Numerical simulation of the head-on collision of two drops in a vertical channel

  • Maryam Hassanzadeh
  • Afshin Ahmadi NadooshanEmail author
  • Morteza Bayareh
Technical Paper


The head-on collision between two oil drops in a vertical channel is investigated numerically by using a volume-of-fluid method. Three-dimensional simulations are examined for laminar, fully developed, unsteady, and incompressible fluid flow. The effects of the Weber and Reynolds numbers and the density ratio on the collision dynamics are investigated before and after the drop coalescence. The results show that the deformation of drops increases and gap thickness decreases as the Weber and Reynolds numbers increase. The drops collide with each other faster for higher density ratios. It is found that the drops elongation has a sinusoidal behavior after collision due to the tendency of the drops to gain a spherical shape. Also, the results demonstrate that the elongation increases with increasing of the Weber and Reynolds numbers and decreasing of the density ratio.


Drop collision Two-phase flow VOF method Reynolds number Weber number Eotvos number 

List of symbols


The minor semi-axes of the drop (m)


Drop diameter (m)


The drop elongation (m)


Eotvos number


Force (N)


Gravity acceleration


Channel height (m)




The major semi-axes of the drop (m)


Channel length (m)


Normal vector (m)


Ohnesorge number


Pressure (Pa)


Reynolds number


Time (s)


Dimensionless time


Velocity (m/s)


Weber number


Position (m)

Greek letters


Density ratio


Viscosity ratio


Dynamic viscosity (N. s/m2)


Kinematic viscosity (m2/s)


Density (kg/m3)


Surface tension (N/s)


1, 2

Number of drop








Surface tension



  1. 1.
    Taylor GI (1934) The deformation of emulsions in definable fields of flow. Proc R Soc (Lond) Ser A 146:501–523CrossRefGoogle Scholar
  2. 2.
    Bayareh M, Mortazavi S (2013) Equilibrium position of a buoyant drop in Couette and Poiseuille flows at finite Reynolds numbers. J Mech 20:53–58CrossRefGoogle Scholar
  3. 3.
    Bayareh M, Mortazavi S (2011) Binary collision of drops in simple shear flow at finite Reynolds numbers. Adv Eng Softw 42:604–611CrossRefGoogle Scholar
  4. 4.
    Jiang X, James AJ (2007) Numerical simulation of the head-on collision of two equal-sized drops with van der Waals forces. J Eng Math 59:99–121MathSciNetCrossRefGoogle Scholar
  5. 5.
    Pan Y, Suga K (2005) Numerical simulation of binary liquid droplet collision. Phys Fluid 17:082105CrossRefGoogle Scholar
  6. 6.
    Bayareh M, Mortazavi S (2011) Three-dimensional numerical simulation of drops suspended in simple shear flow at finite Reynolds numbers. Int J Multiph Flow 37:1315–1330CrossRefGoogle Scholar
  7. 7.
    Wei YK, Li ZH, Zhang YF (2017) Simulations of coalescence of two colliding liquid drops using lattice Boltzmann method. J Comput Multiph Flows 21:147–156MathSciNetCrossRefGoogle Scholar
  8. 8.
    Goodarzi Z, Ahmadi Nadooshan A, Bayareh M (2018) Numerical investigation of off-center binary collision of droplets in a horizontal channel. J Braz Soc Mech Sci Eng 40:1–10CrossRefGoogle Scholar
  9. 9.
    Fortes AF, Joseph DD, Lundgren TS (1987) Nonlinear mechanics of fluidization of beds of spherical particles. J Fluid Mech 177:467–483CrossRefGoogle Scholar
  10. 10.
    Inamuro T, Ogata T, Tajima S, Konishi N (2004) A lattice Boltzmann method for incompressible two-phase flows with large density differences. J Comput Phys 198:628–644CrossRefGoogle Scholar
  11. 11.
    Dai M, Schmidt DP (2005) Numerical simulation of head-on droplet collision: effect of viscosity on maximum deformation. Phys Fluids 17:326–329CrossRefGoogle Scholar
  12. 12.
    Inamuro T, Tajima S, Ogino F (2004) Lattice Boltzmann simulation of droplet collision dynamics. Int J Heat Mass Transf 47:4649–4657CrossRefGoogle Scholar
  13. 13.
    Sun Z, Xi G, Chen X (2009) Mechanism study of deformation and mass transfer for binary droplet collisions with particle method. Phys Fluids 21:296–309CrossRefGoogle Scholar
  14. 14.
    Yoon Y, Borrell M, Park CC, Leal G (2005) Viscosity ratio effects on the coalescence of two equal-sized drops in a two-dimensional linear flow. J Fluid Mech 525:355–379CrossRefGoogle Scholar
  15. 15.
    Mortazavi S, Tryggvasson G (1999) A numerical study of the motion of drop in poiseuille flow, part 1: lateral migration of one drop. J Fluid Mech 411:325–350CrossRefGoogle Scholar
  16. 16.
    Bayareh M, Mortazavi S (2009) Numerical simulation of the motion of a single drop in a shear flow at finite Reynolds numbers. Iran J Sci Technol Trans B Eng 33(B5):441–452Google Scholar
  17. 17.
    Bayareh M, Mortazavi S (2009) Geometry effects on the interaction of two equal-sized drops in simple shear flow at finite Reynolds numbers, 5th international conference: computational methods in multiphase flow. WIT Trans Eng Sci 63:379–388Google Scholar
  18. 18.
    Roisman IV, Planchette C, Lorenceau E, Brenn G (2012) Binary collisions of drops of immiscible liquids. J Fluid Mech 690:512–535CrossRefGoogle Scholar
  19. 19.
    Ray B, Biswas G, Sharma A, Welch SWJ (2013) CLSVOF method to study consecutive drop impact on liquid pool. Int J Numer Methods Heat Fluid Flow 23:143–157MathSciNetCrossRefGoogle Scholar
  20. 20.
    Mortazavi S, Tafreshi MM (2013) On the behavior of suspension of drops on an inclined surface. Phys A 302:58–71CrossRefGoogle Scholar
  21. 21.
    Tasnim SH, Collins MR (2005) Suppressing natural convection in a differentially heated square cavity with an arc shaped baffle. Int Commun Heat Mass Trans 32:94–106CrossRefGoogle Scholar
  22. 22.
    Mousavi Tilehboni SE, Sedighi K, Farhadi M, Fattahi E (2013) Lattice Boltzmann simulation of deformation and breakup of a droplet under gravity using interparticle potential model. Int J Eng 26:781–794CrossRefGoogle Scholar
  23. 23.
    Nikolopoulos N, Theodorakakos A, Bergeles G (2009) Off-center binary collision of droplets: a numerical investigation. Int J Heat Mass Transf 52:4160–4174CrossRefGoogle Scholar
  24. 24.
    Amiri M, Mortazavi S (2013) Three-dimensional numerical simulation of sedimenting drops inside a vertical channel. Int J Multiph Flow 56:40–53CrossRefGoogle Scholar
  25. 25.
    Nobari MR, Jan Y-J, Tryggvason G (1996) Head-on collision of drops—a numerical simulations. Phys Fluid 8(1):29–42CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringShahrekord UniversityShahrekordIran

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