Skip to main content Accessibility help

Colliding drops as coalescing and fragmenting liquid springs

  • C. Planchette (a1), H. Hinterbichler (a1), M. Liu (a2), D. Bothe (a2) and G. Brenn (a1)...


A universal modelling approach of drop fragmentation after head-on drop collisions is presented. In this approach, the colliding drops are seen as liquid springs that coalesce, compress and relax, leading the merged drop to break up if it reaches a critical aspect ratio. Combining energetic balance of the compression and relaxation phases with a Rayleigh-like criterion, we deduce the fragmentation threshold velocity for the collision of two and three drops of the same liquid and of two drops of immiscible liquids. Predictions and experimental results obtained for these three kinds of collisions using various liquids and drop sizes are found to be in good agreement over a wide domain whose boundaries are discussed.


Corresponding author

Email address for correspondence:


Hide All
Ashgriz, N. & Poo, J. Y. 1990 Coalescence and separation in binary collisions of liquid drops. J. Fluid Mech. 221, 183204.
Bazilevskii, A. V., Voronkov, S. I., Entov, V. M. & Rozhkov, A. N. 1981 Orientational effects in the decomposition of streams and strands of diluted polymer solutions. Sov. Phys. Dokl. 26, 333335.
Biance, A.-L., Chevy, F., Clanet, C., Lagubeau, G. & Quéré, D. 2006 On the elasticity of an inertial liquid shock. J. Fluid Mech. 554, 4766.
Brazier-Smith, P. R., Jennings, S. G. & Latham, J. 1972 The interaction of falling water drops: coalescence. Proc. R. Soc. Lond. 326, 393408.
Chen, R.-H. & Chen, C.-T. 2006 Collisions between immiscible drops with large surface tension difference: diesel oil and water. Exp. Fluids 41, 453461.
Dai, M. & Schmidt, D. P. 2005 Numerical simulation of head-on droplet collision: effect of viscosity on maximum deformation. Phys. Fluids 17, 041701.
Focke, C. & Bothe, D. 2011 Computational analysis of binary collisions of shear-thinning droplets. J. Non-Newtonian Fluid Mech. 166, 799810.
Focke, C. & Bothe, D. 2012 Direct numerical simulation of binary off-center collisions of shear thinning droplets at high Weber numbers. Phys. Fluids 24, 073105.
Focke, C., Kuschel, M., Sommerfeld, M. & Bothe, D. 2013 Collision between high and low viscosity droplets: direct numerical simulations and experiments. Intl J. Multiphase Flow 56, 8192.
Gotaas, C., Havelka, P., Jakobsen, H. A., Svendsen, H. F., Hase, M., Roth, N. & Weigand, B. 2007 Effect of viscosity on droplet–droplet collision outcome: experimental study and numerical comparison. Phys. Fluids 19 (10), 102106.
Hinterbichler, H., Planchette, C. & Brenn, G. 2015 Ternary drop collisions. Exp. Fluids 56, 190.
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201225.
Jiang, Y. J., Umemura, A. & Law, C. K. 1992 An experimental investigation in the collision behaviour of hydrocarbon droplets. J. Fluid Mech. 234, 171190.
Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski, S. & Zanetti, G. 1994 Modelling merging and fragmentation in multiphase flows with surfer. J. Comput. Phys. 113, 134147.
Liu, M. & Bothe, D. 2016 Numerical study of head-on droplet collisions at high Weber numbers. J. Fluid Mech. 789, 785805.
Lycett-Brown, D., Luo, K. H., Liu, R. & Lv, P. 2014 Binary droplet collision simulations by a multiphase cascaded lattice Boltzmann method. Phys. Fluids 26 (2), 023303.
Montgomery, D. N. 1970 Collision and coalescence of water drops. J. Atmos. Sci. 28, 291293.
Nikolopoulos, N., Nikas, K.-S. & Bergeles, G. 2009 A numerical investigation of central binary collision of droplets. Comput. Fluids 38, 11911202.
Nobari, M. R., Jan, Y.-J. & Tryggvason, G. 1996 Head-on collision of drops – a numerical investigation. Phys. Fluids 8, 2942.
Okumura, K., Chevy, F., Richard, D., Quéré, D. & Clanet, C. 2003 Water spring: a model for bouncing drops. Europhys. Lett. 62 (2), 237243.
Planchette, C., Lorenceau, E. & Brenn, G. 2012 The onset of fragmentation in binary liquid drop collisions. J. Fluid Mech. 702, 525.
Qian, J. & Law, C. K. 1997 Regimes of coalescence and separation in droplet collision. J. Fluid Mech. 331, 5980.
Rayleigh, Lord 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. 29, 7197.
Richard, D., Clanet, C. & Quéré, D. 2002 Surface phenomena: contact time of a bouncing drop. Nature 417 (6891), 811.
Roisman, I. V. 2004 Dynamics of inertia-dominated binary drop collisions. Phys. Fluids 16 (9), 34383449.
Roisman, I. V. 2009a Inertia dominated drop collisions. i. On the universal flow in the lamella. Phys. Fluids 21 (5), 052103.
Roisman, I. V. 2009b Inertia-dominated drop collisions. ii. An analytical solution of the Navier–Stokes equations for spreading viscous film. Phys. Fluids 21 (5), 052104.
Roisman, I. V., Planchette, C., Lorenceau, E. & Brenn, G. 2011 Binary collisions of drops of immiscible liquids. J. Fluid Mech. 690, 512535.
Saroka, M. D., Ashgriz, N. & Movassat, M. 2012 Numerical investigation of head-on binary drop collisions in a dynamically inert environment. J. Appl. Fluid Mech. 5 (1), 2337.
Stone, H. A. & Leal, L. G. 1989 Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J. Fluid Mech. 198, 399427.
Symon, K. R. 1971 Mechanics, 3rd edn. Addison-Wesley.
Taylor, G. I. 1959 The dynamics of thin sheets of fluid ii. Waves on fluid sheets. Proc. R. Soc. Lond. A 263, 296312.
Willis, K. D. & Orme, M. 2000 Experiments on the dynamics of droplet collisions in a vacuum. Exp. Fluids 29, 347358.
Willis, K. D. & Orme, M. 2003 Binary droplet collisions in a vacuum environment: an experimental investigation on the role of viscosity. Exp. Fluids 34, 2841.
Yeo, Y., Chen, A. U., Basaran, O. A. & Park, K. 2004 Solvent exchange method: a novel microencapsulation technique using dual microdispensers. Pharmaceut. Res. 21, 14191427.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed