Flow transitions in two-dimensional foams

Gilbreth, C. N.; Sullivan, Scott T.; Dennin, Michael

doi:10.1103/physreve.74.051406

Cited by 43 publications

(84 citation statements)

References 27 publications

(53 reference statements)

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“…Non-homogeneous flow, often discussed in terms of "shear banding" or "jammingunjamming transitions", attracted researchers' attention in several areas, because it appears as a generic phenomenon in various systems, such as glassy and granular materials, concentrated suspensions, foams, emulsions, and micellar solutions [1][2][3][4][5][6][7][8][9][10]. This phenomenon is still poorly understood and appropriate theoretical modeling, beyond the phenomenological description, is missing.…”

Section: Pacsmentioning

confidence: 99%

Jamming in Sheared Foams and Emulsions, Explained by Critical Instability of the Films between Neighboring Bubbles and Drops

et al. 2009

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Phenomenon of foam and emulsion jamming at low shear rates is explained by considering the dynamics of thinning of the transient films, formed between neighboring bubbles and drops. After gradually thinning down to a critical thickness, these films undergo instability transition and thin stepwise, forming the so-called "black films", which are only several nanometers thick and, thereby, lead to strong adhesion between the dispersed particles. Theoretical analysis shows that such film thickness instability occurs only if the contact time between the bubbles/drops in sheared foam/emulsion is sufficiently long, which corresponds to sufficiently low (critical) rate of shear. Explicit expression for this critical rate is proposed and compared to experimental data. 83.80.Iz, 83.60.Wc, 47.57.Bc, 82.70.Rr, 82.70.Kj. PACS:Non-homogeneous flow, often discussed in terms of "shear banding" or "jammingunjamming transitions", attracted researchers' attention in several areas, because it appears as a generic phenomenon in various systems, such as glassy and granular materials, concentrated suspensions, foams, emulsions, and micellar solutions [1][2][3][4][5][6][7][8][9][10]. This phenomenon is still poorly understood and appropriate theoretical modeling, beyond the phenomenological description, is missing. Foams and emulsions seem particularly suitable for studying and modeling such nonhomogenous flow and related phenomena, because the behavior of these systems is governed by a relatively well understood interplay of capillary effects and viscous friction in the films, formed between neighboring bubbles and drops [11][12][13][14][15]. This understanding provides the unique possibility for detailed theoretical modeling and experimental studies of these systems at the microstructural level (viz. at the level of single drops, bubbles, and films), which is impossible for the other systems of interest.Recently, several systematic studies were performed [1-10] to clarify the main factors controlling jamming/unjamming transitions in foams and emulsions. Some of the conclusions, relevant to the current study are: (i) Jamming is observed at a certain "critical" shear rate. When this critical rate is reached from above, the bubbles/drops in the dispersion "stick" to each other, thus creating jammed zones. (ii) Critical shear rate depends on several factors, such as the drop and bubble size, volume fraction, and most importantly, on the interaction between dispersed particles. The effect of interparticle forces was convincingly demonstrated with moderately concentrated emulsions (drop volume fraction Φ = 0.73), for which jamming transition was observed in the systems with attractive interdroplet forces only [10]. Until now these observations lack clear explanations and quantitative description.The main purpose of the current letter is to demonstrate that jamming transitions in flowing foams and emulsions could be explained by considering the dynamics of thinning of the films formed 1

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Section: Pacsmentioning

confidence: 99%

Jamming in Sheared Foams and Emulsions, Explained by Critical Instability of the Films between Neighboring Bubbles and Drops

et al. 2009

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“…[76][77][78][79][80][81][93][94][95][96][97][98][99][100] These experiments proved to be very valuable in analyzing several important phenomena (e.g., those related to non-homogeneous flows) and to clarify some common features of the different types of ''yield stress systems'', such as soft glassy materials, granular materials, foams, and emulsions. Also, the theoretical modelling of 2D-foams is technically much simpler, as compared to the 3D-foams, so that the theoretical concepts could be more easily tested with 2D-foams.…”

Section: Steadily Sheared 2d-foams the Role Of Foam Polydispersity mentioning

confidence: 99%

The role of surfactant type and bubble surface mobility in foam rheology

et al. 2009

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This paper is an overview of our recent understanding of the effects of surfactant type and bubble surface mobility on foam rheological properties. The focus is on the viscous friction between bubbles in steadily sheared foams, as well as between bubbles and confining solid wall. Large set of experimental results is reviewed to demonstrate that two qualitatively different classes of surfactants can be clearly distinguished. The first class is represented by the typical synthetic surfactants (such as sodium dodecylsulfate) which are characterised with low surface modulus and fast relaxation of the surface tension after a rapid change of surface area. In contrast, the second class of surfactants exhibits high surface modulus and relatively slow relaxation of the surface tension. Typical examples for this class are the sodium and potassium salts of fatty acids (alkylcarboxylic acids), such as lauric and myristic acids. With respect to foam rheology, the second class of surfactants leads to significantly higher viscous stress and to different scaling laws of the shear stress vs. shear rate in flowing foams. The reasons for these differences are discussed from the viewpoint of the mechanisms of viscous dissipation of energy in sheared foams and the respective theoretical models. The process of bubble breakup in sheared foams (determining the final bubble-size distribution after foam shearing) is also discussed, because the experimental results and their analysis show that this phenomenon is controlled by foam rheological properties.

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“…Foams, which are dispersions of densely packed gas bubbles in a liquid, exhibit an intricate mix of elastic, plastic and viscous behavior reminiscent of the mechanics of other disordered materials such as colloidal suspensions, granular media and emulsions [1,2,3,4,5,6]. When left unperturbed, foams jam into a meta-stable state where surface tension provides the restoring force underlying their elastic response for small strains [1,4,7].…”

Section: Introductionmentioning

confidence: 99%

Flow in linearly sheared two-dimensional foams: From bubble to bulk scale

et al. 2009

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We probe the flow of two dimensional foams, consisting of a monolayer of bubbles sandwiched between a liquid bath and glass plate, as a function of driving rate, packing fraction and degree of disorder. First, we find that bidisperse, disordered foams exhibit strongly rate dependent and inhomogeneous (shear banded) velocity profiles, while monodisperse, ordered foams are also shear banded, but essentially rate independent. Second, we introduce a simple model based on balancing the averaged drag forces between the bubbles and the top plate,F bw and the averaged bubblebubble drag forcesF bb , and assume thatF bw ∼ v 2/3 andF bb ∼ (∂yv) β , where v and (∂yv) denote average bubble velocities and gradients. This model captures the observed rate dependent flows for β ≈ 0.36, and the rate independent flows for β ≈ 0.67. Third, we perform independent rheological measurements ofF bw andF bb , both for ordered and disordered systems, and find these to be fully consistent with the forms assumed in the simple model. Disorder thus modifies the exponent β. Fourth, we vary the packing fraction φ of the foam over a substantial range, and find that the flow profiles become increasingly shear banded when the foam is made wetter. Surprisingly, our model describes flow profiles and rate dependence over the whole range of packing fractions with the same power law exponents -only a dimensionless number k which measures the ratio of the pre-factors of the viscous drag laws is seen to vary with packing fraction. We find that k ∼ (φ − φc)−1 , where φc ≈ 0.84, corresponding to the 2d jamming density, and suggest that this scaling follows from the geometry of the deformed facets between bubbles in contact. Overall, our work shows that the presence of disorder qualitatively changes the effective bubble-bubble drag forces, and suggests a route to rationalize aspects of the ubiquitous Herschel-Bulkley (power law) rheology observed in a wide range of disordered materials.

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Flow transitions in two-dimensional foams

Cited by 43 publications

References 27 publications

Jamming in Sheared Foams and Emulsions, Explained by Critical Instability of the Films between Neighboring Bubbles and Drops

Jamming in Sheared Foams and Emulsions, Explained by Critical Instability of the Films between Neighboring Bubbles and Drops

The role of surfactant type and bubble surface mobility in foam rheology

Flow in linearly sheared two-dimensional foams: From bubble to bulk scale

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