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On the spreading of impacting drops

  • Sander Wildeman (a1), Claas Willem Visser (a1), Chao Sun (a1) (a2) and Detlef Lohse (a1) (a3)
Abstract

The energy budget and dissipation mechanisms during droplet impact on solid surfaces are studied numerically and theoretically. We find that for high impact velocities and negligible surface friction at the solid surface (i.e. free slip), approximately one-half of the initial kinetic energy is transformed into surface energy, independent of the impact parameters and the detailed energy loss mechanism(s). We argue that this seemingly universal rule is related to the deformation mode of the droplet and is reminiscent of pipe flow undergoing a sudden expansion, for which the head loss can be calculated by multiplying the kinetic energy of the incoming flow by a geometrical factor. For impacts on a no-slip surface also dissipation in the shear boundary layer at the solid surface is important. In this case the geometric head loss acts as a lower bound on the total dissipation (i.e. the spreading on a no-slip surface approaches that on a free-slip surface when the droplet viscosity is sent to zero). This new view on the impact problem allows for simple analytical estimates of the maximum spreading diameter of impacting drops as a function of the impact parameters and the properties of the solid surface. It bridges the gap between previous momentum balance approaches and energy balance approaches, which hitherto did not give consistent predictions in the low viscosity limit. Good agreement is found between our models and experiments, both for impacts on ‘slippery’ or lubricated surfaces (e.g. Leidenfrost droplet impacts and head-on droplet–droplet collisions) and for impacts on no-slip surfaces.

Copyright
Corresponding author
Email address for correspondence: swildeman@gmail.com
References
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Antonini C., Amirfazli A. & Marengo M. 2012 Drop impact and wettability: from hydrophilic to superhydrophobic surfaces. Phys. Fluids 24, 102104.
Attané P., Girard F. & Morin V. 2007 An energy balance approach of the dynamics of drop impact on a solid surface. Phys. Fluids 19, 012101.
Aziz S. D. & Chandra S. 2000 Impact, recoil and splashing of molten metal droplets. Intl J. Heat Mass Transfer 43 (16), 28412857.
Bartolo D., Josserand C. & Bonn D. 2006 Singular jets and bubbles in drop impact. Phys. Rev. Lett. 96, 124501.
Batchelor G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Blossey R. 2003 Self-cleaning surfaces virtual realities. Nat. Mater. 2, 301306.
Boyer F., Sandoval-Nava E., Snoeijer J. H., Dijksman J. F. & Lohse D. 2016 Drop impact of shear thickening liquids. Phys. Rev. Fluids 1, 013901.
Chandra S. & Avedisian C. T. 1991 On the collision of a droplet with a solid surface. Proc. R. Soc. Lond. A 432 (1884), 1341.
Clanet C., Béguin C., Richard D. & Quéré D. 2004 Maximal deformation of an impacting drop. J. Fluid Mech. 517, 199208.
Culick F. E. C. 1960 Comments on a ruptured soap film. J. Appl. Phys. 31 (6), 11281129.
De Ruiter J., Lagraauw R., Van den Ende D. & Mugele F. 2014 Wettability-independent bouncing on flat surfaces mediated by thin air films. Nat. Phys. 11 (1), 4853.
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.
Jiang Y. J., Umemura A. & Law C. K. 1992 An experimental investigation on the collision behaviour of hydrocarbon droplets. J. Fluid Mech. 234, 171190.
Josserand C. & Thoroddsen S. T. 2016 Drop impact on solid surface. Annu. Rev. Fluid Mech. 48 (1), 365391.
Kim J. 2007 Spray cooling heat transfer: the state of the art. Intl J. Heat Fluid Flow 28, 753767.
Laan N., De Bruin K. G., Bartolo D., Josserand C. & Bonn D. 2014 Maximum diameter of impacting liquid droplets. Phys. Rev. Appl. 2 (4), 044018.
Lagubeau G., Fontelos M. A., Josserand C., Maurel A., Pagneux V. & Petitjeans P. 2012 Spreading dynamics of drop impacts. J. Fluid Mech. 713, 5060.
Lastakowski H., Boyer F., Biance A.-L., Pirat C. & Ybert C. 2014 Bridging local to global dynamics of drop impact onto solid substrates. J. Fluid Mech. 747, 103118.
Lee J. B., Derome D., Guyer R. & J. Carmeliet 2016 Modelling the maximum spreading of liquid droplets impacting wetting and non-wetting surfaces. Langmuir 32 (5), 12991308.
Marengo M., Antonini C., Roisman I. V. & Tropea C. 2011 Drop collisions with simple and complex surfaces. Curr. Opin. Colloid Interface Sci. 16 (4), 292302.
Mishchenko L., Hatton B., Bahadur V., Taylor J. A., Krupenkin T. & Aizenberg J. 2010 Design of ice-free nanostructured impacting water droplets. ACS Nano 4 (12), 76997707.
Okumura K., Chevy F., Richard D., Quéré D. & Clanet C. 2003 Water spring: a model for bouncing drops. Europhys. Lett. 62 (2), 237243.
Pasandideh-Fard M., Qiao Y. M., Chandra S. & Mostaghimi J. 1996 Capillary effects during droplet impact on a solid surface. Phys. Fluids 8 (3), 650659.
Popinet S. 2003 Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 190 (July), 572600.
Popinet S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228 (16), 58385866.
Quéré D. 2013 Leidenfrost dynamics. Annu. Rev. Fluid Mech. 45, 197215.
Rein M. 1993 Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res. 12 (2), 6193.
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, 6983.
Richard D. & Quéré D. 2000 Bouncing water drops. Europhys. Lett. 50 (6), 769775.
Rioboo R., Marengo M. & Tropea C. 2002 Time evolution of liquid drop impact onto solid, dry surfaces. Exp. Fluids 33 (1), 112124.
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., Berberovi E. & Tropea C. 2009 Inertia dominated drop collisions. I. On the universal flow in the lamella. Phys. Fluids 21 (5), 052103.
Roisman I. V., Planchette C., Lorenceau E. & Brenn G. 2012 Binary collisions of drops of immiscible liquids. J. Fluid Mech. 690, 512535.
Savva N. & Bush J. W. M. 2009 Viscous sheet retraction. J. Fluid Mech. 626 (2009), 211240.
Stow C. D. & Hadfield M. G. 1981 An experimental investigation of fluid flow resulting from the impact of a water drop with an unyielding dry surface. Proc. R. Soc. Lond. A 373 (1755), 419441.
Sünderhauf G., Raszillier H. & Durst F. 2002 The retraction of the edge of a planar liquid sheet. Phys. Fluids 14 (1), 198208.
Taylor G. 1959 The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets. Proc. R. Soc. Lond. A 253 (1274), 313321.
Thoraval M.-J., Takehara K., Etoh T. G., Popinet S., Ray P., Josserand C., Zaleski S. & Thoroddsen S. T. 2012 von Kármán vortex street within an impacting drop. Phys. Rev. Lett. 108 (26), 264506.
Thoraval M.-J., Takehara K., Etoh T. G. & Thoroddsen S. T. 2013 Drop impact entrapment of bubble rings. J. Fluid Mech. 724, 234258.
Thoroddsen S. T., Etoh T. G. & Takehara K. 2008 High-speed imaging of drops and bubbles. Annu. Rev. Fluid Mech. 40, 257285.
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, 203212.
Tran T., Staat H. J. J., Prosperetti A., Sun C. & Lohse D. 2012 Drop impact on superheated surfaces. Phys. Rev. Lett. 108 (3), 036101.
Ukiwe C. & Kwok D. Y. 2005 On the maximum spreading diameter of impacting droplets on well-prepared solid surfaces. Langmuir 21 (31), 666673.
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.
Villermaux E. & Bossa B. 2011 Drop fragmentation on impact. J. Fluid Mech. 668, 412435.
Visser C., 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, 17081722.
Šikalo Š., Wilhelm H.-D., Roisman I. V., Jakirlić S. & Tropea C. 2005 Dynamic contact angle of spreading droplets: experiments and simulations. Phys. Fluids 17 (2005), 062103.
Willis K. & Orme M. 2003 Binary droplet collisions in a vacuum environment: an experimental investigation of the role of viscosity. Exp. Fluids 34 (1), 2841.
Yarin A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing…. Annu. Rev. Fluid Mech. 38, 159192.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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