- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Lattice Boltzmann simulations of droplet breakup in confined and time-dependent flows

Felix Milan1,2,*, Luca Biferale1,†, Mauro Sbragaglia1,‡, and Federico Toschi2,3,4,§

  • 1Department of Physics and INFN, University of Rome “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Rome, Italy
  • 2Department of Applied Physics, Eindhoven University of Technology, Eindhoven 5600 MB, The Netherlands
  • 3Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven 5600 MB, The Netherlands
  • 4CNR-IAC, Via dei Taurini 19, 00185 Rome, Italy

  • *felix.milan@roma2.infn.it
  • †biferale@roma2.infn.it
  • ‡sbragaglia@roma2.infn.it
  • §f.toschi@tue.nl
PDF

Phys. Rev. Fluids 5, 033607 – Published 10 March, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.033607

Abstract

We study droplet dynamics and breakup in generic time-dependent flows via a multicomponent lattice Boltzmann algorithm, with emphasis on flow startup conditions. We first study droplet breakup in a confined oscillatory shear flow via two different protocols. In one setup, we start from an initially spherical droplet and turn on the flow abruptly (“shock method”); in the other protocol, we start from an initially spherical droplet as well, but we progressively increase the amplitude of the flow, by allowing the droplet to relax to the steady state for each increase in amplitude, before increasing the flow amplitude again (“relaxation method”). The two protocols are shown to produce substantially different breakup scenarios. The mismatch between these two protocols is also studied for variations in the flow topology, the degree of confinement, and the inertia of the fluid. All results point to the fact that under extreme conditions of confinement the relaxation protocols can drive the droplets into metastable states, which break only for very intense flow amplitudes, but their stability is prone to external perturbations, such as an oscillatory driving force.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (86)

  1. R. W. Flumerfelt, Drop breakup in simple shear fields of viscoleastic fluids, Ind. Eng. Chem. Fundam. 11, 312 (1972).
  2. J. Rodriguez-Rodriguez, A. Sevilla, C. Martinez-Bazan, and J. M. Gordillo, Generation of microbubbles with applications to industry and medicine, Annu. Rev. Fluid Mech. 47, 405 (2015).
  3. H. Shewan and J. R. Stokes, Review of techniques to manufacture microhydrogel particles for the food industry and their applications, J. Food Eng. 119, 781 (2013).
  4. M. Singh, H. M. Haverinen, and P. Dhagat, Inkjet printing-process and its applications, Adv. Funct. Mater. 22, 673 (2010).
  5. I. Fortelny and J. Juza, Description of the droplet size evolution in flowing immiscible polymer blends, Polymers 11, 761 (2019).
  6. F. Greco, Drop deformation for non-Newtonian fluids in slow flows, J. Non-Newtonian Fluid Mech. 107, 111 (2002).
  7. Stefano Guido and Francesco Greco, Dynamics of a liquid drop in a flowing immiscible liquid, Rheol. Rev. 2, 99 (2004).
  8. P. J. A. Janssen and P. D. Anderson, A boundary-integral model for drop deformation between two parallel plates with nonunit viscosity ratio drops, J. Comput. Phys. 227, 8807 (2008).
  9. G. I. Taylor, The viscosity of a fluid containing small drops of another fluid, Proc. Roy. Soc. A: Math. Phys. Eng. Sci. 138, 41 (1932).
  10. F. Greco, Second-order theory for the deformation of a Newtonian drop in a stationary flow field, Phys. Fluids (1994-present) 14, 946 (2002).
  11. A. Acrivos and T. D. Taylor, The Stokes flow past an arbitrary particle, Chem. Eng. Sci. 19, 445 (1964).
  12. J. Lyngaae-Jørgensen and A. Valenza, Structuring of polymer blends in simple shear flow, Makromol. Chem. Macromol. Symp. 38, 43 (1990).
  13. S. Guido, Shear-induced droplet deformation: Effects of confined geometry and viscoelasticity, Curr. Opin. Colloid Interface Sci. 16, 61 (2011).
  14. P. J. A. Janssen, A. Vananroye, P. Van Puyvelde, P. Moldenaers, and P. D. Anderson, Generalized behavior of the breakup of viscous drops in confinements, J. Rheol. 54, 1047 (2010).
  15. A. Vananroye, R. Cardinaels, P. Van Puyvelde, and P. Moldenaers, Effect of confinement and viscosity ratio on the dynamics of single droplets during transient shear flow, J. Rheol. 52, 1459 (2008).
  16. R. Cardinaels and P. Moldenaers, Droplet relaxation in blends with one viscoelastic component: Bulk and confined conditions, Rheologica Acta 49, 941 (2010).
  17. R. Cardinaels and P. Moldenaers, Critical conditions and breakup of nonsquashed microconfined droplets: Effects of fluid viscoelasticity, Microfluid Nanofluid 10, 1153 (2011).
  18. R. Cardinaels, K. Verhulst, and P. Moldenaers, Influence of confinement on the steady state behavior of single droplets in shear flow for immiscible blends with one viscoelastic component, J. Rheol. (1978-present) 53, 1403 (2009).
  19. R. Cardinaels, A. Vananroye, P. Van Puyvelde, and P. Moldenaers, Breakup criteria for confined droplets: Effects of compatibilization and component viscoelasticity, Macromol. Mater. Eng. 296, 214 (2011).
  20. P. De Bruyn, R. Cardinaels, and P. Moldenaers, The effect of geometrical confinement on coalescence efficiency of droplet pairs in shear flow, J. Colloid Interface Sci. 409, 183 (2013).
  21. P. Van Puyvelde, A. Vananroye, R. Cardinaels, and P. Moldenaers, Review on morphology development of immiscible blends in confined shear flow, Polymer 49, 5363 (2008).
  22. A. Vananroye, P. Van Puyvelde, and P. Moldenaers, Effect of confinement on droplet breakup in sheared emulsions, Langmuir 22, 3972 (2006).
  23. A. Vananroye, P. Van Puyvelde, and P. Moldenaers, Effect of confinement on the steady-state behavior of single droplets during shear flow, J. Rheol. 51, 139 (2007).
  24. A. Vananroye, P. Van Puyvelde, and P. Moldenaers, Deformation and orientation of single droplets during shear flow: Combined effects of confinement and compatibilization, Rheologica acta 50, 231 (2011).
  25. M. Shapira and S. Haber, Low reynolds number motion of a droplet between two parallel plates, Int. J. Multiph. Flow 14, 483 (1988).
  26. M. Shapira and S. Haber, Low reynolds-number motion of a droplet in shear flow including wall effects, Int. J. Multiph. Flow 16, 305 (1990).
  27. G. I. Taylor, The formation of emulsion in definable field of flow, Proc. Roy. Soc. A 146, 501 (1934).
  28. P. L. Maffettone and M. Minale, Equation of change for ellipsoidal drops in viscous flow, J. Non-Newton. Fluid Mech 78, 227 (1998).
  29. M. Minale, A phenomenological model for wall effects on the deformation of an ellipsoidal drop in viscous flow, Rheol. Acta 47, 667 (2008).
  30. M. Minale, Models for the deformation of a single ellipsoidal drop: A review, Rheol. Acta 49, 789 (2010).
  31. V. Sibillo, G. Pasquariello, M. Simeone, V. Cristini, and S. Guido, Drop Deformation in Microconfined Shear Flow, Phys. Rev. Lett. 97, 054502 (2006).
  32. M. Minale, S. Caserta, and S. Guido, Microconfined shear deformation of a droplet in an equiviscous non-Newtonian immiscible fluid: Experiments and modeling, Langmuir 26, 126 (2010).
  33. N. Aggarwal and K. Sarkar, Deformation and breakup of a viscoelastic drop in a Newtonian matrix under steady shear, J. Fluid Mech. 584, 1 (2007).
  34. N. Aggarwal and K. Sarkar, Effects of matrix viscoelasticity on viscous and viscoelastic drop deformation in a shear flow, J. Fluid Mech. 601, 63 (2008).
  35. S. Caserta, S. Reynaud, M. Simeone, and S. Guido, Drop deformation in sheared polymer blends, J. Rheol. 51, 761 (2007).
  36. C. E. Chaffey and H. A. Brenner, A second-order theory for shear deformation of drops, J. Colloid Interface Sci. 24, 258 (1967).
  37. T. Chinyoka, Y. Y. Renardy, M. Renardy, and D. B. Khismatullin, Two-dimensional study of drop deformation under simple shear for Oldroyd-B liquids, J. Non-Newtonian Fluid Mech. 130, 45 (2005).
  38. J. J. Elmendorp and R. J. Maalcke, A study on polymer blending microrheology: Part 1, Polym. Eng. Sci. 25, 1041 (1985).
  39. K. Feigl, S. F. M. Kaufmann, P. Fischer, and E. J. Windhab, A numerical procedure for calculating droplet deformation in dispersing flows and experimental verification, Chem. Eng. Sci. 58, 2351 (2002).
  40. H. P. Grace, Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems, Chem. Eng. Commun. 14, 225 (1982).
  41. A. E. Komrakovaa, O. Shardt, D. Eskinb, and J. J. Derksen, Lattice Boltzmann simulations of drop deformation and breakup in shear flow, Int. J. Multiphase Flow 59, 24 (2014).
  42. H. Li and U. Sundararaj, Does drop size affect the mechanism of viscoelastic drop breakup? Phys. Fluids 20, 053101 (2008).
  43. J. Li, Y. Y. Renardy, and M. Renardy, Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method, Phys. Fluids 12, 269 (2000).
  44. H. Liu, A. J. Valocchi, and Q. Kang, Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations, Phys. Rev. E 85, 046309 (2012).
  45. D. Megias-Alguacil, K. Feigl, M. Dressler, P. Fischer, and E. J. Windhab, Droplet deformation under simple shear investigated by experiment, numerical simulation and modeling, J. Non-Newtonian Fluid Mech. 126, 153 (2005).
  46. F. Mighri and M. A. Huneault, In situ visualization of drop deformation, erosion, and breakup in high viscosity ratio polymeric systems under high shearing stress conditions, J. Appl. Polym. Sci. 42, 25822591 (2006).
  47. F. Mighri, P. J. Carreau, and A. Ajji, Influence of elastic properties on drop deformation and breakup in shear flow, J. Rheol. (1978-present) 42, 1477 (1998).
  48. S. Mukherjee and K. Sarkar, Effects of viscosity ratio on deformation of a viscoelastic drop in a Newtonian matrix under steady shear, J. Non-Newtonian Fluid Mech. 160, 104 (2009).
  49. S. B. Pillapakkam and P. Singh, A level-set method for computing solutions to viscoelastic two-phase flow, J. Comput. Phys. 174, 552 (2001).
  50. Y. Y. Renardy and V. Cristini, Effect of inertia on drop breakup under shear, Phys. Fluids 13, 7 (2001).
  51. V. Sibillo, M. Simeone, and S. Guido, Breakup of a Newtonian drop in a viscoelastic matrix under simple shear flow, Rheol. Acta 43, 449 (2004).
  52. C. L. Tucker and P. Moldenaers, Microstructural evolution in polymer blends, Annu. Rev. Fluid Mech. 34, 177 (2002).
  53. X. Zhao, Drop breakup in dilute Newtonian emulsions in simple shear flow: New drop breakup mechanisms, J. Rheol. 51, 367 (2007).
  54. B. J. Bentley and L. G. Leal, An experimental investigation of drop deformation and breakup in steady two-dimensional linear flows, J. Fluid Mech. 167, 241 (1986).
  55. J. F. Brady and A. Acrivos, The deformation and breakup of a slender drop in an extensional flow: Inertial effects, J. Fluid Mech. 115, 443 (1982).
  56. E. J. Hinch and A. Acrivos, Long slender drops in a simple shear flow, J. Fluid Mech. 98, 305 (1980).
  57. Y. Renardy, Effect of startup conditions on drop breakup under shear with inertia, J. Multiphase Flow 34, 1185 (2008).
  58. S. Torza, R. G. Cox, and S. G. Mason, Particle motions in sheared suspensions XXVII. Transient and steady deformation and burst of liquid drops, J. Colloid Interface Sci. 38, 395 (1972).
  59. R. Cavallo, S. Guido, and M. Simeone, Drop deformation under small-amplitude oscillatory shear flow, Rheol Acta 42, 1 (2002).
  60. R. G. Cox, The deformation of a drop in a general time-dependent fluid flow, J. Fluid Mech. 37, 601 (1969).
  61. A. Farutin and C. Misbah, Rheology of vesicle suspensions under combined steady and oscillating shear flows, J. Fluid Mech. 700, 362 (2012).
  62. F. Milan, M. Sbragaglia, L. Biferale, and F. Toschi, Lattice Boltzmann simulations of droplet dynamics in time-dependent flows, Eur. Phys. J. E 41, 6 (2018).
  63. W. Yu., M. Bousmina, M. Grmela, and C. Zhou, Modeling of oscillatory shear flow of emulsions under small and large deformation fields, J. Rheol. 46, 1401 (2002).
  64. R. Benzi, S. Succi, and M. Vergassola, The lattice Boltzmann equation: Theory and applications, Phys. Rep. 222, 145 (1992).
  65. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Oxford University Press, Oxford, UK, 2001).
  66. M. Sbragaglia, R. Benzi, M. Bernaschi, and S. Succi, The emergence of supramolecular forces from lattice kinetic models of nonideal fluids: Applications to the rheology of soft glassy materials, Soft Matter 8, 10773 (2012).
  67. J. Onishi, Y. Chen, and H. Ohashi, A lattice Boltzmann model for polymeric liquids, Prog. Comp. Fluid Dyn. 5, 75 (2005).
  68. M. Gross, M. E. Cates, F. Varnik, and R. Adhikari, Langevin theory of fluctuations in the discrete Boltzmann equation, J. Stat. Mech. (2011) P03030.
  69. X. Xue, M. Sbragaglia, L. Biferale, and F. Toschi, Effects of thermal fluctuations in the fragmentation of a nanoligament, Phys. Rev. E 98, 012802 (2018).
  70. D. Chiappini, X. Xue, G. Falcucci, and M. Sbragaglia, Ligament breakup simulation through pseudopotential lattice Boltzmann method, In AIP Conference Proceedings, Vol. 1978 (AIP Publishing, 2018), p. 420003.
  71. D. Chiappini, M. Sbragaglia, X. Xue, and G. Falcucci, Hydrodynamic behavior of the pseudopotential lattice Boltzmann method for interfacial flows, Phys. Rev. E 99, 053305 (2019).
  72. S. Farokhirad, T. Lee, and J. F. Morris, Effects of inertia and viscosity on single droplet deformation in confined shear flow, Commun. Comput. Phys. 13, 706 (2013).
  73. A. Gupta and M. Sbragaglia, Deformation and breakup of viscoelastic droplets in confined shear flow, Phys. Rev. E: Stat. Nonlin. Soft Matter Phys. 90, 1 (2014).
  74. A. Gupta, M. Sbragaglia, and A. Scagliarini, Hybrid lattice Boltzmann/finite difference simulations of viscoelastic multicomponent flows in confined geometries, J. Comput. Phys. 291, 177 (2015).
  75. J. Onishi, Y. Chen, and H. Ohashi, Dynamic simulation of multicomponent viscoelastic fluids using the lattice Boltzmann method, Physica A 362, 84 (2006).
  76. H. Xi and C. Duncan, Lattice Boltzmann simulations of three-dimensional single droplet deformation and breakup under simple shear flow, Phys. Rev. E 59, 3022 (1999).
  77. M. Yoshino, Y. Toriumi, and M. Arai, Lattice Boltzmann simulation of two-phase viscoelastic fluid flows, J. Comput. Sci. Technol. 2, 330 (2008).
  78. X. Shan and H. Chen, Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E 47, 1815 (1993).
  79. X. Shan and H. Chen, Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation, Phys. Rev. E 49, 2941 (1994).
  80. M. Sbragaglia and D. Belardinellli, Interaction pressure tensor for a class of multicomponent lattice Boltzmann models, Phys. Rev. E 88, 013306 (2013).
  81. M. Sega, M. Sbragaglia, S. Kantorovich, and A. Ivanov, Interaction pressure tensor for a class of multicomponent lattice Boltzmann models, Soft Matter 9, 10092 (2013).
  82. D. d'Humières, I. Ginzburg, M. Krafczyk, P. Lallemand, and L. Luo, Multiple-relaxation-time lattice Boltzmann models in three dimensions, Roy. Soc. 360, 437 (2002).
  83. M. Hecht and J. Harting, Implementation of on-site velocity boundary conditions for d3q19 lattice Boltzmann simulations, J. Stat. Mech. (2010) P01018.
  84. K. Mattila, J. Hyväluoma, and T. Rossi, Mass-flux-based outlet boundary conditions for the lattice Boltzmann method, J. Stat. Mech. (2009) P06015.
  85. Q. Zou and X. He, On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Phys. Fluids 9, 1591 (1997).
  86. L. Biferale, P. Perlekar, M. Sbragaglia, S. Srivastava, and F. Toschi, A lattice Boltzmann method for turbulent emulsions, J. Phys.: Conf. Ser. 318, 052017 (2011).

Outline

Information

Phys. Rev. Fluids 5, 033607– Published 10 March, 2020
  • Received 15 October 2019
  • Accepted 11 February 2020
Crossmark - Check for updates button

©2020 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation