Journal of Mechanical Science and Technology

, Volume 32, Issue 5, pp 2111–2117 | Cite as

Numerical investigation of dynamic behavior of a compound drop in shear flow

  • Truong V. VuEmail author
  • Luyen V. Vu
  • Binh D. Pham
  • Quan H. LuuEmail author


We present a numerical investigation of the deformation and breakup of a compound drop in shear flow. The numerical method used in this study is a two-dimensional front-tracking/finite difference technique for representing the interface separating two fluids by connected elements. The compound drop with the initially circular and concentric inner and outer fronts is placed at the center of a domain whose top and bottom boundaries move in the opposite direction. Because of the shear rate, the compound drop deforms and can break up into drops, depending on the flow conditions based on the Reynolds number Re, the Capillary number Ca and the interfacial tension ratio σ21 of the outer to inner interfaces. We vary Re in the range of 0.1-3.16, Ca in the range of 0.05-0.6 and σ21 in the range of 0.8-3.2 to reveal the transition from the non-breakup to breakup regimes. Numerical results indicate that the compound drop breaks up into drops when there's an increase in Re or Ca or a decrease in σ21 beyond the corresponding critical values. We also propose a phase diagram of Ca versus Re that shows the region in which the compound drop changes from the deformation mode to the breakup mode.


Compound drop Numerical investigation Front-tracking Breakup Shear flow 


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  1. [1]
    T. V. Vu, H. Takakura, J. C. Wells and T. Minemoto, Production of hollow spheres of eutectic tin-lead solder through a coaxial nozzle, J. of Solid Mechanics and Materials Engineering, 4 (10) (2010) 1530–1538.CrossRefGoogle Scholar
  2. [2]
    R. H. Chen, M. J. Kuo, S. L. Chiu, J. Y. Pu and T. H. Lin, Impact of a compound drop on a dry surface, J. of Mechanical Science and Technology, 21 (11) (2007) 1886–1891.CrossRefGoogle Scholar
  3. [3]
    S. Vellaiyan and K. S. Amirthagadeswaran, Taguchi-Grey relational-based multi-response optimization of the water-indiesel emulsification process, J. of Mechanical Science and Technology, 30 (3) (2016) 1399–1404.CrossRefGoogle Scholar
  4. [4]
    M. L. Fabiilli, J. A. Lee, O. D. Kripfgans, P. L. Carson and J. B. Fowlkes, Delivery of water-soluble drugs using acoustically triggered perfluorocarbon double emulsions, Pharmaceutical Research, 27 (12) (2010) 2753–2765.CrossRefGoogle Scholar
  5. [5]
    L. Sapei, M. A. Naqvi and D. Rousseau, Stability and release properties of double emulsions for food applications, Food Hydrocolloids, 27 (2) (2012) 316–323.CrossRefGoogle Scholar
  6. [6]
    J. Wang, J. Liu, J. Han and J. Guan, Rheology investigation of the globule of multiple emulsions with complex internal structures through a boundary element method, Chemical Engineering Science, 96 (2013) 87–97.CrossRefGoogle Scholar
  7. [7]
    J. Wang, H. Jing and Y. Wang, Possible effects of complex internal structures on the apparent viscosity of multiple emulsions, Chemical Engineering Science, 135 (2015) 381–392.CrossRefGoogle Scholar
  8. [8]
    H. A. Stone, Dynamics of drop deformation and breakup in viscous fluids, Annual Review of Fluid Mechanics, 26 (1) (1994) 65–102.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    H. R. Kim, M. Ha, H. S. Yoon and S. W. Son, Dynamic behavior of a droplet on a moving wall, J. of Mechanical Science and Technology, 28 (5) (2014) 1709–1720.CrossRefGoogle Scholar
  10. [10]
    J. Kim, Characteristics of drag and lift forces on a hemisphere under linear shear, J. of Mechanical Science and Technology, 29 (10) (2015) 4223–4230.CrossRefGoogle Scholar
  11. [11]
    K. Ha and K.-Y. Han, Squeezing of resin droplet with various viscosities between two parallel glasses with very narrow gap, J. of Mechanical Science and Technology, 29 (8) (2015) 3257–3265.CrossRefGoogle Scholar
  12. [12]
    Y. Chen, X. Liu and M. Shi, Hydrodynamics of double emulsion droplet in shear flow, Applied Physics Letters, 102 (5) (2013) 051609.CrossRefGoogle Scholar
  13. [13]
    A. S. Utada, E. Lorenceau, D. R. Link, P. D. Kaplan, H. A. Stone and D. A. Weitz, Monodisperse double emulsions generated from a microcapillary device, Science, 308 (5721) (2005) 537–541.CrossRefGoogle Scholar
  14. [14]
    T. V. Vu, S. Homma, G. Tryggvason, J. C. Wells and H. Takakura, Computations of breakup modes in laminar compound liquid jets in a coflowing fluid, International J. of Multiphase Flow, 49 (2013) 58–69.CrossRefGoogle Scholar
  15. [15]
    C. Goubault, K. Pays, D. Olea, P. Gorria, J. Bibette, V. Schmitt and F. Leal-Calderon, Shear rupturing of complex fluids: Application to the preparation of quasi-monodisperse water-in-oil-in-water double emulsions, Langmuir, 17 (17) (2001) 5184–5188.CrossRefGoogle Scholar
  16. [16]
    S.-Y. Teh, R. Lin, L.-H. Hung and A. P. Lee, Droplet microfluidics, Lab on a Chip, 8 (2) (2008) 198–220.CrossRefGoogle Scholar
  17. [17]
    M. Abkarian, M. Faivre and A. Viallat, Swinging of red blood cells under shear flow, Physical Review Letters, 98 (18) (2007) 188302.CrossRefGoogle Scholar
  18. [18]
    T. V. Vu, J. C. Wells, H. Takakura, S. Homma and G. Tryggvason, Numerical calculations of pattern formation of compound drops detaching from a compound jet in a coflowing immiscible fluid, J. of Chemical Engineering of Japan, 45 (8) (2012) 721–726.CrossRefGoogle Scholar
  19. [19]
    H. Hua, J. Shin and J. Kim, Dynamics of a compound droplet in shear flow, International J. of Heat and Fluid Flow, 50 (2014) 63–71.CrossRefGoogle Scholar
  20. [20]
    Z. Y. Luo, L. He and B. F. Bai, Deformation of spherical compound capsules in simple shear flow, J. of Fluid Mechanics, 775 (2015) 77–104.MathSciNetCrossRefGoogle Scholar
  21. [21]
    S. O. Unverdi and G. Tryggvason, A front-tracking method for viscous, incompressible, multi-fluid flows, J. of Computational Physics, 100 (1) (1992) 25–37.CrossRefzbMATHGoogle Scholar
  22. [22]
    G. Tryggvason, R. Scardovelli and S. Zaleski, Direct numerical simulations of gas-liquid multiphase flows, Cambridge University Press, Cambridge (2011).CrossRefzbMATHGoogle Scholar
  23. [23]
    T. V. Vu, A. V. Truong, N. T. Hoang and D. K. Tran, Numerical investigations of solidification around a circular cylinder under forced convection, J. of Mechanical Science and Technology, 30 (11) (2016) 5019–5028.CrossRefGoogle Scholar
  24. [24]
    G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas and Y.-J. Jan, A fronttracking method for the computations of multiphase flow, J. of Computational Physics, 169 (2) (2001) 708–759.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    T. V. Vu, G. Tryggvason, S. Homma and J. C. Wells, Numerical investigations of drop solidification on a cold plate in the presence of volume change, International J. of Multiphase Flow, 76 (2015) 73–85.MathSciNetCrossRefGoogle Scholar
  26. [26]
    T. V. Vu, Three-phase computation of solidification in an open horizontal circular cylinder, International J. of Heat and Mass Transfer, 111 (2017) 398–409.CrossRefGoogle Scholar
  27. [27]
    C. W. Hirt and B. D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. of Computational Physics, 39 (1) (1981) 201–225.CrossRefzbMATHGoogle Scholar
  28. [28]
    M. Sussman, E. Fatemi, P. Smereka and S. Osher, An improved level set method for incompressible two-phase flows, Computers & Fluids, 27 (5–6) (1998) 663–680.CrossRefzbMATHGoogle Scholar
  29. [29]
    C. S. Peskin, Numerical analysis of blood flow in the heart, J. of Computational Physics, 25 (3) (1977) 220–252.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    S. Homma, J. Koga, S. Matsumoto, M. Song and G. Tryggvason, Breakup mode of an axisymmetric liquid jet injected into another immiscible liquid, Chemical Engineering Science, 61 (12) (2006) 3986–3996.CrossRefGoogle Scholar
  31. [31]
    M. M. Francois, S. J. Cummins, E. D. Dendy, D. B. Kothe, J. M. Sicilian and M. W. Williams, A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework, J. of Computational Physics, 213 (1) (2006) 141–173.CrossRefzbMATHGoogle Scholar
  32. [32]
    S. Choi, M. H. Cho, H. G. Choi and J. Y. Yoo, A Q2Q1 integrated finite element method with the semi-implicit consistent CSF for solving incompressible two-phase flows with surface tension effect, International J. for Numerical Methods in Fluids, 81 (5) (2016) 284–308.MathSciNetCrossRefGoogle Scholar
  33. [33]
    S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, Accurate representation of surface tension using the level contour reconstruction method, J. of Computational Physics, 203 (2) (2005) 493–516.CrossRefzbMATHGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Transportation EngineeringHanoi University of Science and TechnologyHanoiVietnam
  2. 2.Mokpo National UniversityChonnamKorea

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