1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Fluid Mechanics
  4. Volume 55, 2023
  5. Article

Annual Review of Fluid Mechanics

Volume 55, 2023

Gas-Liquid Foam Dynamics: From Structural Elements to Continuum Descriptions

Abstract

Gas-liquid foams are important in applications ranging from oil recovery and mineral flotation to food science and microfluidics. Beyond their practical use, they represent an intriguing prototype of a soft material with a complex, viscoelastic rheological response. Crucially, foams allow detailed access to fluid-dynamical processes on the mesoscale of bubbles underlying the large-scale material behavior. This review emphasizes the importance of the geometry and interaction of mesoscale structural elements for the description of the dynamics of entire foams. Using examples including bulk flow of foam under steady shear, interfacial instabilities, and foam fracture through bubble rupture, this article highlights the wide variety of available theoretical descriptions, ranging from network modeling approaches coupling structural element equations of motion to full continuum models with elastoviscoplastic constitutive relations. Foams offer the opportunity to develop rigorous links between such disparate descriptions, providing a blueprint for physical modeling of dynamical multiscale systems with complex structure.

Keyword(s): fluid mechanics, foams, interfacial mechanics, rheology, soft matter, thin films
Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-032822-125417
2023-01-19
2024-04-25
Loading full text...

Full text loading...

/deliver/fulltext/fluid/55/1/annurev-fluid-032822-125417.html?itemId=/content/journals/10.1146/annurev-fluid-032822-125417&mimeType=html&fmt=ahah

Literature Cited

  1. Abraham FF. 2003. How fast can cracks move? A research adventure in materials failure using millions of atoms and big computers. Adv. Phys. 52:727–90
     [Google Scholar]
  2. Aradian A, Raphael E, De Gennes PG. 2001.. “ Marginal pinching” in soap films. Eur. Phys. Lett. 55:834–40
     [Google Scholar]
  3. Arif S. 2010. Fracture mechanisms in quasi-two-dimensional aqueous foam PhD Thesis, Northwestern Univ. Evanston, IL:
  4. Arif S, Tsai JC, Hilgenfeldt S. 2010. Speed of crack propagation in dry aqueous foam. Eur. Phys. Lett. 92:38001
     [Google Scholar]
  5. Arif S, Tsai JC, Hilgenfeldt S. 2012. Spontaneous brittle-to-ductile transition in aqueous foam. J. Rheol. 56:485–99
     [Google Scholar]
  6. Aubouy M, Jiang Y, Glazier JA, Graner F. 2003. A texture tensor to quantify deformations. Granul. Matter 5:67–70
     [Google Scholar]
  7. Badve M, Barigou M. 2020. Local description of foam flow, deformation and pressure drop in narrow constricted channels. Int. J. Multiph. Flow 128:103279
     [Google Scholar]
  8. Banhart J. 2013. Light-metal foams—history of innovation and technological challenges. Adv. Eng. Mater. 15:82–111
     [Google Scholar]
  9. Barry JD, Weaire D, Hutzler S. 2010. Shear localisation with 2D viscous froth and its relation to the continuum model. Rheol. Acta 49:687–98
     [Google Scholar]
  10. Barry JD, Weaire D, Hutzler S. 2011. Nonlocal effects in the continuum theory of shear localisation in 2D foams. Philos. Mag. Lett. 91:432–40
     [Google Scholar]
  11. Ben Amar M, Corvera Poiré E 1999. Pushing a non-Newtonian fluid in a Hele-Shaw cell: from fingers to needles. Phys. Fluids 11:1757–67
     [Google Scholar]
  12. Ben Salem I, Cantat I, Dollet B 2013a. Response of a two-dimensional liquid foam to air injection: influence of surfactants, critical velocities and branched fracture. Colloids Surf. A 438:41–46
     [Google Scholar]
  13. Ben Salem I, Cantat I, Dollet B 2013b. Response of a two-dimensional liquid foam to air injection: swelling rate, fingering and fracture. J. Fluid Mech. 714:258–82
     [Google Scholar]
  14. Boulogne F, Cox SJ. 2011. Elastoplastic flow of a foam around an obstacle. Phys. Rev. E 83:041404
     [Google Scholar]
  15. Bragg WL, Nye JF. 1947. A dynamical model of a crystal structure. Proc. R. Soc. A 190:474–81
     [Google Scholar]
  16. Brakke K. 1992. The Surface Evolver. Exp. Math. 1:141–65
     [Google Scholar]
  17. Bremond N, Villermaux E. 2005. Bursting thin liquid films. J. Fluid Mech. 524:121–30
     [Google Scholar]
  18. Bretherton FP. 1961. The motion of long bubbles in tubes. J. Fluid Mech. 10:166–88
     [Google Scholar]
  19. Buehler MJ, Tang H, Van Duin AC, Goddard WA III 2007. Threshold crack speed controls dynamical fracture of silicon single crystals. Phys. Rev. Lett. 99:165502
     [Google Scholar]
  20. Burnett G, Chae J, Tam W, De Almeida R, Tabor M 1995. Structure and dynamics of breaking foams. Phys. Rev. E 51:5788–96
     [Google Scholar]
  21. Bussonnière A, Cantat I. 2021. Local origin of the visco-elasticity of a millimetric elementary foam. J. Fluid Mech. 922:A22
     [Google Scholar]
  22. Buzza D, Lu CY, Cates M. 1995. Linear shear rheology of incompressible foams. J. Phys. II 5:37–52
     [Google Scholar]
  23. Cantat I. 2011. Gibbs elasticity effect in foam shear flows: a non quasi-static 2D numerical simulation. Soft Matter 7:448–55
     [Google Scholar]
  24. Cantat I. 2013. Liquid meniscus friction on a wet plate: bubbles, lamellae, and foams. Phys. Fluids 25:031303
     [Google Scholar]
  25. Cantat I, Cohen-Addad S, Elias F, Graner F, Höhler R et al. 2013. Foams: Structure and Dynamics Oxford, UK: Oxford Univ. Press
  26. Cantat I, Delannay R. 2003. Dynamical transition induced by large bubbles in two-dimensional foam flows. Phys. Rev. E 67:031501
     [Google Scholar]
  27. Cantat I, Delannay R. 2005. Dissipative flows of 2D foams. Eur. Phys. J. E 18:55–67
     [Google Scholar]
  28. Cantat I, Kern N, Delannay R. 2004. Dissipation in foam flowing through narrow channels. Eur. Phys. Lett. 65:726–32
     [Google Scholar]
  29. Cantat I, Poloni C, Delannay R. 2006. Experimental evidence of flow destabilization in a two-dimensional bidisperse foam. Phys. Rev. E 73:011505
     [Google Scholar]
  30. Chae J, Tabor M. 1997. Dynamics of foams with and without wall rupture. Phys. Rev. E 55:598–610
     [Google Scholar]
  31. Cheddadi I, Saramito P. 2013. A new operator splitting algorithm for elastoviscoplastic flow problems. J. Non-Newton. Fluid Mech. 202:13–21
     [Google Scholar]
  32. Cheddadi I, Saramito P, Dollet B, Raufaste C, Graner F. 2011. Understanding and predicting viscous, elastic, plastic flows. Eur. Phys. J. E 34:1
     [Google Scholar]
  33. Cheddadi I, Saramito P, Graner F. 2012. Steady Couette flows of elastoviscoplastic fluids are nonunique. J. Rheol. 56:213–39
     [Google Scholar]
  34. Cheddadi I, Saramito P, Raufaste C, Marmottant P, Graner F. 2008. Numerical modelling of foam Couette flows. Eur. Phys. J. E 27:123–33
     [Google Scholar]
  35. Christensen J, Kadic M, Kraft O, Wegener M. 2015. Vibrant times for mechanical metamaterials. MRS Commun. 5:453–62
     [Google Scholar]
  36. Cohen-Addad S, Höhler R. 2014. Rheology of foams and highly concentrated emulsions. Curr. Opin. Colloid Interface Sci. 19:536–48
     [Google Scholar]
  37. Cohen-Addad S, Höhler R, Pitois O. 2013. Flow in foams and flowing foams. Annu. Rev. Fluid Mech. 45:241–67
     [Google Scholar]
  38. Corvera Poiré E, Ben Amar M 1998. Finger behavior of a shear thinning fluid in a Hele-Shaw cell. Phys. Rev. Lett. 81:2048–51
     [Google Scholar]
  39. Coussot P. 1999. Saffman–Taylor instability in yield-stress fluids. J. Fluid Mech. 380:363–76
     [Google Scholar]
  40. Coussot P, Ovarlez G. 2010. Physical origin of shear-banding in jammed systems. Eur. Phys. J. E 33:183–88
     [Google Scholar]
  41. Coussot P, Raynaud J, Bertrand F, Moucheront P, Guilbaud J et al. 2002. Coexistence of liquid and solid phases in flowing soft-glassy materials. Phys. Rev. Lett. 88:218301
     [Google Scholar]
  42. Cox S. 2005. A viscous froth model for dry foams in the surface evolver. Colloids Surf. A 263:81–89
     [Google Scholar]
  43. Cox S, Dollet B, Graner F. 2006. Foam flow around an obstacle: simulations of obstacle–wall interaction. Rheol. Acta 45:403–10
     [Google Scholar]
  44. Debrégeas G, Tabuteau H, Di Meglio JM. 2001. Deformation and flow of a two-dimensional foam under continuous shear. Phys. Rev. Lett. 87:178305
     [Google Scholar]
  45. Denkov ND, Subramanian V, Gurovich D, Lips A. 2005. Wall slip and viscous dissipation in sheared foams: effect of surface mobility. Colloids Surf. A 263:129–45
     [Google Scholar]
  46. Denkov ND, Tcholakova S, Golemanov K, Ananthapadmanabhan K, Lips A. 2008. Viscous friction in foams and concentrated emulsions under steady shear. Phys. Rev. Lett. 100:138301
     [Google Scholar]
  47. Denkov ND, Tcholakova S, Golemanov K, Ananthapadmanabhan K, Lips A. 2009. The role of surfactant type and bubble surface mobility in foam rheology. Soft Matter 5:3389–408
     [Google Scholar]
  48. Dennin M. 2004. Statistics of bubble rearrangements in a slowly sheared two-dimensional foam. Phys. Rev. E 70:041406
     [Google Scholar]
  49. Dollet B. 2010. Local description of the two-dimensional flow of foam through a contraction. J. Rheol. 54:741–60
     [Google Scholar]
  50. Dollet B, Aubouy M, Graner F. 2005a. Anti-inertial lift in foams: a signature of the elasticity of complex fluids. Phys. Rev. Lett. 95:168303
     [Google Scholar]
  51. Dollet B, Cantat I. 2010. Deformation of soap films pushed through tubes at high velocity. J. Fluid Mech. 652:529–39
     [Google Scholar]
  52. Dollet B, Durth M, Graner F. 2006. Flow of foam past an elliptical obstacle. Phys. Rev. E 73:061404
     [Google Scholar]
  53. Dollet B, Elias F, Quilliet C, Huillier A, Aubouy M, Graner F. 2005b. Two-dimensional flows of foam: drag exerted on circular obstacles and dissipation. Colloids Surf. A 263:101–10
     [Google Scholar]
  54. Dollet B, Graner F. 2007. Two-dimensional flow of foam around a circular obstacle: local measurements of elasticity, plasticity and flow. J. Fluid Mech. 585:181–211
     [Google Scholar]
  55. Dollet B, Scagliarini A, Sbragaglia M. 2015. Two-dimensional plastic flow of foams and emulsions in a channel: experiments and lattice Boltzmann simulations. J. Fluid Mech. 766:556–89
     [Google Scholar]
  56. Drenckhan W, Hutzler S. 2015. Structure and energy of liquid foams. Adv. Colloid Interface Sci. 224:1–16
     [Google Scholar]
  57. Durand M, Kraynik AM, Van Swol F, Käfer J, Quilliet C et al. 2014. Statistical mechanics of two-dimensional shuffled foams: geometry–topology correlation in small or large disorder limits. Phys. Rev. E 89:062309
     [Google Scholar]
  58. Durand M, Stone HA. 2006. Relaxation time of the topological T1 process in a two-dimensional foam. Phys. Rev. Lett. 97:226101
     [Google Scholar]
  59. Durian DJ. 1995. Foam mechanics at the bubble scale. Phys. Rev. Lett. 75:4780–83
     [Google Scholar]
  60. Erneux T, Davis S 1993. Nonlinear rupture of free films. Phys. Fluids A 5:1117–22
     [Google Scholar]
  61. Exerowa D, Gochev G, Platikanov D, Liggieri L, Miller R. 2018. Foam Film and Foams: Fundamentals and Applications Boca Raton, FL: CRC
  62. Farrokhpay S. 2011. The significance of froth stability in mineral flotation—a review. Adv. Colloid Interface Sci. 166:1–7
     [Google Scholar]
  63. Gilbreth C, Sullivan S, Dennin M. 2006. Flow transitions in two-dimensional foams. Phys. Rev. E 74:051406
     [Google Scholar]
  64. Goldshtein V, Goldfarb I, Shreiber I. 1996. Drainage waves structure in gas-liquid foam. Int. J. Multiph. Flow 22:991–1003
     [Google Scholar]
  65. Gouldstone A, Van Vliet KJ, Suresh S. 2001. Simulation of defect nucleation in a crystal. Nature 411:656
     [Google Scholar]
  66. Goyon J, Colin A, Bocquet L 2010. How does a soft glassy material flow: finite size effects, non local rheology, and flow cooperativity. Soft Matter 6:2668–78
     [Google Scholar]
  67. Goyon J, Colin A, Ovarlez G, Ajdari A, Bocquet L 2008. Spatial cooperativity in soft glassy flows. Nature 454:84–87
     [Google Scholar]
  68. Graner F, Dollet B, Raufaste C, Marmottant P. 2008. Discrete rearranging disordered patterns. Part I: Robust statistical tools in two or three dimensions. Eur. Phys. J. E 25:349–69
     [Google Scholar]
  69. Green T, Bramley A, Lue L, Grassia P. 2006. Viscous froth lens. Phys. Rev. E 74:051403
     [Google Scholar]
  70. Gros A, Bussonnière A, Nath S, Cantat I. 2021. Marginal regeneration in a horizontal film: instability growth law in the nonlinear regime. Phys. Rev. Fluids 6:024004
     [Google Scholar]
  71. Hele-Shaw H. 1898. Flow of water. Nature 58:520
     [Google Scholar]
  72. Hilgenfeldt S, Arif S, Tsai JC. 2008. Foam: a multiphase system with many facets. Philos. Trans. R. Soc. A 366:2145–59
     [Google Scholar]
  73. Hilgenfeldt S, Koehler S, Stone H. 2001a. Dynamics of coarsening foams: accelerated and self-limiting drainage. Phys. Rev. Lett. 86:4704–7
     [Google Scholar]
  74. Hilgenfeldt S, Kraynik AM, Koehler SA, Stone HA. 2001b. An accurate von Neumann's law for three-dimensional foams. Phys. Rev. Lett. 86:2685–88
     [Google Scholar]
  75. Hill C, Eastoe J. 2017. Foams: from nature to industry. Adv. Colloid Interface Sci. 247:496–513
     [Google Scholar]
  76. Jang WY, Kraynik AM, Kyriakides S. 2008. On the microstructure of open-cell foams and its effect on elastic properties. Int. J. Solids Struct. 45:1845–75
     [Google Scholar]
  77. Janiaud E, Graner F. 2005. Foam in a two-dimensional Couette shear: a local measurement of bubble deformation. J. Fluid Mech. 532:243–67
     [Google Scholar]
  78. Janiaud E, Weaire D, Hutzler S. 2006. Two-dimensional foam rheology with viscous drag. Phys. Rev. Lett. 97:038302
     [Google Scholar]
  79. Janiaud E, Weaire D, Hutzler S. 2007. A simple continuum model for the dynamics of a quasi-two dimensional foam. Colloids Surf. A 309:125–31
     [Google Scholar]
  80. Jiang Y, Swart PJ, Saxena A, Asipauskas M, Glazier JA. 1999. Hysteresis and avalanches in two-dimensional foam rheology simulations. Phys. Rev. E 59:5819
     [Google Scholar]
  81. Jones S, Cox S. 2012. On the effectiveness of a quasistatic bubble-scale simulation in predicting the constriction flow of a two-dimensional foam. J. Rheol. 56:457–71
     [Google Scholar]
  82. Jones S, Dollet B, Slosse N, Jiang Y, Cox S, Graner F. 2011. Two-dimensional constriction flows of foams. Colloids Surf. A 382:18–23
     [Google Scholar]
  83. Kabla A, Debrégeas G. 2003. Local stress relaxation and shear banding in a dry foam under shear. Phys. Rev. Lett. 90:258303
     [Google Scholar]
  84. Kabla A, Scheibert J, Debrégeas G. 2007. Quasi-static rheology of foams. Part 2. Continuous shear flow. J. Fluid Mech. 587:45–72
     [Google Scholar]
  85. Katgert G, Latka A, Möbius M, van Hecke M. 2009. Flow in linearly sheared two-dimensional foams: from bubble to bulk scale. Phys. Rev. E 79:066318
     [Google Scholar]
  86. Katgert G, Möbius ME, van Hecke M. 2008. Rate dependence and role of disorder in linearly sheared two-dimensional foams. Phys. Rev. Lett. 101:058301
     [Google Scholar]
  87. Katgert G, Tighe BP, Möbius ME, van Hecke M. 2010. Couette flow of two-dimensional foams. Eur. Phys. Lett. 90:54002
     [Google Scholar]
  88. Keller JB, Kolodner I. 1954. Instability of liquid surfaces and the formation of drops. J. Appl. Phys. 25:918–21
     [Google Scholar]
  89. Kern N, Weaire D, Martin A, Hutzler S, Cox S. 2004. Two-dimensional viscous froth model for foam dynamics. Phys. Rev. E 70:041411
     [Google Scholar]
  90. Koehler SA, Hilgenfeldt S, Stone HA. 2000. A generalized view of foam drainage: experiment and theory. Langmuir 16:6327–41
     [Google Scholar]
  91. Kraynik AM. 1988. Foam flows. Annu. Rev. Fluid Mech. 20:325–57
     [Google Scholar]
  92. Kraynik AM. 2006. The structure of random foam. Adv. Eng. Mater. 8:900–6
     [Google Scholar]
  93. Krishan K, Dennin M. 2008. Viscous shear banding in foam. Phys. Rev. E 78:051504
     [Google Scholar]
  94. Lai CY, Rallabandi B, Perazzo A, Zheng Z, Smiddy SE, Stone HA. 2018. Foam-driven fracture. PNAS 115:8082–86
     [Google Scholar]
  95. Lauridsen J, Chanan G, Dennin M. 2004. Velocity profiles in slowly sheared bubble rafts. Phys. Rev. Lett. 93:018303
     [Google Scholar]
  96. Le Goff A, Courbin L, Stone HA, Quéré D 2008. Energy absorption in a bamboo foam. Eur. Phys. Lett. 84:036001
     [Google Scholar]
  97. Liger-Belair G, Jeandet P. 2003. Capillary-driven flower-shaped structures around bubbles collapsing in a bubble raft at the surface of a liquid of low viscosity. Langmuir 19:5771–79
     [Google Scholar]
  98. Lindner A. 2000. L'instabilité de Saffman-Taylor dans les fluides complexes: relation entre les propriétés rhéologiques et la formation de motifs. PhD Thesis, Univ. Pierre et Marie Curie Paris:
  99. Lindner A, Bonn D, Poiré EC, Amar MB, Meunier J. 2002. Viscous fingering in non-Newtonian fluids. J. Fluid Mech. 469:237–56
     [Google Scholar]
  100. Lindner A, Rica S, Couder Y 1999. Digitation visqueuse dans une mousse. Comptes rendus de la 18e rencontre du non-linéaire68–72 Paris: Univ. Paris Diderot
     [Google Scholar]
  101. Long R, Hui CY, Gong JP, Bouchbinder E. 2021. The fracture of highly deformable soft materials: a tale of two length scales. Annu. Rev. Condens. Matter Phys. 12:71–94
     [Google Scholar]
  102. Lundberg M, Krishan K, Xu N, O'Hern CS, Dennin M. 2008. Reversible plastic events in amorphous materials. Phys. Rev. E 77:041505
     [Google Scholar]
  103. Marder M. 2004. Effects of atoms on brittle fracture. Int. J. Fract. 130:517–55
     [Google Scholar]
  104. Marder M. 2015. Particle methods in the study of fracture. Int. J. Fract. 196:169–88
     [Google Scholar]
  105. Marmottant P, Graner F. 2007. An elastic, plastic, viscous model for slow shear of a liquid foam. Eur. Phys. J. E 23:337–47
     [Google Scholar]
  106. Marmottant P, Raufaste C, Graner F. 2008. Discrete rearranging disordered patterns. Part II: 2D plasticity, elasticity and flow of a foam. Eur. Phys. J. E 25:371–84
     [Google Scholar]
  107. Matin T 2012. Fire-fighting foam technology. Foam Engineering: Fundamentals and Applications P Stevenson 411–57 New York: Wiley
     [Google Scholar]
  108. McLean JW, Saffman PG. 1981. The effect of surface tension on the shape of fingers in a Hele-Shaw cell. J. Fluid Mech. 102:455–69
     [Google Scholar]
  109. Müller W, Di Meglio J. 1999. Avalanches in draining foams. J. Phys. Condens. Matter 11:L209
     [Google Scholar]
  110. Mysels KJ, Frankel S, Shinoda K. 1959. Soap Films: Studies of Their Thinning and a Bibliography Oxford, UK: Pergamon
  111. Ovarlez G, Cohen-Addad S, Krishan K, Goyon J, Coussot P. 2013. On the existence of a simple yield stress fluid behavior. J. Non-Newton. Fluid Mech. 193:68–79
     [Google Scholar]
  112. Ozbayoglu M, Miska S, Reed T, Takach N. 2005. Using foam in horizontal well drilling: a cuttings transport modeling approach. J. Pet. Sci. Eng. 46:267–82
     [Google Scholar]
  113. Park S, Durian D. 1994. Viscous and elastic fingering instabilities in foam. Phys. Rev. Lett. 72:3347–50
     [Google Scholar]
  114. Paterson L. 1981. Radial fingering in a Hele-Shaw cell. J. Fluid Mech. 113:513–29
     [Google Scholar]
  115. Rabaud M, Couder Y, Gerard N 1988. Dynamics and stability of anomalous Saffman–Taylor fingers. Phys. Rev. A 37:935–47
     [Google Scholar]
  116. Raimbaud Q, Monloubou M, Kerampran S, Cantat I. 2021. Impact of a shock wave on a heterogeneous foam film. J. Fluid Mech. 908:A27
     [Google Scholar]
  117. Raufaste C, Cox S, Marmottant P, Graner F. 2010. Discrete rearranging disordered patterns: prediction of elastic and plastic behavior, and application to two-dimensional foams. Phys. Rev. E 81:031404
     [Google Scholar]
  118. Raufaste C, Dollet B, Cox S, Jiang Y, Graner F. 2007. Yield drag in a two-dimensional foam flow around a circular obstacle: effect of liquid fraction. Eur. Phys. J. E 23:217–28
     [Google Scholar]
  119. Raufaste C, Foulon A, Dollet B. 2009. Dissipation in quasi-two-dimensional flowing foams. Phys. Fluids 21:053102
     [Google Scholar]
  120. Ritacco H. 2020. Complexity and self-organized criticality in liquid foams. A short review. Adv. Colloid Interface Sci. 285:102282
     [Google Scholar]
  121. Ritacco H, Kiefer F, Langevin D. 2007. Lifetime of bubble rafts: cooperativity and avalanches. Phys. Rev. Lett. 98:244501
     [Google Scholar]
  122. Rodts S, Baudez J, Coussot P. 2005. From “discrete” to “continuum” flow in foams. Eur. Phys. Lett. 69:636–42
     [Google Scholar]
  123. Rosenfeld L, Fan L, Chen Y, Swoboda R, Tang SK. 2014. Break-up of droplets in a concentrated emulsion flowing through a narrow constriction. Soft Matter 10:421–30
     [Google Scholar]
  124. Saffman P, Taylor G. 1958. The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. A 245:312–29
     [Google Scholar]
  125. Saramito P. 2007. A new constitutive equation for elastoviscoplastic fluid flows. J. Non-Newton. Fluid Mech. 145:1–14
     [Google Scholar]
  126. Saramito P. 2009. A new elastoviscoplastic model based on the Herschel–Bulkley viscoplastic model. J. Non-Newton. Fluid Mech. 158:154–61
     [Google Scholar]
  127. Schall P, Van Hecke M. 2010. Shear bands in matter with granularity. Annu. Rev. Fluid Mech. 42:67–88
     [Google Scholar]
  128. Stewart PS, Davis SH. 2012. Dynamics and stability of metallic foams: network modeling. J. Rheol. 56:543–74
     [Google Scholar]
  129. Stewart PS, Davis SH. 2013. Self-similar coalescence of clean foams. J. Fluid Mech. 722:645–64
     [Google Scholar]
  130. Stewart PS, Davis SH, Hilgenfeldt S. 2013. Viscous Rayleigh–Taylor instability in aqueous foams. Colloids Surf. A 436:898–905
     [Google Scholar]
  131. Stewart PS, Davis SH, Hilgenfeldt S. 2015. Microstructural effects in aqueous foam fracture. J. Fluid Mech. 785:425–61
     [Google Scholar]
  132. Stewart PS, Hilgenfeldt S. 2017. Cracks and fingers: dynamics of ductile fracture in an aqueous foam. Colloids Surf. A 534:58–70
     [Google Scholar]
  133. Szalewicz K, Leforestier C, van der Avoird A. 2009. Towards the complete understanding of water by a first-principles computational approach. Chem. Phys. Lett. 482:1–14
     [Google Scholar]
  134. Taylor GI. 1934. The mechanism of plastic deformation of crystals. Part I. Theoretical. Proc. R. Soc. A 145:362–87
     [Google Scholar]
  135. Taylor GI. 1950. The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. R. Soc. A 201:192–96
     [Google Scholar]
  136. Thakur RK, Vial C, Djelveh G. 2003. Influence of operating conditions and impeller design on the continuous manufacturing of food foams. J. Food Eng. 60:9–20
     [Google Scholar]
  137. Thomas GL, Belmonte JM, Graner F, Glazier JA, de Almeida RM. 2015. 3D simulations of wet foam coarsening evidence a self similar growth regime. Colloids Surf. A 473:109–14
     [Google Scholar]
  138. Thomson W. 1887. On the division of space with minimum partitional area. Philos. Mag. 24:503–14
     [Google Scholar]
  139. Van De Fliert B, Howell P, Ockendon J. 1995. Pressure-driven flow of a thin viscous sheet. J. Fluid Mech. 292:359–76
     [Google Scholar]
  140. Vandewalle N, Lentz J, Dorbolo S, Brisbois F. 2001. Avalanches of popping bubbles in collapsing foams. Phys. Rev. Lett. 86:179–82
     [Google Scholar]
  141. Verbist G, Weaire D, Kraynik A. 1996. The foam drainage equation. J. Phys. Condens. Matter 8:3715–31
     [Google Scholar]
  142. Wang J, Joseph DD. 2004. Potential flow of a second-order fluid over a sphere or an ellipse. J. Fluid Mech. 511:201–15
     [Google Scholar]
  143. Wang Y, Krishan K, Dennin M. 2006. Impact of boundaries on velocity profiles in bubble rafts. Phys. Rev. E 73:031401
     [Google Scholar]
  144. Weaire D. 1993. On the motion of vertices in two-dimensional grain growth. Philos. Mag. Lett. 68:93–98
     [Google Scholar]
  145. Weaire D, Phelan R. 1994. A counter-example to Kelvin's conjecture on minimal surfaces. Philos. Mag. Lett. 69:107–10
     [Google Scholar]
  146. Weaire DL, Hutzler S. 2001. The Physics of Foams Oxford, UK: Univ. Press
  147. Yanagisawa N, Kurita R. 2019. In-situ observation of collective bubble collapse dynamics in a quasi-two-dimensional foam. Sci. Rep. 9:5152
     [Google Scholar]
  148. Yanagisawa N, Tani M, Kurita R 2021. Dynamics and mechanism of liquid film collapse in a foam. Soft Matter 17:1738–46
     [Google Scholar]
  149. Zehnder AT. 2012. Fracture Mechanics Berlin: Springer
  150. Zhuang Z, Liu Z, Cui Y. 2019. Dislocation Mechanism–Based Crystal Plasticity: Theory and Computation at the Micron and Submicron Scale San Diego, CA: Academic
/content/journals/10.1146/annurev-fluid-032822-125417
Loading
Gas-Liquid Foam Dynamics: From Structural Elements to Continuum Descriptions
Annual Review of Fluid Mechanics 55, 323 (2023); https://doi.org/10.1146/annurev-fluid-032822-125417
/content/journals/10.1146/annurev-fluid-032822-125417
/content/journals/10.1146/annurev-fluid-032822-125417
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error