Hostname: page-component-89b8bd64d-x2lbr Total loading time: 0 Render date: 2026-05-09T00:43:56.730Z Has data issue: false hasContentIssue false
  • English
  • Français

Regimes of wettability-dependent and wettability-independent bouncing of a drop on a solid surface

Published online by Cambridge University Press:  11 December 2020

Praveen K. Sharma  and
Harish N. Dixit Open the ORCID record for Harish N. Dixit [Opens in a new window]
Praveen K. Sharma
Affiliation:
Department of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Telangana 502285, India
Harish N. Dixit*
Affiliation:
Department of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Telangana 502285, India
*
†Email address for correspondence: hdixit@mae.iith.ac.in
Get access Rights & Permissions [Opens in a new window]

Abstract

Tiny drops of millimetre size are known to bounce on a solid surface if the surface is superhydrophobic. Recent experiments show that bouncing can occur even on hydrophilic surfaces under conditions where the drop is supported on a thin cushion of gas preventing it from making contact with the surface. We present a detailed insight into this observation by simulating bouncing dynamics of a drop on a flat solid surface using axisymmetric direct numerical simulations. The dynamics of drop motion is governed by three important dimensionless parameters, namely, Reynolds number, $Re$, Weber number, $We$, and capillary number, $Ca_g$. We generate a phase diagram in the $We\text {--}Re$ plane separating the wettability-independent (non-contact bouncing) and wettability-dependent (contact bouncing) regions. We show that $We=2.14$ is the optimum value of Weber number which can support a gas cushion for the widest range of Reynolds numbers. The phase diagram is further divided into five sub-regions based on the shape of the drop and the gas film beneath it. The simulations can reproduce experimentally reported gas films of ${\sim }1\ \mathrm {\mu }\textrm {m}$ with excellent agreement spatially and temporally. Simulations also reproduce well-known scaling laws for a variety of parameters characterising the gas film. New scaling laws for the radial extent of the gas film as well as time taken for impact are derived. For higher Weber and Reynolds numbers, a bouncing drop captures a gas bubble inside it consistent with simple experiments carried out for water drops bouncing on superhydrophobic surfaces.

JFM classification

Drops and Bubbles: Drops Multiphase and Particle-laden Flows: Multiphase flow Low-Reynolds-number flows: Lubrication theory

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A37
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Bartolo, D., Josserand, C. & Bonn, D. 2006 Singular jets and bubbles in drop impact. Phys. Rev. Lett. 96, 124501.CrossRefGoogle ScholarPubMed
Bouwhuis, W., van der Veen, R. C. A., Tran, T., Keij, D. L., Winkels, K. G., Peters, I. R., van der Meer, D., Sun, C., Snoeijer, J. H. & Lohse, D. 2012 Maximal air bubble entrainment at liquid-drop impact. Phys. Rev. Lett. 109, 264501.CrossRefGoogle ScholarPubMed
Chandra, S. & Avedisian, C. T. 1991 On the collision of a droplet with a solid surface. Proc. R. Soc. Lond. A 432, 13–41.Google Scholar
Clanet, C., Béguin, C., Richard, D. & Quéré, D. 2004 Maximal deformation of an impacting drop. J. Fluid Mech. 517, 199–208.CrossRefGoogle Scholar
Connor, J. N. & Horn, R. G. 2003 The influence of surface forces on thin film drainage between a fluid drop and a flat solid. Faraday Discuss. 123, 193–206.CrossRefGoogle Scholar
Duchemin, L. & Josserand, C. 2011 Curvature singularity and film-skating during drop impact. Phys. Fluids 23, 091701.CrossRefGoogle Scholar
Falkovich, G., Fouxon, A. & Stepanov, M. G. 2002 Acceleration of rain initiation by cloud turbulence. Nature 419, 151.CrossRefGoogle ScholarPubMed
Farsoiya, P. K., Mayya, Y. S. & Dasgupta, R. 2017 Axisymmetric viscous interfacial oscillations–theory and simulations. J. Fluid Mech. 826, 797–818.CrossRefGoogle Scholar
Footte, G. B. 1975 The water drop rebound problem: dynamics of collision. J. Atmos. Sci. 32 (2), 390–402.2.0.CO;2>CrossRefGoogle Scholar
Gopinath, A. & Koch, D. L. 2002 Collision and rebound of small droplets in an incompressible continuum gas. J. Fluid Mech. 454, 145–201.CrossRefGoogle Scholar
Grabowski, W. W. & Wang, L.-P. 2013 Growth of cloud droplets in a turbulent environment. Annu. Rev. Fluid Mech. 45, 293–324.CrossRefGoogle Scholar
Hendrix, M. H. W., Manica, R., Klaseboer, E., Chan, D. Y. C. & Ohl, C.-D. 2012 Spatiotemporal evolution of thin liquid films during impact of water bubbles on glass on a micrometer to nanometer scale. Phys. Rev. Lett. 108, 247803.Google Scholar
Hicks, P. D. & Purvis, R. 2010 Air cushioning and bubble entrapment in three-dimensional droplet impacts. J. Fluid Mech. 649, 135–163.Google Scholar
Hicks, P. D. & Purvis, R. 2013 Liquid–solid impacts with compressible gas cushioning. J. Fluid Mech. 735, 120–149.CrossRefGoogle Scholar
Huang, J. J., Shu, C. & Chew, Y. T. 2011 Lattice Boltzmann study of bubble entrapment during droplet impact. Intl J. Numer. Meth. Fluids 65, 655–682.CrossRefGoogle Scholar
Israelachvili, J. N. 2011 Intermolecular and Surface Forces. Academic Press.Google Scholar
Josserand, C. & Thoroddsen, S. T. 2016 Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48, 365–391.CrossRefGoogle Scholar
Klaseboer, E., Manica, R. & Chan, D. Y. C. 2014 Universal behavior of the initial stage of drop impact. Phys. Rev. Lett. 113, 194501.CrossRefGoogle ScholarPubMed
Kolinski, J. M., Mahadevan, L. & Rubinstein, S. M. 2014 Drops can bounce from perfectly hydrophilic surfaces. Europhys. Lett. 108, 24001.CrossRefGoogle Scholar
Kolinski, J. M., Rubinstein, S. M., Mandre, S., Brenner, M. P., Weitz, D. A. & Mahadevan, L. 2012 Skating on a film of air: drops impacting on a surface. Phys. Rev. Lett. 108, 074503.Google ScholarPubMed
Langley, K., Li, E. Q. & Thoroddsen, S. T. 2017 Impact of ultra-viscous drops: air-film gliding and extreme wetting. J. Fluid Mech. 813, 647–666.CrossRefGoogle Scholar
Langley, K. R., Li, E. Q., Vakarelski, I. U. & Thoroddsen, S. T. 2018 The air entrapment under a drop impacting on a nano-rough surface. Soft Matt. 14, 7586–7596.CrossRefGoogle Scholar
Langley, K. R. & Thoroddsen, S. T. 2019 Gliding on a layer of air: impact of a large-viscosity drop on a liquid film. J. Fluid Mech. 878, R2.Google Scholar
Leal, L. G. 2007 Advanced Transport Phenomena: Fluid Mechanics and Convective Transport processes, vol. 7. Cambridge University Press.CrossRefGoogle Scholar
Li, E. Q., Langley, K. R., Tian, Y. S., Hicks, P. D. & Thoroddsen, S. T. 2017 Double contact during drop impact on a solid under reduced air pressure. Phys. Rev. Lett. 119 (21), 214502.CrossRefGoogle ScholarPubMed
Li, E. Q. & Thoroddsen, S. T. 2015 Time-resolved imaging of a compressible air disc under a drop impacting on a solid surface. J. Fluid Mech. 780, 636–648.CrossRefGoogle Scholar
Li, E. Q., Vakarelski, I. U. & Thoroddsen, S. T. 2015 Probing the nanoscale: the first contact of an impacting drop. J. Fluid Mech. 785, R2.CrossRefGoogle Scholar
Liu, Y., Tan, P. & Xu, L. 2013 Compressible air entrapment in high-speed drop impacts on solid surfaces. J. Fluid Mech. 716, R9.CrossRefGoogle Scholar
Mandre, S., Mani, M. & Brenner, M. P. 2009 Precursors to splashing of liquid droplets on a solid surface. Phys. Rev. Lett. 102, 134502.CrossRefGoogle ScholarPubMed
Mani, M., Mandre, S. & Brenner, M. P. 2010 Events before droplet splashing on a solid surface. J. Fluid Mech. 647, 163–185.CrossRefGoogle Scholar
Manica, R., Hendrix, M. H. W., Gupta, R., Klaseboer, E., Ohl, C.-D. & Chan, D. Y. C. 2013 Effects of hydrodynamic film boundary conditions on bubble–wall impact. Soft Matt. 9, 9755–9758.CrossRefGoogle Scholar
Manica, R., Hendrix, M. H. W., Gupta, R., Klaseboer, E., Ohl, C.-D. & Chan, D. Y. C. 2014 Modelling bubble rise and interaction with a glass surface. Appl. Math. Model. 38, 4249–4261.CrossRefGoogle Scholar
Manica, R., Klaseboer, E. & Chan, D. Y. C. 2016 The impact and bounce of air bubbles at a flat fluid interface. Soft Matt. 12, 3271–3282.CrossRefGoogle Scholar
Mehdi-Nejad, V., Mostaghimi, J. & Chandra, S. 2003 Air bubble entrapment under an impacting droplet. Phys. Fluids 15, 173–183.CrossRefGoogle Scholar
Nobari, M. R., Jan, Y.-J. & Tryggvason, G. 1996 Head-on collision of drops—a numerical investigation. Phys. Fluids 8 (1), 29–42.CrossRefGoogle Scholar
Pack, M., Hu, H., Kim, D., Zheng, Z., Stone, H. A. & Sun, Y. 2017 Failure mechanisms of air entrainment in drop impact on lubricated surfaces. Soft Matt. 13, 2402–2409.CrossRefGoogle ScholarPubMed
Pan, K.-L., Law, C. K. & Zhou, B. 2008 Experimental and mechanistic description of merging and bouncing in head-on binary droplet collision. J. Appl. Phys. 103 (6), 064901.CrossRefGoogle Scholar
Popinet, S. 2003 Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 190, 572–600.CrossRefGoogle Scholar
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228, 5838–5866.CrossRefGoogle Scholar
Renardy, Y., Popinet, S., Duchemin, L., Renardy, M., Zaleski, S., Josserand, C., Drumright-Clarke, M. A., Richard, D., Clanet, C. & Quéré, D. 2003 Pyramidal and toroidal water drops after impact on a solid surface. J. Fluid Mech. 484, 69.Google Scholar
Richard, D. & Quéré, D. 2000 Bouncing water drops. Europhys. Lett. 50, 769–775.CrossRefGoogle Scholar
de Ruiter, J., van den Ende, D. & Mugele, F. 2015 a Air cushioning in droplet impact. II. Experimental characterization of the air film evolution. Phys. Fluids 27, 012105.CrossRefGoogle Scholar
de Ruiter, J., Lagraauw, R., Mugele, F. & van den Ende, D. 2015 b Bouncing on thin air: how squeeze forces in the air film during non-wetting droplet bouncing lead to momentum transfer and dissipation. J. Fluid Mech. 776, 531–567.CrossRefGoogle Scholar
de Ruiter, J., Lagraauw, R., van den Ende, D. & Mugele, F. 2015 c Wettability-independent bouncing on flat surfaces mediated by thin air films. Nat. Phys. 11, 48–53.CrossRefGoogle Scholar
de Ruiter, J., Oh, J. M., van den Ende, D. & Mugele, F. 2012 Dynamics of collapse of air films in drop impact. Phys. Rev. Lett. 108, 074505.CrossRefGoogle ScholarPubMed
San Lee, J., Weon, B. M., Je, J. H. & Fezzaa, K. 2012 How does an air film evolve into a bubble during drop impact? Phys. Rev. Lett. 109, 204501.Google Scholar
Smith, F. T., Li, L. & Wu, G. X. 2003 Air cushioning with a lubrication/inviscid balance. J. Fluid Mech. 482, 291–318.CrossRefGoogle Scholar
Thoroddsen, S. T., Etoh, T. G., Takehara, K., Ootsuka, N. & Hatsuki, Y. 2005 The air bubble entrapped under a drop impacting on a solid surface. J. Fluid Mech. 545, 203–212.CrossRefGoogle Scholar
Thoroddsen, S. T., Takehara, K. & Etoh, T. G. 2010 Bubble entrapment through topological change. Phys. Fluids 22, 051701.CrossRefGoogle Scholar
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, 1708–1722.CrossRefGoogle ScholarPubMed
Wildeman, S., Visser, C. W., Sun, C. & Lohse, D. 2016 On the spreading of impacting drops. J. Fluid Mech. 805, 636–655.CrossRefGoogle Scholar
Xu, L., Zhang, W. W. & Nagel, S. R. 2005 Drop splashing on a dry smooth surface. Phys. Rev. Lett. 94, 184505.CrossRefGoogle ScholarPubMed
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159–192.CrossRefGoogle Scholar

Sharma and Dixit supplementary movie 1

See pdf file for movie caption

Download Sharma and Dixit supplementary movie 1(Video)
Video 965.1 KB

Sharma and Dixit supplementary movie 2

See pdf file for movie caption

Download Sharma and Dixit supplementary movie 2(Video)
Video 929 KB

Sharma and Dixit supplementary movie 3

See pdf file for movie caption

Download Sharma and Dixit supplementary movie 3(Video)
Video 255.1 KB

Sharma and Dixit supplementary movie 4

See pdf file for movie caption

Download Sharma and Dixit supplementary movie 4(Video)
Video 2.8 MB
Supplementary material: File

Sharma and Dixit supplementary figure

See pdf file for figure caption

Download Sharma and Dixit supplementary figure(File)
File 277.2 KB
Supplementary material: PDF

Sharma and Dixit supplementary material

Captions for movies 1-4 and supplementary figure 1

Download Sharma and Dixit supplementary material(PDF)
PDF 71.4 KB