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Oscillations of small bubbles and medium yielding in elastoviscoplastic fluids

Marco De Corato1,*, Brice Saint-Michel1, George Makrigiorgos2,†, Yannis Dimakopoulos2, John Tsamopoulos2,‡, and Valeria Garbin1,§

  • 1Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
  • 2Fluid Mechanics and Rheology Laboratory, Department of Chemical Engineering, University of Patras, Patras 26500, Greece

  • *Present address: Institute for Bioengineering of Catalonia (IBEC), Baldiri i Reixac 10-12, 08028 Barcelona, Spain.
  • †Present address: Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA.
  • ‡tsamo@chemeng.upatras.gr
  • §v.garbin@imperial.ac.uk
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Phys. Rev. Fluids 4, 073301 – Published 1 July, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.073301

Abstract

We investigate the radial oscillations of small gas bubbles trapped in yield-stress fluids and driven by an acoustic pressure field. We model the rheological behavior of the yield-stress fluid using the recently developed elastoviscoplastic constitutive equation that takes into account the elastic and viscoplastic deformations of the material [Saramito, J. Non-Newton. Fluid Mech. 158, 154 (2009)]. Assuming that the bubble remains spherical during the pressure driving, we reduce the problem to a set of ordinary differential equations and an integrodifferential equation, which we solve numerically for the case of two yield-stress fluids, i.e., a soft Carbopol gel and a stiffer kaolin suspension. We find that depending on the amplitude and frequency of the pressure field, the radial oscillations of the bubble produce elastic stresses that may or may not suffice to yield the surrounding material. We evaluate the critical amplitude of the acoustic pressure required to achieve yielding and we find a good agreement between numerical simulations and an analytical formula derived under the assumption of linear deformations. Finally, we examine the bubble oscillation amplitude for a very wide range of applied pressures both below and above the critical value to assess the impact of yielding on the bubble dynamics. This analysis could be used to identify a signature of yielding in experiments where the radial dynamics of a bubble is measured. More generally, these results can be used to rationalize the optimal conditions for pressure-induced bubble release from yield-stress fluids, which is relevant to various biomedical and industrial applications, including the oil industry and food processing.

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References (71)

  1. P. Coussot, Yield-stress fluid flows: A review of experimental data, J. Non-Newton. Fluid Mech. 211, 31 (2014).
  2. D. Bonn, M. M. Denn, L. Berthier, T. Divoux, and S. Manneville, Yield-stress materials in soft condensed matter, Rev. Mod. Phys. 89, 035005 (2017).
  3. A. Beris, J. Tsamopoulos, R. Armstrong, and R. Brown, Creeping motion of a sphere through a Bingham plastic, J. Fluid Mech. 158, 219 (1985).
  4. N. Dubash and I. Frigaard, Conditions for static bubbles in viscoplastic fluids, Phys. Fluids 16, 4319 (2004).
  5. N. Dubash and I. Frigaard, Propagation and stopping of air bubbles in Carbopol solutions, J. Non-Newton. Fluid Mech. 142, 123 (2007).
  6. J. P. Singh and M. M. Denn, Interacting two-dimensional bubbles and droplets in a yield-stress fluid, Phys. Fluids 20, 040901 (2008).
  7. J. Tsamopoulos, Y. Dimakopoulos, N. Chatzidai, G. Karapetsas, and M. Pavlidis, Steady bubble rise and deformation in Newtonian and viscoplastic fluids and conditions for bubble entrapment, J. Fluid Mech. 601, 123 (2008).
  8. D. Sikorski, H. Tabuteau, and J. R. de Bruyn, Motion and shape of bubbles rising through a yield-stress fluid, J. Non-Newton. Fluid Mech. 159, 10 (2009).
  9. Y. Dimakopoulos, M. Pavlidis, and J. Tsamopoulos, Steady bubble rise in Herschel-Bulkley fluids and comparison of predictions via the augmented Lagrangian method with those via the Papanastasiou model, J. Non-Newton. Fluid Mech. 200, 34 (2013).
  10. M. K. Tripathi, K. C. Sahu, G. Karapetsas, and O. K. Matar, Bubble rise dynamics in a viscoplastic material, J. Non-Newton. Fluid Mech. 222, 217 (2015).
  11. W. F. Lopez, M. F. Naccache, and P. R. de Souza Mendes, Rising bubbles in yield-stress materials, J. Rheol. 62, 209 (2018).
  12. R. P. Sofjan and R. W. Hartel, Effects of overrun on structural and physical characteristics of ice cream, Int. Dairy J. 14, 255 (2004).
  13. H. Luyten, J. Plijter, and T. Van Vliet, Crispy/crunchy crusts of cellular solid foods: A literature review with discussion, J. Texture Stud. 35, 445 (2004).
  14. S. H. Kostmaka and M. L. Wilson, Design and Control of Concrete Mixtures (Portland Cement Association, Skokie, USA, 2011).
  15. A. D. Mazzeo, Centrifugal casting and fast curing of polydimethylsiloxane (PDMS) for the manufacture of micro and nano featured components, Ph.D. thesis, Massachusetts Institute of Technology, 2009.
  16. A. Bonett and D. Pafitis, Getting to the root of gas migration, Oilfield Rev. 8, 36 (1996).
  17. BP Investigation team, Deepwater Horizon Accident Investigation Report, British Petroleum, 2010.
  18. A. Johnson and D. White, Gas-rise velocities during kicks, SPE Drill. Eng. 6, 257 (1991).
  19. T. J. Lin, Mechanisms and control of gas bubble formation in cosmetics, J. Soc. Cosmet. Chem. 22, 323 (1971).
  20. J. A. Koch, D. I. Castaneda, R. H. Ewoldt, and D. A. Lange, Vibration of fresh concrete understood through the paradigm of granular physics, Cem. Concr. Res. 115, 31 (2019).
  21. S. Stein and H. Buggisch, Rise of pulsating bubbles in fluids with a yield stress, Z. Angew. Math. Mech. 80, 827 (2000).
  22. G. Karapetsas, D. Photeinos, Y. Dimakopoulos, and J. Tsamopoulos, Dynamics and motion of a gas bubble in a viscoplastic medium under acoustic excitation, J. Fluid Mech. 865, 381 (2019).
  23. S. Iwata, Y. Yamada, T. Takashima, and H. Mori, Pressure-oscillation defoaming for viscoelastic fluid, J. Non-Newton. Fluid Mech. 151, 30 (2008).
  24. S. Iwata, T. Takahashi, T. Onuma, R. Nagumo, and H. Mori, Local flow around a tiny bubble under a pressure-oscillation field in a viscoelastic worm-like micellar solution, J. Non-Newton. Fluid Mech. 263, 24 (2019).
  25. G. Astarita and G. Apuzzo, Motion of gas bubbles in non-Newtonian liquids, AIChE J. 11, 815 (1965).
  26. O. Hassager, Negative wake behind bubbles in non-Newtonian liquids, Nature (London) 279, 402 (1979).
  27. C. Pilz and G. Brenn, On the critical bubble volume at the rise velocity jump discontinuity in viscoelastic liquids, J. Non-Newton. Fluid Mech. 145, 124 (2007).
  28. J. Papaioannou, A. Giannousakis, Y. Dimakopoulos, and J. Tsamopoulos, Bubble deformation and growth inside viscoelastic filaments undergoing very large extensions, Ind. Eng. Chem. Res. 53, 7548 (2014).
  29. D. Fraggedakis, M. Pavlidis, Y. Dimakopoulos, and J. Tsamopoulos, On the velocity discontinuity at a critical volume of a bubble rising in a viscoelastic fluid, J. Fluid Mech. 789, 310 (2016).
  30. A. Ellis, J. G. Waugh, and R. Y. Ting, Cavitation suppression and stress effects in high-speed flows of water with dilute macromolecule additives, J Basic Eng. 92, 459 (1970).
  31. H. S. Fogler and J. D. Goddard, Collapse of spherical cavities in viscoelastic fluids, Phys. Fluids 13, 1135 (1970).
  32. A. C. Papanastasiou, L. E. Scriven, and C. W. Macosko, Bubble growth and collapse in viscoelastic liquids analyzed, J. Non-Newton. Fluid Mech. 16, 53 (1984).
  33. C. Kim, Collapse of spherical bubbles in Maxwell fluids, J. Non-Newton. Fluid Mech. 55, 37 (1994).
  34. J. Jimenez-Fernandez and A. Crespo, Bubble oscillation and inertial cavitation in viscoelastic fluids, Ultrasonics 43, 643 (2005).
  35. J. Naude and F. Mendez, Periodic and chaotic acoustic oscillations of a bubble gas immersed in an upper convective Maxwell fluid, J. Non-Newton. Fluid Mech. 155, 30 (2008).
  36. H. A. Kafiabad and K. Sadeghy, Chaotic behavior of a single spherical gas bubble surrounded by a Giesekus liquid: A numerical study, J. Non-Newton. Fluid Mech. 165, 800 (2010).
  37. F. R. Cunha and D. L. Albernaz, Oscillatory motion of a spherical bubble in a non-Newtonian fluid, J. Non-Newton. Fluid Mech. 191, 35 (2013).
  38. J. S. Allen and R. A. Roy, Dynamics of gas bubbles in viscoelastic fluids. II. Nonlinear viscoelasticity, J. Acoust. Soc. Am. 108, 1640 (2000).
  39. J. S. Allen and R. A. Roy, Dynamics of gas bubbles in viscoelastic fluids. I. Linear viscoelasticity, J. Acoust. Soc. Am. 107, 3167 (2000).
  40. R. G. Holt and R. A. Roy, Measurements of bubble-enhanced heating from focused, MHz-frequency ultrasound in a tissue-mimicking material, Ultrasound Med. Biol. 27, 1399 (2001).
  41. X. Yang and C. C. Church, A model for the dynamics of gas bubbles in soft tissue, J. Acoust. Soc. Am. 118, 3595 (2005).
  42. C. Hua and E. Johnsen, Nonlinear oscillations following the Rayleigh collapse of a gas bubble in a linear viscoelastic (tissue-like) medium, Phys. Fluids 25, 083101 (2013).
  43. M. Warnez and E. Johnsen, Numerical modeling of bubble dynamics in viscoelastic media with relaxation, Phys. Fluids 27, 063103 (2015).
  44. R. Gaudron, M. Warnez, and E. Johnsen, Bubble dynamics in a viscoelastic medium with nonlinear elasticity, J. Fluid Mech. 766, 54 (2015).
  45. P. Movahed, W. Kreider, A. D. Maxwell, S. B. Hutchens, and J. B. Freund, Cavitation-induced damage of soft materials by focused ultrasound bursts: A fracture-based bubble dynamics model, J. Acoust. Soc. Am. 140, 1374 (2016).
  46. E. Zilonova, M. Solovchuk, and T. Sheu, Bubble dynamics in viscoelastic soft tissue in high-intensity focal ultrasound thermal therapy, Ultrason. Sonochem. 40, 900 (2018).
  47. F. Hamaguchi and K. Ando, Linear oscillation of gas bubbles in a viscoelastic material under ultrasound irradiation, Phys. Fluids 27, 113103 (2015).
  48. A. Jamburidze, M. De Corato, A. Huerre, A. Pommella, and V. Garbin, High-frequency linear rheology of hydrogels probed by ultrasound-driven microbubble dynamics, Soft Matter 13, 3946 (2017).
  49. J. B. Estrada, C. Barajas, D. L. Henann, E. Johnsen, and C. Franck, High strain-rate soft material characterization via inertial cavitation, J. Mech. Phys. Solids 112, 291 (2018).
  50. B. Dollet, P. Marmottant, and V. Garbin, Bubble dynamics in soft and biological matter, Annu. Rev. Fluid Mech. 51, 331 (2019).
  51. N. Mougin, A. Magnin, and J.-M. Piau, The significant influence of internal stresses on the dynamics of bubbles in a yield stress fluid, J. Non-Newton. Fluid Mech. 171-172, 42 (2012).
  52. W. J. Yang and H. Yeh, Theoretical study of bubble dynamics in purely viscous fluids, AlChE J. 12, 927 (1966).
  53. T. C. Papanastasiou, Flows of materials with yield, J. Rheol. 31, 385 (1987).
  54. Y. Dimakopoulos, G. Makrigiorgos, G. Georgiou, and J. Tsamopoulos, The PAL (Penalized Augmented Lagrangian) method for computing viscoplastic flows: A new fast converging scheme, J. Non-Newton. Fluid Mech. 256, 23 (2018).
  55. P. Saramito, A new elastoviscoplastic model based on the Herschel-Bulkley viscoplastic model, J. Non-Newton. Fluid Mech. 158, 154 (2009).
  56. D. Fraggedakis, Y. Dimakopoulos, and J. Tsamopoulos, Yielding the yield stress analysis: A thorough comparison of recently proposed elasto-visco-plastic (EVP) fluid models, J. Non-Newton. Fluid Mech. 236, 104 (2016).
  57. D. Fraggedakis, Y. Dimakopoulos, and J. Tsamopoulos, Yielding the yield-stress analysis: A study focused on the effects of elasticity on the settling of a single spherical particle in simple yield-stress fluids, Soft Matter 12, 5378 (2016).
  58. G. Ovarlez, Q. Barral, and P. Coussot, Three-dimensional jamming and flows of soft glassy materials, Nat. Mater. 9, 115 (2010).
  59. L. Martinie, H. Buggisch, and N. Willenbacher, Apparent elongational yield stress of soft matter, J. Rheol. 57, 627 (2013).
  60. X. Zhang, O. Fadoul, E. Lorenceau, and P. Coussot, Yielding and Flow of Soft-Jammed Systems in Elongation, Phys. Rev. Lett. 120, 048001 (2018).
  61. A. Prosperetti, A generalization of the Rayleigh-Plesset equation of bubble dynamics, Phys. Fluids 25, 409 (1982).
  62. L. Lacaze, A. Filella, and O. Thual, Steady and unsteady shear flows of a viscoplastic fluid in a cylindrical Couette cell, J. Non-Newton. Fluid Mech. 220, 126 (2015).
  63. L. H. Luu and Y. Forterre, Drop impact of yield-stress fluids, J. Fluid Mech. 632, 301 (2009).
  64. M. Dinkgreve, M. Fazilati, M. M. Denn, and D. Bonn, Carbopol: From a simple to a thixotropic yield-stress fluid, J. Rheol. 62, 773 (2018).
  65. E. Zana and L. Leal, Dissolution of a stationary gas bubble in a quiescent, viscoelastic liquid, Ind. Eng. Chem. Fundam. 14, 175 (1975).
  66. A. Prosperetti, Thermal effects and damping mechanisms in the forced radial oscillations of gas bubbles in liquids, J. Acoust. Soc. Am. 61, 17 (1977).
  67. J. Magnaudet and I. Eames, The motion of high-Reynolds-number bubbles in inhomogeneous flows, Annu. Rev. Fluid Mech. 32, 659 (2000).
  68. O. Vincent, P. Marmottant, P. A. Quinto-Su, and C.-D. Ohl, Birth and Growth of Cavitation Bubbles within Water under Tension Confined in a Simple Synthetic Tree, Phys. Rev. Lett. 108, 184502 (2012).
  69. O. Vincent, P. Marmottant, S. R. Gonzalez-Avila, K. Ando, and C.-D. Ohl, The fast dynamics of cavitation bubbles within water confined in elastic solids, Soft Matter 10, 1455 (2014).
  70. N. Louvet, D. Bonn, and H. Kellay, Nonuniversality in the Pinch-Off of Yield-Stress Fluids: Role of Nonlocal Rheology, Phys. Rev. Lett. 113, 218302 (2014).
  71. V. T. O'Brien and M. E. Mackay, Shear and elongation flow properties of kaolin suspensions, J. Rheol. 46, 557 (2002).

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Phys. Rev. Fluids 4, 073301– Published 1 July, 2019
  • Received 18 March 2019
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