Rigidity Percolation in Particle-Laden Foams

Cohen-Addad, Sylvie; Krzan, Marcel; Höhler, Reinhard; Herzhaft, Benjamin

doi:10.1103/physrevlett.99.168001

Cited by 29 publications

(33 citation statements)

References 20 publications

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“…Moreover, the few existing experimental studies have focused on very specific material e.g. particles in a clay dispersion [Coussot (1997), Ancey and Jorrot (2001)], a cement paste [Geiker et al (2002)], a foam [Cohen-Addad et al (2007)] or coal slurries [Sengun and Probstein (1989a,b)]. This poses a problem: can we use the results obtained in studies performed with noncolloidal particles in clay dispersions to predict the behavior of a mortar (i.e.…”

Section: Introductionmentioning

confidence: 99%

Yield stress and elastic modulus of suspensions of noncolloidal particles in yield stress fluids

Mahaut¹,

Château²,

Coussot³

et al. 2008

Journal of Rheology

169

138

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SynopsisWe study experimentally the behavior of isotropic suspensions of noncolloidal particles in yield stress fluids. This problem has been poorly studied in the literature, and only on specific materials. In this paper, we manage to develop procedures and materials that allow focusing on the purely mechanical contribution of the particles to the yield stress fluid behavior, independently of the physicochemical properties of the materials. This allows us to relate the macroscopic properties of these suspensions to the mechanical properties of the yield stress fluid and the particle volume fraction, and to provide results applicable to any noncolloidal particle in any yield stress fluid. We find that the elastic modulus/concentration relationship follows a Krieger-Dougherty law, and show that the yield stress/concentration relationship is related to the elastic modulus/concentration relationship through a very simple law, in agreement with results from a micromechanical analysis. * corresponding author: guillaume.ovarlez@lcpc.fr † Support from the Agence Nationale de la Recherche (ANR) is acknowledged (grant ANR-05-JCJC-0214). I IntroductionDense suspensions arising in industrial processes (concrete casting, drilling muds, foodstuff transport...) and natural phenomena (debris-flows, lava flows...) often involve a broad range of particle sizes. The behavior of these materials reveal many complex features which are far from being understood (for a recent review, see Stickel and Powell (2005)). This complexity originates from the great variety of interactions between the particles (colloidal, hydrodynamic, frictional, collisional...) and of physical properties of the particles (volume fraction, deformability, sensitivity to thermal agitation, shape, buoyancy...) involved in the material behavior.Basically, these materials exhibit a yield stress and have a solid viscoelastic behavior below this yield stress; above the yield stress they behave as liquids, and their flow behavior is usually well fitted to a Herschel-Bulkley law [Larson (1999)] although the exact details of the constitutive law seem more complex at the approach of the transition between the liquid and the solid regimes [Coussot (2005)]. The yielding behavior originates from the colloidal interactions which create a jammed network of interacting particles [Larson (1999);Coussot (2005)]. If the behavior of dense colloidal suspensions, and more generally of yield stress fluids, have received considerable interest and been widely studied, the influence of the large particles on this behavior have been poorly studied. Moreover, the few existing experimental studies have focused on very specific material e.g. particles in a clay dispersion [Coussot (1997), Ancey and Jorrot (2001)], a cement paste [Geiker et al. (2002)], a foam [Cohen-Addad et al. (2007)] or coal slurries [Sengun and Probstein (1989a,b)]. This poses a problem: can we use the results obtained in studies performed with noncolloidal particles in clay dispersions to predict the behavior of a m...

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Section: Introductionmentioning

confidence: 99%

Yield stress and elastic modulus of suspensions of noncolloidal particles in yield stress fluids

Mahaut¹,

Château²,

Coussot³

et al. 2008

Journal of Rheology

169

138

View full text Add to dashboard Cite

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“…In this case, the surfactant adsorbs at the air/water interface causing effects such as Marangoni stresses and interfacial dilational elasticity which stabilize the foam. There have also been several recent examples of aqueous foams stabilized by partially hydrophobic particles 3–9. Such particles adsorb at the air/water interface and form a rigid shell (“armored bubbles”10) that protects bubbles against coalescence.…”

Section: Introductionmentioning

confidence: 99%

Polymer Foams Stabilized by Particles Adsorbed at the Air/Polymer Interface

Thareja¹,

Ising²,

Kingston³

et al. 2008

Macromol. Rapid Commun.

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In aqueous systems, partially hydrophobic particles are known to stabilize foams even in the absence of any added surfactant. This paper shows that the same principle can be applied to polymeric systems: particles that are partially wetted by a polymer melt can stabilize a foam of that polymer. The foam stability is attributable to the adsorption of the particles at the air/polymer interface. Remarkably, stable foams are realized even from polymers that are liquid at room temperature, and hence are otherwise unfoamable. The implications of this result to practical foaming operations are discussed.

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“…With respect to previous work, our results highlight a critical size ratio below which a new elastic regime, characterized by unequaled modulus values as well as independence of size ratio, has been identified. This behavior, which has been clearly correlated to the formation of a thick granular skeleton of tightly packed particles, is not correctly described by the so-called rigidity percolation model [26]. We have shown that this increased elasticity originates from the strong synergistic effects that can be brought about in those particleloaded foams: the particles are small enough for forming an interstitial granular skeleton and the bubbles interface imposes a small but crucial confinement pressure on the packed particles, therefore providing significant mechanical strength to the granular skeleton.…”

Section: Resultsmentioning

confidence: 99%

“…In contrast, filling of molds requires an appropriate workability of the fresh foamy paste. In this regard, rheology of aqueous foams [7,23] and rheology of suspensions [24,25] have been studied mostly separately and only few recent studies have however tackled the issue of coupling of interstitial rheology and bubble elasticity in foams [9,26]. Whereas a satisfactory modeling of the global rheology is still lacking, unusual and interesting rheological behaviors have been reported.…”

Section: Introductionmentioning

confidence: 99%

“…Whereas a satisfactory modeling of the global rheology is still lacking, unusual and interesting rheological behaviors have been reported. Cohen-Addad et al [26] provided a very enlightening example of the strong synergistic effects that can be brought about in complex liquid foams: it is shown that adding a tiny amount of non-colloidal particles in aqueous foams allows for elastic and loss shear moduli to be enhanced by more than one order of magnitude. Particle-size dependence is reported, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Optimal strengthening of particle-loaded liquid foams

et al. 2017

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Foams made of complex fluids such as particle suspensions have a great potential for the development of advanced aerated materials. In this paper, we study the rheological behavior of liquid foams loaded with granular suspensions. We focus on the effect of small particles, i.e., particle-to-bubble size ratio smaller than 0.1, and we measure the complex modulus as a function of particle size and particle volume fraction. With respect to previous work, the results highlight a new elastic regime characterized by unequaled modulus values as well as independence of size ratio. A careful investigation of the material microstructure reveals that particles organize through the network between the gas bubbles and form a granular skeleton structure with tightly packed particles. The latter is proven to be responsible for the reported new elastic regime. Rheological probing performed by strain sweep reveals a two-step yielding of the material: The first one occurs at small strain and is clearly attributed to yielding of the granular skeleton; the second one corresponds to the yielding of the bubble assembly, as observed for particle-free foams. Moreover, the elastic modulus measured at small strain is quantitatively described by models for solid foams in assuming that the granular skeleton possesses a bulk elastic modulus of order 100 kPa. Additional rheology experiments performed on the bulk granular material indicate that this surprisingly high value can be understood as soon as the magnitude of the confinement pressure exerted by foam bubbles on packed grains is considered.

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Rigidity Percolation in Particle-Laden Foams

Cited by 29 publications

References 20 publications

Yield stress and elastic modulus of suspensions of noncolloidal particles in yield stress fluids

Yield stress and elastic modulus of suspensions of noncolloidal particles in yield stress fluids

Polymer Foams Stabilized by Particles Adsorbed at the Air/Polymer Interface

Optimal strengthening of particle-loaded liquid foams

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