The continuum theory of shear localization in two-dimensional foam

Journal of Physics Condensed Matter

Volumn 22, Issue 19, 2010, Pages

  Weaire, Denis ^a   Barry, Joseph D ^a   Hutzler, Stefan ^a  

^a TRINITY COLLEGE DUBLIN   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUUM MODEL; CONTINUUM THEORY; HERSCHEL-BULKLEY; LIQUID FOAM; LOW STRAIN RATES; MECHANICAL SYSTEMS; QUASISTATIC SIMULATIONS; SEMI-EMPIRICAL; SHEAR LOCALIZATIONS; STEADY SHEAR; TWO-DIMENSIONAL FOAMS; WALL DRAG;

CONTINUUM MECHANICS; EXPERIMENTS; STRESSES; TWO DIMENSIONAL; YIELD STRESS;

STRAIN RATE;

CHEMICAL MODEL; CHEMISTRY; COMPUTER SIMULATION; FLOW KINETICS; GAS; METHODOLOGY; REVIEW; SHEAR STRENGTH; VISCOSITY; YOUNG MODULUS;

COMPUTER SIMULATION; ELASTIC MODULUS; GASES; MODELS, CHEMICAL; RHEOLOGY; SHEAR STRENGTH; VISCOSITY;

EID: 77951614373     PISSN: 09538984     EISSN: 1361648X     Source Type: Journal    
DOI: 10.1088/0953-8984/22/19/193101     Document Type: Review

References (82)

1. Kraynik A M 1988 Foam flows Annu. Rev. Fluid Mech. 20 325-57
2. Smith C S 1952 The shapes of metal grains, with some other metallurgical applications of topology Metal Interfaces (Cleveland: ASM)
3. Bragg L and Nye J F 1947 A dynamical model of a crystal structure Proc. R. Soc. A 190 474-81
4. Abd El Kader A and Earnshaw J C 1997 Evolution of a two-dimensional foam containing a single topological defect: an experimental study Phys. Rev. E 56 3251-5
5. Vaz M F and Fortes M A 1997 Experiments on defect spreading in hexagonal foams J. Phys.: Condens. Matter 9 8921
6. Weaire D and Hutzler S 1999 The Physics of Foams (Oxford: Clarendon)
7. Durian D J 1995 Foam mechanics at the bubble scale Phys. Rev. Lett. 75 4780-3
8. Durian D J 1997 Bubble-scale model of foam mechanics: melting, nonlinear behavior, and avalanches Phys. Rev. E 55 1739-51
9. Ono I K, OHern C S, Durian D J, Langer S A, Liu A J and Nagel S R 2002 Effective temperatures of a driven system near jamming Phys. Rev. Lett. 89 095703
10. Cantat I and Delannay R 2003 Dynamical transition induced by large bubbles in 2d foam flows Phys. Rev. E 67 031501
11. Cantat I, Kern N and Delannay R 2004 Dissipation in foam flowing through narrow channels Europhys. Lett. 65 726-32 (Pubitemid 38361193)
12. Cantat I and Delannay R 2005 Dissipative flows of 2d foams Eur. Phys J. E 18 55-67
13. Dollet B, Elias F, Quilliet C, Raufaste C, Aubouy M and Graner F 2005 Two-dimensional flow of foam around an obstacle: force measurements Phys. Rev. E 71 031403
14. Dollet B, Aubouy M and Graner F 2005 Anti-inertial lift in foams: a signature of the elasticity of complex fluids Phys. Rev. Lett. 95 168303
15. Dollet B and 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 (Pubitemid 47232967)
16. Raufaste C, Dollet B, Cox S, Jiang Y and Graner F 2007 Yield drag in a two-dimensional flow of foam around a circular obstacle: effect of fluid fraction Eur. Phys. J. E 23 217-28
17. Graner F, Marmottant P and Raufaste C 2008 Discrete rearranging disordered patterns, part ii: 2d plasticity, elasticity and flow of a foam Eur. Phys. J. E 25 371384
18. Caps H, Traberlsi S, Dorbolo S and Vandewalle N 2004 Bubble and granular flows: differences and similarities Physica A 344 424-30
19. Denkov N D, Subramanian V, Gurovich D and Lips A 2005 Wall slip and viscous dissipation in sheared foams: effect of surface mobility Colloids Surf. A 263 129-45
20. Denkov N D, Tcholakova S, Golemanov K, Ananthapadmanabhan K P and Lips A 2008 Viscous friction in foams and concentrated emulsions under steady shear Phys. Rev. Lett. 100 138301
21. Tcholakova S, Denkov N D, Golemanov K, Ananthapadmanabhan K P and Lips A 2008 Theoretical model of viscous friction inside steadily sheared foams and concentrated emulsions Phys. Rev. E 78 011405
22. Debrégeas G, Tabuteau H and di Meglio J-M 2001 Deformation and flow of a two-dimensional foam under continuous shear Phys. Rev. Lett. 87 178305
23. Janiaud E, Weaire D and Hutzler S 2006 Two-dimensional foam rheology with viscous drag Phys. Rev. Lett. 97 038302
24. Clancy R J, Janiaud E, Weaire D and Hutzler S 2006 The response of 2d foams to continuous applied shear in a Couette rheometer Eur. Phys. J. E 21 123-32
25. Janiaud E, Weaire D and Hutzler S 2007 A simple continuum model for the dynamics of a quasi-two-dimensional foam Colloids Surf. A 309 125-31
26. Weaire D, Hutzler S, Langlois V J and Clancy R J 2008 Velocity dependence of shear localisation in a 2d foam Phil. Mag. Lett. 88 387-96
27. Langlois V J, Hutzler S and Weaire D 2008 Rheological properties of the soft disk model of 2d foams Phys. Rev. E 78 021401
28. Katgert G, Möbius M E and van Hecke M 2008 Rate dependence and role of disorder in linearly sheared two-dimensional foams Phys. Rev. Lett. 101 058301
29. Katgert G, Möbius M E and van Hecke M 2008 Relaxation and flow in linearly sheared two-dimensional foams Eur. Phys. Lett. submitted
30. Katgert G, Latka A, Möbius M E and van Hecke M 2009 Flow in linearly sheared two-dimensional foams: from bubble to bulk scale Phys. Rev. E 79 066318
31. Kabla A and Debrégeas G 2003 Local stress relaxation and shear banding in dry foam under shear Phys. Rev. Lett. 90 258303
32. Kabla A and Debrégeas G 2007 Quasi-static rheology of foams. Part 1. Oscillating strain J. Fluid Mech. 587 23-44
33. Kabla A, Scheibert J and Debrégeas G 2007 Quasistatic rheology of foams. Part 2. Continuous shear flow J. Fluid Mech. 587 45-72
34. Cox S J 2005 A viscous froth model for dry foams in the surface evolver Colloids Surf. A 263 81-9
35. Wyn A, Davies I T and Cox S J 2008 Simulations of two-dimensional foam rheology: localization in linear Couette flow and the interaction of settling discs Eur. Phys. J. E 26 81-9
36. Cox S J and Wyn A 2008 Localization of topological changes in Couette and Poiseuille flows of two-dimensional foams AIP Conf. Proc. 1027 836-8
37. Schall P and van Hecke M 2010 Shear bands in matter with granularity Annu. Rev. Fluid Mech. 42 67-88
38. Weaire D and Fortes M A 1994 Stress and strain in liquid and solid foams Adv. Phys. 43 685-738
39. Cox S J and Janiaud E 2008 On the structure of quasi-two-dimensional foams Phil. Mag. Lett. 88 693-701
40. Wang Y, Krishan K and Dennin M 2006 Impact of boundaries on velocity profiles in bubble rafts Phys. Rev. E 73 031401
41. Dennin M 2008 Discontinuous jamming transitions in soft materials: coexistence of flowing and jammed states J. Phys.: Condens. Matter 20 283103
42. Lauridsen J, Chanan G and Dennin M 2004 Velocity profiles in slowly sheared bubble rafts Phys. Rev. Lett. 93 018303
43. Gilbreth C, Sullivan S and Dennin M 2006 Flow transitions in two-dimensional foams Phys. Rev. E 74 051406
44. Krishan K and Dennin M 2008 Viscous shear banding in foam Phys. Rev. E 78 051504
45. Lauridsen J, Twardos M and Dennin M 2002 Shear-induced stress relaxation in a two-dimensional wet foam Phys. Rev. Lett. 89 098303
46. Goyon J, Colin A, Ovarlez G, Ajdari A and Bocquet L 2008 Spatial cooperativity in soft glassy flows Nature 454 84-7
47. Weaire D and Kermode J P 1983 The evolution of the structure of a two-dimensional soap froth Phil. Mag. B 47 L29-31
48. Weaire D and Kermode J P 1983 Computer simulation of a two-dimensional soap froth. I. Method and motivation Phil. Mag. B 48 245-59
49. Weaire D and Kermode J P 1984 Computer simulation of a two-dimensional soap froth. II. Analysis of results Phil. Mag. B 50 379-95
50. Barry J D, Weaire D and Hutzler S 2010 Shear localisation with 2d visous froth and its relation to the continuum model Rheol. Acta at press (doi:10.1007/s00397-010-0449-6)
51. Fu T-L, Weaire D and Kermode J P 1986 On the shear elastic constant of a two-dimensional froth Phil. Mag. B 54 L39-43
52. Bolton F and Weaire D 1990 Rigidity loss transition in a disordered 2d froth Phys. Rev. Lett. 65 3449
53. Bolton F and Weaire D 1992 The effects of Plateau borders in the two-dimensional soap froth. II. General simulation and analysis of rigidity loss transition. Phil. Mag. B 65 473-87
54. Hutzler S, Weaire D and Bolton F 1995 The effects of Plateau borders in the two-dimensional soap froth, III. Further results Phil. Mag. B 71 277
55. Wyn A 2010 Topological changes in sheared two-dimensional foams PhD Thesis University of Wales Aberystwyth
56. Kern N, Weaire D, Martin A, Hutzler S and Cox S J 2004 Two-dimensional viscous froth model for foam dynamics Phys. Rev. E 70 041411
57. Bretherton F P 1961 The motion of long bubbles in tubes J. Fluid Mech. 10 166-88
58. Khan S A, Schnepper C A and Armstrong R C 1988 Foam rheology: III. Measurement of shear flow properties J. Rheol. 32 69-92
59. Hunter R J 1993 Introduction to Modern Colloid Science (Oxford: Oxford University Press)
60. Weaire D 2008 The rheology of foam Curr. Opin. Colloid Interface Sci. 13 171-6
61. Weaire D, Clancy R J and Hutzler S 2009 A simple analytical theory of localisation in 2d foam rheology Phil. Mag. Lett. 89 294-9
62. Marmottant P and Graner F 2007 An elastic, plastic, viscous model for slow shear of a liquid foam Eur. Phys. J. E 23 337-47
63. Weaire D, Clancy R J and Hutzler S 2009 The origin of the strain-rate discontinuity in 2d foam rheometry with circular geometry arXiv:0907.1624v1 [cond-mat.soft]
64. Glazier J A and Weaire D 1992 The kinetics of cellular patterns J. Phys.: Condens. Matter 4 1867-94
65. Weaire D and McMurry S 1996 Some fundamentals of grain growth Solid State Phys. 50 1-36
66. Drenckhan W, Cox S J, Delaney G, Holste H, Weaire D and Kern N 2005 Rheology of ordered foams-on the way to discrete microfluidics Colloids Surf. A 263 52-64
67. Brakke K A 1992 The surface evolver Exp. Math. 1 141-65
68. Brakke K http://www.susqu.edu/brakke/evolver/evolver.html
69. Larson R G 1999 The Structure and Rheology of Complex Fluids (Oxford: Oxford University Press)
70. Bocquet L, Colin A and Ajdari A 2009 Kinetic theory of plastic flow in soft glassy materials Phys. Rev. Lett. 103 036001
71. Weaire D and Hutzler S 2009 Foam as a complex system J. Phys.: Condens. Matter 21 4227
72. Goldenberg C, Atman A P F, Claudin P, Combe G and Goldhirsch I 2006 Scale separation in granular packings: stress plateaus and fluctuations Phys. Rev. Lett. 96 168001
73. Morse D C and Witten T A 1993 Droplet elasticity in weakly compressed emulsions Europhys. Lett. 22 549
74. Lacasse M D, Grest G S and Levine D 1996 Deformation of small compressed droplets Phys. Rev. E 54 5436-46
75. Weaire D, Langlois V, Saadatfar M and Hutzler S 2007 Foam as granular matter Granular and Complex Materials, World Scientific Lecture Notes in Complex Systems vol 8 ed T Di Matteo, T Aste and A Tordesillas (New Jersey: World Scientific) pp1-26
76. Picard G, Ajdari A, Lequeux F and Bocquet L 2005 Complex spatiotemporal behavior within a simple elastoplastic model Phys. Rev. E 71 010501
77. Behringer R P 2007 Fluctuations in granular materials Granular and Complex Materials, World Scientific Lecture Notes in Complex Systems vol 8 ed T Di Matteo, T Aste and A Tordesillas (New Jersey: World Scientific) pp187-215
78. Lagrée P-Y and Lhuilliera D 2006 The Couette flow of dense and fluid-saturated granular media Eur. J. Mech. B 25 960-70
79. Weaire D and Rivier N 1984 Soap, cells and statistics: random patterns in two dimensions Contemp. Phys. 25 59
80. Durand M and Stone H A 2006 Relaxation time of the topological t1 process in a two-dimensional foam Phys. Rev. Lett. 97 226101
81. Dennin M and Knobler C M 1997 Experimental studies of bubble dynamics in a slowly driven monolayer foam Phys. Rev. Lett. 78 2485-8
82. Wang Y, Krishan K and Dennin M 2007 Statistics of microscopic yielding in sheared aqueous foams Phil. Mag. Lett. 87 125-33