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Events before droplet splashing on a solid surface

Published online by Cambridge University Press:  18 March 2010

MADHAV MANI ,
SHREYAS MANDRE  and
MICHAEL P. BRENNER
MADHAV MANI
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge MA 02138, USA
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]
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Abstract

A high-velocity (≈1 ms−1) impact between a liquid droplet (≈1 mm) and a solid surface produces a splash. Classical observations traced the origin of this splash to a thin sheet of fluid ejected near the impact point, though the fluid mechanical mechanism leading to the sheet is not known. Mechanisms of sheet formation have heretofore relied on initial contact of the droplet and the surface. In this paper, we theoretically and numerically study the events within the time scale of about 1 μs over which the coupled dynamics between the gas and the droplet becomes important. The droplet initially tries to contact the substrate by either draining gas out of a thin layer or compressing it, with the local behaviour described by a self-similar solution of the governing equations. This similarity solution is not asymptotically consistent: forces that were initially negligible become relevant and dramatically change the behaviour. Depending on the radius and impact velocity of the droplet, we show that the solution is overtaken by initially subdominant physical effects such as the surface tension of the liquid–gas interface or viscous forces in the liquid. At low impact velocities surface tension stops the droplet from impacting the surface, whereas at higher velocities viscous forces become important before surface tension. The ultimate dynamics of the interface once droplet viscosity cannot be neglected is not yet known.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 647: Dedicated to Professor S. H. Davis on his 70th birthday , 25 March 2010 , pp. 163 - 185
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Bach, G. A., Koch, D. L. & Gopinath, A. 2004 Coalescence and bouncing of small aerosol droplets. J. Fluid Mech. 518, 157–185.CrossRefGoogle Scholar
Bowden, F. P. & Field, J. E. 1964 The deformation of solids by liquid impact, by solid impact and by shock. Proc. R. Soc. Lond. A 282, 331–352.Google Scholar
Bussmann, M., Chandra, S. & Mostaghimi, J. 2000 Modeling the splash of a droplet impacting a solid surface. Phys. Fluids 12, 3121.Google Scholar
Cohen, I., Brenner, M. P., Eggers, J. & Nagel, S. R. 1999 Two fluid drop snap-off problem: experiments and theory. Phys. Rev. Lett. 83, 1147.CrossRefGoogle Scholar
Deegan, R. D., Brunet, P. & Eggers, J. 2008 Complexities of splashing. Nonlinearity 21, C1–C11.Google Scholar
Field, J. E., Dear, J. P. & Ogren, J. E. 1989 The effects of target compliance on liquid drop impact. J. Appl. Phys. 65, 533–540.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
Haller, K. K., Poulikakos, D., Ventikos, Y. & Monkewitz, P. 2003 Shock wave formation in droplet impact on a rigid surface. J. Fluid. Mech. 490, 1–14.CrossRefGoogle Scholar
Jenkins, D. C. & Booker, J. D. 1960 In Aerodynamic Capture Particles (ed. Richardson, E. G.), pp. 97–103. Permagon.Google Scholar
Lesser, M. B. 1981 Analytic solutions of liquid-drop impact problems. Proc. R. Soc. Lond. A 377, 289–308.Google Scholar
Lesser, M. B. & Field, J. E. 1983 The impact of compressible liquids. Annu. Rev. Fluid Mech. 15, 97–122.CrossRefGoogle Scholar
Levin, Z. & Hobbs, P. V. 1971 Splashing of water drops on solid and wetted surfaces. Philos. Trans. R. Soc. Lond. A 269, 555.Google Scholar
Mandre, S., Mani, M. & Brenner, M. P. 2009 Precursors to splashing of liquid droplets on a solid surface. Phys. Rev. Lett. 102, 134502-1–134502-4.CrossRefGoogle ScholarPubMed
Pan, K. L. & Law, C. K. 2007 Dynamics of droplet-film collision. J. Fluid Mech. 587, 1–22.CrossRefGoogle Scholar
Rein, M. 1993 Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res. 12, 6193.CrossRefGoogle Scholar
Rein, M. & Delplanque, J. P. 2008 The role of air entrainment on the outcome of drop impact on a solid surface. Acta Mech. 201, 105–118.CrossRefGoogle Scholar
Smith, F. T., Li, L. & Wu, G. X. 2003 Air cushioning with a lubrication inviscid balance. J. Fluid Mech., 291–318.Google Scholar
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.Google Scholar
Taylor, G. I. & Saffman, P. G. 1957 Effects of compressibility at low Reynolds number. J. Aeronaut. Sci. 24, 553.CrossRefGoogle Scholar
Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2003 Air entrapment under an impacting drop. J. Fluid Mech 478, 125–134.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.Google Scholar
Xu, L., Zhang, W. W. & Nagel, S. R. 2005 Drop splashing on a dry smooth surface. Phys. Rev. Lett. 94, 184505.Google Scholar
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.Google Scholar