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Two-Dimensional Lattice Boltzmann Model for Droplet Impingement and Breakup in Low Density Ratio Liquids

Published online by Cambridge University Press:  20 August 2015

Amit Gupta  and
Ranganathan Kumar
Amit Gupta*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology, New Delhi, India 110016
Ranganathan Kumar*
Affiliation:
Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, FL 32816, USA
*
Email:[email protected]
Corresponding author.Email:[email protected]
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Abstract

A two-dimensional lattice Boltzmann model has been employed to simulate the impingement of a liquid drop on a dry surface. For a range of Weber number, Reynolds number and low density ratios, multiple phases leading to breakup have been obtained. An analytical solution for breakup as function of Reynolds and Weber number based on the conservation of energy is shown to match well with the simulations. At the moment breakup occurs, the spread diameter is maximum; it increases with Weber number and reaches an asymptotic value at a density ratio of 10. Droplet breakup is found to be more viable for the case when the wall is non-wetting or neutral as compared to a wetting surface. Upon breakup, the distance between the daughter droplets is much higher for the case with a non-wetting wall, which illustrates the role of the surface interactions in the outcome of the impact.

Keywords

76T10Lattice Boltzmanndroplet impingementspread factorbreakup
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 3 , September 2011 , pp. 767 - 784
Copyright
Copyright © Global Science Press Limited 2011

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References

[1]Yarin, A. L., Drop impact dynamics: splashing, spreading, receding, bouncing •••, Ann. Rev. Fluid Mech., 38 (2006), 159–192.CrossRefGoogle Scholar
[2]Wachters, L. H. J. and Westerling, N. A. J., The heat transfer from a hot wall to impinging water drops in the spheroidal state, Chem. Eng. Sci., 21 (1966), 1047–1056.Google Scholar
[3]Stow, C. D. and Hadfield, M. G., An experimental investigation of fluid flow resulting from the impact of a water drop with an unyielding dry surface, Proc. R. Soc. Lond. A, 373 (1981), 419–441.Google Scholar
[4]Yarin, A. L. and Weiss, D. A., Impact of drops on solid surfaces: self-similar capillary waves, and splashing as a new type of kinematic discontinuity, J. Fluid Mech., 283 (1995), 141–173.Google Scholar
[5]Scheller, B. L. and Bousfield, D. W., Newtonian drop impact with a solid surface, AIChE J., 41 (1995), 1357–1367.Google Scholar
[6]Rioboo, R., Marengo, M. and Tropea, C., Time evolution of liquid drop impact onto solid, dry surfaces, Expt. Fluids, 33 (2002), 112–124.Google Scholar
[7]Pasandideh-Fard, M., Qiao, Y. M., Chandra, S. and Mostaghimi, J., Capillary effects during droplet impact on a solid surface, Phys. Fluids, 8 (1996), 650–659.Google Scholar
[8]Xu, L., Zhang, W. W. and Nagel, S. R., Drop splashing on a dry smooth surface, Phys. Rev. Lett., 94 (2005), 184505.Google Scholar
[9]Mundo, C., Sommerfeld, M. and Tropea, C., Droplet-wall collisions: experimental studies of the deformation and breakup process, Int. J. Multiphase Flow, 21 (1995), 151–173.CrossRefGoogle Scholar
[10]Chandra, S. and Avedisian, C. T., On the collision of a droplet with a solid surface, Proc. R. Soc. Lond. A, 432 (1991), 13–41.Google Scholar
[11]Josserand, C. and Zaleski, S., Droplet splashing on a thin liquid film, Phys. Fluids, 15 (2003), 1650–1657.CrossRefGoogle Scholar
[12]Morton, D., Rudman, M. and Jong-Leng, L., An investigation of the flow regimes resulting from splashing drops, Phys. Fluids, 12 (2000), 747–763.CrossRefGoogle Scholar
[13]Lee, T. and Lin, C.-L., A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio, J. Comput. Phys., 206 (2005), 16–47.CrossRefGoogle Scholar
[14]Mukherjee, S. and Abraham, J., Lattice Boltzmann simulations of two-phase flow with high density ratio in axially symmetric geometry, Phys. Rev. E, 75 (2007), 026701.Google Scholar
[15]Mukherjee, S. and Abraham, J., Crown behavior in drop impact on wet walls, Phys. Fluids, 19 (2007), 052103.CrossRefGoogle Scholar
[16]Mukherjee, S. and Abraham, J., Investigations of drop impact on dry walls with a lattice-Boltzmann model, J. Coll. Inter. Sci., 312 (2007), 341–354.Google Scholar
[17]Benzi, R., Succi, S. and Vergassola, M., The lattice Boltzmann equation: theory and applications, Phys. Rep., 222 (1992), 145–197.CrossRefGoogle Scholar
[18]Succi, S., The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, 2001.Google Scholar
[19]Noble, D. R., Chen, S., Georgiadis, J. G. and Buckius, R. O., A consistent hydrodynamic boundary condition for the lattice Boltzmann method, Phys. Fluids, 7 (1995), 203–209.CrossRefGoogle Scholar
[20]Rothman, D. and Keller, J., Immiscible cellular-automaton fluids, J. Stat. Phys., 52 (1988), 1119–1127.Google Scholar
[21]Shan, X. and Chen, H., Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E, 47 (1993), 1815–1819.Google Scholar
[22]Hou, S., Shan, X., Zou, Q., Doolen, G. D. and Soll, W. E., Evaluation of two lattice Boltzmann models for multiphase flows, J. Comput. Phys., 138 (1997), 695–713.CrossRefGoogle Scholar
[23] M.Swift, Osborne, W. and Yeomans, J., Lattice Boltzmann simulation of nonideal fluids, Phys. Rev. Lett., 75 (1995), 830–833.Google Scholar
[24]Inamuro, T., Tajima, S. and Ogino, F., Lattice Boltzmann simulation of droplet collision dynamics, Int. J. Heat Mass Trans., 47 (2004), 4649–4657.Google Scholar
[25]Kurtoglo, I. O. and Lin, C. L.., Lattice Boltzmann simulation of bubble dynamics, Num. Heat Trans. B, 50 (2006), 333–351.Google Scholar
[26]He, X., Chen, S. and Zhang, R., A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability, J. Comput. Phys., 152 (1999), 642–663.CrossRefGoogle Scholar
[27]Lishchuk, S. V., Care, C. M. and Halliday, I., Lattice Boltzmann algorithm for surface tension with greatly reduced microcurrents, Phys. Rev. E, 67 (2003), 036701.Google Scholar
[28]Falcucci, G., Bella, G., Chiatti, G., Chibbaro, S., Sbragaglia, M. and Succi, S., Lattice Boltzmann models with mid-range interactions, Commun. Comput. Phys., 1 (2006), 1–13.Google Scholar
[29]Falcucci, G., Chibbaro, S., Succi, S., Shan, X. and Chen, H., Lattice Boltzmann spray-like fluids, Europhys. Lett., 82 (2008), 24005.Google Scholar
[30]Gupta, A., Murshed, S. M. S. and Kumar, R., Droplet formation and stability of flows in a microfluidic T-junction, Appl. Phys. Lett., 94 (2009), 164107.Google Scholar
[31]Gupta, A. and Kumar, R., Effect of geometry on droplet formation in the squeezing regime in a microfluidic T-junction, Microfluidics Nanofluidics, 8 (2010), 799–812.CrossRefGoogle Scholar
[32]Kang, Q., Zhang, D. and Chen, S., Displacement of a two-dimensional immiscible droplet in a channel, Phys. Fluids, 14 (2002), 3203–3214.CrossRefGoogle Scholar
[33]Kang, Q., Zhang, D. and Chen, S., Displacement of a three-dimensional immiscible droplet in a duct, J. Fluid Mech., 545 (2005), 41–66.CrossRefGoogle Scholar
[34]Huang, H., Thorne, D. T., Schaap, M. G. and Sukop, M. C., Proposed approximation for contact angles in Shan-and-Chen-type multicomponent multiphase lattice Boltzmann models, Phys. Rev. E, 76 (2007), 066701.Google Scholar
[35]Martys, N. S. and Chen, H., Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method, Phys. Rev. E, 53 (1996), 743–750.Google Scholar
[36]Sankaranarayanan, K., Shan, X., Kevrekidis, I. G. and Sundaresan, S., Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltz-mann method, J. Fluid Mech., 452 (2002), 61–96.Google Scholar
[37]Buick, J. M. and Greated, C. A., Gravity in a lattice Boltzmann model, Phys. Rev. E, 61 (2000), 5307–5320.Google Scholar
[38]Gupta, A. and Kumar, R., Lattice Boltzmann simulation to study multiple bubble dynamics, Int. J. Heat Mass Trans., 51 (2008), 5192–5203.Google Scholar
[39]Yuan, P. and Schaefer, L., Equations of state in a lattice Boltzmann model, Phys. Fluids, 18 (2006), 042101.Google Scholar