Abstract
The investigation of the underlying physical processes involved in the impact of droplets has various practical applications in engineering and science. In this research, the spreading velocities within droplet impingement on a sapphire glass were investigated for a wide range of Weber numbers using particle image velocimetry (PIV), which involves tracking the movement of polymeric fluorescent particles (6 µm) within the droplet. The experiments were carried out at room temperature, and the droplets had impact velocities ranging from 0.41 to 2.37 m/s, which corresponded to Weber numbers of 5–183. The results showed that the radial velocity was generally linear over a wide range of spreading radius but the velocity at the exterior radial positions became nonlinear over time due to the influence of capillary and viscous forces. This nonlinearity was more pronounced for lower Weber numbers because the viscosity effects in the droplet were more significant compared to the inertia forces. As the Weber number decreases, the spreading and receding of the droplets are completed faster, leading to different trends in the radial velocity profiles.
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Abbreviations
- \({D}_{o}\) :
-
Initial droplet diameter (mm)
- R :
-
Spreading radius (mm)
- \(\overline{r }\) :
-
Dimensionless radius
- T :
-
Time (s)
- U :
-
Radial velocity (m/s)
- \({U}_{o}\) :
-
Initial droplet velocity (m/s)
- \(\overline{u }\) :
-
Dimensionless radial velocity
- We :
-
Weber number
- μ :
-
Dynamic viscosity (Ns/m2)
- ρ :
-
Density (kg/m3)
- σ :
-
Surface tension (N/m)
- τ :
-
Dimensionless time
- δ:
-
Uncertainty
References
Adrian RJ (2005) Twenty years of particle image velocimetry. Exp Fluids 39:159–169. https://doi.org/10.1007/s00348-005-0991-7
Al-Sharafi A, Yilbas BS (2019) Thermal and flow analysis of a droplet heating by multi-walls. Int J Therm Sci 138:247–262. https://doi.org/10.1016/j.ijthermalsci.2018.12.048
Erkan N (2019) Full-field spreading velocity measurement inside droplets impinging on a dry solid-heated surface. Exp Fluids 60:1–17. https://doi.org/10.1007/s00348-019-2735-0
Erkan N, Okamoto K (2014) Full-field spreading velocity measurement inside droplets impinging on a dry solid surface. Exp Fluids 55:1–9. https://doi.org/10.1007/s00348-014-1845-y
Frommhold PE, Mettin R, Ohl CD (2015) Height-resolved velocity measurement of the boundary flow during liquid impact on dry and wetted solid substrates. Exp Fluids 56:76. https://doi.org/10.1007/s00348-015-1944-4
Gultekin A, Erkan N, Colak U, Suzuki S (2020) PIV measurement inside single and double droplet interaction on a solid surface. Exp Fluids 61:1–18. https://doi.org/10.1007/s00348-020-03051-0
Gultekin A, Erkan N, Ozdemir E et al (2021) Simultaneous multiple droplet impact and their interactions on a heated surface. Exp Therm Fluid Sci 120:110255. https://doi.org/10.1016/j.expthermflusci.2020.110255
He M, Qiu H (2016) Internal flow patterns of an evaporating multicomponent droplet on a flat surface. Int J Therm Sci 100:10–19. https://doi.org/10.1016/j.ijthermalsci.2015.09.006
Jung J, Jeong S, Kim H (2016) Investigation of single-droplet/wall collision heat transfer characteristics using infrared thermometry. Int J Heat Mass Transf 92:774–783. https://doi.org/10.1016/j.ijheatmasstransfer.2015.09.050
Kang KH, Lim HC, Lee HW, Lee SJ (2013) Evaporation-induced saline Rayleigh convection inside a colloidal droplet. Phys Fluids 25:042001. https://doi.org/10.1063/1.4797497
Kim S, Wu Z, Esmaili E, et al (2020) How a raindrop gets shattered on biological surfaces. The Proceedings of the National Academy of Sciences 117:13901–13907. https://doi.org/10.17605/OSF.IO/6RD8K.y
Liang G, Mudawar I (2016) Review of mass and momentum interactions during drop impact on a liquid film. Int J Heat Mass Transf 101:577–599. https://doi.org/10.1016/j.ijheatmasstransfer.2016.05.062
Liang G, Mudawar I (2017) Review of drop impact on heated walls. Int J Heat Mass Transf 106:103–126. https://doi.org/10.1016/j.ijheatmasstransfer.2016.10.031
Ma D, Zhou J, Wang Z, Wang Y (2020) Block copolymer ultrafiltration membranes by spray coating coupled with selective swelling. J Memb Sci 598:117656. https://doi.org/10.1016/j.memsci.2019.117656
Morozov VS, Volkov RS, Misyura SY (2018) Visualizing the velocity inside a drop when a cold droplet falls on a sessile drop on a hotwall. Interfacial Phenom Heat Transf 6:209–218. https://doi.org/10.1615/InterfacPhenomHeatTransfer.2018026188
Otsu N (1979) A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern SMC 9:62–66. https://doi.org/10.1109/TSMC.1979.4310076
Pasandideh-Fard M, Pershin V, Chandra S, Mostaghimi J (2002) Splat shapes in a thermal spray coating process: simulations and experiments. J Therm Spray Technol 11:206–217. https://doi.org/10.1361/105996302770348862
Roisman IV, Rioboo R, Tropea C (2002) Normal impact of a liquid drop on a dry surface: model for spreading and receding. Proc Royal Soc Math Phys Eng Sci 458:1411–1430. https://doi.org/10.1098/rspa.2001.0923
Sakai M, Hashimoto A, Yoshida N et al (2007) Image analysis system for evaluating sliding behavior of a liquid droplet on a hydrophobic surface. Rev Sci Inst 78:045103. https://doi.org/10.1063/1.2716005
Schneider CA, Rasband WS, Eliceiri KW (2012) NIH image to imageJ: 25 years of image analysis. Nat Methods 9:671–675. https://doi.org/10.1038/nmeth.2089
Shahmohammadi M, Zhao J, Yu KN (2018) Investigation of droplet behaviors for spray cooling using level set method. Ann Nucl Energy 113:162–170. https://doi.org/10.1016/j.anucene.2017.09.046
Smith MI, Bertola V (2011) Particle velocimetry inside Newtonian and non-Newtonian droplets impacting a hydrophobic surface. Exp Fluids 50:1385–1391. https://doi.org/10.1007/s00348-010-0998-6
Wang Y, Bourouiba L (2017) Drop impact on small surfaces: thickness and velocity profiles of the expanding sheet in the air. J Fluid Mech 814:510–534. https://doi.org/10.1017/jfm.2017.18
Wang Y, Bourouiba L (2018) Unsteady sheet fragmentation: droplet sizes and speeds. J Fluid Mech 848:946–967. https://doi.org/10.1017/jfm.2018.359
Yarin AL (2006) Drop impact dynamics: splashing. The Annual Review of Fluid Mechanics, Spreading, Receding, Bouncing. https://doi.org/10.1146/annurev.fluid.38.050304.092144
Yarin AL, Weiss DA (1995) Impact of drops on solid surfaces: self-similar capillary waves, and splashing as a new type of kinematic discontinuity. J Fluid Mech 283:141–173. https://doi.org/10.1017/S0022112095002266
Zhang Z, Li J, Jiang PX (2013) Experimental investigation of spray cooling on flat and enhanced surfaces. Appl Therm Eng 51:102–111. https://doi.org/10.1016/j.applthermaleng.2012.08.057
Acknowledgements
This work is financially supported by the Nuclear Energy Science & Technology and Human Resource Development Project from the Japan Atomic Energy Agency/Collaborative Laboratories for Advanced Decommissioning Science. The financial support from the Scientific and Technological Research Council of Turkey (TUBITAK/2214-A—Research Fellowship Programme for PhD Students) for providing scholarship to the first author is gratefully acknowledged.
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Gultekin, A., Erkan, N., Colak, U. et al. Investigating the dynamics of droplet spreading on a solid surface using PIV for a wide range of Weber numbers. J Vis 26, 999–1007 (2023). https://doi.org/10.1007/s12650-023-00920-8
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DOI: https://doi.org/10.1007/s12650-023-00920-8