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Introduction to Drop-Surface Interactions

  • Martin Rein
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 456)

Abstract

The interaction of drops with surfaces is an everyday occurrence that comprises a rich variety of fluid mechanical facets. Almost two and a half millenniums ago the phrase gutta cavat lapidem (dripping water hollows out a stone) was coined reflecting the erosive action of repetitively impinging drops. The first scientific investigations into certain aspects of drop impact were then conducted in the second half of the nineteenth century. Topics addressed at those times include the formation of vortex rings by drops impinging on liquid surfaces, drops floating on or bouncing off pools, the spreading of a drop of one liquid on the surface of another liquid, splashing and an instability of drops spreading on solid surfaces, the result of the instability being well-known from the formation of ink blots. These and further phenomena of drop-surface interactions will be discussed in the present and in the other chapters of this book. In this we will limit ourselves to the interaction of single drops with different surfaces. It will become clear that processes occurring during drop-surface interactions are governed by a great number of different branches not only of fluid mechanics but also of thermal sciences. Often, a detailed understanding of the processes of drop-surface interactions is not yet available.

Keywords

Vortex Ring Froude Number Cold Spray Cavitation Bubble Weber Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Adler, W. F. (1999). Rain impact retrospective and vision for the future. Wear 233–235:25.Google Scholar
  2. Alkhimov, A. P., Kosarev, V. F. and Papyrin, A. N. (1990). A new method of ‘cold’ gas dynamic deposition. Sov. Phys. Dokl. 35:1047–1049.Google Scholar
  3. Anilkumar, A. V., Lee C. P. and Wang, T. G. (1991). Surface-tension-induced mixing following coalescence of initially stationary drops. Phys. Fluids A 3:2587–2591.CrossRefGoogle Scholar
  4. Armster, S. Q., Delplanque, J.-P., Rein, M. and Lavernia, E. J. (2002). Thermo-fluid mechanisms controlling droplet-based materials processes. Int. Materials Rev. (accepted for publication)Google Scholar
  5. Baird, M. H. I. (1960). The stability of inverse soap bubbles. Trans. Faraday Soc. 15:91–96.Google Scholar
  6. Benjamin, T. B. and Ellis, A. T. (1966). The collapse of cavitation bubbles and the pressure thereby produced against solid boundaries. Phil. Trans. R. Soc. Lond. A 260:221–240.CrossRefGoogle Scholar
  7. Bennet, T. and Poulikakos, D. (1993). Splat-quench solidification: estimating the Maximum spreading of a droplet impacting a solid surface. J. Materials Science 28:963–970.CrossRefGoogle Scholar
  8. Birkhoff, G. (1960). Hydrodynamics. A Study in Logic, Fact and Similitude. Princeton University Press, Princeton, 1960.Google Scholar
  9. Borner, H. and Schmidt, D. W. (1985). Investigation of large-scale vortex rings in He II by acoustic measurements of circulation. In: Meier, G. E. A. and Obermeier, F. (eds.), Flow of real fluids, Springer-Verlag, Berlin, 135–146.CrossRefGoogle Scholar
  10. Brunton, J. H. and Camus, J. J. (1970). The flow of a liquid drop during impact. In: Fyall, A. A. and King, R. B. (eds.) Proc. 3rd Int. Conf. Rain Erosion and Associated Phenomena Meersburg, West-Germany (RAE, 1970)Google Scholar
  11. Chandra, S. and Avedesian, C. T. (1991). On the collision of a droplet with a solid surface. Proc. R. Soc. London 432:13–41.CrossRefGoogle Scholar
  12. Chow, L. C., Sehmbey, M. S., and Pais, M. R. (1997). High Heat Flux Spray Cooling. In: Tien, C.-L. (ed.), Ann. Rev. Heat Transfer 8, Begell House, New York, 291–318.Google Scholar
  13. Cresswell, R. W. and Morton, B. R. (1995). Drop-formed vortex rings — The generation of vorticity. Phys. Fluids 7:1363. (Enlarged photographs are presented in a preprint, published as: Applied Mathematics Reports and Preprints 94/21, Monash University, 1994.)MathSciNetCrossRefGoogle Scholar
  14. Dell’Aversana, P., Banavar J. R. and Koplik, J. (1996). Suppression of coalescence by shear and temperature gradients. Phys. Fluids 8:15.CrossRefGoogle Scholar
  15. Dooley, B. S., Warncke, A. E., Gharib M. and Tryggvason, G. (1997). Vortex ring generation due to the coalescence of a water drop at a free surface. Exp. in Fluids 22:369.CrossRefGoogle Scholar
  16. Elliot, T. A. and Ford, D. M. (1972). Dynamic contact angles. Trans. Faraday Soc. 681:1814–1823.CrossRefGoogle Scholar
  17. Engel, O. G. (1955). Waterdrop Collisions With Solid Surfaces. J. Research NBS 54:281–298.CrossRefMATHGoogle Scholar
  18. Fukumoto, M. and Huang, Y. (1999). Flattening mechanism in thermal sprayed nickel particle impinging on flat substrate surface. J. Thermal Spray Techn. 8:427–432.CrossRefGoogle Scholar
  19. Gilbarg, D. and Anderson, R. A. (1948). Influence of Atmospheric Pressure on the Phenomena Accompanying the Entry of Spheres in Water. J. Appl. Phys. 19:127.CrossRefGoogle Scholar
  20. Hsiao, M., Lichter, S. and Quintero, L. G. (1988). The critical Weber number for vortex and jet formation for drops impinging on a liquid pool. Phys. Fluids 31:3560–3562.CrossRefGoogle Scholar
  21. Kientzler, J. C., Arons, A. B., Blanchard, D. C. and Woodcock, A. H. (1954). Photographic Investigation of the Projection of Droplets by Bubbles Bursting at a Water Surface. Tellus 6:1–7.CrossRefGoogle Scholar
  22. Kutter, V. (1916). Die Anwendung von Wirbelringen zur Bestimmung von Oberflächenspannungen. Phys. Zeitschrift 17:573–579.Google Scholar
  23. Lesser, M. and Field, J. E. (1983). The impact of compressible liquids. Annu. Rev. Fl. Mech. 15:97–122.CrossRefGoogle Scholar
  24. Mao, T., Kuhn, D. C. S., and Honghi Tran (1997). Spread and Rebound of Liquid Droplets upon Impact on Flat Surfaces. AlChE J. 43(9):2169–2179.CrossRefGoogle Scholar
  25. May, A. (1952). Vertical Entry of Missiles into Water. J. Appl. Phys. 23:1362.CrossRefGoogle Scholar
  26. Mundo, C., Sommerfeld, M. and Tropea, C. (1995). Droplet wall collisions: experimental studies of the deformation and breakup process. Int. J. Multiphase Flow 21:151–173.CrossRefMATHGoogle Scholar
  27. Pizolla, P. A., Roth, S. and De Forest, P. R. (1986a). Blood Droplet Dynamics — I. J. Forensic Sciences 31:36.Google Scholar
  28. Pizolla, P. A., Roth, S. and De Forest, P. R. (1986b). Blood Droplet Dynamics — II. J. Forensic Sciences 31:50.Google Scholar
  29. Poddubenko, V. V. and Yablonik, R. M. (1990). Impact of a droplet on a solid surface. Fluid Mech. Sov. Res. 19(3): 111–116.Google Scholar
  30. Poulikakos, D. and Waldvogel, J. M. (1996). Heat Transfer and Fluid Dynamics in the Process of Spray Deposition. Advance in Heat Transfer 28:1.CrossRefGoogle Scholar
  31. Prosperetti, A. and Oguz, H. N. (1993). The impact of drops on liquid surfaces and the underwater noise of rain. Ann. Rev. Fluid Mech. 25:577–602.CrossRefGoogle Scholar
  32. Pumphrey, H. C. and Elmore, P. A. (1990). The entrainment of bubbles by drop impacts. J. Fluid Mech. 220:539–567.CrossRefGoogle Scholar
  33. Pumphrey, H. C. and Walton, A. J. (1988). Experimental study of the sound emitted by water drops impacting on a water surface. European J. Phys. 9:225–231.CrossRefGoogle Scholar
  34. Rein, M. and Meier, G.E.A. (1988). Numerical Simulation of the Dynamics of Cavitation Bubble Fields Generated by Strong Expansion Waves. In: Furuya, O. (ed.), Cavitation and Multiphase Flow Forum — 1988, ASME, New York, 40–44.Google Scholar
  35. Rein, M. and Meier, G.E.A. (1990a). On the Dynamics of Heterogeneous Shock Cavitation. Acustica 71:1–13.Google Scholar
  36. Rein, M. and Meier, G.E.A. (1990b). On the Influence of Different Parameters on Heterogeneous Shock Cavitation. J. Acoust. Soc. Am. 88:1921–1928.CrossRefGoogle Scholar
  37. Rein, M. (1993). Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res. 12:61.CrossRefGoogle Scholar
  38. Rein, M. (1995a). Wave phenomena during droplet impact. In: Morioka, S. and van Wijngaarden, L. (eds.), IUTAM Symposium on Waves in Liquid/Gas and Liquia/Vapor Two-Phase Systems, Kluwer Academic Publishers, 171–190.CrossRefGoogle Scholar
  39. Rein, M. (1995b). Nonlinear analysis of two-dimensional compressible liquid-liquid impact. European J. Mech. B/Fluids 14:301–322.MathSciNetMATHGoogle Scholar
  40. Rein, M. (1996). The transitional regime between coalescing and splashing drops. J. Fluid Mech. 306:145.CrossRefGoogle Scholar
  41. Rein, M. (2002). Capillary effects at newly formed liquid-liquid contacts. Phys. Fluids 14:411–414.MathSciNetCrossRefGoogle Scholar
  42. Richard, D. and Quéré, D. (2000). Bouncing water drops. Europhysics Letters 50:769–775.CrossRefGoogle Scholar
  43. Scheller, B. L. and Bousfield, D. W. (1995). Newtonian Drop Impact with a Solid surface. AIChE J. 41(6): 1357–1367.CrossRefGoogle Scholar
  44. Schotland, R. M. (1960). Experimental Results Relating to the Coalescence of Water Droplets with Water Surfaces. Disc. Faraday Soc. 30:72.CrossRefGoogle Scholar
  45. Sigler, J. and Mesler, R. (1990). The Behavior of the Gas Film Formed upon Drop Impact with a Liquid Surface. J. Colloid Interface Sci. 134:459.CrossRefGoogle Scholar
  46. Stow, C. D. and 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. London A 373:419–441.CrossRefGoogle Scholar
  47. Stuhlman Jr., O. (1932). The Mechanics of Effervescence. Physics (J. Appl. Phys.) 2:457–466.Google Scholar
  48. Thompson, J. J. and Newall, H. F. (1885). On the Formation of Vortex Rings by Drops falling into Liquids, and some allied Phenomena. Proc. R. Soc. London 39:417.CrossRefGoogle Scholar
  49. Thoroddson, S. T. and Sakakibara, J. (1998). Evolution of the fingering pattern of an impacting drop. Phys. Fluids 10:1359–1374.CrossRefGoogle Scholar
  50. Tomlinson, C. (1861). On the cohesion figures of liquids. Phil. Mag. Ser.4 22:249–261.Google Scholar
  51. Tomlinson, C. (1864). On the cohesion figures of liquids. Phil. Mag. Ser.4 28:354–364.Google Scholar
  52. van Wijngaarden, L. (1968). On the equations of motion for mixtures of liquid and gas bubbles. J. Fluid Mech. 33:465–474.CrossRefMATHGoogle Scholar
  53. Vardelle, A., Themelis, N. J., Dussoubs, B., Vardelle, M. and Fauchais, P. (1997). Transport and chemical rate phenomena in plasma sprays. High Temp. Material Processes 1:295–313.Google Scholar
  54. Walzel, P. (1980). Zerteilgrenze beim Tropfenaufprall. Chem.-Ing. Tech. 52:338–339.CrossRefGoogle Scholar
  55. Worthington, A. M. (1876). On the forms assumed by drops of liquids falling vertically on a horizontal plate. Proc. R. Soc. London 25:261–271.CrossRefGoogle Scholar
  56. Wu, J. Z. and Wu, J. M. (1996). Vorticity dynamics on boundaries. Adv. Appl. Mech. 32:119.CrossRefGoogle Scholar
  57. Yao, S.-C. (1994). Dynamics and Heat Transfer of Impacting Sprays. In: Tien, C.-L. (ed.), Ann. Rev. Heat Transfer, Begell House, New York, 351–382.Google Scholar

Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • Martin Rein
    • 1
  1. 1.Deutsches Zentrum für Luft- und RaumfahrtGöttingenGermany

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