Liquid foam exhibits surprisingly high viscosity, higher than each of its phases. This dissipation enhancement has been rationalized by invoking either a geometrical confinement of the shear in the liquid phase, or the influence of the interface viscosity. However, a precise localization of the dissipation, and its mechanism, at the bubble scale is still lacking. To this aim, we simultaneously monitored the evolution of the local flow velocity, film thickness and surface tension of a five films assembly, induced by different controlled deformations. These measurements allow us to build local constitutive relations for this foam elementary brick. We first show that, for our millimetric foam films, the main part of the film has a purely elastic, reversible behavior, thus ruling out the interface viscosity to explain the observed dissipation. We then highlight a generic frustration at the menisci, controlling the interface transfer between neighbor films and resulting in the localization of a bulk shear flow close to the menisci. A model accounting for surfactant transport in these small sheared regions is developed. It is in good agreement with the experiment, and demonstrate that most of the dissipation is localized in these domains. The length of these sheared regions, determined by the physico-chemical properties of the solution, sets a transition between a large bubble regime in which the films are mainly stretched and compressed, and a small bubble regime in which they are sheared. Finally, we discuss the parameter range where a model of foam viscosity could be built on the basis of these local results.
We study experimentally the pressure drop needed to push a bubble train in a millimetric channel, as a function of the velocity. For dry liquid foams, the influence of the amount of liquid and of the bubble size is pointed out and we predict theoretically that this influence is closely related to the power law obtained for the force/velocity relation. This model is in fair agreement with our experimental data and provides a new interpretation of previous results.
Like emulsions, pastes and many other forms of soft condensed matter, aqueous foams present slow mechanical relaxations when subjected to a stress too small to induce any plastic flow. To identify the physical origin of this viscoelastic behaviour, we have simulated how dry disordered coarsening 2D foams respond to a small applied stress. We show that the mechanism of long time relaxation is driven by coarsening induced rearrangements of small bubble clusters. These findings are in full agreement with a scaling law previously derived from experimental creep data for 3D foams. Moreover, we find…
Many microfluidics devices, coating processes or diphasic flows involve the motion of a liquid meniscus on a wet wall. This motion induces a specific viscous force, that exhibits a non-linear dependency in the meniscus velocity. We propose a review of the theoretical and experimental work made on this viscous force, for simple interfacial properties. The interface is indeed assumed either perfectly compressible (mobile interface) or perfectly incompressible (rigid interface). We show that, in the second case, the viscous force exerted by the wall on the meniscus is a combination of two power l…
Using 2D numerical simulations as well as analytical modelling, we show how slow viscoelastic dynamics of aqueous foam are linked to coarsening induced intermittent bubble rearrangements. The macroscopic strain rate is expressed in terms of mesoscopic dynamics where local rearrangements are represented by strain fields induced by force dipoles. We relate these dipoles quantitatively to local geometrical features of the corresponding bubble rearrangements. We also explain how applying a small macroscopic stress biases the outcome of coarsening induced rearrangements.
The Cellular Potts Model (CPM) succesfully simulates drainage and shear in foams. Here we use the CPM to investigate instabilities due to the flow of a single large bubble in a dry, monodisperse two-dimensional flowing foam. As in experiments in a Hele-Shaw cell, above a threshold velocity the large bubble moves faster than the mean flow. Our simulations reproduce analytical and experimental predictions for the velocity threshold and the relative velocity of the large bubble, demonstrating the utility of the CPM in foam rheology studies.
We describe a numerical model to predict the rheology of two-dimensional dry foams. The model accurately describes soap film curvature, viscous friction with the walls, and includes the transport of surfactant within the films and across the vertices where films meet. It accommodates the changes in foam topology that occur when a foam flows and, in particular, accurately represents the relaxation of the foam following a topological change. The model is validated against experimental data, allowing the prediction of elastic and viscous parameters associated with different surfactant solutions.
We describe the extension of a "viscous froth" model to the dynamics of a wet foam in a Hele-Shaw cell. The two-dimensional model includes the friction experienced by the soap films as they are dragged along the cell walls, while retaining accurate geometrical information. To explore the consequences of changing the liquid content in this situation, we consider a simple foam geometry known as a bubble lens: a bubble partially filling a narrow, straight channel with a single film spanning the gap between the bubble and the opposite wall. The triple vertices of this structure are decorated with …
The elementary topological T1 process in a two-dimensional foam corresponds to the "flip" of one soap film with respect to the geometrical constraints. From a mechanical point of view, this T1 process is an elementary relaxation process through which the entire structure of an out-of-equilibrium foam evolves. The dynamics of this elementary relaxation process has been poorly investigated and is generally neglected during simulations of foams. We study both experimentally and theoretically the T1 dynamics in a dry two-dimensional foam. We show that the dynamics is controlled by the surface visc…
In a recent letter (Denkov et al., Phys. Rev. Lett., vol. 100 (2008) p. 138301) we calculated theoretically the macroscopic viscous stress of steadily sheared foam/emulsion from the energy dissipated inside the transient planar films, formed between neighboring bubbles/drops in the shear flow. The model predicts that the viscous stress in these systems should be a proportional to Ca^1/2, where Ca is the capillary number and n = 1/2 is the power-law index. In the current paper we explain in detail our model and develop it further in several aspects: First, we extend the model to account for the…
A Stokes experiment for foams is proposed. It consists in a two-dimensional flow of a foam, confined between a water subphase and a top plate, around a fixed circular obstacle. We present systematic measurements of the drag exerted by the flowing foam on the obstacle, \emph{versus} various separately controlled parameters: flow rate, bubble volume, solution viscosity, obstacle size and boundary conditions. We separate the drag into two contributions, an elastic one (yield drag) at vanishing flow rate, and a fluid one (viscous coefficient) increasing with flow rate. We quantify the influence of…
The highly confined flow of the liquid phase, trapped between the gas bubbles, is at the origin of the large effective viscosity of the liquid foams. Despite the industrial relevance of this complex fluid, the foam viscosity remains difficult to predict, because of the lack of flow characterization at the bubble scale. Using an original deformable frame, we provide the first experimental evidence of the interface transfer between a compressed film (resp. a stretched film) and its first neighbour, across their common meniscus. We measure this transfer velocity, which is a key boundary condition…
A variety of complex fluids consist in soft, round objects (foams, emulsions, assemblies of copolymer micelles or of multilamellar vesicles -- also known as onions). Their dense packing induces a slight deviation from their prefered circular or spherical shape. As a frustrated assembly of interacting bodies, such a material evolves from one conformation to another through a succession of discrete, topological events driven by finite external forces. As a result, the material exhibits a finite yield threshold. The individual objects usually evolve spontaneously (colloidal diffusion, object coal…
The role of surface tension gradients in the apparent viscosity of liquid foams remains largely unexplained. In this article, we develop a toy-model based on a periodic array of 2D hexagonal bubbles, each bubble being separated from its neighbors by a liquid film of uniform thickness. The two interfaces of this thin liquid film are allowed to slide relatively to each other, thus shearing the liquid phase in between. We solve the dynamics under external shear of this minimal system and we show that the continuity of the surface tension around the whole bubble is the relevant condition to determ…
We report measurements of viscoelastic properties of thin polymer films of 10-100 nm at the MHz range. These thin films are confined between a quartz crystal resonator and a millimetric bead layer, producing an increase of both resonance frequency and dissipation of the quartz resonator. The shear modulus and dynamic viscosity of thin films extracted from these measurements are consistent with the bulk values of the polymer. This modified quartz resonator provides an easily realizable and effective tool for probing the rheological properties of thin films at ambient environment.
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 s…
The 2D flow of a foam confined in a Hele-Shaw cell through a contraction is investigated. Its rheological features are quantified using image analysis, with measurements of the elastic stress, rate of plasticity, and velocity. The behavior of the velocity strongly differs at the contraction entrance, where the flow is purely convergent, and at the contraction exit, where a velocity undershoot and a re-focussing of the streamlines are unraveled. The yielded region, characterized by a significant rate of plasticity and a maximal stress amplitude, is concentrated close to the contraction. These q…
Multiscale stress dynamics in sheared liquid foams revealed by tomo-rheoscopy
Lund University（隆德大学）；Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；ENS de Lyon, Université de Lyon（里昂高等师范学校，里昂大学）；Paul Scherrer Institut（保罗谢尔研究所）；Université Côte d’Azur（蔚蓝海岸大学）；Institut Universitaire de France (IUF)（法国大学学院）；Technical University of Denmark（丹麦技术大学）
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 and the averaged bubble-bubble drag forces. This model …
Liquid foams are widely used in industry for their high effective viscosity, whose local origin is still unclear. This Letter presents new results on the extension of a suspended soap film, in a configuration mimicking the elementary deformation occurring during foam shearing. We evidence a surprising two-step evolution: the film first extends homogeneously, then its extension stops, and a new thicker film is extracted from the meniscus. The second step is independent of the nature of the surfactant solution, whereas the initial extension is only observed for surfactant solutions with negligib…
Hypothesis Saponins are natural surfactants which can provide highly viscoelastic interfaces. This property can be used to quantify precisely the effect of interfacial dilatational elasticity on the various rheological properties of bulk emulsions. Experiments We measured the interfacial dilatational elasticity of adsorption layers from four saponins (Quillaja, Escin, Berry, Tea) adsorbed on hexadecane-water and sunflower oil-water interfaces. In parallel, the rheological properties under steady and oscillatory shear deformations were measured for bulk emulsions, stabilized by the same saponin…
