Here the SPH method is applied to simulate in the three-dimensional space the multiple hydrodynamics collisions and formation of clusters of equal-size liquid drops in a vacuum environment. For a range of velocity values from 0.2 mm/ms to 30.0 mm/ms we observe three possible scenarios, such as: coalescence and cluster formation of drops. When the collision velocity is too low the droplets interact only through their deformed surfaces. If this velocity is around 15.0 mm/ms the coalescence of the drops is observed, and after some time starting on t=0 a flat circular section is observed between the colliding drops. This interface disappears when the dynamics runs and the drops finally coalesce. The velocity vector fields were computed for the different scenarios showing some zones inside the drops where the fluid velocity is diminished and other zones where the SPH particles are accelerated.
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. A287, 1978, 635–642.
5.
LiD., Coalescence between two small bubbles or drops, J. Colloid Interface Sci. 163, 1994, 108–119.
6.
ChenJ.D., A model of coalescence between two equal-sized spherical drops or bubbles, J. Colloid Interface Sci. 107, 1985, 209–220.
7.
AshgrizN. and GiviP., Binary collision dynamics of fuel droplets, Int. J. Heat Fluid Flow8, 1987, 205–208.
8.
AshgrizN. and GiviP., Coalescence efficiencies of fuel droplets in binary collisions, Int. Commun. Heat Mass Transfer16, 1989, 11–17.
9.
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, 1–11.
10.
FooteG.B., The water drop rebound problem: Dynamics of collision, J. Atmos. Sci.32, 1974, 390–401.
11.
EggersJ.ListerJ.R. and StoneH.A., Coalescence of liquid drops, J. Fluid Mech. 401, 1999, 293–310.
12.
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.
13.
AshgrizN. and PooJ.Y., Coalescence and separation of binary collisions of liquid drops, J. Fluid Mech. 221, 1990, 183–204.
14.
RekvigL. and FrenkelD., Molecular simulations of droplet coalescence in oil/water/surfactant systems, J. Chem. Phys.127, 2007, 1–13.
15.
MashayekF.AshgrizN.MinkowyczW.J. and ShotorbanB., Coalescence collision of liquid drops, Int. J. Heat Mass Trans. 46, 2003, 77–89.
16.
Mohamed-KassimZ. and LongmireE.K., Drop coalescence through a liquid/liquid interface, Phys. Fluids, 2004, 1–9.
17.
AartsD.LekkerkerkerH.GuoH.WegdamG. and BonnD., Hydrodynamics of Droplet Coalescence, Phys. Rev. Lett.95, 2005, 1–11.
18.
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.
19.
NarsimhanG., Model for drop coalescence in a locally isotropic turbulent flow field, J. Coll. Interf. Sci.272, 2004, 197–209.
20.
CristiniV.BawzdziewiczJ. and LoewenbergM., An Adaptive Mesh Algorithm for Evolving Surfaces: Simulations of Drop Breakup and Coalescence, J. Comput. Phys.168, 2001, 445–463.
21.
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.
22.
JiaX.McLaughlinJ.B. and KontomarisK., Lattice Boltzmann simulations of drop coalescence and chemical mixing, Physica A362, 2006, 62–67.
23.
ZhangF.H.LiE.Q. and ThoroddsenS.T., Satellite formation during coalescence of unequal size drops, Phys. Rev. Lett.102, 2009, 1–12.
24.
QianJ. and LawC.K., Regimes of coalescence and separation in droplet collision, J. Fluid Mech. 331, 1997, 59–.
25.
YoonY.BaldessariF.CenicerosH.D. and LealL.G., Coalescence of two equal-sized deformable drops in an axisymmetric flow, Phys. Fluids19, 2007, 1–8.
26.
WuM.CubaudT. and HoC., Scaling law in liquid drop coalescence driven by surface tension, Phys. Fluids16, 2004, 51–54.
27.
DucheminL.EggersJ. and JosserandC., Inviscid coalescence of drops, J. Fluid Mech. 487, 2003, 167–180.
28.
SunZ.XiG. and ChenX., Mechanism study of deformation and mass transfer for binary droplet collisions with particle method, Phys. Fluids21, 2009, 1–12.
29.
ThoroddsenS.T.QianB.EtohT.G. and TakeharaK., The initial coalescence of miscible drops, Phys. Fluids19, 2007, 1–10.
30.
Acevedo-MalavéA. and García-SucreM., 3D Coalescence Collision of Liquid Drops using Smoothed Particle Hydrodynamics, In: Schulz, HarryE. (ed.). INTECH Publishers, 2011. In Press.
31.
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.
32.
Acevedo-MalavéA. and García-SucreM., Coalescence Collision of Liquid Drops I: Off-Center Collisions of equal-size drops, AIP Advances1, 2011, 032117.
33.
Acevedo-MalavéA. and García-SucreM., Coalescence Collision of Liquid Drops II: Off-Center Collisions of unequal-size drops, AIP Advances1, 2011, 032118.
34.
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.
35.
Acevedo-MalavéA. and García-SucreM., Many Drops Interactions II: Simulation of Coalescence, Flocculation and Fragmentation of Multiple Colliding Drops with Smoothed Particle Hydrodynamics, J. Comput. Multiphase Flows, 2012. Submitted.
36.
MonaghanJJ., Extrapolating B splines for interpolation, J. Comput. Phys.60, 1985, 253–262.
37.
LiuGR. and LiuMB., Smoothed Particle Hydrodynamics – A Meshfree Particle Method, World Scientific, 2003.
