Droplet Collision

  • G. BrennEmail author


We put together the state of knowledge on binary collisional interactions of droplets in a gaseous environment. Phenomena observed experimentally after drop collisions, such as coalescence, bouncing, reflexive separation and stretching separation, are discussed. Collisions of drops of the same liquid and of different – miscible or immiscible – liquids, as well as collisions of drops of equal and different size are addressed. Collisions of drops of immiscible liquids may lead to an unstable interaction which is not observed with drops of equal or miscible liquids. Regimes characterized by the various phenomena are depicted in nomograms of the Weber number and the non-dimensional impact parameter. The state-of-the-art in the simulation of binary droplet collisions is reviewed. Overall three different methods are represented in the literature on these simulations. We discuss models derived from numerical simulations and from experiments, which are presently in use for simulations of spray flows to account for the influence of collisional interactions of the spray droplets on the drop size spectrum of the spray.


Binary drop collisions Bouncing Coalescence Collision model Crossing separation Gaseous environment Immiscible liquids Lattice-Boltzmann simulation Miscible liquids Navier–Stokes simulation Reflexive separation Satellite droplets Spray flow simulation SPH simulation Stretching separation 


  1. 1.
    P. R. Brazier-Smith, S. G. Jennings, J. Latham: Accelerated rates of rainfall, Nature 232, 112–113 (1971).CrossRefGoogle Scholar
  2. 2.
    D. M. Whelpdale, R. List: The coalescence process in raindrop growth, J. Geophys. Res. 76, 2836–2856 (1971).CrossRefGoogle Scholar
  3. 3.
    R. List, J. R. Gillespie: Evolution of raindrop spectra with collision-induced breakup, J. Atmos. Sci. 33, 2007–2013 (1976).CrossRefGoogle Scholar
  4. 4.
    S. G. Bradley, C.D Stow: On the production of satellite droplets during collisions between water drops falling in still air, J. Atmos. Sci. 36, 494–500 (1979).CrossRefGoogle Scholar
  5. 5.
    T. B. Low, R. List: Collision, coalescence and breakup of raindrops. Part I: Experimentally established coalescence efficiencies and fragment size distributions in breakup, J. Atmos. Sci. 39, 1591–1606 (1982).CrossRefGoogle Scholar
  6. 6.
    D. J. Ryley, B. N. Bennett-Cowell: The collision behaviour of steam-borne water drops, Int. J. Mech. Sci. 9, 817–833 (1967).CrossRefGoogle Scholar
  7. 7.
    P. R. Brazier-Smith, S. G. Jennings, J. Latham: An investigation of the behaviour of drops and drop-pairs subjected to strong electrical forces, Proc. R. Soc. Lond. A 325, 363–376 (1971).CrossRefGoogle Scholar
  8. 8.
    A. M. Podvysotsky, A. A. Shraiber: Coalescence and break-up of drops in two-phase flows, Int. J. Multiphase Flow 10, 195–209 (1984).CrossRefGoogle Scholar
  9. 9.
    N. Ashgriz, P. Givi: Binary collision dynamics of fuel droplets, Heat Fluid Flow 8, 205–210 (1987).CrossRefGoogle Scholar
  10. 10.
    N. Ashgriz, P. Givi: Coalescence efficiencies of fuel droplets in binary collisions, Int. Commun. Heat Mass Transfer 16, 11–20 (1989).CrossRefGoogle Scholar
  11. 11.
    G. Brenn, A. Frohn: Collision and merging of two equal droplets of propanol, Exp. Fluids 7, 441–446 (1989).CrossRefGoogle Scholar
  12. 12.
    G. Brenn, A. Frohn: Collision and coalescence of droplets of various liquids, J. Aerosol Sci. 20, 1027–1030 (1989).CrossRefGoogle Scholar
  13. 13.
    A. Menchaca-Rocha, A. Cuevas, M. Chapa, M. Silva: Rotating-liquid-drop model limit tested on macroscopic drops, Phys. Rev. E 47, 1433–1436 (1993).CrossRefGoogle Scholar
  14. 14.
    C. K. Law: Dynamics of droplet collision, Proceedings of the IUTAM Symposium Mechanics and Combustion of Droplets and Sprays, Tainan, Taiwan, pp. 99–118 (1994).Google Scholar
  15. 15.
    J. Qian, C. K. Law: Effects of liquid and ambient gas properties on droplet collision, AIAA paper 94–0681 (1994).Google Scholar
  16. 16.
    A. Menchaca-Rocha, F. Huidobro, A. Martinez-Davalos, K. Michaelian, A. Perez, V. Rodriguez, N. Cârjan: Coalescence and fragmentation of colliding mercury drops, J. Fluid Mech. 346, 291–318 (1997).CrossRefGoogle Scholar
  17. 17.
    M. Orme: Experiments on droplet collisions, bounce, coalescence and disruption, Prog. Energy Combust. Sci. 23, 65–79 (1997).CrossRefGoogle Scholar
  18. 18.
    C. C. Hung, J. K. Martin: Collisional behavior of hydrocarbon droplets, Proceedings of the 10th Annual Conference Liquid Atomization and Spray Systems (ILASS Americas), Ottawa, Ontario (CDN) 1997, pp. 62–66 (1997).Google Scholar
  19. 19.
    J. Eggers, J. R. Lister, H. A. Stone: Coalescence of liquid drops, J. Fluid Mech. 401, 293–310 (1999).zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    L. Duchemin, J. Eggers, C. Josserand: Inviscid coalescence of drops, J. Fluid Mech. 487, 167–178 (2003).zbMATHCrossRefGoogle Scholar
  21. 21.
    F. Mashayek, N. Ashgriz, W. J. Minkowycz, B. Shotorban: Coalescence collision of liquid drops, Int. J. Heat Mass Transfer 46, 77–89 (2003).zbMATHCrossRefGoogle Scholar
  22. 22.
    G. A. Bach, D. L. Koch, A. Gopinath: Coalescence and bouncing of small aerosol droplets, J. Fluid Mech. 518, 157–185 (2004).zbMATHCrossRefGoogle Scholar
  23. 23.
    P. Duru, D. L. Koch, C. Cohen: Experimental study of turbulence-induced coalescence in aerosols, Int. J. Multiphase Flow 33, 987–1005 (2007).CrossRefGoogle Scholar
  24. 24.
    C. Gotaas, P. Havelka, H. A. Jakobsen, H. F. Svendsen, M. Hase, N. Roth, B. Weigand: Effect of viscosity on droplet-droplet collision outcome: experimental study and numerical comparison, Phys. Fluids 19, paper 102106 (2007).Google Scholar
  25. 25.
    F.-C. Wang, J.-T. Feng, Y.-P. Zhao: The head-on colliding process of binary liquid droplets at low velocity: high-speed photography experiments and modelling, J. Colloid Interface Sci. 326, 196–200 (2008).CrossRefGoogle Scholar
  26. 26.
    C. Planchette, E. Lorenceau, G. Brenn: Liquid encapsulation by binary collisions of immiscible liquid drops, Colloids Surf. A: Physicochem. Eng. Aspects 365, 89–94 (2010).Google Scholar
  27. 27.
    R. W. Park, E. J., Crosby: A device for producing controlled collisions between pairs of drops, Chem. Eng. Sci. 20, 39–45 (1965).CrossRefGoogle Scholar
  28. 28.
    J. M. Schneider, N. R. Lindblad, C. D. Hendricks: An apparatus to study the collision and coalescence of liquid aerosols, J. Colloid Sci. 20, 610–616 (1965).CrossRefGoogle Scholar
  29. 29.
    J. R. Adam, N. R. Lindblad, C. D. Hendricks: The collision, coalescence, and disruption of water droplets, J. Appl. Phys. 39, 5173–5180 (1968).CrossRefGoogle Scholar
  30. 30.
    J. Qian, C. K. Law: Regimes of coalescence and separation in droplet collision, J. Fluid Mech. 331, 59–80 (1997).CrossRefGoogle Scholar
  31. 31.
    K. D. Willis, M. Orme: Experiments on the dynamics of droplet collisions in a vacuum, Exp. Fluids 29, 347–358 (2000).CrossRefGoogle Scholar
  32. 32.
    K. Willis, M. Orme: Binary droplet collisions in a vacuum environment: an experimental investigation of the role of viscosity, Exp. Fluids 34, 28–41 (2003).Google Scholar
  33. 33.
    G. Brenn, St. Kalenderski, I. Ivanov: Investigation of the stochastic collisions of drops produced by Rayleigh breakup of two laminar liquid jets, Phys. Fluids 9, 349–364 (1997).CrossRefGoogle Scholar
  34. 34.
    Y. J. Jiang, A. Umemura, C. K. Law: An experimental investigation on the collision behaviour of hydrocarbon droplets, J. Fluid Mech. 234, 171–190 (1992).CrossRefGoogle Scholar
  35. 35.
    Y. Pan, K. Suga: Numerical simulation of binary liquid droplet collision, Phys. Fluids 17, paper 082105 (2005).Google Scholar
  36. 36.
    N. Ashgriz, J. Y. Poo: Coalescence and separation in binary collisions of liquid drops, J. Fluid Mech. 221, 183–204 (1990).CrossRefGoogle Scholar
  37. 37.
    A. Y. Tong, Z. Y. Wang: Relaxation dynamics of a free elongated liquid ligament, Phys. Fluids 19, paper 092101 (2007).Google Scholar
  38. 38.
    G. Brenn, V. Kolobaric: Satellite droplet formation by unstable binary drop collisions, Phys. Fluids 18, paper 087101 (2006).Google Scholar
  39. 39.
    N. Roth, M. Rieber, A. Frohn: High energy head-on collision of droplets, Proceedings of the Annual Conference Liquid Atomization and Spray Systems (ILASS Europe), Toulouse, July 1999.Google Scholar
  40. 40.
    J.-P. Estrade, H. Carentz, G. Lavergne, Y. Biscos: Experimental investigation of dynamic binary collision of ethanol droplets – a model for droplet coalescence and bouncing, Int. J. Heat Fluid Flow 20, 486–491 (1999).CrossRefGoogle Scholar
  41. 41.
    J.-P. Estrade, P. Berthoumieu, G. Lavergne, Y. Biscos: Experimental investigation of dynamic binary collision of various liquids, Proceedings of the 8th International Symposium Flow Visualization, Sorrento, Italy, September 1998.Google Scholar
  42. 42.
    P. R. Brazier-Smith, S. G. Jennings, J. Latham: The interaction of falling water drops: coalescence, Proc. R. Soc. Lond. A 326, 393–408 (1972).CrossRefGoogle Scholar
  43. 43.
    V. A. Arkhipov, G. S. Ratanov, V. F. Trofimov: Experimental investigation of the interaction of colliding droplets, J. Appl. Mech. Tech. Phys. 2, 73–77 (1978).Google Scholar
  44. 44.
    V. A. Arkhipov, I. M. Vasenin, V. F. Trofimov: Stability of colliding drops of ideal liquid, J. Appl. Mech. Tech. Phys. 3, 95–98 (1983).Google Scholar
  45. 45.
    T.-C. Gao, R.-H. Chen, J.-Y. Pu, T.-H. Lin: Collision between an ethanol drop and a water drop, Exp. Fluids 38, 731–738 (2005).CrossRefGoogle Scholar
  46. 46.
    R. H. Chen: Diesel-diesel and diesel-ethanol drop collisions, Appl. Thermal Eng. 27, 604–610 (2007).CrossRefGoogle Scholar
  47. 47.
    C. H. Wang, W. G. Hung, S. Y. Fu, W. C. Huang, C. K. Law: On the burning and microexplosion of collision-generated two-component droplets: miscible fuels, Combust. Flame 134, 289–300 (2003).CrossRefGoogle Scholar
  48. 48.
    S. F. Simpson, J. R. Kincaid, F. J. Holler: Microdroplet mixing for rapid reaction kinetics with Raman spectrometric detection, Anal. Chem. 55, 1420–1422 (1983).CrossRefGoogle Scholar
  49. 49.
    R. H. Chen, C. T. Chen: Collision between immiscible drops with large surface tension difference: diesel oil and water, Exp. Fluids 41, 453–461 (2006).CrossRefGoogle Scholar
  50. 50.
    C. Planchette, G. Brenn: Liquid encapsulation by binary collisions of immiscible liquid drops, Proceedings of the 11th International Conference Liquid Atomization Spray Systems (ICLASS 2009), Vail, abstract ICLASS2009–243.Google Scholar
  51. 51.
    P. T. Yue, J. J. Feng, C. Liu, J. Shen: Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids, J. Non-Newtonian Fluid Mech. 129, 163–176 (2005).zbMATHCrossRefGoogle Scholar
  52. 52.
    M. Motzigemba, N. Roth, D. Bothe, H.-J. Warnecke, J. Prüss, K. Wielage, B. Weigand: The effect of non-Newtonian flow behaviour on binary droplet collisions: vof-simulation and experimental analysis, Proceedings of the 18th Annual Conference Liquid Atomization Spray Systems (ILASS Europe), Zaragoza, Spain, pp. 559–564 (2002).Google Scholar
  53. 53.
    O. Kurt, U. Fritsching, G. Schulte: Secondary droplet formation during binary suspension droplet collision, Atomization Sprays 19, 457–472 (2009).CrossRefGoogle Scholar
  54. 54.
    M. Rieber, A. Frohn: Three-dimensional Navier-Stokes simulation of binary collisions between droplets of equal size, J. Aerosol Sci. 26(Suppl. 1), S929–S930 (1995).CrossRefGoogle Scholar
  55. 55.
    M. R. Nobari, Y.-J. Jan, G. Tryggvason: Head-on collision of drops – a numerical investigation, Phys. Fluids 8, 29–42 (1996).zbMATHCrossRefGoogle Scholar
  56. 56.
    M. R. H. Nobari, G. Tryggvason: Numerical simulations of three-dimensional drop collisions, AIAA J. 34, 750–755 (1996).CrossRefGoogle Scholar
  57. 57.
    M. Rieber, A. Frohn: Navier-Stokes simulation of droplet collision dynamics, Proceedings of the 7th International Symposium CFD, Beijing, China, pp. 520–525 (1997).Google Scholar
  58. 58.
    M. Z. Dai, D. P. Schmidt: Numerical simulation of head-on droplet collision: effect of viscosity on maximum deformation, Phys. Fluids 17, paper 041701 (2005).Google Scholar
  59. 59.
    S. Tanguy, A. Berlemont: Application of a level set method for simulation of droplet collisions, Int. J. Multiphase Flow 31, 1015–1035 (2005).zbMATHGoogle Scholar
  60. 60.
    S. P. Decent, G. Sharpe, A. J. Shaw, P. M. Suckling: The formation of a liquid bridge during the coalescence of drops, Int. J. Multiphase Flow 32, 717–738 (2006).zbMATHCrossRefGoogle Scholar
  61. 61.
    X. Jiang, A. J. James: Numerical simulation of the head-on collision of two equal-sized drops with van der Waals forces, J. Eng. Math. 59, 99–121 (2007).zbMATHCrossRefMathSciNetGoogle Scholar
  62. 61.
    N. Nikolopoulos, K.-S. Nikas, G. Bergeles: A numerical investigation of central binary collision of droplets, Comp. Fluids 38, 1191–1202 (2009).CrossRefGoogle Scholar
  63. 63.
    M. Schelkle, M. Rieber, A. Frohn: Numerische Simulation von Tropfenkollisionen, Spektrum der Wissenschaft 1, 72–79 (1999).Google Scholar
  64. 64.
    T. Inamuro, S. Tajima, F. Ogino: Lattice Boltzmann simulation of droplet collision dynamics, Int. J. Heat Mass Transfer 47, 4649–4657 (2004).zbMATHCrossRefGoogle Scholar
  65. 65.
    B. Sakakibara, T. Inamuro: Lattice Boltzmann simulation of collision dynamics of two unequal-size droplets, Int. J. Heat Mass Transfer 51, 3207–3216 (2008).zbMATHCrossRefGoogle Scholar
  66. 66.
    M. Schelkle: Lattice-Boltzmann-Verfahren zur Simulation dreidimensionaler Zweiphasenströmungen mit freien Oberflächen, Ph.D. thesis University of Stuttgart, Shaker, Aachen, Germany (1997).Google Scholar
  67. 67.
    M. Schelkle, A. Frohn: Three-dimensional lattice Boltzmann simulations of binary collisions between equal droplets, J. Aerosol Sci. 26(Suppl. 1), S145–S146 (1995).CrossRefGoogle Scholar
  68. 68.
    Y. Meleán, L. Di G. Sigalotti: Coalescence of colliding van der Waals liquid drops, Int. J. Heat Mass Transfer 48, 4041–4061 (2005).zbMATHCrossRefGoogle Scholar
  69. 69.
    J. K. Dukowicz: A particle-fluid numerical model for liquid sprays, J. Comp. Phys. 35, 229–253 (1980).zbMATHCrossRefMathSciNetGoogle Scholar
  70. 70.
    G. H. Ko, H. S. Ryou: Modeling of droplet collision-induced breakup process, Int. J. Multiphase Flow 31, 723–738 (2005).zbMATHCrossRefGoogle Scholar
  71. 71.
    L. E. Kollár, M. Farzaneh, A. R. Karev: Modeling droplet collision and coalescence in an icing wind tunnel and the influence of these processes on droplet size distribution, Int. J. Multiphase Flow 31, 69–92 (2005).zbMATHCrossRefGoogle Scholar
  72. 72.
    A. Kitron T. Elperin, A. Tamir: Stochastic modelling of the effects of liquid droplet collisions in impinging streams absorbers and combustors, Int. J. Multiphase Flow 17, 247–265 (1991).zbMATHCrossRefGoogle Scholar
  73. 73.
    M. Gavaises, A. Theodorakakos, G. Bergeles, G. Brenn: Evaluation of the effect of droplet colllisions on spray mixing, Proc. Inst. Mech. Eng. 210, 465–475 (1996).CrossRefGoogle Scholar
  74. 74.
    P. Villedieu, J. Hylkema: Une méthode particulaire aléatoire reposant sur une équation cinétique pour la simulation numérique des sprays denses de gouttelettes liquides, C.R. Acad. Sci. Paris vol. 325, Série I, 323–328 (1997).Google Scholar
  75. 75.
    J. Dohmann: Dispersion and coagulation of droplets in intersecting sprays, Chem. Eng. Technol. 21, 341–345 (1998).CrossRefGoogle Scholar
  76. 76.
    R. Kaesemann, H. Fahlenkamp: The meaning of droplet-droplet interaction for the wet flue-gas cleaning process, Chem. Eng. Technol. 25, 739–742 (2002).CrossRefGoogle Scholar
  77. 77.
    D. P. Schmidt, C. J. Rutland: Reducing grid dependency in droplet collision modelling, J. Eng. Gas Turbines Power 126, 227–233 (2004).CrossRefGoogle Scholar
  78. 78.
    G. H. Ko, H. S. Ryou: Droplet collision processes in an inter-spray impingement system, J. Aerosol Sci. 36, 1300–1321 (2005).CrossRefGoogle Scholar
  79. 79.
    C. Bautsch, H. Fahlenkamp: Detailed simulation of wet flue-gas-desulphurisation scrubbers with CFD, Proceedings of the International Conference on Liquid Atomization Spray Systems (ICLASS 2006), Kyoto, Japan, paper ICLASS06–238.Google Scholar
  80. 80.
    S. Hou, D. P. Schmidt: Adaptive collision meshing and satellite droplet formation in spray simulations, Int. J. Multiphase Flow 32, 935–956 (2006).zbMATHCrossRefGoogle Scholar
  81. 81.
    L. E. Kollár, M. Farzaneh: Modeling the evolution of droplet size distribution in two-phase flows, Int. J. Multiphase Flow 33, 1255–1270 (2007).CrossRefGoogle Scholar
  82. 82.
    S. Hou, D. P. Schmidt: Interaction mechanisms between closely spaced sprays, SAE Technical Paper 2008-01-0946 (2008).Google Scholar
  83. 83.
    P. J. O’Rourke, F. V. Bracco: Modelling of drop interactions in thick sprays and a comparison with experiments, Proc. Inst. Mech. Eng. 9, 101–116 (1980).Google Scholar
  84. 84.
    D. P. Schmidt, C. J. Rutland: A new droplet collision algorithm. J. Comp. Phys. 164, 62–80 (2000).zbMATHCrossRefGoogle Scholar
  85. 85.
    H.-Y. Zhang, Y.-S. Zhang, B. Xu, C.-I. Mo: Extension of O’Rourke droplet collision model: application to diesel spray of single-hole injector, SAE Technical Paper 2006-01-3335 (2006).Google Scholar
  86. 86.
    P. Stralin, F. Wahlin, N. Nordin, H.-E. Angström: A Lagrangian collision model applied to an impinging spray nozzle, SAE Technical Paper 2006-01-3331 (2006).Google Scholar
  87. 87.
    A. Munnannur, R. D. Reitz: A new predictive model for fragmenting and non-fragmenting binary droplet collisions, Int. J. Multiphase Flow 33, 873–896 (2007).CrossRefGoogle Scholar
  88. 88.
    S. L. Post, J. Abraham: Modeling the outcome of drop-drop collisions in Diesel sprays, Int. J. Multiphase Flow 28, 997–1019 (2002).zbMATHCrossRefGoogle Scholar
  89. 89.
    T. L. Georjon, R. D. Reitz: A drop-shattering collision model for multidimensional spray computations, Atomization Sprays 9, 231–254 (1999).Google Scholar
  90. 90.
    G. Brenn, D. Valkovska, K. D. Danov: The formation of satellite droplets by unstable binary drop collisions, Phys. Fluids 13, 2463–2477 (2001).CrossRefGoogle Scholar

Copyright information

© Springer US 2011

Authors and Affiliations

  1. 1.Graz University of TechnologyInstitute of Fluid Mechanics and Heat TransferGrazAustria

Personalised recommendations