Shear induced normal stress differences in aqueous foams

A finite simple shear deformation of an elastic solid induces unequal normal stresses. This nonlinear phenomenon, known as the Poynting effect, is governed by a universal relation between shear strain and first normal stresses difference, valid for non-dissipative elastic materials. We provide the first experimental evidence that an analog of the Poynting effect exists in aqueous foams where besides the elastic stress, there are significant viscous or plastic stresses. These results are interpreted in the framework of a constitutive model, derived from a physical description of foam rheology

Investigation of shear banding in three-dimensional foams

We study the steady flow properties of different three-dimensional aqueous foams in a wide gap Couette geometry. From local velocity measurements through Magnetic Resonance Imaging techniques and from viscosity bifurcation experiments, we find that these foams do not exhibit any observable signature of shear banding. This contrasts with two previous results (Rodts et al., Europhys. Lett., 69 (2005) 636 and Da Cruz et al., Phys. Rev. E, 66 (2002) 051305); we discuss possible reasons for this dicrepancy. Moreover, the foams we studied undergo steady flow for shear rates well below the critical shear rate recently predicted (Denkov et al., Phys. Rev. Lett., 103 (2009) 118302). Local measurements of the constitutive law finally show that these foams behave as simple Herschel-Bulkley yield stress fluids

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

Rhéologie multiéchelle des mousses liquides

Les mousses aqueuses sont des fluides complexes constitués de dispersions concentrées de bulles de gaz dans une solution de tensioactifs. A l'instar d'autres fluides complexes comme les émulsions ou les pâtes, une mousse se comporte comme un solide viscoélastique lorsque la fraction volumique de la phase continue est suffisamment faible pour que l'empilement des bulles soit bloqué. Ses propriétés mécaniques résultent de couplages entre processus se produisant à plusieurs échelles de temps et d'espace : celles des tensioactifs adsorbés aux interfaces liquide-gaz, celles d'une bulle de gaz ou de mouvements collectifs à une échelle mésoscopique. A partir de trois expériences, nous avons mis en évidence l'impact du désordre de leur structure d'une part, et celui des tensioactifs d'autre part, sur les propriétés viscoélastiques des mousses. Nous avons mis au point un rhéomètre oscillatoire qui permet de mesurer la relation contrainte-déformation-fréquence d'une monocouche de bulles confinées entre deux parois planes parallèles tout en contrôlant sa pression osmotique. Nous avons montré que les relaxations de ces mousses de structure modèle sont pilotées par la rhéologie interfaciale de cisaillement que nous avons caractérisée indépendamment. Nous proposons un modèle quantitatif de ce couplage. Dans une deuxième expérience, nous avons sondé la réponse viscoélastique des mousses de structure 3D désordonnées. Nos résultats montrent que selon la rigidité des interfaces, le facteur de perte d'une mousse est décrit par une loi d'échelle en fréquence. Son évolution avec la taille des bulles et la viscosité du liquide permet de déterminer le mécanisme à l'origine de la dissipation. Dans une troisième expérience, Nous avons élaboré des mousses monodisperses de structure 3D ordonnées et de pression osmotique contrôlée. De manière remarquable, la variation de leur facteur de perte en fonction de la fréquence est similaire à celle des mousses désordonnées de même composition chimique. Ces résultats démontrent que le désordre de l'empilement des bulles n'est pas à l'origine des relaxations viscoélastiques linéaires des mousses, comme l'avaient suggéré plusieurs modèles théoriques, et ouvrent la voie à une modélisation quantitative du lien entre la viscoélasticité des interfaces et celle des mousses 3DAqueous foams are constituted of concentrated gas bubble dispersions in a surfactant solution. Like other complex fluids, such as emulsions or pastes, foam behaves as a viscoelastic solid if the volume fraction of the continuous phase is sufficiently small for the bubble packing to be jammed. The mechanical properties of the foam are due to couplings between processes at a wide range of time and length scales: The ones of the surfactant molecules that are adsorbed to the gas-liquid interfaces, the ones of the bubbles or collective motions at a mesoscopic scale. On the basis of three experiments, we have evidenced the impact of structural disorder and surfactant properties on foam viscoelasticity. We have constructed an oscillatory rheometer to measure the frequency and strain dependent stress response of a bubble monolayer confined between two parallel plates, subjected to an imposed osmotic pressure. We have shown that the relaxation of these model foams are governed by the interfacial shear rheology which we have probed in independent experiments and, we present a quantitative model of this coupling. In a second experiment, we have probed the viscoelastic response of disordered 3D foams. Our results show that, depending on interfacial rigidity, the mechanical loss factor of a foam is described by a scaling law depending on frequency. Its dependence on bubble size and liquid viscosity helps to determine the origin of the dissipation. In our third experiment, we have produced monodispersed ordered foams, subjected to a controlled osmotic pressure. Remarkably, the frequency scaling of their loss factor is similar to the one of disordered foams of the same chemical composition. These results demonstrate that the linear viscoelastic response of foams is not the consequence of disorder on the bubble scale as suggested by several previous theories, and they thus open the way for quantitative models linking the viscoelasticity of the interfaces to that of 3D foamsPARIS-EST-Université (770839901) / SudocSudocFranceF

Glissement à la paroi d'une mousse humide

Les mousses aqueuses sont des assemblées compactes de bulles de gaz dans une solution de tensioactifs. Pour décrire les propriétés rhéologiques de ces fluides complexes utilisés dans de nombreuses applications, il est nécessaire de comprendre les mécanismes de dissipation aux petites échelles, au niveau des bulles ou des films liquides. En particulier, on observe que ces matériaux glissent le long de parois lisses. D'autre part, la rhéologie des mousses dépend fortement de leur fraction volumique de liquide ; nous nous intéressons donc ici au cas des mousses humides, proches de la transition de (dé)blocage, quand les contacts entre bulles disparaissent et que la pression de confinement de la mousse tend vers zéro. Pour élucider les mécanismes de friction en jeu dans les mousses humides, nous étudions le glissement de monocouches de bulles ou de mousses 3D le long d'un plan incliné immergé. Deux régimes de friction sont mis en évidence : en plus d'une friction non-linéaire de type Bretherton, déjà observée dans les mousses, nous montrons l'existence d'une friction linéaire en vitesse de type Stokes (Le Merrer et al. Soft Matter 2015). La transition entre ces deux régimes est pilotée par l'écrasement des bulles contre la paroi

A high rate flow-focusing foam generator

We use a rigid axisymetric microfluidic flow focusing device to produce monodisperse bubbles, dispersed in a surfactant solution. The gas volume fraction of the dispersion collected out of this device can be as large as 90%, demonstrating that foam with solid-like viscoelastic properties can be produced in this way. The polydispersity of the bubbles is so low that we observe crystallization of our foam. We measure the diameter of the bubbles and compare these data to recent theoretical predictions. The good control over bubble size and foam gas volume fraction shows that our device is a flexible and promising tool to produce calibrated foam at a high flow rate

Coarsening transitions of wet liquid foams under microgravity conditions

We report foam coarsening studies which were performed in the International Space Station (ISS) to suppress drainage due to gravity. Foams and bubbly liquids with controlled liquid fractions $\phi$ between 15 and 50\% were investigated to study the transition between bubble growth laws previously reported near the dry limit $\phi \rightarrow 0$ and the dilute limit $\phi \rightarrow 1$ (Ostwald ripening). We determined the coarsening rates; for the driest foams and the bubbly liquids, they are in close agreement with theoretical predictions. We observe a sharp cross-over between the respective laws at a critical value $\phi^*$. At liquid fractions beyond this transition, neighboring bubbles are no longer all in contact, like at a jamming transition. Remarkably $\phi^*$ is significantly larger than the random close packing volume fraction of the bubbles $\phi_{\text{rcp}}$ which was determined independently. We attribute the differences between $\phi^*$ and $\phi_{\text{rcp}}$ to a weakly adhesive bubble interaction that we have studied in complementary ground-based experiments

Aqueous foams in microgravity, measuring bubble sizes

The paper describes a study of wet foams in microgravity whose bubble size distribution evolves due to diffusive gas exchange. We focus on the comparison between the size of bubbles determined from images of the foam surface and the size of bubbles in the bulk foam, determined from Diffuse Transmission Spectroscopy (DTS). Extracting the bubble size distribution from images of a foam surface is difficult so we have used three different procedures : manual analysis, automatic analysis with a customized Python script and machine learning analysis. Once various pitfalls were identified and taken into account, all the three procedures yield identical results within error bars. DTS only allows the determination of an average bubble radius which is proportional to the photon transport mean free path $\ell^*$. The relation between the measured diffuse transmitted light intensity and {$\ell^*$} previously derived for slab-shaped samples of infinite lateral extent does not apply to the cuboid geometry of the cells used in the microgravity experiment. A new more general expression of the diffuse intensity transmitted with specific optical boundary conditions has been derived and applied to determine the average bubble radius. The temporal evolution of the average bubble radii deduced from DTS and of the same average radii of the bubbles measured at the sample surface are in very good agreement throughout the coarsening. Finally, ground experiments were performed to compare bubble size distributions in a bulk wet foam and at its surface at times so short that diffusive gas exchange is insignificant. They were found to be similar, confirming that bubbles seen at the surface are representative of the bulk foam bubbles