Abstract
Liquid droplet impacts onto solid surfaces have attracted enormous amount of attention from wide range of research fields including experimental and numerical investigations. Unlike experimental efforts, numerical and analytical studies generated various sets of data. In this study, we investigated the spreading velocities inside the water droplets impinging onto a dry glass substrate using time-resolved PIV. The method, together with the high spatiotemporal resolution and the additional treatments improving the robustness, allowed us to resolve the radial velocity profiles efficiently in the spreading phase. Several impact velocity cases ranging from 0.40 to 0.96 m/s were studied. They correspond to low and moderate level Weber numbers (4.9–27.6). We observed that instantaneous radial velocity distributions exhibit linear and nonlinear modes. The nonlinearity is caused by the vortical flows formed at outer regions of the spreading liquid lamella. We demonstrated that even at low impact velocities the linear parts of the profiles obey a quasi-one-dimensional theory proposed in the literature. The comparison of obtained results with a literature-based numerical study, performed for high range of Weber numbers, confirmed the simultaneous existence of linear and nonlinear parts in the radial velocity profiles. In spite of the scale differences in terms of Weber number, the agreements in the tendencies of the profiles imply the validity of the mechanism considered in the numerical study even at low and moderate level range of Weber numbers.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adrian R (1986) Image shifting technique to resolve directional ambiguity in double-pulsed velocimetry. Appl Opt 25:3855–3858
Adrian R (2005) Twenty years of particle image velocimetry. Exp Fluids 39(2):159–169
Biance A-L, Clanet C, Quere D (2004) First steps in the spreading of a liquid droplet. Phys Rev E 69:016301
Buchmüller I, Roisman I V, Tropea C (2012) Influence of elevated pressure on impingement of a droplet upon a hot surface. ICLASS-2012, Heidelberg
Clanet C, Beguin C, Richard D, Quere D (2004) Maximal deformation of an impacting drop. J Fluid Mech 517:199–208
Erkan N, Shinohara K, Someya S, Okamoto K (2008) Threecomponent velocity measurement in microscale flows using time-resolved PIV. Meas Sci Technol 19(057):003
Fukai J, Shiiba Y, Yamamoto T, Miyatake O (1995) Wetting effects on the spreading of a liquid droplet colliding with a flatsurface: experiment and modeling. Phys Fluids 7(2):236–247
Hao P, Lv C, Yao Z, He F (2010) Sliding behavior of water droplet on superhydrophobic surface. EPL 90:66003
Harvie DJE, Fletcher DF (2001) A hydrodynamic and thermodynamic simulation of droplet impacts on hot surfaces, part II: validation and applications. Int J Heat Mass Transf 44:2643–2659
Kamnis S, Gu S (2005) Numerical modelling of droplet impingement. J Phys D Appl Phys 38:3664–3673
Kang KH, Lim HC, Lee HW, Lee SJ (2013) Evaporation-induced saline Rayleigh convection inside a colloidal droplet. Phys Fluids 25:042001
Lecordier B, Trinite M (2004) Advanced PIV algorithms with image distortion validation and comparison using synthetic images of turbulent flow. In: Particle image velocimetry: recent improvements, Springer, pp 115–132
Mao T, Kuhn D, Tran H (1997) Spread and rebound of liquid droplets upon impact on flat surfaces. AIChE J 43(9):2169–2179
Pasandideh-Fard M, Chandra S, Mostaghimi J (2002) A three-dimensional model of droplet impact and solidification. Int J Heat Mass Transf 45(11):2229–2242
Raffel M, Willert CE, Wereley ST, Kompenhans J (2007) Particle image velocimetry—a practical guide. Springer, Berlin
Rioboo R, Marengo M, Tropea C (2002) Time evolution of liquid drop impact onto solid, dry surfaces. Exp Fluids 33:112–124
Roisman IV, Rioboo R, Tropea C (2002) Normal impact of a liquid drop on a dry surface: model for spreading and receding. Proc R Soc Lond Ser A Math Phys Eng Sci 458(2022):1411–1430
Roisman VI, Berberović E, Tropea C (2009) Inertia dominated drop collisions. I. On the universal flow in the lamella. Phys Fluids 21:052103
Saha A, Basu S, Kumar R (2012) Velocity and rotation measurements in acoustically levitated droplets. Phys Lett A 376:3185–3191
Sakai M, Hashimoto A, Yoshito N, Suzuki S, Kameshima Y, Nakajima A (2007) Image analysis system for evaluating sliding behavior of a liquid droplet on a hydrophobic surface. Rev Sci Instrum 78(045):103
Scarano F (2002) Iterative image deformation methods in piv. Meas Sci Technol 13(1):R1
Sen S, Vaikuntanathan V, Sivakumar D (2014) Experimental investigation of biofuel drop impact on stainless steel surface. Exp Thermal Fluid Sci 54:38–46
Smith MI, Bertola V (2011) Particle velocimetry inside Newtonian and non-Newtonian droplets impacting a hydrophobic surface. Exp Fluids 50:1385–1391
Stanton DW, Rutland CJ (1998) Multi-dimensional modeling of thin liquid films and spray-wall interactions resulting from impinging sprays. Int J Heat Mass Transf 41(20):3037–3054
Stow C, Hadfield M (1981) An experimental investigation of fluid flow resulting from the impact of a water drop with an unyielding dry surface. Proc R Soc Lond Ser A Math Phys Sci 373(1755):419–441
Worthington A (1876) On the forms assumed by drops of liquids falling vertically on a horizontal plate. Proc R Soc Lond 25(171–178):261–272
Xu L, Zhang WW, Nagel SR (2005) Drop splashing on a dry smooth surface. Phys Rev Lett 94(18):184–505
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Erkan, N., Okamoto, K. Full-field spreading velocity measurement inside droplets impinging on a dry solid surface. Exp Fluids 55, 1845 (2014). https://doi.org/10.1007/s00348-014-1845-y
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-014-1845-y