Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-02-05T07:57:22.873Z Has data issue: false hasContentIssue false
  • English
  • Français

The mechanism of a splash on a dry solid surface

Published online by Cambridge University Press:  28 November 2011

Shreyas Mandre  and
Michael P. Brenner
Shreyas Mandre*
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
Michael P. Brenner
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

From rain storms to ink jet printing, it is ubiquitous that a high-speed liquid droplet creates a splash when it impacts on a dry solid surface. Yet, the fluid mechanical mechanism causing this splash is unknown. About fifty years ago it was discovered that corona splashes are preceded by the ejection of a thin fluid sheet very near the vicinity of the contact point. Here we present a first-principles description of the mechanism for sheet formation, the initial stages of which occur before the droplet physically contacts the surface. We predict precisely when sheet formation occurs on a smooth surface as a function of experimental parameters, along with conditions on the roughness and other parameters for the validity of the predictions. The process of sheet formation provides a semi-quantitative framework for studying the subsequent events and the influence of liquid viscosity, gas pressure and surface roughness. The conclusions derived from this framework are in quantitative agreement with previous measurements of the splash threshold as a function of impact parameters (the size and velocity of the droplet) and in qualitative agreement with the dependence on physical properties (liquid viscosity, surface tension, ambient gas pressure, etc.) Our analysis predicts an as yet unobserved series of events within micrometres of the impact point and microseconds of the splash.

JFM classification

Interfacial Flows (free surface): Capillary flows Drops and Bubbles: Drops
Type
Papers
Information
Journal of Fluid Mechanics , Volume 690 , 10 January 2012 , pp. 148 - 172
Copyright
Copyright © Cambridge University Press 2011

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.)

References

1. Bird, J. C., Tsai, S. S. H. & Stone, H. A. 2009 Inclined to splash: triggering and inhibiting a splash with tangential velocity. New J. Phys. 11, 063017.CrossRefGoogle Scholar
2. Bussmann, M., Chandra, S. & Mostaghimi, J. 2000 Modelling the splash of a droplet impacting a solid surface. Phys. Fluids 12, 3121–3132.CrossRefGoogle Scholar
3. Cawthorn, C. J. & Balmforth, N. J. 2010 Contact in a viscous fluid. Part 1. A falling wedge. J. Fluid Mech. 646, 327–338.CrossRefGoogle Scholar
4. Chandra, S. & Avedisian, C. T. 1991 On the collision of a droplet with a solid surface. Proc. Math. Phys. Sci. 432 (1884), 13–41.Google Scholar
5. Chen, A. U., Notz, P. K. & Basaran, O. A. 2002 Computational and experimental analysis of pinch-off and scaling. Phys. Rev. Lett. 88 (17), 174501.CrossRefGoogle ScholarPubMed
6. Deegan, R. D., Prunet, P. & Eggers, J. 2008 Complexities of splashing. Nonlinearity 21, C1–C11.CrossRefGoogle Scholar
7. Dhiman, R. & Chandra, S. 2008 Rupture of radially spreading liquid films. Phys. Fluids 20, 092104.CrossRefGoogle Scholar
8. Eggers, J., Fontelos, M. A., Josserand, C. & Zaleski, S. 2010 Drop dynamics after impact on a solid wall: theory and simulations. Phys. Fluids 22, 062101.CrossRefGoogle Scholar
9. Fullana, J. M. & Zaleski, S. 1999 Stability of a growing end rim in a liquid sheet of uniform thickness. Phys. Fluids 11, 952–954.CrossRefGoogle Scholar
10. Gopinath, A., Chen, S. B. & Koch, D. L. 1997 Lubrication flows between spherical particles colliding in a compressible non-continuum gas. J. Fluid Mech. 344, 245–269.CrossRefGoogle Scholar
11. Haller, K. K., Poulikakos, D., Ventikos, Y. & Monkewitz, P. 2003 Shock wave formation in droplet impact on a rigid surface: lateral liquid motion and multiple wave structure in the contact line region. J. Fluid Mech. 490, 1–14.CrossRefGoogle Scholar
12. Harlow, F. H. & Shannon, J. P. 1967 The splash of a liquid drop. J. Appl. Phys. 38, 3855.CrossRefGoogle Scholar
13. Josserand, C., Lemoyne, L., Troeger, R. & Zaleski, S. 2005 Droplet impact on a dry surface: triggering the splash with a small obstacle. J. Fluid Mech. 524, 47–56.CrossRefGoogle Scholar
14. Keller, J. B. & Kolodner, I. 1954 Instability of liquid surfaces and the formation of drops. J. Appl. Phys. 25 (7), 918–921.CrossRefGoogle Scholar
15. Lesser, M. B. 1981 Analytic solutions of liquid-drop impact problems. Proc. R. Soc. Lond. A 377, 289–308.Google Scholar
16. Lesser, M. B. & Field, J. E. 1983 The impact of compressible liquids. Annu. Rev. Fluid Mech. 15, 97–122.CrossRefGoogle Scholar
17. Levin, Z. & Hobbs, P. V. 1971 Splashing of water drops on solid and wetted surfaces: hydrodynamics and charge separation. Phil. Trans. R. Soc. Lond. A 269, 555–585.Google Scholar
18. Mandre, S., Mani, M. & Brenner, M. P. 2009 Precursors to splashing of liquid droplets on a solid surface. Phys. Rev. Lett. 102 (13), 134502.CrossRefGoogle ScholarPubMed
19. Mani, M., Mandre, S. & Brenner, M. P. 2010 Events before droplet splashing on a solid surface. J. Fluid Mech. 647, 163–185.CrossRefGoogle Scholar
20. Maxwell, J. C. 1879 On stresses in rarified gases arising from inequalities of temperature. Phil. Trans. R. Soc. Lond. A 170, 231–256.Google Scholar
21. Mongruel, A., Daru, V., Feuillebois, F. & Tabakova, S. 2009 Early post-impact time dynamics of viscous drops onto a solid dry surface. Phys. Fluids 21, 032101.CrossRefGoogle Scholar
22. Mundo, C. H. R., Sommerfeld, M. & Tropea, C. 1995 Droplet–wall collisions: experimental studies of the deformation and breakup process. Intl J. Multiphase Flow 21 (2), 151–173.CrossRefGoogle Scholar
23. North, S. H., Lock, E. H., King, T. R., Franek, J. B., Walton, S. G. & Taitt, C. R. 2009 Effect of physicochemical anomalies of soda-lime silicate slides on biomolecule immobilization. Analyt. Chem. 82 (1), 406–412.CrossRefGoogle Scholar
24. Range, K. & Feuillebois, F. 1998 Influence of surface roughness on liquid drop impact. J. Colloid Interface Sci. 203 (1), 16–30.CrossRefGoogle Scholar
25. Rein, M. & Delplanque, J. P. 2008 The role of air entrainment on the outcome of drop impact on a solid surface. Acta Mechanica 201, 105–118.CrossRefGoogle Scholar
26. Reyssat, M., Richard, D., Clanet, C. & Quéré, D. 2010 Dynamical superhydrophobicity. Faraday Discuss. 146, 19–33.CrossRefGoogle ScholarPubMed
27. Rioboo, R., Marengo, M. & Tropea, C. 2002 Time evolution of liquid drop impact onto solid, dry surfaces. Exp. Fluids 33 (1), 112–124.CrossRefGoogle Scholar
28. Rioboo, R., Tropea, C. & Marengo, M. 2001 Outcomes from a drop impact on solid surfaces. Atomiz. Sprays 11 (2), 155–166.Google Scholar
29. de Ruiter, J., Pepper, R. E. & Stone, H. A. 2010 Thickness of the rim of an expanding lamella near the splash threshold. Phys. Fluids 22, 022104.CrossRefGoogle Scholar
30. Schroll, R. D., Josserand, C., Zaleski, S. & Zhang, W. W. 2010 Impact of a viscous liquid drop. Phys. Rev. Lett. 104 (3), 34504.CrossRefGoogle ScholarPubMed
31. Song, M. & Tryggvason, G. 1999 The formation of thick borders on an initially stationary fluid sheet. Phys. Fluids 11, 2487–2493.CrossRefGoogle Scholar
32. 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, 419–441.Google Scholar
33. Taylor, G. I. & Saffman, P. G. 1957 Effects of compressibility at low Reynolds number. J. Aeronaut. Sci. 24, 553.CrossRefGoogle Scholar
34. Thoroddsen, S. T. 2002 The ejecta sheet generated by the impact of a drop. J. Fluid Mech. 451, 373–381.CrossRefGoogle Scholar
35. Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2006 Crown breakup by marangoni instability. J. Fluid Mech. 557 (-1), 63–72.CrossRefGoogle Scholar
36. Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2008 High-speed imaging of drops and bubbles. Annu. Rev. Fluid Mech. 40, 257–285 ISSN 0066-4189.CrossRefGoogle Scholar
37. 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
38. Thoroddsen, S. T., Thoraval, M. J., Takehara, K. & Etoh, T. G. 2011 Droplet splashing by a slingshot mechanism. Phys. Rev. Lett. 106 (3), 34501 ISSN 1079-7114.CrossRefGoogle ScholarPubMed
39. Tsai, P., van der Veen, R. C. A., Van De Raa, M. & Lohse, D. 2010 How micropatterns and air pressure affect splashing on surfaces. Langmuir 26 (20), 16090–16095.CrossRefGoogle ScholarPubMed
40. Vander Wal, R. L., Berger, G. M. & Mozes, S. D. 2006 Droplets splashing upon films of the same fluid of various depths. Exp. Fluids 40 (1), 33–52.CrossRefGoogle Scholar
41. Worthington, A. M. 1876 On the forms assumed by drops of liquids falling vertically on a horizontal plate. Proc. R. Soc. Lond. A 25, 261–272.Google Scholar
42. Xu, L. 2007 Liquid drop splashing on smooth, rough, and textured surfaces. Phys. Rev. E 75 (5), 56316.CrossRefGoogle ScholarPubMed
43. Xu, L., Zhang, W. W. & Nagel, S. R. 2005 Drop splashing on a dry smooth surface. Phys. Rev. Lett. 94, 184505.CrossRefGoogle ScholarPubMed
44. Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159–192 ISSN 0066-4189.CrossRefGoogle Scholar
45. Yarin, A. L. & Weiss, D. A. 1995 Impact of drops on solid surfaces: self similar capillary waves and splashing as a new type of kinetic discontinuity. J. Fluid Mech. 283, 141–173.CrossRefGoogle Scholar
46. Yokoi, K. 2011 Numerical studies of droplet splashing on a dry surface: triggering a splash with the dynamic contact angle. Soft Matt. 7, 5120–5123.CrossRefGoogle Scholar
47. Zhang, L. V., Brunet, P., Eggers, J. & Deegan, R. D. 2010 Wavelength selection in the crown splash. Phys. Fluids 22, 122105.CrossRefGoogle Scholar