H., et al.: Asymmetric heat transfer characteristics of a double droplet impact on a moving liquid film. Int. J. Heat Mass Tran. 126, 649–659 (2018). https://doi.org/10.1016/j.ijheatmasstransfer.2018.05.161
Wang, X., Xu, B., Chen, Z., et al.: Effects of Gravitational Force and Surface Orientation on the Jumping Velocity and Energy Conversion Efficiency of Coalesced Droplets. Microgravity Sci. Technol. 32, 1185–1197 (2020). https://doi.org/10.1007/s12217-020-09841-9
Xie, H., Zeng, Z., Zhang, L., et al.: Simulation on Thermocapillary-Driven Drop Coalescence by Hybrid Lattice Boltzmann Method. Microgravity Sci. Technol. 28, 67–77 (2016). https://doi.org/10.1007/s12217-015-9483-4
Xu, B., Chen, Z.: Droplet Movement on a Composite Wedge-Shaped Surface with Multi-Gradients and Different Gravitational Field by Molecular Dynamics. Microgravity Sci. Technol. 30, 571–579 (2018). https://doi.org/10.1007/s12217-018-9641-6
Xu, B., Chen, Z.: Condensation on Composite V-Shaped Surface with Different Gravity in Nanoscale. Microgravity Sci. Technol. 31(5), 603–613 (2019). https://doi.org/10.1007/s12217-019-09731-9
Yarin, A.L.: DROP IMPACT DYNAMICS: Splashing, Spreading, Receding, Bouncing…. Annu. Rev. Fluid Mech. 38(1), 159–192 (2006). https://doi.org/10.1146/annurev.fluid.38.050304.09214
Yuan, W., Zhang, L.: A Lattice Boltzmann Simulation of Droplet Impacting on Superhydrophobic Surfaces with Randomly Distributed Rough Structures. Langmuir 33(3), 820–829 (2016). https://doi.org/10.1021/acs.langmuir.6b04041
Yin, C., Wang, T., Che, Z., et al.: Oblique impact of droplets on microstructured superhydrophobic surfaces. Int. J. Heat Mass Tran. 123, 693–704 (2018). https://doi.org/10.1016/j.ijheatmasstransfer.2018.02.06
Yin, Z., Ding, Z., Ma, X., et al.: Molecular Dynamics Simulations of Single Water Nanodroplet Impinging Vertically on Curved Copper Substrate. Microgravity Sci. Technol. 31(40), 749–757 (2019). https://doi.org/10.1007/s12217-019-9696-z
Yin, Z., Ding, Z., Zhang, W., et al.: Dynamic behaviors of nanoscale binary water droplets simultaneously impacting on flat surface. Comp. Mater. Sci. 183, 109814 (2020). https://doi.org/10.1016/j.commatsci.2020.109814
Zhao, Y.: Moving contact line problem: Advances and perspectives. Theor. Appl. Mech. Lett. 4(3), 034002 (2014). https://doi.org/10.1063/2.1403402
Zhu, L., Ge, J.R., Qi, Y.Y., et al.: Droplet impingement behavior analysis on the leaf surface of, shu-chazao, under different pesticide formulations. Comput. Electron. Agr. 144, 16–25 (2018). https://doi.org/10.1016/j.compag.2017.11.030
Zhou, J., Wang, Y., Geng, J., et al.: Characteristic oscillation phenomenon after head-on collision of two nanofluid droplets. Phys. Fluids 30, 072107 (2018). https://doi.org/10.1063/1.5040027
Acknowledgements
The authors thank the reviewers and Gerris developers for the hard work. This work was supported by the University Natural Science Research Project of Anhui Province under Grant No. KJ2020A0826 and No. KJ2019A1294.
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Zongjun Yin: Data curation, Formal analysis, Writing—original draft. Rong Su: Validation, Software. Wenfeng Zhang: Conceptualization, Project administration, Writing—review & editing. Zhenglong Ding: Funding acquisition, Validation. Qiannan Chen: Validation, Software. Futong Chai: Investigation, Data curation. Qingqing Wang: Validation, Software. Fengguang Liu: Project administration.
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Yin, Z., Su, R., Zhang, W. et al. Oscillation Characteristics of Single Droplet Impacting Vertically on Smooth Surfaces Using Volume of Fluid Method. Microgravity Sci. Technol. 33, 58 (2021). https://doi.org/10.1007/s12217-021-09901-8
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DOI: https://doi.org/10.1007/s12217-021-09901-8