Moghtadernejad, Sara
(2014)
*Dynamics of Droplet Shedding and Coalescence under the Effect of Shear Flow.*
PhD thesis, Concordia University.

Preview |
Text (application/pdf)
7MBMoghtadernejad_PhD_F2014.pdf - Accepted Version Available under License Spectrum Terms of Access. |

## Abstract

Droplet shedding and coalescence has various industrial applications from ink-jet printing to ice accretion on wind turbine blades, power lines or aircrafts. It is known that the incipience of icing phenomenon in the mentioned applications arises from the shedding and coalescence of the rain droplets. The coalesced droplets then start to form a runback flow and when temperature is below the water freezing point, ice can be accumulated on these structures which alters the performance in the mentioned technologies. Accordingly this work is dedicated to a fundamental study on dynamics of droplet shedding and coalescence as a preliminary stage of ice formation.

Sessile droplets are deposited on surfaces where various air flows are introduced to them for analyzing their shedding behavior. As it is believed that using superhydrophobic coatings decreases the amount of ice accumulation on the solid surfaces, the effect of different surface wettabilities ranging from hydrophilic to superhydrophobic is also studied on droplet dynamics.

It is shown that on a hydrophilic substrate when the air speed is high enough, rivulets are formed from merging droplets. In contrast, on a superhydrophobic substrate there is no rivulet formation. Instead coalesced droplets roll on the surface and detach from it if the air speed is sufficiently high. In addition, the results indicate a contrast in the mechanism of the coalescence and subsequent detachment between a single and two droplets on a superhydrophobic surface. At low air speeds, the two droplets coalesce by attracting each other before detaching with successive rebounds on the substrate, while at higher speeds the detachment occurs almost instantly after coalescence, with a detachment time decreasing exponentially with the air speed.

A wind tunnel experiment was designed to characterize the rivulet dynamics on various surface wettabilities. Smoothed Particle Hydrodynamics method was performed and its results were compared with the ones obtained from the experiments. The results indicate that increasing the air speed results in formation of waves with higher frequency in comparison with the lower air speeds. It was also demonstrated that as on superhydrophobic substrates instead of rivulets series of droplets are formed these substrates can be suitable candidates for anti-icing purposes.

Divisions: | Concordia University > Gina Cody School of Engineering and Computer Science > Mechanical and Industrial Engineering |
---|---|

Item Type: | Thesis (PhD) |

Authors: | Moghtadernejad, Sara |

Institution: | Concordia University |

Degree Name: | Ph. D. |

Program: | Mechanical Engineering |

Date: | 29 August 2014 |

Thesis Supervisor(s): | Esmail, Nabil and Dolatabadi, Ali |

ID Code: | 978915 |

Deposited By: | SARA MOGHATDER |

Deposited On: | 26 Nov 2014 14:36 |

Last Modified: | 18 Jan 2018 17:47 |

## References:

R. Li, N., Ashgriz, S., Chandra, J.R., Andrews, and S., Drappel, Coalescing of two droplets impacting a solid surface. Exp. Fluids, 2010. 48: p. 1025-1035.R. Li, N., Ashgriz, S., Chandra, J.R., Andrews, and J., Williams, Drawback during deposition of overlapping molten wax droplets. J. Manuf. Sci. Eng., 2008. 130(4).

R. Dhiman, S., Chandra, Freezing-induced splashing during impact of molten metal droplets with high Weber numbers. Int. J. Heat and Mass Transfer, 2005. 48(25-26): p. 5625–5638.

D. Soltman, V., Subramanian, Ink-jet printed line morphologies and temperature control of the coffee ring effect. Langmuir, 2008. 24(5): p. 2224–2231.

A. Alizadeh, M., Yamada, R., Li, W., Shang, S., Otta, S., Zhong, L., Ge, A., Dhinojwala, K.R., Conway, V., Bahadur, A.J., Vinciquerra, B., Stephens, and M.L., Blohm, Dynamics of ice nucleation on water repellent surfaces. Langmuir, 2012. 28(6): p. 3180-3186.

M. Holl, Z., Patek, and L., Smrcek, Wind tunnel testing of performance degradation of ice contaminated airfoils. ICAS Technical Paper 3.1.1, 2000.

Young, T., An essay on the cohesion of fluids. Phil. Trans. R. Soc. London 1805. 95: p. 65-87

G. Wolansky, A., Marmur, The actual contact angle on a hetrogeneous rough surface in three dimensions Langmuir, 1998. 14(18): p. 5292-5297.

B. Bhushan, Y.C., Jung and K., Koch, Micro-nano and hierarchical structures for superhydrophobicity, self-cleaning and low adhesion. Philos. Trans. A. Math. Phys. Eng. Sci., 2009. 367: p. 1631-1672.

Wenzel, R.N., Resistance of solid surfaces to wetting by water. Indust. Eng. Chem., 1936. 28: p. 988-994.

Marmur, A., Wetting of hydrophobic rough surfaces: To be heterogeneous or not to be Langmuir, 2003. 19(20): p. 8343–8348.

E. Bormashenko, T., Stein, R., Pogreb, and D., Aurbach, "Petal effect"on surfaces based on lycopodium: High-stick surfaces demonstrating high apparent contact angles. J. Physical Chem. C, 2009. 113(14): p. 5568-5572.

B. Bhushan, Y.C., Jung, Micro and nanoscale characterization of hydrophobic and hydrophilic leaf surfaces Nanotechnology, 2006. 17(11): p. 2758-2772

A.B.D. Cassie, C., Baxter, Wettability of porous surfaces. Trans. Faraday Soc., 1944. 40(546-551).

M. Nosonovsky, B., Bhushan, Patterned nonadhesive surfaces: Superhydrophobicity and wetting regime transitions. Langmuir, 2008. 24: p. 1525-1533.

A.J. Meuler, J.D., Smith, K.K., Varanasi, J.M., Mabry, G.H., McKinley and R.E., Cohen, Relationships between water wettability and ice adhesion. ACS Appl. Materials and Interfaces, 2010. 2: p. 3100-3110.

S. Kulinich, M., Farzaneh, Ice adhesion on superhydrophobic surfaces. Appl. Surf. Sci., 2009. 225(18): p. 8153-8157.

X. Li, D., Reinhoudt and M., Crego-Calama, What do we need for a superhydrophobic surface? A review on the recent progress in the preparation of superhydrophobic surfaces. Chem. Soc. Rev., 2007. 36: p. 1350-1368.

J. Genzer, K., Efimenko, Recent developments in superhydrophobic surfaces and their relevance to marine fouling: A review. Biofouling, 2006. 22: p. 339-360.

W. Barthlott, C., Neinhuis, Purity of the sacred lotus, or escape from contamination in biological surfaces. Planta, 1997. 202(1): p. 1-8.

J.A. Nychka, M.M., Gentleman, Implications of wettability in biological materials science. JOM, 2010. 62: p. 39-48.

X. Zhang, F., Shi, J., Niu, Y., Jiang, and Z., Wang, Superhydrophobic surfaces: From structural control to functional application. J. Mater. Chem., 2008. 18: p. 621-633.

M. Farhangi, P.J., Graham, N.R., Choudhury, and A., Dolatabadi, Induced detachment of coalescing droplets on superhydrophobic surfaces Langmuir, 2012. 28(2): p. 1290–1303.

M. Callies, D., Quéré, On water repellency. Soft Matter, 2005. 1: p. 55-61.

A. Lafuma, D., Quéré, Superhydrophobic states. Nature Materials, 2003. 2: p. 457-460.

D.Oner, T.J., McCarthy, Ultrahydrophobic surfaces; Effects of topography length scales on wettability Langmuir, 2000. 16(20): p. 7777-7782.

J. Drelich, J.L., Wilbur, J.D., Miller, and G.M., Whitesides, Contact angles for liquid drops at a model heterogeneous surface consisting of alternating and parallel hydrophobic/hydrophilic strips. Langmuir, 1996. 12(7): p. 1913-1922.

A. Frohn, N., Roth, Dynamics of droplets. 2000, Berlin: Springer

Ashgriz, N., Handbook of atomization and sprays. 2011, Heidelberg, NY Springer.

L. Duchemin, J., Eggers, and C., Josserand, Inviscid coalescence of drops. J. Fluid Mech., 2003. 487: p. 167–178.

Yarin, A.L., Drop impact dynamics: Splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech., 2006. 38: p. 159-192.

Worthington, A.M., The splash of a drop. 1895, London: Society for promoting christian knowledge.

Worthington, A.M., A study of splashes 1908, Davenport: The Royal Naval Engineering College.

S. Chandra, C.T., Avedisian, On the collision of a droplet with a solid surface. Math. Phys. Sci., 1991. 432: p. 13-41.

M. Pasandideh-Fard, Y.M., Qiao, S., Chandra, and J., Mostaghimi, Capillary effects during droplet impact on a solid surface. Phys. Fluids, 1996. 8(3): p. 650-659.

D.C. Vadillo, A., Soucemarianadin, C., Delattre, and D.C.D, Roux, Dynamic contact angle effects onto the maximum drop impact spreading on solid surfaces. Phys. Fluids, 2009. 21: p. 1-8.

C. Ukiwe, D., Kwok, On the maximum spreading diameter of impacting droplets on well-prepared solid surfaces. Langmuir, 2005. 21(2): p. 666-673.

L. Chen, Z., Xiao, P.C.H., Chan, Y.K., Lee, and Z., Li, A comparative study of droplet impact dynamics on a dual-scaled superhydrophobic surface and lotus leaf. Appl. Surf. Sci., 2011. 257(21): p. 8857-8863.

J.B. Lee, S.H., Lee, Dynamic of wetting and spreading characteristics of a liquid droplet impinging on hydrophobic textured surfaces. Langmuir, 2011. 27(11): p. 6565-6573.

A. Menchaca-Rocha, A., Martinez-Davalos, and R., Nunez, Coalescence of liquid drops by surface tension. Phys. Rev. E 2001. 63: p. 046309

S.G. Bradley, C.D., Stow, Collisions between liquid drops, in Philos. Trans. R. Soc. . 1978: London. p. 635-675

A. Brandes, G., Zhang, and J., Vivekanadan, Drop size distribution retrieval with polarimetric radar model and application. J. Appl. Meteorol., 2004. 43(461).

E.B. White, J.A.J., Schmucker, A runback criterion for water drops in a turbulent accelerated boundary layer. J. Fluids Eng., 2008. 130: p. 061302–6.

A.J.B. Milne, A., Amirfazli, Drop shedding by shear flow for hydrophilic to superhydrophobic surfaces. Langmuir, 2009. 25(24): p. 14155–14164.

M.W. Lee, D.K., Kang, S.S., Yoon, and A.L., Yarin, Coalescence of two drops on partially wettable substrates. Langmuir, 2012. 28: p. 3791–3798.

Frenkel, J., Viscous flow of crystalline bodies under the action of surface tension. J. Phys. Moscow, 1945. 9: p. 385-391.

J. Eggers, J.R., Lister, and H.A., Stone, Coalescence of liquid drops. J. Fluid Mech., 1999. 401: p. 293–310.

Eggers, J., Coalescence of spheres by surface diffusion. Phys. Rev. Lett., 1998. 80: p. 2634-2637.

Vorst, G.A.L., Integral method for a two-dimensional Stokes flow with shrinking holes applied to viscous sintering. J. Fluid Mech., 1993. 257: p. 667-689

Vorst, G.A.L., Modeling and numerical simulation of viscous sintering. 1994, TU Eidhoven.

W.D. Ristenpart, P.D., McCalla, R.V., Roy, and H.A., Stone, Coalescence of spreading drops on a wettable substrate. Phys. Rev. Lett., 2006. 97: p. 064501.

S.T. Thoroddsen, K., Takehara, and T.G., Etoh, The coalescence speed of a pendant and a sessile drop. J. Fluid Mech., 2005. 527: p. 85–114

M. Wu, T., Cubad, and C.M., Ho, Scaling law in liquid drop coalescence driven by surface tension. Phys. Fluids, 2004. 16: p. 51-54.

R.D. Narhe, D.A., Beysens, and Y.D., Pomeau, Dynamic drying in the early-stage coalescence of drops sitting on a plate. Europhys. Lett., 2008(81): p. 46002

P.J. Graham, M., Farhangi, and A., Dolatabadi, Dynamics of droplet coalescence in response to increasing hydrophobicity. Phys. Fluids, 2012. 24: p. 112105.

H.Y. Kim, J.H., Kim, and B.H., Kang, Meandering instability of a rivulet. J. Fluid Mech., 2004. 498: p. 245-256.

Diez, J.A., Contact line instabilities of thin liquid films. Phys. Rev. Lett., 2001. 86(4): p. 632-635.

P. Schmuki, M., Laso, On the stability of rivulet flow. J. Fluid Mech., 1990. 215: p. 125-143.

S. Schiaffino, A.A.S., Formation and stability of liquid and molten beads on a solid surface. J. Fluid Mech, 1997. 343: p. 95-11-.

G.W. Young, S.H., Davis, Rivulet instabilities. J. Fluid Mech, 1987. 176: p. 1-31.

E. Momoniat, T.G., Myers, and S., Abelman, New solutions for surface driven spreading of thin film Int. J. Non-Linear Mech., 2005. 40(4): p. 523-529.

A. Oron, S.H., Davis, and S.G., Banko, Long-scale evolution of thin liquid films. Rev. Modern Phys., 1997. 69(3): p. 931-980.

J.S. Marshall, R., Ettema Rivulet dynamics with variable gravity and wind shear. 2004.

Gajewski, A., Contact angle and rivulet width hysteresis on metallic surfaces. Part I : With heated surface. Int. J. Heat and Mass Transfer, 2008. 51(25-26): p. 5762-5771.

Gajewski, A., Contact angle and rivulet width hysteresis on metallic surfaces. Part II : With cooled surface. Int. J. Heat and Mass Transfer 2009. 52(13-14): p. 3197-3204.

J.A. Diez, A.G., Gonzalez, and L., Kondic, On the breakup of fluid rivulets. Phys. Fluids, 2009. 21(8): p. 082105.

A. Daerr, J., Eggers, L., Limat, and N., Valade, General mechanism for the meandering instability of rivulets of newtonian fluids. Phys. Rev. Lett., 2011. 106(18): p. 184501.

H.H. Saber, M.S., El-Genk On the breakup of a thin liquid film subject to interfacial shear. J. Fluid Mech., 2004. 500: p. 113-133.

Politovich, M.K., Aircarft icing 2003, National Center for Atomospheric Reasrch: Boulder, CO, USA. p. 68-75.

S.A. Kulinich, S., Farhadi, K., Nose, K., and X.W., Du, Superhydrophobic surfaces: Are they really ice-repellent? Langmuir, 2010. 27(1): p. 25-29.

C. Antonini, M., Innocenti, T., Horn, M., Marengo, and A., Amirfazli, Understanding the effect of superhydrophobic coatings on energy reduction in anti-icing system. Cold Reg. Sci. Technol., 2011. 67(1-2): p. 58-67.

L. Boinovich, A.M., Emelyanenko, V.V., Korolev, and S.A., Pashinin, Effect of wettability on sessile drop freezing: When superhydrophobicity stimulates an extreme freezing delay. Langmuir 2014. 30(6): p. 1659–1668.

L. Cao, A.K., Jones, V.K., Sikka, J., Wu, and D., Gao, Anti-icing superhydrophobic coatings. Langmuir, 2009. 25(21): p. 12444-12448.

S. Moghtadernejad, M., Mohammadi, M., Jadidi, M., Tembely, and A., Dolatabadi Shear driven droplet shedding on surfaces with various wettabilities. SAE Int. J. Aerosp., 2013. 6(2): p. 459-464.

A.D. Schleizer, R.T.J., Bonnecaze, Displacement of a two-dimensional immiscible droplet adhering to a wall in shear and pressure-driven flows. J. Fluid Mech., 1999. 383(1): p. 29-54.

T.G. Myersa, H.X., Liang, and B., Wetton, The stability and flow of a rivulet driven by interfacial shear and gravity. Int. J. Non-Linear Mech., 2004. 39(8): p. 1239-1249.

C. Antonini, F.J., Carmona, E.M., Pierce, M., Marengo, and A., Amirfazli General methodology for evaluating the adhesion force of drops and bubbles on solid surfaces. Langmuir, 2009. 25(11): p. 6143–6154.

M.D. Abramo, P.J., Magelhaes, and J.S., Ram, Image processing with ImageJ. Biophotonics Int., 2004. 11(7): p. 36-42.

S. Moghtadernejad, M., Jadidi, N., Esmail, and A., Dolatabadi, Shear driven droplet coalescence and rivulet formation. J. Mech. Eng. Sci., 2015, doi: 10.1177/0954406215590186.

S. Moghtadernejad, M., Jadidi, M., Tembely, N., Esmail, and A., Dolatabadi, Concurrent droplet coalescence and solidification on surfaces with various wettabilities in 4th Joint US-European Fluids Engineering Summer Meeting. 2014: Chicago, IL, USA

S. Jung, K.M., Tiwari, V.N., Doan, and D., Poulikakos Mechanism of supercooled droplet freezing on surfaces. Nature Commun., 2012. 3(615).

D. Aarts, H., Lekkerkerker, H., Guo, G., Wegdam, and D., Bonn, Hydrodynamics of droplet coalescence. Phys. Rev. Lett., 2005. 95: p. 164503.

S. Moghtadernejad, M., Tembely, M., Jadidi, N., Esmail, and A., Dolatabadi, Shear driven droplet shedding and coalescence on a superhydrophobic surface. Phys. Fluids, 2015. 27(3).

ESI-OpenCFD. Home OpenFOAM. 2014; Available from: http://www.openfoam.com.

R. Scardovelli, S., Zaleski, Direct numerical simulation of free-surface and interfacial flow. Annu. Rev. Fluid Mech., 1999. 31(1): p. 567-603.

J.U. Brackbill, D.B., Kothe, and C., Zemach, A continuum method for modeling surface tension. J. Comput. Phys., 1992. 100(2): p. 335-354

Rusche, H., Computational fluid dynamics of dispersed two phase flows at high phase fractions 2002, Imperial College University of London.

Kistler, S.F., Hydrodynamics of wetting 1993, Marcel Dekker Inc.: New York. p. 311–429.

Vreman, A.W., An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications. Phys. Fluids 2004. 16(10): p. 3670.

C. Fureby, G., Tabor, H.G., Weller, and A.D., Gosman, A comparative study of subgrid scale models in homogeneous isotropic turbulence. Phys. Fluids, 1997. 9: p. 1416.

Yoshizawa, K., Horiuti, A statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation of turbulent flows J. Phys. Soci. Japan, 1985. 54: p. 2834-2839

S. Moghtadernejad, M., Jadidi, M., Tembely, N., Esmail, and A., Dolatabadi, Concurrent droplet coalescence and solidification on surfaces with various wettabilities. ASME J. Fluids. Eng, 2015. 137(7).

B. Carroll, C., Hidrovo, Droplet detachment mechanism in a high-speed gaseous micro flow. J. Fluids Eng, 2013. 135(7): p. 071206-8.

F. Capizzano, E., Luliano, A Eulerian method for water droplet impingement by means of an immersed boundary technique. J. Fluids Eng., 2014. 136(4): p. 040906-8.

R. Li, N., Ashgriz, and S., Chandra, Maximum spread of droplet on solid surface: Low Reynolds and Weber numbers. J. Fluids Eng., 2010. 132(6): p. 061302-5.

Rein, M., Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res., 1993. 12: p. 61-93.

Y.P. Wan, H., Zhang, X.Y., Jiang, S., Sampath, and V., Prasad, Role of solidification, substrate temperature and Reynolds number on droplet spreading in thermal spray deposition: Measurements and modeling. J. Heat Transfer, 2000. 123(2): p. 382-389.

D. Li, Z., Chen Experimental study on instantaneously shedding frozen water droplets from cold vertical surface by ultrasonic vibration. Exp. Therm. Fluid Sci., 2014. 53: p. 17-25.

G. McAlister, R., Ettema, and J.S., Marshall, Wind-driven rivulet breakoff and droplet flows in microgravity and terrestrial gravity conditions. J. Fluids Eng., 2004. 127(2): p. 257-266.

D.M. Anderson, M.G., Worster, and S.H., Davis, The case for a dynamic contact angle in containerless solidification. J. Cryst. Growth, 1996. 163(3): p. 329-338.

O.R. Enríquez, A.G., Marín, K.G., Winkels, H., Jacco, and J.H., Snoeijer Freezing singularities in water drops. Phys. Fluids, 2012. 24(9): p. 091102.

S. Jung, K.M., Tiwari, and D., Poulikakos, Frost halos from supercooled water droplets. PNAS, 2012. 109(40): p. 16073-16078.

S. Farhadi, M., Farzaneh, and S.A., Kulinich, Anti-icing performance of superhydrophobic surfaces. Appl. Surf. Sci., 2011. 257(14): p. 6264-6269.

K.A. Wier, T.J., McCarthy, Condensation on ultrahydrophobic surfaces and its effect on droplet mobility: Ultrahydrophobic surfaces are not always water repellant. Langmuir, 2006. 22(6): p. 2433-2436.

X. Xio, Y.T., Cheng, B.W., Sheldon, and J., Rankin, Condensed water on superhydrophobic carbon films. J. Mater. Res., 2008. 23(8): p. 2174-2178.

R. Karmouch, G.G., Ross, Experimental study on the evolution of contact angles with temperature near the freezing point. J. Phys. Chem. C., 2010. 114(9): p. 4063-4066.

R.D. Nareh, D.A., Beysens, Growth dynamics of water drops on a square-pattern rough hydrophobic surface. Langmuir, 2007. 23(12): p. 6486-6489.

B. Mockenhaupt, H., Ensikat, M., Spaeth, and W., Barthlott, Superhydrophobicity of biological and technical surfaces under moisture condensation: stability in relation to surface structure. Langmuir, 2008. 24(23): p. 13591-13597.

K. Varanasi, T., Deng, J.D., Smith, M., Hsu, and N., Bhate, Frost formation and ice adhesion on superhydrophobic surfaces. Appl. Phys. Lett., 2010. 97(23): p. 234102-234102-3.

R. Menini, Z., Ghalmi, and M., Farzaneh, Highly resistant icephobic coatings on aluminum alloys. Cold Reg. Sci. Technol., 2011. 65(1): p. 65-69.

S.A. Kulinich, M., Farzaneh, On ice-releasing properties of rough hydrophobic coatings. Cold Reg. Sci. Technol., 2011. 65(1): p. 60-64.

H.J. Ensikat, A.J., Schulte, K., Koch, and W., Barthlott, Droplets on superhydrophobic surfaces: Visualization of the contact area by cryo-scanning electron microscopy. Langmuir, 2009. 25(22): p. 13077-13083.

S. Moghtadernejad, M.J., N., Esmail, and A. Dolatabadi, SPH simulation of rivulet dynamics on surfaces with various wettabilities. SAE Int. J. Aerosp, 2015. 8(1): p. 160-173.

S. Moghtadernejad, M., Jadidi, N., Esmail, and A., Dolatabadi. Shear driven rivulet dynamics on surfaces with various wettabilities. in ASME 2014 International Mechanical Engineering Congress & Exhibition. 2014. Montreal, QC, Canada.

Lucy, L.B., A numerical approach to the testing of the fission hypothesis. The Astronomical J., 1977. 82: p. 1013-1024.

R.A. Gingold, J.J., Monaghan, Smoothed particle hydrodynamics-theory and application to non-spherical stars. Monthly Notices of the R. Astronomical Soci., 1977. 181: p. 375-389.

Monaghan, J.J., Smoothed particle hydrodynamics. Annu. Rev. of Astronomy and Astrophysics, 1992. 30: p. 543-574.

Monaghan, J.J., Simulating free surface flows with SPH. J. Comput. Phys., 1994. 110(2): p. 399-406.

A. Crespo, M., Gómez-Gesteira, and R., Dalrymple, Boundary conditions generated by dynamic particles in SPH methods. CMC Tech. Sci. Press, 2007. 5(3): p. 173.

Monaghan, J.J., Smoothed particle hydrodynamics and its diverse applications. Annu. Rev. Fluid Mech., 2012. 44: p. 323-346.

J.J. Monaghan, A., Kocharyan, SPH simulation of multi-phase flow. Computer Phys. Commun., 1995. 87(1): p. 225-235.

Monaghan, J.J., Why particle methods work. SIAM J. on Scientific and Statistical Computing, 1982. 3(4): p. 422-433.

G. Liu, M.B., Liu, Smoothed particle hydrodynamics: A meshfree particle method. 2003: World Scientific.

Monaghan, J.J., Smoothed particle hydrodynamics. Reports on progress in physics, 2005. 68(8): p. 1703.

M.B. Liu, G.R., Liu, Smoothed particle hydrodynamics (SPH): An overview and recent developments. Archives of Comput. methods in Eng., 2010. 17(1): p. 25-76.

Benz, W., Applications of Smoothed Particle Hydrodynamics (SPH) to astrophysical problems. Computer Phys. Commun., 1988. 48(1): p. 97-105.

F. Sun, M., Tan, and J.T., Xing. Air-water two phase flow simulation using smoothed particle hydrodynamics. in 2nd International Conference on Violent Flows. 2012.

M. Müller, D., Charypar, and M., Gross. Particle-based fluid simulation for interactive applications. in Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation. 2003. Eurographics Association.

M. Müller, B., Solenthaler, R., Keiser, and M., Gross. Particle-based fluid-fluid interaction. in Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation. 2005. ACM.

Crespo, A., Application of the Smoothed Particle Hydrodynamics model SPHysics to free-surface hydrodynamics. 2008, PhD thesis.

P.W. Randles, L.D., Libersky, Smoothed particle hydrodynamics: Some recent improvements and applications. Computer methods in Appl. Mech. and Eng., 1996. 139(1): p. 375-408.

J.J. Monaghan, a.J.C., Lattanzio, A refined particle method for astrophysical problems. Astronomy and Astrophysics, 1985. 149: p. 135-143.

H. Xiong, J., Zhu, Study of droplet deformation, heat-conduction and solidification using incompressible smoothed particle hydrodynamics method. J. Hydrodynamics, Ser. B, 2010. 22(5): p. 150-153.

M. Ellero, M., Serrano, and P., Espanol, Incompressible smoothed particle hydrodynamics. J. Comput. Phys., 2007. 226(2): p. 1731-1752.

S. Lind, R., Xu, P., Stansby, and B., Rogers, Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves. J. Comput. Phys., 2012. 231(4): p. 1499-1523.

J. Morris, P., Fox, and Y., Zhu, Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys., 1997. 136(1): p. 214-226.

B. Solenthaler, R., Pajarola, Predictive-corrective incompressible SPH. ACM Trans. Graph., 2009. 28(3): p. 1-6.

X. Hu, N., Adams, An incompressible multi-phase SPH method. J. Comput. Phys., 2007. 227(1): p. 264-278.

Zhang, M., Simulation of surface tension in 2D and 3D with smoothed particle hydrodynamics method. J. Comput. Phys., 2010. 229(19): p. 7238-7259.

S. Šikalo, H.D., Wilhelm, I.V., Roisman, S., Jakirliæ, and C., Tropea, Dynamic contact angle of spreading droplets: Experiments and simulations. Phys. Fluids, 2005. 17(6): p. 062103.

S. Afkhami, S., Zaleski, and M., Bussmann, A mesh-dependent model for applying dynamic contact angles to VOF simulations. J. Comput. Phys., 2009. 228(15): p. 5370-5389.

A. Tartakovsky, P., Meakin, Modeling of surface tension and contact angles with smoothed particle hydrodynamics. Phys. Rev. E, 2005. 72(2): p. 026301.

Verlet, L., Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev., 1967. 159(1): p. 98.

T.R. Saitoh, J., Makino, A necessary condition for individual time steps in SPH simulations. The Astrophysical J. Lett., 2009. 697(2): p. L99.

H. Xiong, L., Chenand, and J., Lin, Smoothed particle hydrodynamics modeling of free surface flow. J. Hydrodynamics, Ser. B, 2006. 18(3): p. 443-445.

Roy, T.M., Physically based fluid modeling using smoothed particle hydrodynamics. 1995, University of Illinois at Chicago.

Liu, G., Meshfree methods: Moving beyond the finite element method. 2010: CRC press.

Z. Yao, J., Wang, G., Liu, and M., Cheng, Improved neighbor list algorithm in molecular simulations using cell decomposition and data sorting method. Computer Phys. Commun., 2004. 161(1): p. 27-35.

R.A. Dalrymple, B.D., Rogers, Numerical modeling of water waves with the SPH method. Coastal Eng., 2006. 53(2): p. 141-147.

A. Colagrossi, M., Landrini, Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J. Comput. Phys., 2003. 191(2): p. 448-475.

M. Liu, J., Shao, and J., Chang, On the treatment of solid boundary in smoothed particle hydrodynamics. Sci. China Technol. Sci., 2012. 55(1): p. 244-254.

Repository Staff Only: item control page