Journal of Theoretical
and Applied Mechanics

56, 3, pp. 675-686, Warsaw 2018
DOI: 10.15632/jtam-pl.56.3.675

Smoothed particle hydrodynamics modelling of the Rayleigh-Plateau instability

Michał Olejnik, Kamil Szewc
The break-up of liquid ligaments and formation of droplets are elementary phenomena in
multiphase flows which are of high importance in industrial and medical applications. From
the numerical point of view, they require proper interface and surface tension treatment.
In the present work, we apply Smoothed Particle Hydrodynamics, a meshless approach, to
simulate the break-up of a liquid cylinder inside the gaseous phase, i.e. the Rayleigh-Plateau
instability. Results obtained in 3D show that even a relatively coarse resolution allows one
to predict correctly the size of droplets formed in the process. The detailed analysis of the
break-up time in 2D setup implies that a certain level of spatial discretisation needs to be
reached to determine this moment precisely.
Keywords: meshless methods, SPH, capillary jet break-up, interfacial flows

References


Abate A.R., Poitzsch A., Hwang Y., Lee J., Czerwinska J., Weitz D.A., 2009, Impact

of inlet channel geometry on microfluidic drop formation, Physical Review E, 80, 026310

Adami S., Hu X.Y., Adams N.A., 2012, A generalized wall boundary condition for smoothed

particle hydrodynamics, Journal of Computational Physics, 231, 7057-7075

Boeck T., Li J., López-Pag´es E., Yecko P., Zaleski S., 2007, Ligament formation in sheared

liquid-gas layers, Theoretical and Computational Fluid Dynamics, 21, 59-76

Brackbill J.U., Kothe D.B., Zemach C., 1992, A continuum method for modeling surface

tension, Journal of Computational Physics, 100, 335-354

Dai M., Schmidt S.P., 2005, Adaptive tetrahedral meshing in free-surface flow, Journal of Com-

putational Physics, 208, 228-252

Das A.K., Das P.K., 2010a, Equilibrium shape and contact angle of sessile drops of different

volumes – Computation by SPH and its further improvement by DI, Chemical Engineering Science, 65, 4027-4037

Das A.K., Das P.K., 2010b, Incorporation of diffuse interface in smoothed particle hydrodyna-

mics: Implementation of the scheme and case studies, International Journal for Numerical Methods

in Fluids, 67, 671-699

Dehnen W., Aly H., 2012, Improving convergence in smoothed particle hydrodynamics simula-

tions without pairing instability, Monthly Notices of Royal Astronomical Society, 425, 1068-1082

Guzowski J., Jakiela S., Korczyk P.M., Garstecki P., 2013, Custom tailoring multiple

droplets one-by-one, Lab on a Chip, 13, 4308-4311

Hu X.Y., Adams N.A., 2006, A multi-phase SPH method for macroscopic and mesoscopic flows,

Journal of Computational Physics, 213, 844-861

Hunter J.D., 2007, Matplotlib: A 2D Graphics Environment, Computing in Science and Engine-

ering, 9, 90-95

Monaghan J.J., 1992, Smoothed Particle Hydrodynamics, Annual Review of Astronomy and

Astrophysics, 30, 543-574

Monaghan J.J., 2012, Smoothed Particle Hydrodynamics and its diverse applications, Annual

Review of Fluid Mechanics, 44, 323-346

Morris J.P., 2000, Simulating surface tension with smoothed particle hydrodynamics, Interna-

tional Journal for Numerical Methods in Fluids, 33, 333-353

Olejnik M., Szewc K., Pozorski J., 2016, Modelling of the flow regime transition with the

Smoothed Particle Hydrodynamics, Proceedings of 9th International Conference on Multiphase

Flow, Florence, Italy, paper No. 1037

Olejnik M., Szewc K., Pozorski J., 2017, SPH with dynamical smoothing length adjustment

based on the local flow kinematics, Journal of Computational Physics, 348, 23-44

Ordoubadi M., Yaghoubi M., Yeganehdoust F., 2017, Surface tension simulation of free

surface flows using smoothed particle hydrodynamics, Scientia Iranica, Transactions B: Mechanical

Engineering, 24, 2019-2033

Ramachandran P., Varoquaux G., 2011,Mayavi: 3D visualization of scientific data, Computing

in Science and Engineering, 13, 40-51

Sirotkin F.V., Yoh J.J, 2012, A new particle method for simulating breakup of liquid jets,

Journal of Computational Physics, 231, 1650-1674

Szewc K., 2014, Smoothed Particle Hydrodynamics simulations using Graphics Processing Units,

TASK Quarterly, 18, 67-80

Szewc K., Pozorski J., Minier J.-P., 2012a, Analysis of the incompressibility constraint in the

SPH method, International Journal for Numerical Methods in Engineering, 91, 343-369

Szewc K., Pozorski J., Minier J.-P., 2013, Simulations of single bubbles rising through viscous

liquids using Smoothed Particle Hydrodynamics, International Journal of Multiphase Flow, 50, 98-105

Szewc K., Pozorski J., Minier J.-P., 2015, Spurious interface fragmentation in multiphase

SPH, International Journal for Numerical Methods in Engineering, 103, 625-649

Szewc K., Tani`ere A., Pozorski J., Minier J.-P., 2012b, A study on application of Smoothed

Particle Hydrodynamics to multi-phase flows, International Journal of Nonlinear Sciences and

Numerical Simulation, 13(6), 383-395

Tryggvason G., Scardovelli R., Zaleski S., 2011, Direct Numerical Simulations of Gas-

Liquid Multiphase Flows, Cambridge University Press

Wendland H., 1995, Piecewise polynomial, positive definite and compactly supported radial

functions of minimal degree, Advances in Computational Mathematics, 4, 389-396

Wieth L., Kelemen K., Braun S., Koch R., Bauer H.J., Schuchmann H.P., 2016, Smo-

othed Particle Hydrodynamics (SPH) simulation of a high-pressure homogenization process, Mi-

crofluidics and Nanofluidics, 20, 42

Vacondio R., Rogers B.D., Stansby P.K., Mignosa P., 2016, Variable resolution for SPH

in three dimensions: Towards optimal splitting and coalescing for dynamic adaptivity, Computer

Methods in Applied Mechanics and Engineering, 300, 442-460

Violeau D., 2012, Fluid Mechanics and the SPH Method, Oxford University Press, Oxford

Violeau D., Rogers B.D., 2016, Smoothed particle hydrodynamics (SPH) for free-surface flows:

past, present and future, Journal of Hydraulic Research, 54, 1-26

Yeganehdoust F., Yaghoubi M., Emdad H., Ordoubadi M., 2016, Numerical study of mul-

tiphase droplet dynamics and contact angles by smoothed particle hydrodynamics, Applied Mathe-

matical Modelling, 40, 8493-8512