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

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

Comportement rhéologique des fluides à seuil aérés

The rheological behaviour of suspensions of bubbles in yield stress fluids is investigated through experiments on model systems. Model foamed yield stress fluids are prepared by adding monodisperse bubbles in model yield stress fluids, which behave as soft visco-elastic solids for small deformation and flow with a Herschel-Bulkley law above their yield stress. The complex modulus, yield stress and flow curve of those model foamed yield stress fluids is characterised by rheometrical measurements. For gas volume fractions lower than the percolation threshold of the bubbles in the suspending yield stress fluid, the macroscopic behaviour of the bubble suspensions results from the coupling of the fluid rheology to capillarity acting on the surface of the bubbles. The rheological properties of the suspensions decrease all the more with the gas volume fraction as capillarity is weak. This coupling is quantified through capillary numbers which also allow us to compare our experimental results to micro-mechanical estimates. For higher gas volume fractions, beyond the percolation threshold of the bubbles, the aerated material turns into an actual foam of yield stress fluid in which the interstitial fluid is confined in the Plateau borders. This confinement leads to the onset of finite-size effects as the foam is sheared, and the macroscopic behaviour of the foam depends on the micro-structure of the interstitial yield stress fluidNous étudions le comportement rhéologique de suspensions de bulles dans un fluide à seuil. Des suspensions modèles sont formulées par l'incorporation de bulles d'air monodisperses dans un fluide à seuil modèle, qui se comporte comme un solide visco-élastique pour de faibles déformations et s'écoule en suivant une loi de Herschel-Bulkley si la contrainte appliquée est supérieure à sa contrainte seuil. Nous caractérisons le module complexe, la contrainte seuil et la loi de comportement en écoulement de ces fluides à seuil aérés modèles. Pour des fractions volumiques en gaz inférieures à la fraction critique de percolation des bulles dans le fluide à seuil, la réponse macroscopique des suspensions de bulles est le résultat d'un couplage entre la rhéologie du fluide à seuil interstitiel et la capillarité qui s'exerce à la surface des bulles. Les grandeurs rhéologiques mesurées sur les suspensions décroissent d'autant plus avec la fraction volumique en gaz que les effets capillaires sont faibles. L'introduction de plusieurs nombres capillaires permet de quantifier ce couplage et de comparer les résultats expérimentaux obtenus à une estimation micro-mécanique. Au-delà de la fraction volumique critique de percolation des bulles, le matériau aéré devient une mousse de fluide à seuil dans laquelle le fluide à seuil interstitiel est confiné dans les bords de Plateau. Ce confinement entraîne l'apparition d'effets de taille finie lorsque la mousse de fluide à seuil est cisaillée, et la réponse macroscopique de la mousse dépend de la microstructure du fluide à seuil interstitie

Rheological behaviour of foamed yield stress fluids

Nous étudions le comportement rhéologique de suspensions de bulles dans un fluide à seuil. Des suspensions modèles sont formulées par l'incorporation de bulles d'air monodisperses dans un fluide à seuil modèle, qui se comporte comme un solide visco-élastique pour de faibles déformations et s'écoule en suivant une loi de Herschel-Bulkley si la contrainte appliquée est supérieure à sa contrainte seuil. Nous caractérisons le module complexe, la contrainte seuil et la loi de comportement en écoulement de ces fluides à seuil aérés modèles. Pour des fractions volumiques en gaz inférieures à la fraction critique de percolation des bulles dans le fluide à seuil, la réponse macroscopique des suspensions de bulles est le résultat d'un couplage entre la rhéologie du fluide à seuil interstitiel et la capillarité qui s'exerce à la surface des bulles. Les grandeurs rhéologiques mesurées sur les suspensions décroissent d'autant plus avec la fraction volumique en gaz que les effets capillaires sont faibles. L'introduction de plusieurs nombres capillaires permet de quantifier ce couplage et de comparer les résultats expérimentaux obtenus à une estimation micro-mécanique. Au-delà de la fraction volumique critique de percolation des bulles, le matériau aéré devient une mousse de fluide à seuil dans laquelle le fluide à seuil interstitiel est confiné dans les bords de Plateau. Ce confinement entraîne l'apparition d'effets de taille finie lorsque la mousse de fluide à seuil est cisaillée, et la réponse macroscopique de la mousse dépend de la microstructure du fluide à seuil interstitielThe rheological behaviour of suspensions of bubbles in yield stress fluids is investigated through experiments on model systems. Model foamed yield stress fluids are prepared by adding monodisperse bubbles in model yield stress fluids, which behave as soft visco-elastic solids for small deformation and flow with a Herschel-Bulkley law above their yield stress. The complex modulus, yield stress and flow curve of those model foamed yield stress fluids is characterised by rheometrical measurements. For gas volume fractions lower than the percolation threshold of the bubbles in the suspending yield stress fluid, the macroscopic behaviour of the bubble suspensions results from the coupling of the fluid rheology to capillarity acting on the surface of the bubbles. The rheological properties of the suspensions decrease all the more with the gas volume fraction as capillarity is weak. This coupling is quantified through capillary numbers which also allow us to compare our experimental results to micro-mechanical estimates. For higher gas volume fractions, beyond the percolation threshold of the bubbles, the aerated material turns into an actual foam of yield stress fluid in which the interstitial fluid is confined in the Plateau borders. This confinement leads to the onset of finite-size effects as the foam is sheared, and the macroscopic behaviour of the foam depends on the micro-structure of the interstitial yield stress flui

A mechanism of strain hardening and Bauschinger effect: shear-history-dependent microstructure of elasto-plastic suspensions

Dispersing solid hard particles in an elasto-plastic material leads to important shear-history dependence of the behavior, namely strain hardening and Bauschinger effect. Strain hardening is observed as the progressive strengthening of a material during its plastic deformation and is usually associated with ductility, a property often sought after in composite materials to postpone fractures and failure. In addition, anisotropic mechanical properties are developed, the material resistance being larger in the direction of the imposed flow, which is referred to as the Bauschinger effect. We show that this is related here to shear-history-dependent particle-pair distribution functions. Roughness and interparticle contacts likely play a major role, as replacing hard particles by nondeformable bubbles modifies the suspension microstructure and suppresses strain hardening. Beyond suspensions, our study provides new insight in the understanding and control of strain hardening and Bauschinger effect in composite materials

A mechanism of strain hardening and Bauschinger effect: shear-history-dependent microstructure of elasto-plastic suspensions

Dispersing solid hard particles in an elasto-plastic material leads to important shear-history dependence of the behavior, namely strain hardening and Bauschinger effect. Strain hardening is observed as the progressive strengthening of a material during its plastic deformation and is usually associated with ductility, a property often sought after in composite materials to postpone fractures and failure. In addition, anisotropic mechanical properties are developed, the material resistance being larger in the direction of the imposed flow, which is referred to as the Bauschinger effect. We show that this is related here to shear-history-dependent particle-pair distribution functions. Roughness and interparticle contacts likely play a major role, as replacing hard particles by nondeformable bubbles modifies the suspension microstructure and suppresses strain hardening. Beyond suspensions, our study provides new insight in the understanding and control of strain hardening and Bauschinger effect in composite materials