Shear induced drainage in foamy yield-stress fluids

Shear induced drainage of a foamy yield stress fluid is investigated using MRI techniques. Whereas the yield stress of the interstitial fluid stabilizes the system at rest, a fast drainage is observed when a horizontal shear is imposed. It is shown that the sheared interstitial material behaves as a viscous fluid in the direction of gravity, the effective viscosity of which is controlled by shear in transient foam films between bubbles. Results provided for several bubble sizes are not captured by the R^2 scaling classically observed for liquid flow in particulate systems, such as foams and thus constitute a remarkable demonstration of the strong coupling of drainage flow and shear induced interstitial flow. Furthermore, foam films are found to be responsible for the unexpected arrest of drainage, thus trapping irreversibly a significant amount of interstitial liquid.Comment: Published in Physical Review Letters. http://prl.aps.org/abstract/PRL/v104/i12/e12830

Coupling of elasticity to capillarity in soft aerated materials

We study the elastic properties of soft solids containing air bubbles. Contrary to standard porous materials, the softness of the matrix allows for a coupling of the matrix elasticity to surface tension forces brought in by the bubbles. Thanks to appropriate experiments on model systems, we show how the elastic response of the dispersions is governed by two dimensionless parameters: the gas volume fraction and a capillary number comparing the elasticity of the matrix to the stiffness of the bubbles. We also show that our experimental results are in good agreement with computations of the shear modulus through a micro-mechanical approach.Comment: submitted to Soft Matte

Rheological behaviour of suspensions of bubbles in yield stress fluids

The rheological properties of suspensions of bubbles in yield stress fluids are investigated through experiments on model systems made of monodisperse bubbles dispersed in concentrated emulsions. Thanks to this highly tunable system, the bubble size and the rheological properties of the suspending yield stress fluid are varied over a wide range. We show that the macroscopic response under shear of the suspensions depends on the gas volume fraction and the bubble stiffness in the suspending fluid. This relative stiffness can be quantified through capillary numbers comparing the capillary pressure to stress scales associated with the rheological properties of the suspending fluid. We demonstrate that those capillary numbers govern the decrease of the elastic and loss moduli, the absence of variation of the yield stress and the increase of the consistency with the gas volume fraction, for the investigated range of capillary numbers. Micro-mechanical estimates are consistent with the experimental data and provide insight on the experimental results.Comment: submitted to Journal of non Newtonian Fluid Mechanic

On the existence of a simple yield stress fluid behavior

Materials such as foams, concentrated emulsions, dense suspensions or colloidal gels, are yield stress fluids. Their steady flow behavior, characterized by standard rheometric techniques, is usually modeled by a Herschel-Bulkley law. The emergence of techniques that allow the measurement of their local flow properties (velocity and volume fraction fields) has led to observe new complex behaviors. It was shown that many of these materials exhibit shear banding in a homogeneous shear stress field, which cannot be accounted for by the standard steady-state constitutive laws of simple yield stress fluids. In some cases, it was also observed that the velocity fields under various conditions cannot be modeled with a single constitutive law and that nonlocal models are needed to describe the flows. Doubt may then be cast on any macroscopic characterization of such systems, and one may wonder if any material behaves in some conditions as a Herschel-Bulkley material. In this paper, we address the question of the existence of a simple yield stress fluid behavior. We first review experimental results from the literature and we point out the main factors (physical properties, experimental procedure) at the origin of flow inhomogeneities and nonlocal effects. It leads us to propose a well-defined procedure to ensure that steady-state bulk properties of the materials are studied. We use this procedure to investigate yield stress fluid flows with MRI techniques. We focus on nonthixotropic dense suspensions of soft particles (foams, concentrated emulsions, Carbopol gels). We show that, as long as they are studied in a wide (as compared to the size of the material mesoscopic elements) gap geometry, these materials behave as 'simple yield stress fluids': they are homogeneous, they do not exhibit steady-state shear banding, and their steady flow behavior in simple shear can be modeled by a local continuous monotonic constitutive equation which accounts for flows in various conditions and matches the macroscopic response.Comment: Journal of Non-Newtonian Fluid Mechanics (2012) http://dx.doi.org/10.1016/j.jnnfm.2012.06.00

Yielding and flow of foamed metakaolin pastes

Metakaolin is a broadly used industrial raw material, with applications in the production of ceramics and geopolymers, and the partial replacement of Portland cement. The early stages of the manufacturing of some of these materials require the preparation and processing of a foamed metakaolin-based slurry. In this study, we propose to investigate the rheology of a foamed metakaolin-based fresh paste by performing well-controlled experiments. We work with a non-reactive metakaolin paste containing surfactant, in which we disperse bubbles of known radius at a chosen volume fraction. We perform rheometry measurements to characterize the minimum stress required for the foamed materials to flow (yield stress), and the dissipation occurring during flow. We show that the yield stress of the foamed samples is equal to the one of the metakaolin paste, and that dissipation during flow increases quadratically with the bubble volume fraction. Comparison with yielding and flow of model foamed yield stress fluids allows us to understand these results in terms of coupling between the bubbles' surface tension and the metakaolin paste's rheology

Mixtures of foam and paste: suspensions of bubbles in yield stress fluids

We study the rheological behavior of mixtures of foams and pastes, which can be described as suspensions of bubbles in yield stress fluids. Model systems are designed by mixing monodisperse aqueous foams and concentrated emulsions. The elastic modulus of the suspensions decreases with the bubble volume fraction. This decrease is all the sharper as the elastic capillary number (defined as the ratio of the paste elastic modulus to the bubble capillary pressure) is high, which accounts for the softening of the bubbles as compared to the paste. By contrast, the yield stress of most studied materials is not modified by the presence of bubbles. Their plastic behavior is governed by the plastic capillary number, defined as the ratio of the paste yield stress to the bubble capillary pressure. At low plastic capillary number values, bubbles behave as nondeformable inclusions, and we predict that the suspension dimensionless yield stress should remain close to unity. At large plastic capillary number values, we observe bubble breakup during mixing: bubbles are deformed by shear. Finally, at the highest bubble volume fractions, the yield stress increases abruptly: this is interpreted as a 'foamy yield stress fluid' regime, which takes place when the paste mesoscopic constitutive elements are strongly confined in the films between the bubbles

Rayleigh-Taylor Instability in Elastoplastic Solids: A Local Catastrophic Process

International audienceWe show that the Rayleigh-Taylor instability in elastoplastic solids takes the form of local perturbations penetrating the material independently of the interface size, in contrast with the theory for simple elastic materials. Then, even just beyond the stable domain, the instability abruptly develops as bursts rapidly moving through the other medium. We show that this is due to the resistance to penetration of a finger which is minimal for a specific finger size and drops to a much lower value beyond a small depth (a few millimeters). The Rayleigh-Taylor instability (RTI) is a well-known instability which occurs when a denser fluid rests on top of a lighter one [1]. As it develops, the two fluids penetrate one another, in the form of fingers. Instability is driven by the density difference and the acceleration to which the fluids are submitted, while surface tension provides a stabilizing effect. In contrast, RTI in solids is much less studied and understood, even though it relates to many application fields and can cause irreversible damage to structures. Examples include metal plates submitted to strong pressure or acceleration in high-energy density physics experiments [2], magnetic implosion of impactor liners [3,4], assessment of solid strength under high strain rate [5], slowly accreting neutron stars [6]. Other applications are found in geology: volcanic island formation [7], salt dome formation [8], and more generally, magmatic diapirism in Earth's mantle and continental crust [9,10], correspond to situations where a liquid opens its way through a layer of denser solid material above it. In most approaches to this problem [7–9,11], the upper material was considered as a highly viscous fluid, which allowed simple simulations of the process, but could also be misleading. Another situation concerns oil well cementing operations, in which yield stress fluids of different densities (drilling muds and cement, e.g.), which behave as solids at rest, may be pumped into the well in an ill-favored density order [12]. The basic approach to RTI for solids assumes linear elastic materials. The problem appears similar to that for simple fluids, except that the role of surface tension effects, neglected for solids, is played by elasticity. For a single solid above a liquid with a (positive) density difference Δρ, the instability criterion (A) is given by gΔρ > 4απG=L, where G and L are the shear modulus and length of the sample, respectively, and g denotes the gravitational acceleration. Depending on boundary conditions, factor α was found to be 1 [3,13], 1.6 [14], or 2 [15]. A couple of experiments on metal plates [16] and with a yogurt [17] provided some support to this theory. From a more complete study [18] using soft elastic solids, the overall validity of this approach was proved but the wavelength was shown to be smaller than expected from theory and dependent on uncontrollable, slight disturbances of the surface [19]. RTI for solids is further complicated by the fact that yielding may occur beyond a critical deformation. So far, this aspect has been considered separately, leading to the conclusion that instability results from a sufficiently large initial perturbation amplitude ε 0 (penetration depth). The instability criterion (B) then reads gΔρ > βτ c =ε 0 , where τ c denotes the material's yield stress (in simple shear), and where 0.5 ≤ β ≤ 2 depending on the sample aspect ratio [13–15,18,24,25]. Some tests with a single material were apparently in agreement with this criterion [17] but the plastic regime for this material was not so well-defined [19]. Finally, it was suggested [2] that elastic and plastic stability criteria should be taken into account successively, and deep theoretical analysis [26] predicted that for plastic materials, once the threshold is reached somewhere, the perturbation grows unlimitedly. These approaches have the advantage of considering independently the elasticity and the yielding effects. However, one cannot exclude that the interplay of both mechanisms could play a crucial role in the early stage of the perturbation growth. Here we aim at clarifying this problem through experiments on well-characterized materials, linearly elastic below a critical deformation and elastoplastic beyond this deformation. We show that the RTI in solids does not develop as predicted by the theory for simple elastic materials, but results from the ability of local perturbations to penetrate the material by involving, from the start, both elastic and plastic effects. At some point during the process, resistance to penetration drops, causing an abrup

Propriétés rhéologiques de suspensions floculéees modèles

Ces travaux s'intéressent à la compréhension et à la caractérisation macroscopique et microscopique des phénomènes de floculation dans des suspensions colloïdales modèles. Plusieurs paramètres et leur impact sont étudiés : intensité des forces électrostatiques, fraction volumique en particules, histoire de chargement, taille et forme des particules. Le comportement macroscopique de chaque suspension est caractérisé par une mesure de la contrainte seuil et une mesure du module élastique après différents temps de repos. Pour chaque matériau, on obtient une unique courbe en traçant les contraintes seuil mesurées en fonction des modules élastiques mesurées pour diverses valeurs de l'intensité des forces électrostatiques, de l'age du système et de la fraction volumique en particules. Ces différentes courbes se rassemblent en une unique courbe maîtresse en normalisant la contrainte seuil par le diamètre au carré des particules et le module élastique par le diamètre des particules

Wall Slip of Soft-Jammed Systems: A Generic Simple Shear Process

International audienceFrom well-controlled long creep tests we show that the residual apparent yield stress observed with soft-jammed systems along smooth surfaces is an artefact due to edge effects. By removing these effects we can determine the stress solely associated with steady state wall slip below the material yield stress. This stress is found to vary linearly with the slip velocity for a wide range of materials whatever the structure, the interaction types between the elements and with the wall, and the concentration. Thus wall slip results from the laminar flow of some given free liquid volume remaining between the (rough) jammed structure formed by the elements, and the smooth wall. This phenomenon may be described by the simple shear flow in a Newtonian liquid layer of uniform thickness. For various systems this equivalent thickness varies in a narrow range (35 ± 15 nm)