In this study, the SPH method is applied to simulate for the first time the multiple hydrodynamics collisions and the formation of clusters of equally sized liquid drops in three-dimensional space. Smoothed Particle Hydrodynamics is a Lagrangian mesh-free formalism and has been useful to model continuous fluid. This formalism is employed to solve the Navier-Stokes equations by replacing the fluid with a set of particles. These particles are interpolation points from which properties of the fluid can be determined. We observe that when the velocity of collision varies between 0.2 mm/ms and 30.0 mm/ms different results may arise, such as: coalescence, fragmentation and formation of clusters of liquid drops. The velocity vector fields formed inside the drops during the collision process are shown.
References
1.
ShahP.S.FanL.T.KaoI.C. and EricksonL.E., Modeling of growth processes with two liquid phases: A review of drop phenomena, mixing, and growth, Adv. Appl. Microbiol. 15, 1972, 367–414.
2.
ParkJ.Y. and BlairL.M., The effect of coalescence on drop size distribution in an agitated liquid–liquid dispersion, Chem. Eng. Sci.30, 1975, 1057–1064.
3.
RourkeP.J. and BraccoF.V., Modelling of drop interactions in thick sprays and a comparison with experiments, in: Stratified Charged Auto Engineering Conference, Institute of Mechanical Engineering Publications101, 1980.
4.
BradleyS.G. and StowC.D., Collision between liquid drops, Philos. Trans. R. Soc. London Ser. A.287, 1978, 635–642.
5.
AshgrizN. and PooJ.Y., Coalescence and separation of binary collisions of liquid drops, J. Fluid Mech. 221, 1990, 183–204.
6.
LiD., Coalescence between two small bubbles or drops, J. Colloid Interface Sci. 163, 1994, 108–119.
7.
ChenJ.D., A model of coalescence between two equal-sized spherical drops or bubbles, J. Colloid Interface Sci. 107, 1985, 209–220.
8.
FooteG.B., The water drop rebound problem: Dynamics of collision, J. Atmos. Sci.32, 1974, 390–401.
9.
AshgrizN. and GiviP., Binary collision dynamics of fuel droplets, Int. J. Heat Fluid Flow8, 1987, 205–208.
10.
AshgrizN. and GiviP., Coalescence efficiencies of fuel droplets in binary collisions, Int. Commun. Heat Mass Transfer16, 1989, 11–17.
11.
BrennG. and FrohnA., Collision and merging of two equal droplets of propanol, Exp. Fluids7, 1989, 441–446.
12.
JiangY.J.UmemuraA. and LawC.K., An experimental investigation on the collision behaviour of hydrocarbon droplets, J. Fluid Mech. 234, 1992, 171–190.
13.
Menchaca-RochaA.Martinez-DavalosA. and NuñezR., Coalescence of liquid drops by surface tension, Phys. Rev. E.63, 2001, 1–11.
14.
CristiniV.BawzdziewiczJ. and LoewenbergM., An Adaptive Mesh Algorithm for Evolving Surfaces: Simulations of Drop Breakup and Coalescence, J. Comput. Phys.168, 2001, 445–463.
15.
MashayekF.AshgrizN.MinkowyczW.J. and ShotorbanB., Coalescence collision of liquid drops, Int. J. Heat Mass Trans. 46, 2003, 77–89.
16.
Menchaca-RochaA.HuidobroF.Martinez-DavalosA.MichaelianK.PerezA.RodriguezV. and CarjanN., Coalescence and fragmentation of colliding mercury drops, J. Fluid Mech. 346, 1997, 291–318.
17.
EggersJ.ListerJ.R. and StoneH.A., Coalescence of liquid drops, J. Fluid Mech. 401, 1999, 293–310.
GokhaleS.J.DasguptaS.PlawskyJ.L. and WaynerP.C., Reflectivity-based evaluation of the coalescence of two condensing drops and shape evolution of the coalesced drop, Phys. Rev. E.70, 2004, 1–12.
20.
LealL.G., Flow induced coalescence of drops in a viscous fluid, Phys. Fluids16, 2004, 1833–1851.
21.
WuM.CubaudT. and HoC., Scaling law in liquid drop coalescence driven by surface tension, Phys. Fluids16, 2004, 51–54.
22.
DucheminL.EggersJ. and JosserandC., Inviscid coalescence of drops, J. Fluid Mech. 487, 2003, 167–180.
23.
BaldessariF. and LealL.G., Effect of overall drop deformation on flow-induced coalescence at low capillary numbers, Phys. Fluids18, 2006, 1–9.
24.
YiantsiosS.G. and DavisR.H., Close approach and deformation of two viscous drops due to gravity and van der Waals forces, J. Colloid Interface Sci. 144, 1991, 412–433.
25.
BrennG. and KolobaricV., Satellite droplet formation by unstable binary drop collisions, Phys. Fluids18, 2006, 1–11.
26.
DecentS.P.SharpeG.ShawA.J. and SucklingP.M., The formation of a liquid bridge during the coalescence of drops, Int. J. Multi-phase Flow32, 2006, 717–738.
27.
Mohamed-KassimZ. and LongmireE.K., Drop coalescence through a liquid/liquid interface, Phys. Fluids, 2004, 1–8.
28.
YoonY.BaldessariF.CenicerosH.D. and LealL.G., Coalescence of two equal-sized deformable drops in an axisymmetric flow, Phys. Fluids19, 2007, 1–9.
29.
RekvigL. and FrenkelD., Molecular simulations of droplet coalescence in oil/water/surfactant systems, J. Chem. Phys.127, 2007, 1–16.
30.
ThoroddsenS.T.QianB.EtohT.G. and TakeharaK., The initial coalescence of miscible drops, Phys. Fluids19, 2007, 1–9.
31.
XingX.Q.ButlerD.L.NgS.H.WangZ.DanylukS. and YangC., Simulation of droplet formation and coalescence using lattice Boltzmann-based single-phase model, J. Coll. Interf. Sci.311, 2007, 609–618.
32.
SunZ.XiG. and ChenX., Mechanism study of deformation and mass transfer for binary droplet collisions with particle method, Phys. Fluids21, 2009, 1–11.
33.
WangW.GongJ.NganK.H. and AngeliP., Effect of glycerol on the binary coalescence of water drops in stagnant oil phase, Chem. Eng. Res. Design87, 2009, 1640–1648.
34.
Acevedo-MalavéA. and García-SucreM., 3D Coalescence Collision of Liquid Drops using Smoothed Particle Hydrodynamics, In: SchulzHarry E. (ed.). INTECH Publishers (2011). In Press.
35.
Acevedo-MalavéA. and García-SucreM., Head-on Binary Collisions of Unequal size Liquid Drops with Smoothed Particle Hydrodynamics, In: García-SucreMéximo (ed.). Transworld Research Network, 2011. In Press.
36.
Acevedo-MalavéA. and García-SucreM., Coalescence Collision of Liquid Drops I: Off-Center Collisions of equal-size drops, AIP Advances1, 2011, 032117.
37.
Acevedo-MalavéA. and García-SucreM., Coalescence Collision of Liquid Drops II: Off-Center Collisions of unequal-size drops, AIP Advances1, 2011, 032118.
38.
LucyLB., A numerical approach to the testing of the fission hypothesis, Astron. J.82, 1977, 1013–1024.
39.
GingoldRA. and MonaghanJJ., Smoothed particle hydrodynamics: Theory and application to non-spherical stars, Roy Astronom Soc181, 1977, 375–389.
40.
Acevedo-MalavéA. and García-SucreM., Many Drops Interactions I: Simulation of Coalescence, Flocculation and Fragmentation of Multiple Colliding Drops with Smoothed Particle Hydrodynamics, J. Comput. Multiphase Flows, 2012. Submitted.
41.
MonaghanJJ., Extrapolating B splines for interpolation, J. Comput. Phys.60, 1985, 253–262.
