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Annual Review of Fluid Mechanics

Volume 50, 2018

Hydrodynamic Interactions Among Bubbles, Drops, and Particles in Non-Newtonian Liquids

Abstract

The understanding of hydrodynamic forces around particles, drops, or bubbles moving in Newtonian liquids is modestly mature. It is possible to obtain predictions of the attractive–repulsive interaction for moving ensembles of dispersed particulate objects. There is a certain intuition of what the effects of viscous, inertial, and surface tension forces should be. When the liquid is non-Newtonian, this intuition is gone. In this review, we summarize recent efforts at gaining fundamental understanding of hydrodynamic interactions in non-Newtonian liquids. Due to the complexity of the problem, most investigations rely on experimental observations. However, computations of non-Newtonian fluid flow have made increasingly significant contributions to our understanding of particle, drop, and bubble interactions. We focus on gravity-driven flows: rise or sedimentation of single spheroidal objects, pairs, and dispersions. We identify the effects of two main rheological attributes—viscoelasticity and shear-dependent viscosity—on the interaction and potential aggregation of particles, drops, and bubbles. We end by highlighting the open questions in the subject and by suggesting future directions toward the fundamental physics as well as applications.

Keyword(s): bubble velocity discontinuity, bubbles, clustering, negative wake, pairwise interaction, particles, shear thinning, viscoelasticity

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2018-01-05
2024-04-26
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Literature Cited

  1. Acharya A, Ulbrecht J. 1978. Note on the influence of viscoelasticity on the coalescence rate of bubbles and drops. AIChE J 24:348–51 [Google Scholar]
  2. Ardekani AM, Rangel RH, Joseph DD. 2008. Two spheres in a free stream of a second-order fluid. Phys. Fluids 20:063101 [Google Scholar]
  3. Arigo M, McKinley G. 1998. An experimental investigation of negative wakes behind spheres settling in a shear-thinning viscoelastic fluid. Rheol. Acta 37:307–27 [Google Scholar]
  4. Astarita G, Apuzzo G. 1965. Motion of gas bubbles in non-Newtonian liquids. AIChE J 11:815–20 [Google Scholar]
  5. Barnes H, Hutton JF, Walters K. 1989. An Introduction to Rheology Amsterdam: Elsevier
  6. Bartram E, Goldsmith HL, Mason SG. 1975. Particle motions in non-Newtonian media. III. Further observations in elasticoviscous fluids. Rheol. Acta 14:776–82 [Google Scholar]
  7. Binous H, Phillips RJ. 1999. Dynamic simulation of one and two particles sedimenting in viscoelastic suspensions of FENE dumbbells. J. Non-Newton. Fluid Mech. 83:93–130 [Google Scholar]
  8. Bird RB, Armstrong RC, Hassager O. 1987. Dynamics of Polymeric Liquids 1 Fluid Mechanics New York: Wiley
  9. Blomley MJK, Cooke JC, Unger EC, Monaghan MJ, Cosgrove DO. 2001. Microbubble contrast agents: a new era in ultrasound. BMJ 322:1222–25 [Google Scholar]
  10. Bobroff S, Phillips RJ. 1998. Nuclear magnetic resonance imaging investigation of sedimentation of concentrated suspensions in non-Newtonian fluids. J. Rheol. 42:1419–36 [Google Scholar]
  11. Bot ETG, Hulsen M, van den Brule B. 1998. The motion of two spheres falling along their line of centres in a Boger fluid. J. Non-Newton. Fluid Mech. 79:191–212 [Google Scholar]
  12. Brunn P. 1977. Interaction of spheres in a viscoelastic fluid. Rheol. Acta 16:461–75 [Google Scholar]
  13. Brunn P. 1980. The motion of rigid particles in viscoelastic fluids. J. Non-Newton. Fluid Mech. 7:271–88 [Google Scholar]
  14. Buchholz H, Buchholz R, Lucke J, Schugerl K. 1978. Bubble swarm behavior and gas absortion in non-Newtonian fluids in sparged columns. Chem. Eng. Sci. 33:1061–70 [Google Scholar]
  15. Cerri MO, Futiwaki L, Jesus CDF, Cruz AJG, Badino AC. 2008. Average shear rate for non-Newtonian fluids in a concentric-tube airlift bioreactor. Biochem. Eng. J. 39:51–57 [Google Scholar]
  16. Chehata D. 2004. Estudio de la discontinuidad en la velocidad de ascenso de una burbuja en un liquido no-Newtoniano MSc Thesis, Univ. Nac. Auton. Mex.
  17. Chhabra RP. 2006. Bubbles, Drops, and Particles in Non-Newtonian Fluids Boca Raton, FL: CRC, 2nd ed..
  18. Clift R, Grace JR, Weber ME. 2005. Bubbles, Drops, and Particles Mineola, NY: Dover
  19. Daugan S, Talini L, Herzhaft B, Allain C. 2002a. Aggregation of particles settling in shear-thinning fluids. Eur. Phys. J. E 7:73–81 [Google Scholar]
  20. Daugan S, Talini L, Herzhaft B, Allain C. 2002b. Aggregation of particles settling in shear-thinning fluids, part 2. Three-particle aggregation. Eur. Phys. J. E 9:55–62 [Google Scholar]
  21. Daugan S, Talini L, Herzhaft B, Peysson Y, Allain C. 2004. Sedimentation of suspensions in shear-thinning fluids. Oil Gas Sci. Technol. 59:71–80 [Google Scholar]
  22. D'Avino G, Maffettone PL. 2015. Particle dynamics in viscoelastic liquids. J. Non-Newton. Fluid Mech. 215:80–104 [Google Scholar]
  23. De Kee D Carreau PJ, Mordarski J. 1986. Bubble velocity and coalescence in vicoelastic liquids. Chem. Eng. Sci. 41:2273–83 [Google Scholar]
  24. De Kee D, Chhabra RP. 2002. Transport Processes in Bubbles, Drops, and Particles New York: Taylor & Francis, 2nd ed..
  25. De Kee D, Chhabra RP, Dajan A. 1990. Motion and coalescence of gas bubbles in non-Newtonian polymer solutions. J. Non-Newton. Fluid Mech. 37:1–18 [Google Scholar]
  26. Dealy JM. 2010. Weissenberg and Deborah numbers—their definition and use. Rheol. Bull. 79:14–18 [Google Scholar]
  27. Denn MM, Morris JF. 2014. Rheology of non-Brownian suspensions. Annu. Rev. Chem. Biomol. Eng. 5:203–28 [Google Scholar]
  28. Dreher TM, Glass J, O'Connor AJ, Stevens GW. 1999. Effect of rheology on coalescence rates and emulsion stability. AIChE J 40:1182–90 [Google Scholar]
  29. Dziubinski M, Fidos H, Sosno M. 2004. The flow pattern map of two-phase non-Newtonian liquid–gas flow in the vertical pipe. Int. J. Multiph. Flow 30:551–63 [Google Scholar]
  30. Eisenberg DA, Klink IM, Phillips RJ. 2013. Axisymmetric sedimentation of spherical particles in a viscoelastic fluid: sphere-wall and sphere-sphere interactions. J. Rheol. 57:857–80 [Google Scholar]
  31. Ern P, Risso F, Fabre D, Magnaudet J. 2012. Wake-induced oscillatory paths of bodies freely rising or falling in fluids. Annu. Rev. Fluid Mech. 44:97–121 [Google Scholar]
  32. Fabris D, Muller S, Liepmann D. 1999. Wake measurements for flow around a sphere in a viscoelastic fluid. Phys. Fluids 11:3599–612 [Google Scholar]
  33. Fan W, Ma Y, Li X, Li H. 2009. Study on the flow field around two parallel moving bubbles and interaction between bubbles rising in CMC solutions by PIV. Chin. J. Chem. Eng. 17:904–13 [Google Scholar]
  34. Feng J, Huang PY, Joseph DD. 1996. Dynamic simulations of sedimentation of solid particles in an Oldroyd-B fluid. J. Non-Newton. Fluid Mech. 63:63–88 [Google Scholar]
  35. Feng J, Joseph DD, Glowinski R, Pan TW. 1995. A three-dimensional computation of the force and torque on an ellipsoid settling slowly through a viscoelastic fluid. J. Fluid Mech. 283:1–16 [Google Scholar]
  36. Folkes MJ, Hope PS. 1993. Polymer Blends and Alloys London: Chapman & Hall
  37. Fraggedakis D, Dimakopoulos Y, Tsamopoulos J. 2016a. 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 12:5378–401 [Google Scholar]
  38. Fraggedakis D, Dimakopoulos Y, Tsamopoulos J. 2016b. Yielding the yield stress analysis: a thorough comparison of recently proposed elasto-visco-plastic (EVP) fluid models. J. Non-Newton. Fluid Mech. 236:104–22 [Google Scholar]
  39. Fraggedakis D, Pavlidis M, Dimakopoulos Y, Tsamopoulos J. 2016c. On the velocity discontinuity at a critical volume of a bubble rising in a viscoelastic fluid. J. Fluid Mech. 789:310–46 [Google Scholar]
  40. Frank X, Li HZ, Funfschilling D. 2005. An analytical approach to the rise velocity of periodic bubble trains in non-Newtonian fluids. Eur. Phys. J. E 16:29–35 [Google Scholar]
  41. Gauthier F, Goldsmith HL, Mason SG. 1971a. Particle motions in non-Newtonian media. I: Couette flow. Rheol. Acta 10:344–64 [Google Scholar]
  42. Gauthier F, Goldsmith HL, Mason SG. 1971b. Particle motions in non-Newtonian media. II. Poiseuille flow. Trans. Soc. Rheol. 15:297–330 [Google Scholar]
  43. Gheissary G, van den Brule BHAA. 1996. Unexpected phenomena observed in particle settling in non-Newtonian media. J. Non-Newton. Fluid Mech. 67:1–18 [Google Scholar]
  44. Goyal N, Derksen J. 2012. Direct simulations of spherical particles sedimenting in viscoelastic fluids. J. Non-Newton. Fluid Mech. 183–184:1–13 [Google Scholar]
  45. Guazzelli E, Hinch J. 2011. Fluctuations and instability in sedimentation. Annu. Rev. Fluid Mech. 43:97–116 [Google Scholar]
  46. Gueslin B, Talini L, Herzhaft B, Peysson Y, Allain C. 2006. Aggregation behaviour of two spheres falling through an aging fluid. Phys. Rev. E 74:042501 [Google Scholar]
  47. Guido S. 2011. Shear-induced droplet deformation: effects of confined geometry and viscoelasticity. Curr. Opin. Colloid Interface Sci. 16:61–70 [Google Scholar]
  48. Gummalam S, Chhabra RP. 1987. Rising velocity of a swarm of spherical bubbles in a power law non-Newtonian liquid. Can. J. Chem. Eng. 65:1004–8 [Google Scholar]
  49. Gumulya MM, Horsley RR, Pareek V, Lichti DD. 2011. The effects of fluid viscoelasticity on the settling behaviour of horizontally aligned spheres. Chem. Eng. Sci. 66:5822–31 [Google Scholar]
  50. Hadamard JS. 1911. Mouvement permanent lent d'une sphere liquide et visqueuse dans un liquide visqueux. C.R. Acad. Sci. 152:1735–38 [Google Scholar]
  51. Hallez Y, Legendre D. 2011. Interaction between two spherical bubbles rising in a viscous liquid. J. Fluid Mech. 673:406–31 [Google Scholar]
  52. Hao J, Pan TW, Glowinski R, Joseph DD. 2009. A fictitious domain/distributed Lagrange multiplier method for the particulate flow of Oldroyd-B fluids: a positive definiteness preserving approach. J. Non-Newton. Fluid Mech. 156:95–111 [Google Scholar]
  53. Happel J, Brenner H. 1965. Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media Englewood Cliffs, NJ: Prentice Hall
  54. Hassager O. 1979. Negative wake behind bubbles in non-Newtonian liquids. Nature 279:402–3 [Google Scholar]
  55. Haward SJ, Odell JA. 2004. Molecular orientation in non-Newtonian flow of dilute polymer solutions around spheres. Rheol. Acta 43:350–63 [Google Scholar]
  56. Herrera-Velarde JR, Zenit R, Chehata D, Mena B. 2003. The flow of non-Newtonian fluids around bubbles and its connection to the jump discontinuity. J. Non-Newton. Fluid Mech. 111:199–209 [Google Scholar]
  57. James D. 2009. Boger fluids. Annu. Rev. Fluid Mech. 41:129–42 [Google Scholar]
  58. Joseph DD, Liu YJ. 1993. Orientation of long bodies falling in a viscoelastic liquid. J. Rheol. 37:1–22 [Google Scholar]
  59. Joseph DD, Liu YJ, Poletto M, Feng J. 1994. Aggregation and dispersion of spheres falling in viscoelastic liquids. J. Non-Newton. Fluid Mech. 54:45–86 [Google Scholar]
  60. Khair A, Squires TM. 2010. Active microrheology: a proposed technique to measure normal stress coefficients of complex fluids. Phys. Rev. Lett. 105:156001 [Google Scholar]
  61. Kim S, Karrila SJ. 1991. Microhydrodynamics: Principles and Selected Applications Boston: Butterworth-Heinemann
  62. Leal LG. 1979. The motion of small particles in non-Newtonian fluids. J. Non-Newton. Fluid Mech. 5:33–78 [Google Scholar]
  63. Lee HM, Park OO. 1994. Rheology and dynamics of immiscible polymer blends. J. Rheol. 38:1405–25 [Google Scholar]
  64. Legendre D, Magnaudet J, Mougin G. 2003. Hydrodynamic interactions between two spherical bubbles rising side by side in a viscous liquid. J. Fluid Mech. 497:133–43 [Google Scholar]
  65. Legendre D, Zenit R, Vélez-Cordero J. 2012. On the deformation of gas bubbles in liquids. Phys. Fluids 24:043303 [Google Scholar]
  66. Li HZ, Frank X, Funfschilling D, Mouline Y. 2001. Towards the understanding of bubble interactions and coalescence in non-Newtonian fluids: a cognitive approach. Chem. Eng. Sci. 56:6419–25 [Google Scholar]
  67. Li HZ, Mouline Y, Funfschilling D, Marchal P, Choplin L, Midoux N. 1998. Evidence for in-line bubble interactions in non-Newtonian fluids. Chem. Eng. Sci. 53:2219–30 [Google Scholar]
  68. Lin TJ, Lin GM. 2003. The mechanisms of bubble coalescence in a non-Newtonian fluid. Can. J. Chem. Eng. 81:476–82 [Google Scholar]
  69. Lin TJ, Lin GM. 2009. Mechanisms of in-line coalescence of two-unequal bubbles in a non-Newtonian fluid. Chem. Eng. J. 155:750–56 [Google Scholar]
  70. Liu YJ, Joseph DD. 1993. Sedimentation of particles in polymer solutions. J. Fluid Mech. 255:565–95 [Google Scholar]
  71. Liu YJ, Liao TY, Joseph DD. 1995. A two-dimensional cusp at the trailing edge of an air bubble rising in a viscoelastic liquid. J. Fluid Mech. 304:321–42 [Google Scholar]
  72. Magnaudet J, Eames I. 2000. The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32:659–708 [Google Scholar]
  73. Martinez-Mercado J, Palacios-Morales CA, Zenit R. 2007. Measurement of pseudoturbulence intensity in monodispersed bubbly liquids for 10 < Re < 500. Phys. Fluids 19:103302 [Google Scholar]
  74. McKinley GH. 2002. Steady and transient motion of spherical liquids. See De Kee & Chhabra 2002 338–75
  75. Mena B, Manero O, Leal L. 1987. The influence of rheological properties on the slow flow past spheres. J. Non-Newton. Fluid Mech. 26:247–75 [Google Scholar]
  76. Mendoza-Fuentes A, Zenit R, Manero O. 2009. On the flow of associative polymers past a sphere: evaluation of negative wake criteria. Phys. Fluids 21:033104 [Google Scholar]
  77. Mendoza-Fuentes AJ, Zenit R, Manero O. 2010. Evaluation of the drag correction factor for spheres settling in associative polymers. Rheol. Acta 49:979–84 [Google Scholar]
  78. Mora S, Talini L, Allain C. 2005. Structuring sedimentation in a shear-thinning fluid. Phys. Rev. Lett. 95:088301 [Google Scholar]
  79. Ohta M, Kobayashi N, Shigekane Y, Yoshida Y, Iwata S. 2015. The dynamic motion of single bubbles with unique shapes rising freely in hydrophobically modified alkali-soluble emulsion polymer solutions. J. Rheol. 59:303–16 [Google Scholar]
  80. Ortiz S, Lee J, Figueroa B, Mena B. 2016. An experimental note on the deformation and breakup of viscoelastic droplets rising in non-Newtonian fluids. Rheol. Acta 55:879–87 [Google Scholar]
  81. Phillips RJ. 1996. Dynamic simulation of hydrodynamically interacting spheres in a quiescent second-order fluid. J. Fluid Mech. 315:345–65 [Google Scholar]
  82. Phillips RJ. 2010. Structural instability in the sedimentation of particulate suspensions through viscoelastic fluids. J. Non-Newton. Fluid Mech. 165:479–88 [Google Scholar]
  83. Phillips RJ, Talini L. 2007. Chaining of weakly interacting particles suspended in viscoelastic fluids. J. Non-Newton. Fluid Mech. 147:175–88 [Google Scholar]
  84. Pillapakkam SB, Singh P, Blackmore D, Aubry N. 2007. Transient and steady state of a rising bubble in a viscoelastic fluid. J. Fluid Mech. 589:215–52 [Google Scholar]
  85. Pilz C, Brenn G. 2007. On the critical bubble volume at the rise velocity jump discontinuity in viscoelastic liquids. J. Non-Newton. Fluid Mech. 145:124–38 [Google Scholar]
  86. Prieto J. 2015. Stochastic particle level set simulations of buoyancy-driven droplets in non-Newtonian fluids. J. Non-Newton. Fluid Mech. 226:16–31 [Google Scholar]
  87. Riddle MJ, Narvaez C, Bird R. 1977. Interactions between two spheres falling along their line of centers in a viscoelastic fluid. J. Non-Newton. Fluid Mech. 2:23–35 [Google Scholar]
  88. Rodrigue D, Blanchet J. 2006. The effect of viscoelasticity and surface tension on the motion of liquid drops Presented at IUTAM Symp. Interact. Dispersed Syst. Newton. Viscoelastic Fluids, March 26–30 Guanajuato Mexico:
  89. Rodrigue D, De Kee D, Chan Man Fong CF. 1996a. An experimental study of the effect of surfactants on the free rise velocity of gas bubbles. J. Non-Newton. Fluid Mech. 66:213–32 [Google Scholar]
  90. Rodrigue D, De Kee D, Chan Man Fong CF. 1996b. The slow motion of a spherical particle in a Carreau fluid. Chem. Eng. Comm. 154:203–15 [Google Scholar]
  91. Rybczyński W. 1911. Über die fortschreitende Bewegung einer flüssigen Kugel in einem zähen Medium. Bull. Int. Acad. Sci. Crac. Ser. A 1911:40–46 [Google Scholar]
  92. Shah SN. 1993. Rheological characterization of hydraulic fracturing slurries. SPE Prod. Fac. 8:123–30 [Google Scholar]
  93. Singh P, Joseph DD, Hesla TI, Glowinski R, Pan TW. 2000. A distributed Lagrange multiplier/fictitious domain method for viscoelastic particulate flows. J. Non-Newton. Fluid Mech. 91:165–88 [Google Scholar]
  94. Solomon M, Muller S. 1996. Flow past a sphere in polystyrene-based Boger fluids: the effect on the drag coefficient of finite extensibility, solvent quality and polymer molecular weight. J. Non-Newton. Fluid Mech. 62:81–94 [Google Scholar]
  95. Soto E. 2008. Flow of single air bubbles in complex fluids PhD Thesis, Univ. Nac. Auton. Mex.
  96. Soto E, Goujon C, Zenit R, Manero O. 2006. A study of velocity discontinuity for single air bubbles rising in an associative polymer. Phys. Fluids 18:121510 [Google Scholar]
  97. Stone HA, Leal LG. 1990. The effects of surfactants on drop deformation and breakup. J. Fluid Mech. 220:161–86 [Google Scholar]
  98. Takagi S, Ogasawara T, Matsumoto Y. 2008. The effects of surfactant on the multiscale structure of bubbly flows. Philos. Trans. R. Soc. A 366:2117–29 [Google Scholar]
  99. Vélez-Cordero JR, Lantenet J, Hernández-Cordero J, Zenit R. 2014. Compact bubble clusters in Newtonian and non-Newtonian liquids. Phys. Fluids 26:053101 [Google Scholar]
  100. Vélez-Cordero JR, Sámano D, Yue P, Feng JJ, Zenit R. 2011. Hydrodynamic interaction between a pair of bubbles ascending in shear-thinning inelastic fluids. J. Non-Newton. Fluid Mech. 166:118–32 [Google Scholar]
  101. Vélez-Cordero JR, Sámano D, Zenit R. 2012. Study of the properties of bubbly flows in Boger-type fluids. J. Non-Newton. Fluid Mech. 175–76:1–9 [Google Scholar]
  102. Vélez-Cordero JR, Zenit R. 2011. Bubble cluster formation in shear-thinning inelastic bubbly columns. J. Non-Newton. Fluid Mech. 166:32–41 [Google Scholar]
  103. Verneuil E, Phillips RJ, Talini L. 2007. Axisymmetric two-sphere sedimentation in a shear thinning viscoelastic fluid: particle interactions and induced fluid velocity fields. J. Rheol. 51:1343–59 [Google Scholar]
  104. Yu Z, Wachs A, Peysson Y. 2006. Numerical simulation of particle sedimentation in shear-thinning fluids with a fictitious domain method. J. Non-Newton. Fluid Mech. 136:126–39 [Google Scholar]
  105. Yue P, Feng JJ, Liu C, Shen J. 2005. Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids. J. Non-Newton. Fluid Mech. 129:163–76 [Google Scholar]
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Hydrodynamic Interactions Among Bubbles, Drops, and Particles in Non-Newtonian Liquids
Annual Review of Fluid Mechanics 50, 505 (2018); https://doi.org/10.1146/annurev-fluid-122316-045114
/content/journals/10.1146/annurev-fluid-122316-045114
/content/journals/10.1146/annurev-fluid-122316-045114
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