Aqueous foams are suspensions of bubbles inside aqueous phases. Their multiphasic composition leads to a complex rheological behavior that is useful in numerous applications, from oil recovery to food/cosmetic processing. Their structure is very similar to the one of emulsions, so that both materials share common mechanical properties. In particular, the presence of surfactants at the gas–liquid interfaces leads to peculiar interfacial and dissipative properties. Foam rheology has been an active research topics and is already reported in several reviews, most of them covering rheometry measurements at the scale of the foam, coupled with interpretations at the local scale of bubbles or interfaces. In this review, we start following this approach, then we try to cover the multiscale features of aqueous foam flows, emphasizing regimes where intermediate length scales need to be taken into account or regimes fast enough regarding internal time scales so that the flow goes beyond the quasi-static limit.
Les mousses aqueuses sont des suspensions de bulles à l'intérieur de phases aqueuses. Leur caractère multiphasique conduit à un comportement rhéologique complexe qui est utile dans de nombreuses applications, depuis la récupération du pétrole jusqu'aux industries alimentaire et cosmétique. Leur structure est très similaire à celle des émulsions, de telle sorte que ces deux types de matériaux partagent des propriétés mécaniques communes. En particulier, la présence de surfactants aux interfaces gaz–liquide mène à des propriétés interfaciales et dissipatives particulières. La rhéologie des mousses constitue un champ de recherche actif et a déjà été évoquée dans plusieurs revues, la plupart d'entre elles couvrant des mesures rhéométriques à l'échelle de la mousse, couplées avec des interprétations à l'échelle locale des bulles et des interfaces. Nous commençons cette revue en suivant cette approche, puis nous tentons de couvrir les caractéristiques multi-échelles des écoulements de mousses liquides, en insistant sur les régimes où des échelles de longueur intermédiaires doivent être prises en compte, ou sur les régimes suffisamment rapides pour que l'écoulement sorte de la limite quasi statique.
Mot clés : Mousses aqueuses, Rhéologie, Élasticité, Plasticité, Dissipation, Multiéchelle
Benjamin Dollet 1; Christophe Raufaste 2
@article{CRPHYS_2014__15_8-9_731_0, author = {Benjamin Dollet and Christophe Raufaste}, title = {Rheology of aqueous foams}, journal = {Comptes Rendus. Physique}, pages = {731--747}, publisher = {Elsevier}, volume = {15}, number = {8-9}, year = {2014}, doi = {10.1016/j.crhy.2014.09.008}, language = {en}, }
Benjamin Dollet; Christophe Raufaste. Rheology of aqueous foams. Comptes Rendus. Physique, Volume 15 (2014) no. 8-9, pp. 731-747. doi : 10.1016/j.crhy.2014.09.008. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2014.09.008/
[1] The jamming perspective on wet foams, Soft Matter, Volume 9 (2013), pp. 9739-9743
[2] Foams, Oxford University Press, 2013
[3] The Physics of Foams, Oxford University Press, 1999
[4] Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires, Gauthier–Villars, 1873
[5] Yield drag in a two-dimensional foam flow around a circular obstacle: effect of liquid fraction, Eur. Phys. J. E, Volume 23 (2007), pp. 217-228
[6] Rheometry of Pastes, Suspensions and Granular Materials, Wiley, 2005
[7] Rheology: Principles, Measurements and Applications, Wiley–VCH, 1994
[8] The Structure and Rheology of Complex Fluids, Oxford University Press, 1999
[9] Foam flows, Annu. Rev. Fluid Mech., Volume 20 (1988), pp. 325-357
[10] Rheology of liquid foams, J. Phys. Condens. Matter, Volume 17 (2005), p. R1041-R1069
[11] The role of surfactant type and bubble surface mobility in foam rheology, Soft Matter, Volume 5 (2009), pp. 3389-3408
[12] Flow in foams and flowing foams, Annu. Rev. Fluid Mech., Volume 45 (2013), pp. 241-267
[13] Foam Engineering: Fundamentals and Applications (P. Stevenson, ed.), Wiley, 2012
[14] Theory of mobilization pressure gradient of flowing foams in porous media. I. Incompressible foam, J. Colloid Interface Sci., Volume 136 (1990), pp. 1-16
[15] Structure-dependent mobility of a dry aqueous foam flowing along two parallel channels, Phys. Fluids, Volume 25 (2013), p. 063101
[16] Microfluidics with foams, Soft Matter, Volume 5 (2009), pp. 3385-3388
[17] Foams: Fundamentals and Applications in the Petroleum Industry, American Chemical Society, 1994
[18] Experimental studies of bubble dynamics in a slowly driven monolayer foam, Phys. Rev. Lett., Volume 78 (1997), pp. 2485-2488
[19] Two-dimensional shear modulus of a Langmuir foam, Europhys. Lett., Volume 64 (2003), pp. 709-715
[20] Coarsening foams robustly reach a self-similar growth regime, Phys. Rev. Lett., Volume 104 (2010), p. 248304
[21] Liquid flow through aqueous foams: the node-dominated foam drainage equation, Phys. Rev. Lett., Volume 82 (1999), pp. 4232-4235
[22] Élasticité, morphologie et drainage magnétique dans les mousses liquides, Université Paris-7, 2004 (PhD thesis)
[23] Origin of the slow linear viscoelastic response of aqueous foams, Phys. Rev. Lett., Volume 93 (2004), p. 028302
[24] Oscillatory rheology of aqueous foams: surfactant, liquid fraction, experimental protocol and aging effects, Soft Matter, Volume 5 (2009), pp. 1937-1946
[25] Elasticity of compressed emulsions, Phys. Rev. Lett., Volume 75 (1995), pp. 2051-2054
[26] Anomalous viscous loss in emulsions, Phys. Rev. Lett., Volume 76 (1996), pp. 3017-3020
[27] Relaxing in foam, Phys. Rev. Lett., Volume 91 (2003), p. 188303
[28] Fast relaxations in foam, Phys. Rev. E, Volume 82 (2010), p. 011405
[29] Vanishing elasticity for wet foams: equivalence with emulsions and role of polydispersity, J. Rheol., Volume 43 (1999), pp. 1411-1422
[30] Is the yield stress of aqueous foam a well-defined quantity?, Colloids Surf. A, Volume 263 (2005), pp. 111-116
[31] The large amplitude oscillatory strain response of aqueous foam: strain localization and full stress fourier spectrum, Eur. Phys. J. E, Volume 27 (2008), pp. 309-321
[32] Rheology of foams and highly concentrated emulsions. IV. An experimental study of the shear viscosity and yield stress of concentrated emulsions, J. Colloid Interface Sci., Volume 128 (1989), pp. 176-187
[33] Aqueous foam slip and shear regimes determined by rheometry and multiple light scattering, J. Rheol., Volume 52 (2008), pp. 1091-1111
[34] Wide-gap Couette flows of dense emulsions: local concentration measurements, and comparison between macroscopic and local constitutive law measurements through magnetic resonance imaging, Phys. Rev. E, Volume 78 (2008), p. 036307
[35] Theoretical model of viscous friction inside steadily sheared foams and concentrated emulsions, Phys. Rev. E, Volume 78 (2008), p. 011405
[36] Investigation of shear banding in three-dimensional foams, Europhys. Lett., Volume 91 (2010), p. 68005
[37] Yielding and flow of monodisperse emulsions, J. Colloid Interface Sci., Volume 179 (1996), pp. 439-448
[38] Rheology of foams and highly concentrated emulsions. III. Static shear modulus, J. Colloid Interface Sci., Volume 112 (1986), pp. 427-437
[39] Simple shearing flow of a dry kelvin soap foam, J. Fluid Mech., Volume 311 (1996), pp. 327-343
[40] Simple shearing flow of dry soap foams with tetrahedrally close-packed structure, J. Rheol., Volume 44 (2000), pp. 453-471
[41] Topological transition dynamics in a strained bubble cluster, Soft Matter, Volume 5 (2009), pp. 4672-4679
[42] The stress system in a suspension of force-free particles, J. Fluid Mech., Volume 41 (1970), pp. 545-570
[43] Rheology of foams and highly concentrated emulsions. I. Elastic properties and yield stress of a cylindrical model system, J. Colloid Interface Sci., Volume 91 (1983), pp. 160-175
[44] Rheology of foams I. Theory for dry foams, J. Non-Newton. Fluid Mech., Volume 22 (1986), pp. 1-22
[45] Relaxation time of the topological T1 process in a two-dimensional foam, Phys. Rev. Lett., Volume 97 (2006), p. 226101
[46] Statistics of bubble rearrangement dynamics in a coarsening foam, Phys. Rev. E, Volume 78 (2008), p. 066303
[47] Bubble rearrangement duration in foams near the jamming point, Phys. Rev. Lett., Volume 108 (2012), p. 188301
[48] Rheology of foams IV. Effect of gas volume fraction, J. Rheol., Volume 33 (1989), pp. 881-911
[49] Linear elastic behavior of dry soap foams, J. Colloid Interface Sci., Volume 181 (1996), pp. 511-520
[50] Die elastischen Eigenschaften der Schäume, Kolloid Z., Volume 64 (1933), pp. 1-6
[51] A model of foam elasticity based upon the laws of Plateau, J. Colloid Interface Sci., Volume 145 (1991), pp. 255-259
[52] On the shear modulus of two-dimensional liquid foams: a theoretical study of the effect of geometrical disorder, J. Appl. Mech., Volume 74 (2007), pp. 560-567
[53] Shear modulus of two-dimensional foams: the effect of area dispersity and disorder, Eur. Phys. J. E, Volume 21 (2006), pp. 49-56
[54] Structure of random foams, Phys. Rev. Lett., Volume 93 (2004), p. 208301
[55] Statistical mechanics of two-dimensional shuffled foams: prediction of the correlation between geometry and topology, Phys. Rev. Lett., Volume 107 (2011), p. 168304
[56] Analytical results for size–topology correlations in 2D disk and cellular packings, Phys. Rev. Lett., Volume 108 (2012), p. 015502
[57] Rheology of foams and highly concentrated emulsions. II. Experimental study of the yield stress and wall effects for concentrated oil-in-water emulsions, J. Colloid Interface Sci., Volume 105 (1985), pp. 150-171
[58] Model for the elasticity of compressed emulsions, Phys. Rev. Lett., Volume 76 (1996), p. 3448
[59] Osmotic pressure and viscoelastic shear moduli of concentrated emulsions, Phys. Rev. E, Volume 56 (1997), pp. 3150-3166
[60] Rheology of adsorbed surfactant monolayers at fluid surfaces, Annu. Rev. Fluid Mech., Volume 46 (2014), pp. 47-65
[61] Linear shear rheology of incompressible foams, J. Phys., Volume 5 (1995), pp. 37-52
[62] A theory of extensional viscosity for flowing foams and concentrated emulsions, J. Colloid Interface Sci., Volume 118 (1987), pp. 201-211
[63] Viscous effects in the rheology of foams and concentrated emulsions, J. Colloid Interface Sci., Volume 132 (1989), pp. 491-503
[64] Intermolecular and Surface Forces, Academic Press, 1991
[65] Disjoining pressure in thin liquid foam and emulsion films—new concepts and perspectives, J. Phys. Condens. Matter, Volume 15 (2003), p. R1197-R1232
[66] Viscous friction in foams and concentrated emulsions under steady shear, Phys. Rev. Lett., Volume 100 (2008), p. 138301
[67] Soap Films: Study of Their Thinning and a Bibliography, Pergamon, 1959
[68] How topological rearrangements and liquid fraction control liquid foam stability, Phys. Rev. Lett., Volume 106 (2011), p. 068301
[69] Extension of a suspended soap film: a homogeneous dilatation followed by new film extraction, Phys. Rev. Lett., Volume 111 (2013), p. 094501
[70] What is the mechanism of soap film entrainment?, Langmuir, Volume 27 (2011), pp. 13406-13409
[71] Theoretical study of the generation of soap films: role of interfacial visco-elasticity, J. Fluid Mech., Volume 739 (2014), pp. 124-142
[72] Coating flows, Annu. Rev. Fluid Mech., Volume 36 (2004), pp. 29-53
[73] The motion of long bubbles in tubes, J. Fluid Mech., Volume 10 (1961), pp. 166-188
[74] Wall slip and viscous dissipation in sheared foams: effect of surface mobility, Colloids Surf. A, Volume 263 (2005), pp. 129-145
[75] Foam-wall friction: effect of air volume fraction for tangentially immobile bubble surface, Colloids Surf. A, Volume 282 (2006), pp. 329-347
[76] Liquid meniscus friction on a wet plate: bubbles, lamellae, and foams, Phys. Fluids, Volume 25 (2013), p. 031303
[77] Rheology of soft glassy materials, Phys. Rev. Lett., Volume 78 (1997), pp. 2020-2023
[78] Dynamics of viscoplastic deformation in amorphous solids, Phys. Rev. E, Volume 57 (1998), pp. 7192-7205
[79] Bubble-scale model of foam mechanics: melting, nonlinear behavior, and avalanches, Phys. Rev. E, Volume 55 (1997), pp. 1739-1751
[80] Model for the scaling of stresses and fluctuations in flows near jamming, Phys. Rev. Lett., Volume 105 (2010), p. 088303
[81] Elasticity of floppy and stiff random networks, Phys. Rev. Lett., Volume 101 (2008), p. 215501
[82] Jamming of soft particles: geometry, mechanics, scaling and isostaticity, J. Phys. Condens. Matter, Volume 22 (2010), p. 033101
[83] Microscopic approach to the nonlinear elasticity of compressed emulsions, Phys. Rev. Lett., Volume 110 (2013), p. 048302
[84] Relaxations and rheology near jamming, Phys. Rev. Lett., Volume 107 (2011), p. 158303
[85] Deformation and flow of a two-dimensional foam under continuous shear, Phys. Rev. Lett., Volume 87 (2001), p. 178305
[86] Velocity profiles in slowly sheared bubbles rafts, Phys. Rev. Lett., Volume 93 (2004), p. 018303
[87] Impact of boundaries on velocity profiles in bubble rafts, Phys. Rev. E, Volume 73 (2006), p. 031401
[88] Rate dependence and role of disorder in linearly sheared two-dimensional foams, Phys. Rev. Lett., Volume 101 (2008), p. 058301
[89] Statistics of bubble rearrangements in a slowly sheared two-dimensional foam, Phys. Rev. E, Volume 70 (2004), p. 041406
[90] Two-dimensional flow of foam around a circular obstacle: local measurements of elasticity, plasticity and flow, J. Fluid Mech., Volume 585 (2007), pp. 181-211
[91] Local description of the two-dimensional flow of foam through a contraction, J. Rheol., Volume 54 (2010), pp. 741-760
[92] Anti-inertial lift in foams: a signature of the elasticity of complex fluids, Phys. Rev. Lett., Volume 95 (2005), p. 168303
[93] Dense bubble flow in a silo: an unusual flow of a dispersed medium, Phys. Rev. E, Volume 73 (2006), p. 056309
[94] Local stress relaxation and shear banding in a dry foam under shear, Phys. Rev. Lett., Volume 90 (2003), p. 258303
[95] Shear-induced stress relaxation in a two-dimensional wet foam, Phys. Rev. Lett., Volume 89 (2002), p. 098303
[96] Coexistence of liquid and solid phases in flowing soft-glassy materials, Phys. Rev. Lett., Volume 88 (2002), p. 218301
[97] Couette flow of two-dimensional foams, Europhys. Lett., Volume 90 (2010), p. 54002
[98] Flow in linearly sheared two-dimensional foams: from bubble to bulk scale, Phys. Rev. E, Volume 79 (2009), p. 066318
[99] Two-dimensional foam rheology with viscous drag, Phys. Rev. Lett., Volume 97 (2006), p. 038302
[100] The response of 2D foams to continuous applied shear in a Couette rheometer, Eur. Phys. J. E, Volume 21 (2006), pp. 123-132
[101] Velocity dependence of shear localisation in a 2D foam, Philos. Mag. Lett., Volume 88 (2008), pp. 387-396
[102] A simple analytical theory of localisation in 2D foam rheology, Philos. Mag. Lett., Volume 89 (2009), pp. 294-299
[103] Numerical modelling of foam Couette flows, Eur. Phys. J. E, Volume 27 (2008), pp. 123-133
[104] Steady Couette flows of elastoviscoplastic fluids are non-unique, J. Rheol., Volume 56 (2012), pp. 213-239
[105] Understanding and predicting viscous, elastic, plastic flows, Eur. Phys. J. E, Volume 34 (2011), p. 1
[106] Elastic consequences of a single plastic event: a step towards the microscopic modeling of the flow of yield stress fluids, Eur. Phys. J. E, Volume 15 (2004), pp. 371-381
[107] Topological rearrangements and stress fluctuations in quasi-two-dimensional hopper flow of emulsions, Soft Matter, Volume 8 (2012), pp. 10486-10492
[108] Screening in dry two-dimensional foams, Soft Matter, Volume 4 (2008), pp. 1871-1878
[109] Networklike propagation of cell-level stress in sheared random foams, Phys. Rev. Lett., Volume 111 (2013), p. 138301
[110] Experimental study of forces between quasi-two-dimensional emulsion droplets near jamming, Soft Matter, Volume 9 (2013), pp. 3424-3436
[111] Spatial cooperativity in soft glassy flows, Nature, Volume 454 (2008), pp. 84-87
[112] How does a soft glassy material flow: finite size effects, non local rheology, and flow cooperativity, Soft Matter, Volume 6 (2010), pp. 2668-2678
[113] Kinetic theory of plastic flow in soft glassy materials, Phys. Rev. Lett., Volume 103 (2009), p. 036001
[114] Boundary conditions for soft glassy flows: slippage and surface fluidization, Soft Matter, Volume 10 (2014), pp. 6984-6989
[115] Microscale rheology of a soft glassy material close to yielding, Phys. Rev. Lett., Volume 108 (2012), p. 148301
[116] A molecular dynamics study of non-local effects in the flow of soft jammed particles, Soft Matter, Volume 9 (2013), pp. 7489-7500
[117] Shear-induced “melting” of an aqueous foam, J. Colloid Interface Sci., Volume 213 (1999), pp. 169-178
[118] Dynamics of yielding observed in a three-dimensional aqueous dry foam, Phys. Rev. E, Volume 267 (2003), p. 021405
[119] Plastic and viscous dissipations in foams: cross-over from low to high shear rates, Soft Matter, Volume 9 (2013), pp. 9602-9607
[120] Two-dimensional viscous froth model for foam dynamics, Phys. Rev. E, Volume 70 (2004), p. 041411
[121] Rheology of ordered foams—on the way to discrete microfluidics, Colloids Surf. A, Volume 263 (2005), pp. 52-64
[122] The viscous froth model: steady states and the high-velocity limit, Proc. R. Soc. A, Volume 465 (2010), pp. 2391-2405
[123] Viscous froth simulations with surfactant mass transfer and Marangoni effects: deviations from Plateau's rules, Colloids Surf. A, Volume 382 (2011), pp. 8-17
[124] Speed of crack propagation in dry aqueous foams, Europhys. Lett., Volume 92 (2010), p. 38001
[125] Spontaneous brittle-to-ductile transition in aqueous foam, J. Rheol., Volume 56 (2012), pp. 485-499
[126] Response of a two-dimensional liquid foam to air injection: swelling rate, fingering and fracture, J. Fluid Mech., Volume 714 (2013), pp. 258-282
[127] Gibbs elasticity effect in foam shear flows: a non quasi-static 2D numerical simulation, Soft Matter, Volume 7 (2011), pp. 448-455
[128] Foam rheology: a model of viscous phenomena, J. Rheol., Volume 31 (1987), pp. 175-205
[129] A Princen hexagonal foam out of physicochemical equilibrium, J. Rheol., Volume 56 (2012), pp. 501-526
[130] Surfactant mixtures for control of bubble surface mobility in foam studies, Langmuir, Volume 24 (2008), pp. 9956-9961
[131] Laser-speckle-visibility acoustic spectroscopy in soft turbid media, Phys. Rev. E, Volume 89 (2014), p. 012308
[132] Investigating acoustic-induced deformations in a foam using multiple light scattering, Phys. Rev. E, Volume 82 (2010), p. 021409
[133] Heat transfer effect on sound propagation in foam, J. Acoust. Soc. Am., Volume 92 (1992), pp. 2756-2769
[134] Sound and weak shock wave propagation in gas–liquid foams, Shock Waves, Volume 7 (1997), pp. 77-88
[135] Sound velocity and absorption in a coarsening foam, Phys. Rev. E, Volume 66 (2002), p. 021404
[136] A Textbook on Sound, Bell, 1944
[137] The attenuation of acoustic signals by aqueous and particulate foams, Appl. Acoust., Volume 24 (1988), pp. 193-209
[138] Sound waves in foams, Colloids Surf. A, Volume 263 (2005), pp. 315-319
[139] Acoustical observation of bubble oscillations induced by bubble popping, Phys. Rev. E, Volume 75 (2007), p. 041601
[140] Propagation of ultrasound in aqueous foams: bubble size dependence and resonance effects, Soft Matter, Volume 9 (2013), pp. 1194-1202
[141] Resonant acoustic propagation and negative density in liquid foams, Phys. Rev. Lett., Volume 112 (2014), p. 148307
[142] The reduction of blast noise with aqueous foams, J. Acoust. Soc. Am., Volume 74 (1983), pp. 1757-1763
[143] Mitigation of sound waves by wet aqueous foams, Colloids Surf. A, Volume 344 (2009), pp. 48-55
[144] Blast wave mitigation by dry aqueous foams, Shock Waves, Volume 23 (2013), pp. 39-53
[145] Real-time tomography at the swiss light source, AIP Conf. Proc., Volume SRI2009 (2009)
[146] Quantitative 3D characterization of cellular materials: segmentation and morphology of foam, Colloids Surf. A, Volume 415 (2012), pp. 230-238
[147] The formation of emulsions in definable fields of flow, Proc. R. Soc. Lond. A, Volume 146 (1934), pp. 501-523
[148] Rheology of emulsions, Adv. Colloid Interface Sci., Volume 151 (2009), pp. 1-23
[149] Propagation of drop coalescence in a two-dimensional emulsion: a route towards phase inversion, Phys. Rev. Lett., Volume 106 (2011), p. 214502
Cited by Sources:
Comments - Policy