Skip to main content Accessibility help
×
Home

Spreading and oscillation dynamics of drop impacting liquid film

  • Xiaoyu Tang (a1), Abhishek Saha (a1) (a2), Chao Sun (a3) and Chung K. Law (a1)

Abstract

We herein report an experimental study to explore the effects of impact inertia, film thickness and viscosity on the dynamics of shape deformation of a drop impacting a liquid film. We have identified that the spreading dynamics shows a weak dependence on impact inertia, but strongly depends on the film thickness. For a thick film, the liquid surface deforms and absorbs part of the impact energy, and hence inhibits spreading of the drop. For a thin film, the drop motion is restricted by the bottom solid substrate, promoting spreading. The periodicity of the capillary controlled shape oscillation, on the other hand, is found to be independent of impact inertia and film thickness. The damping of the shape oscillation shows strong dependence on the film thickness, in that the oscillation decays faster for smaller film thicknesses, due to the enhanced viscous loss.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Spreading and oscillation dynamics of drop impacting liquid film
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Spreading and oscillation dynamics of drop impacting liquid film
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Spreading and oscillation dynamics of drop impacting liquid film
      Available formats
      ×

Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corresponding author

Email addresses for correspondence: asaha@eng.ucsd.edu, cklaw@princeton.edu

References

Hide All
Basaran, O. A. 1992 Nonlinear oscillations of viscous liquid drops. J. Fluid Mech. 241, 169198.
Basaran, O. A., Scott, T. C. & Byers, C. H. 1989 Drop oscillations in liquid–liquid systems. AIChE J. 35 (8), 12631270.
Becker, E., Hiller, W. J. & Kowalewski, T. A. 1991 Experimental and theoretical investigation of large-amplitude oscillations of liquid droplets. J. Fluid Mech. 231, 189210.
Becker, E., Hiller, W. J. & Kowalewski, T. A. 1994 Nonlinear dynamics of viscous droplets. J. Fluid Mech. 258, 191216.
Clanet, C., Béguin, C., Richard, D. & Quéré, D. 2004 Maximal deformation of an impacting drop. J. Fluid Mech. 517, 199208.
Cossali, G. E., Coghe, A. & Marengo, M. 1997 The impact of a single drop on a wetted solid surface. Exp. Fluids 22 (6), 463472.
van Dam, D. B. & Le Clerc, C. 2004 Experimental study of the impact of an ink-jet printed droplet on a solid substrate. Phys. Fluids 16 (9), 34033414.
Davidson, M. R. 2002 Spreading of an inviscid drop impacting on a liquid film. Chem. Engng Sci. 57 (17), 36393647.
Eggers, J., Fontelos, M. A., Josserand, C. & Zaleski, S. 2010 Drop dynamics after impact on a solid wall: theory and simulations. Phys. Fluids 22 (6), 062101.
Gao, X. & Li, R. 2015 Impact of a single drop on a flowing liquid film. Phys. Rev. E 92, 053005.
Geppert, A., Terzis, A., Lamanna, G., Marengo, M. & Weigand, B. 2017 A benchmark study for the crown-type splashing dynamics of one-and two-component droplet wall–film interactions. Exp. Fluids 58 (12), 172.
Josserand, C. & Thoroddsen, S. T. 2016 Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48 (1), 365391.
Josserand, C. & Zaleski, S. 2003 Droplet splashing on a thin liquid film. Phys. Fluids 15 (6), 16501657.
Lagubeau, G., Fontelos, M. A., Josserand, C., Maurel, A., Pagneux, V. & Petitjeans, P. 2010 Flower patterns in drop impact on thin liquid films. Phys. Rev. Lett. 105, 184503.
Lifshitz, E. M. & Landau, L. D.1959 Fluid Mechanics, Course of Theoretical Physics, vol. 6. (2nd ed.). Butterworth-Heinemann.
Lundgren, T. S. & Mansour, N. N. 1988 Oscillations of drops in zero gravity with weak viscous effects. J. Fluid Mech. 194, 479510.
Marcotte, F., Michon, G.-J., Séon, T. & Josserand, C. 2019 Ejecta, corolla, and splashes from drop impacts on viscous fluids. Phys. Rev. Lett. 122, 014501.
Mashayek, F. & Ashgriz, N. 1998 Nonlinear oscillations of drops with internal circulation. Phys. Fluids 10 (5), 10711082.
Miller, C. A. & Scriven, L. E. 1968 The oscillations of a fluid droplet immersed in another fluid. J. Fluid Mech. 32 (3), 417435.
Pan, K. & Law, C. K. 2007 Dynamics of droplet–film collision. J. Fluid Mech. 587, 122.
Prosperetti, A. 1980 Free oscillations of drops and bubbles: the initial-value problem. J. Fluid Mech. 100 (2), 333347.
Reid, W. H. 1960 The oscillations of a viscous liquid drop. Q. J. Math. 18 (1), 8689.
Rieber, M. & Frohn, A. 1999 A numerical study on the mechanism of splashing. Intl J. Heat Fluid Flow 20 (5), 455461.
Rioboo, R., Bauthier, C., Conti, J., Voue, M. & De Coninck, J. 2003 Experimental investigation of splash and crown formation during single drop impact on wetted surfaces. Exp. Fluids 35 (6), 648652.
Roisman, I. V. 2009 Inertia dominated drop collisions. II. An analytical solution of the Navier–Stokes equations for a spreading viscous film. Phys. Fluids 21 (5), 052104.
Roisman, I. V., van Hinsberg, N. P. & Tropea, C. 2008 Propagation of a kinematic instability in a liquid layer: capillary and gravity effects. Phys. Rev. E 77, 046305.
Roisman, I. V., Rioboo, R. & Tropea, C. 2002 Normal impact of a liquid drop on a dry surface: model for spreading and receding. Proc. R. Soc. Lond. A 458 (2022), 14111430.
Saha, A., Wei, Y., Tang, X. & Law, C. K. 2019 Kinematics of vortex ring generated by a drop upon impacting a liquid pool. J. Fluid Mech. 875, 842853.
Schiaffino, S. & Sonin, A. A. 1997 Molten droplet deposition and solidification at low Weber numbers. Phys. Fluids 9 (11), 31723187.
Son, Y. & Kim, C. 2009 Spreading of inkjet droplet of non-Newtonian fluid on solid surface with controlled contact angle at low Weber and Reynolds numbers. J. Non-Newtonian Fluid Mech. 162 (1), 7887.
Tang, X., Saha, A., Law, C. K. & Sun, C. 2016 Nonmonotonic response of drop impacting on liquid film: mechanism and scaling. Soft Matt. 12 (20), 45214529.
Tang, X., Saha, A., Law, C. K. & Sun, C. 2018 Bouncing-to-merging transition in drop impact on liquid film: role of liquid viscosity. Langmuir 34 (8), 26542662.
Tang, X., Saha, A., Law, C. K. & Sun, C. 2019 Bouncing drop on liquid film: dynamics of interfacial gas layer. Phys. Fluids 31 (1), 013304.
Tran, A. T. T., Hyland, M. M., Shinoda, K. & Sampath, S. 2011 Influence of substrate surface conditions on the deposition and spreading of molten droplets. Thin Solid Films 519 (8), 24452456.
Tran, T., de Maleprade, H., Sun, C. & Lohse, D. 2013 Air entrainment during impact of droplets on liquid surfaces. J. Fluid Mech. 726, R3.
Tran, T., Staat, H. J. J., Prosperetti, A., Sun, C. & Lohse, D. 2012 Drop impact on superheated surfaces. Phys. Rev. Lett. 108 (3), 036101.
Trinh, E. & Wang, T. G. 1982 Large-amplitude free and driven drop-shape oscillations: experimental observations. J. Fluid Mech. 122, 315338.
Trinh, E. H., Thiessen, D. B. & Holt, R. G. 1998 Driven and freely decaying nonlinear shape oscillations of drops and bubbles immersed in a liquid: experimental results. J. Fluid Mech. 364, 253272.
Tsamopoulos, J. A. & Brown, R. A. 1983 Nonlinear oscillations of inviscid drops and bubbles. J. Fluid Mech. 127, 519537.
Vadillo, D. C., Soucemarianadin, A., Delattre, C. & Roux, D. C. D. 2009 Dynamic contact angle effects onto the maximum drop impact spreading on solid surfaces. Phys. Fluids 21 (12), 122002.
Visser, C. W., Frommhold, P. E., Wildeman, S., Mettin, R., Lohse, D. & Sun, C. 2015 Dynamics of high-speed micro-drop impact: numerical simulations and experiments at frame-to-frame times below 100 ns. Soft Matt. 11 (9), 17081722.
Wildeman, S., Visser, C. W., Sun, C. & Lohse, D. 2016 On the spreading of impacting drops. J. Fluid Mech. 805, 636655.
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing …. Annu. Rev. Fluid Mech. 38, 159192.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Spreading and oscillation dynamics of drop impacting liquid film

  • Xiaoyu Tang (a1), Abhishek Saha (a1) (a2), Chao Sun (a3) and Chung K. Law (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed