How topological rearrangements and liquid fraction control liquid foam stability

Scraping of foam on a substrate

HYPOTHESIS

Foam is not only an industrially important form of matter, but also one of soft jammed system such as colloidal suspensions and emulsion suspensions. Since foams are composed of gas bubbles and liquid, it is expected that the coupling of bubbles and liquid strongly affects rheology of foams, which is different from simple liquids. To reveal this coupling effect and considering the importance of foam applications, we studied the scraping of foam by a rigid plate on a substrate.

EXPERIMENT

We mainly used 5.0 wt% solution of ionic surfactant TTAB (tetradecyltrimethylammonium bromide). We systematically investigate the scraping behaviors by the rigid plate as a function of scraping velocity, gap height, confinement length, amount of foam and wettability of the substrate.

FINDINGS

The results show that there are three distinguishable scraping patterns: homogeneous scraping, no scraping, and slendered scraping. These behaviors are clearly different from those of simple liquid systems. Of these, the upper limit of homogeneous scraping could be explained theoretically by the competition between dewetting and shear, which is not previously discussed. Furthermore, the theory is applicable to the scraping of other soft jammed systems such as colloidal and emulsion suspensions.

Micro and Macroscopic Stress-Strain Relations in Disordered Tessellated Networks

We demonstrate that for a rigid and incompressible network in mechanical equilibrium, the microscopic stress and strain follows a simple relation, σ=pE, where σ is the deviatoric stress, E is a mean-field strain tensor, and p is the hydrostatic pressure. This relationship arises as the natural consequence of energy minimization or equivalently, mechanical equilibration. The result suggests not only that the microscopic stress and strain are aligned in the principal directions, but also microscopic deformations are predominantly affine. The relationship holds true regardless of the different (foam or tissue) energy model considered, and directly leads to a simple prediction for the shear modulus, μ=⟨p⟩/2, where ⟨p⟩ is the mean pressure of the tessellation, for general randomized lattices.

Cross over to collective rearrangements near the dry-wet transition in two-dimensional foams

Liquid foams respond plastically to external perturbations over some critical magnitude. This rearrangement process is directly related to the mechanical properties of the foams, playing a significant role in determining foam lifetime, deformability, elasticity, and fluidity. In this paper, we experimentally investigate the rearrangement dynamics of foams near a dry-wet transition. When a foam transforms from a dry state to a wet state, it is found that considering collective events, separated T1 events propagate in dry foams, while T1 events occur simultaneously in wet foams. This cross over to collective rearrangements is closely related to the change in local bubble arrangements and mobility. Furthermore, it is also found that a probability of collective rearrangement events occurring follows a Poisson distribution, suggesting that there is little correlation between discrete collective rearrangement events. These results constitute progress in understanding the dynamical properties of soft jammed systems, relevant for biological and material sciences as well as food science.

Probing foams from the nanometer to the millimeter scale by coupling small-angle neutron scattering, imaging, and electrical conductivity measurements

Liquid foams are multi-scale structures whose structural characterization requires the combination of very different techniques. This inherently complex task is made more difficult by the fact that foams are also intrinsically unstable systems and that their properties are highly dependent on the production protocol and sample container. To tackle these issues, a new device has been developed that enables the simultaneous time-resolved investigation of foams by small-angle neutron scattering (SANS), electrical conductivity, and bubbles imaging. This device allows the characterization of the foam and its aging from nanometer up to centimeter scale in a single experiment. A specific SANS model was developed to quantitatively adjust the scattering intensity from the dry foam. Structural features such as the liquid fraction, specific surface area of the Plateau borders and inter-bubble films, and thin film thickness were deduced from this analysis, and some of these values were compared with values extracted from the other applied techniques. This approach has been applied to a surfactant-stabilized liquid foam under free drainage and the underlying foam destabilization mechanisms were discussed with unprecedented detail. For example, the information extracted from the image analysis and SANS data allows for the first time to determine the disjoining pressure vs. thickness isotherm in a real, draining foam.

Polyelectrolyte/Surfactant Mixtures: A Pathway to Smart Foams

This review deals with liquid foams stabilized by polyelectrolyte/surfactant (PS) complexes in aqueous solution. It briefly reviews all the important aspects of foam physics at several scales, from interfaces to macroscopic foams, needed to understand the basics of these complex systems, focusing on those particular aspects of foams stabilized by PS mixtures. The final section includes a few examples of smart foams based on PS complexes that have been reported recently in the literature. These PS complexes open an opportunity to develop new intelligent dispersed materials with potential in many fields, such as oil industry, environmental remediation, and pharmaceutical industry, among others. However, there is much work to be done to understand the mechanism involved in the stabilization of foams with PS complexes. Understanding those underlying mechanisms is vital to successfully formulate smart systems. This review is written in the hope of stimulating further work in the physics of PS foams and, particularly, in the search for responsive foams based on polymer-surfactant mixtures.

From Individual Liquid Films to Macroscopic Foam Dynamics: A Comparison between Polymers and a Nonionic Surfactant

Foams can resist destabilizaton in ways that appear similar on a macroscopic scale, but the microscopic origins of the stability and the loss thereof can be quite diverse. Here, we compare both the macroscopic drainage and ultimate collapse of aqueous foams stabilized by either a partially hydrolyzed poly(vinyl alcohol) (PVA) or a nonionic low-molecular-weight surfactant (BrijO10) with the dynamics of individual thin films at the microscale. From this comparison, we gain significant insight regarding the effect of both surface stresses and intermolecular forces on macroscopic foam stability. Distinct regimes in the lifetime of the foams were observed. Drainage at early stages is controlled by the different stress-boundary conditions at the surfaces of the bubbles between the polymer and the surfactant. The stress-carrying capacity of PVA-stabilized interfaces is a result of the mutual contribution of Marangoni stresses and surface shear viscosity. In contrast, surface shear inviscidity and much weaker Marangoni stresses were observed for the nonionic surfactant surfaces, resulting in faster drainage times, both at the level of the single film and the macroscopic foam. At longer times, the PVA foams present a regime of homogeneous coalescence where isolated coalescence events are observed. This regime, which is observed only for PVA foams, occurs when the capillary pressure reaches the maximum disjoining pressure. A final regime is then observed for both systems where a fast coalescence front propagates from the top to the bottom of the foams. The critical liquid fractions and capillary pressures at which this regime is obtained are similar for both PVA and BrijO10 foams, which most likely indicates that collapse is related to a universal mechanism that seems unrelated to the stabilizer interfacial dynamics.

Active T1 transitions in cellular networks

In amorphous solids as in tissues, neighbor exchanges can relax local stresses and allow the material to flow. In this paper, we use an anisotropic vertex model to study T1 rearrangements in polygonal cellular networks. We consider two different physical realizations of the active anisotropic stresses: (i) anisotropic bond tension and (ii) anisotropic cell stress. Interestingly, the two types of active stress lead to patterns of relative orientation of T1 transitions and cell elongation that are different. Our work suggests that these two realizations of anisotropic active stresses can be observed in vivo. We describe and explain these results through the lens of a continuum description of the tissue as an anisotropic active material. We furthermore discuss the energetics of the dynamic tissue and express the energy balance in terms of internal elastic energy, mechanical work, chemical work and heat. This allows us to define active T1 transitions that can perform mechanical work while consuming chemical energy.

Pinch-off from a foam droplet in a Hele-Shaw cell

Placing some foam on a vertical surface is a ubiquitous situation, for example, such as in shaving and wall cleaning in daily life, and in egg-laying or making foam nests for some animals or insects in nature. In such a situation, one may prefer that the foam remains in the initial position. Moreover, losing solution via liquid pinch-off from the bottom of the foam is undesirable. To address the pinching off condition and mechanism, we conducted a model experiment: we confined an amount of foam in a Hele-Shaw cell. Two sliding down modes, both with and without liquid pinch-off, were observed under gravity. We fabricated morphology phase diagrams, and theoretically clarified the onset of liquid pinch-off from a foamy droplet.

Hydrogel foams from liquid foam templates: Properties and optimisation

Hydrogel foams are an important sub-class of macroporous hydrogels. They are commonly obtained by integrating closely-packed gas bubbles of 10-1000 μm into a continuous hydrogel network, leading to gas volume fractions of more than 70% in the wet state and close to 100% in the dried state. The resulting wet or dried three-dimensional architectures provide hydrogel foams with a wide range of useful properties, including very low densities, excellent absorption properties, a large surface-to-volume ratio or tuneable mechanical properties. At the same time, the hydrogel may provide biodegradability, bioabsorption, antifungal or antibacterial activity, or controlled drug delivery. The combination of these properties are increasingly exploited for a wide range of applications, including the biomedical, cosmetic or food sector. The successful formulation of a hydrogel foam from an initially liquid foam template raises many challenging scientific and technical questions at the interface of hydrogel and foam research. Goal of this review is to provide an overview of the key notions which need to be mastered and of the state of the art of this rapidly evolving field at the interface between chemistry and physics.

Dynamics and mechanism of liquid film collapse in a foam

Foams have unique properties that distinguish them from ordinary liquids and gases, and are ubiquitously observed in nature, both in biological systems and industrial products. Foams are known to eventually collapse over time; given their wide-range industrial application, understanding how bubbles in a foam collapse is an important aspect for product longevity and tailoring physical properties. Previously, it was shown that droplets are emitted during the collective bubble collapse, however the mechanism of the droplet emission in a foam is not yet clearly understood. It is directly related to the stability of the foam, thus we quantitatively investigate collapse dynamics in liquid films in a foam, and identify some unique features. When one film breaks, we see that the oscillation of the vertical Plateau border to which it is connected induces anomalous liquid transport from the edge of the border to the center. Once a crack appears near the border and a collapse front is formed, we find that the curvature of the front reverses as it migrates, followed by the emergence and emission of droplets. We elucidate the origins of this behavior and discuss the stability of foams, establishing how the characteristic time scales of the process relate to each other.

Size distribution dependence of collective relaxation dynamics in a two-dimensional wet foam

Foams can be ubiquitously observed in nature and in industrial products. Despite the relevance of their properties to deformation, fluidity, and collapse, all of which are essential for applications, there are few experimental studies of collective relaxation dynamics in a wet foam. Here, we directly observe how the relaxation dynamics changes with increasing liquid fraction in both monodisperse and polydisperse two-dimensional foams. As we increase the liquid fraction, we quantitatively characterize the slowing-down of the relaxation, and the increase of the correlation length. We also find two different relaxation modes which depend on the size distribution of the bubbles. It suggests that the bubbles which are simply near to each other play an important role in large rearrangements, not just those in direct contact. Finally, we confirm the generality of our experimental findings by a numerical simulation for the relaxation process of wet foams.

Scaling Laws in the Dynamics of Collapse of Single Bubbles and 2D Foams

Avalanches of rupturing bubbles play an important role in the dynamics of collapse of macroscopic liquid foams. We hypothesized that the occurrence of cascades of rupturing bubbles in foams depends, at least in part, on the power released during the rupture of a bubble. In this paper, we present results on the dynamics of single bubble bursting obtained by analyzing the pressure wave (sound) emitted by the bubble when collapsing. We found that the released energy varies linearly with bubble size, the frequency of the emitted sound follows a power law with exponent 3/2 (compatible with the Helmholtz resonator model) and the duration of a rupturing event seems to be independent of bubble size. To correlate the dynamics of individual bubbles with the dynamics of foams, we studied the occurrence of avalanches on bubble rafts and found that the phenomenon appears to be a self-organized criticality (SOC) process. The distribution functions for the size of the avalanches are a power law with exponents between 2 and 3, depending on the surfactant concentration. The distribution of times between ruptures also follows a power law with exponents close to 1, independently of the surfactant concentration.

Deposits from evaporating emulsion drops

The processes in which droplets evaporate from solid surfaces, leaving behind distinct deposition patterns, have been studied extensively for variety of solutions. In this work, by combining different microscopy techniques (confocal fluorescence, video and Raman) we investigate pattern formation and evaporation-induced phase change in drying oil-in-water emulsion drops. This combination of techniques allows us to perform drop shape analysis while visualizing the internal emulsion structure simultaneously. We observe that drying of the continuous water phase of emulsion drops on hydrophilic surfaces favors the formation of ring-like zones depleted of oil droplets at the contact line, which originate from geometrical confinement of oil droplets by the meniscus. From such a depletion zone, a “coffee ring” composed of surfactant molecules forms as the water evaporates. On all surfaces drying induces emulsion destabilization by coalescence of oil droplets, commencing at the drop periphery. For hydrophobic surfaces, the coalescence of the oil droplets leads to a uniform oil film spreading out from the initial contact line. The evaporation dynamics of these composite drops indicate that the water in the continuous phase of the emulsion drops evaporates predominantly by diffusion through the vapor, showing no large differences to the evaporation of simple water drops.

Complexity and self-organized criticality in liquid foams. A short review

This short review deals with the work done on liquid foams within the framework of the physics of complexity. It aims to stimulate new theoretical and experimental work on foam dynamics as complex dynamical systems. In particular, it examines these systems in relation to Self-Organized Criticality (SOC), for which foams could be used as an accessible experimental model system.

Emulsion Destabilization by Squeeze Flow

There is a large debate on the destabilization mechanism of emulsions. We present a simple technique using mechanical compression to destabilize oil-in-water emulsions. Upon compression of the emulsion, the continuous aqueous phase is squeezed out, while the dispersed oil phase progressively deforms from circular to honeycomb-like shapes. The films that separate the oil droplets are observed to thin and break at a critical oil/water ratio, leading to coalescence events. Electrostatic interactions and local droplet rearrangements do not determine film rupture. Instead, the destabilization occurs like an avalanche propagating through the system, starting at areas where the film thickness is smallest.

On the rupture of thin films made from aqueous surfactant solutions

This short review describes the work on aqueous foam film stability with the important past contributions of Dotchi Exerowa and Dimo Platikanov, together with advances from other research groups. The review is focused on film rupture, for which few controlled experiments can be found in the literature and as a consequence, our understanding is still limited. The work on rupture of films in foams is described, together with the correlations with the rupture of isolated films. The review addresses mainly the case of aqueous films and foams, but analog studies of emulsions and emulsion films are also briefly discussed.

In-situ observation of collective bubble collapse dynamics in a quasi-two-dimensional foam

The stability of foams is an important subject not only for fundamental science, but for applications in daily life. The most destructive phenomenon underpinning foam collapse is a collective bubble collapse, yet the mechanism behind this is unclear. In this study, we clarify the dynamics of the collective bubble collapse in a quasi-two-dimensional foam by in-situ observation with a high speed camera. We find two modes for collective bubble collapse: one is the propagation of liquid film breakage via impact with the stream of another broken liquid film. The other is breakage of a distant liquid film due to penetration by a liquid droplet, emitted by impact with the flow of a broken liquid film. As the liquid fraction increases, the velocity of liquid droplets decreases. Instead of penetration, the liquid droplet bounces like a billiard ball or it is absorbed into other films.

Coalescence in Two-Dimensional Foams: A Purely Statistical Process Dependent on Film Area

While coalescence is ultimately the most drastic destabilization process in foams, its underlying processes are still unclear. To better understand them, we track individual coalescence events in two-dimensional foams at controlled capillary pressure. We obtain statistical information revealing the influence of the different parameters which have been previously proposed to explain coalescence. Our main conclusion is that coalescence probability is simply proportional to the area of the thin film separating two bubbles, suggesting that coalescence is mostly stochastic.

Critical exponents of the yielding transition of amorphous solids

We investigate numerically the yielding transition of a two-dimensional model amorphous solid under external shear. We use a scalar model in terms of values of the total local strain, derived from the full (tensorial) description of the elastic interactions in the system, in which plastic deformations are accounted for by introducing a stochastic "plastic disorder" potential. This scalar model is seen to be equivalent to a collection of Prandtl-Tomlinson particles, which are coupled through an Eshelby quadrupolar kernel. Numerical simulations of this scalar model reveal that the strain rate versus stress curve, close to the critical stress, is of the form γ[over ̇]∼(σ-σ_{c})^{β}. Remarkably, we find that the value of β depends on details of the microscopic plastic potential used, confirming and giving additional support to results previously obtained with the full tensorial model. To rationalize this result, we argue that the Eshelby interaction in the scalar model can be treated to a good approximation in a sort of "dynamical" mean field, which corresponds to a Prandtl-Tomlinson particle that is driven by the applied strain rate in the presence of a stochastic noise generated by all other particles. The dynamics of this Prandtl-Tomlinson particle displays different values of the β exponent depending on the analytical properties of the microscopic potential, thus giving support to the results of the numerical simulations. Moreover, we find that other critical exponents that depend on details of the dynamics show also a dependence with the form of the disorder, while static exponents are independent of the details of the disorder. Finally, we show how our scalar model relates to other elastoplastic models and to the widely used mean-field version known as the Hébraud-Lequeux model.

Foaming of Transient Polymer Hydrogels

Foams made with polymer hydrogels can be used in a variety of applications, such as scaffolds for biomedical applications or decontamination processes. However, from a practical point of view, it is difficult to introduce bubbles into viscous or viscoelastic fluids and to produce large volumes of hydrogel foams. In the present article, we investigate the foaming process of poly(vinyl alcohol) (PVA)/borax transient hydrogels, where PVA chains reversibly bind to borax molecules. In a previous article, we showed that foams obtained with PVA/borax mixtures are highly stable because of both high interfacial and bulk viscosities and can be used to quickly absorb liquids, which make them suitable for detergency or decontamination processes. To produce these foams, we use a two-step foaming process which consists in first shearing a PVA solution to obtain a PVA foam and second adding borax to the PVA foam under continuous shearing. The obtained PVA/borax foams are stable for weeks. In this study, we observe a shear-induced collapse of the foams for formulations containing a low borax/PVA ratio, whereas they remain stable under shear for high PVA/borax ratios. Using scaling arguments, we find that the shear-induced collapse of the foams and bubbles is obtained below a critical ratio, N E/N B = 15, of the number of entanglements per chain, N E, and the number of borax per chain, N B. Rheology measurements show that the samples present a shear-thickening behavior that increases with the borax concentration. We suggest that during the foaming process when the shearing rate is of the order of 100 s-1, the viscosity of these samples diverges, leading to a viscous to fragile transition. To mimic the fast stretching of the PVA/borax thin films during the foaming process, we study the stretching of individual PVA/borax catenoid-shaped thin films at high stretching rates. We observe that the films containing low PVA/borax ratios do not minimize their surface area unlike what is theoretically expected for standard surfactant films. Moreover, the films tend to be unstable and fracture because the PVA/borax network does not have time to rearrange and relax stresses for high stretching rates.

Electrokinetic transport in liquid foams

Investigating electrokinetic transport in a liquid foam is at the confluence of two well developed research areas. On one hand, the study of electrokinetic flows (i.e. surface-driven flows generated close to a charged interface) is fairly well understood in regards the solid/liquid interface. On the other hand, the flow of liquid in a 3D deformable network, i.e a foam, under a volume force such as gravity has been thoroughly studied over the past decade. The overlapping zone of these two frameworks is of great interest for both communities as it gives rise to challenging new questions such as: what is the importance of the nature of the charged interface, created by mobile and soluble surfactants in the case of foam, on electrokinetic transport? How does a foam behave when submitted to a surface-driven flow? Can we compensate a volume-driven flow, i.e. gravity, by a surface-driven flow, i.e. electroosmosis? In this review, we will explore these questions on three different scales: a surfactant laden interface, a foam film and a macroscopic foam.

Oleofoams: Properties of Crystal-Coated Bubbles from Whipped Oleogels-Evidence for Pickering Stabilization

Interfacially stabilized nonaqueous lipid-based foams, which we name here oleofoams, are rarely encountered as opposed to the large number of aqueous foams stabilized by molecular or particulate emulsifiers. There is no case well described in the literature with a convincing characterization of the interfacial contribution to oleofoam stability. Methods for filling this gap are described here, which reach out to a large part of the lipid phase diagram. We bring here complete evidence that lipidic crystals made of a high fraction of fully soluble monoglyceride (MG) in oil do not only adsorb at the oil-air interface but also can easily form a jammed, closely packed layer of crystals around the bubbles of a foam produced by whipping (Pickering effect). Very fine bubbles, soft textures, or firmer ones such as for shaving foams could be obtained, with a high air fraction (up to 75%), which is unprecedented. A thin, jammed layer of crystals on bubbles can cause bubbles to retain nonspherical shapes in the absence of bulk effects for times much longer than the characteristic capillary relaxation time for bare bubbles, which is actual evidence for Pickering-type interfacial stabilization. By comparing to foams obtained by depressurization, we show that whipping is necessary for bubble wrapping with a layer of crystals. The origin of high stability against Ostwald ripening at long times is also discussed. Furthermore, we show that these Pickering whipped foams have rheological properties dominated by interfacial or film contributions, which is of high interest for food and cosmetics applications because of their high moduli. This system can be considered to be a model of the crystallization behavior of MG in oil, which is similar to that in many fats. Our methods are very general in the context of lipid-based foaming, in particular, from food materials, and were used in patent applications.

Coalescence In Draining Foams Made of Very Small Bubbles

We studied the stability of foams containing small bubbles (radius ≲ 50  μm). The foams are made from aqueous surfactant solutions containing various amounts of glycerol. The foams start breaking at their top, when the liquid volume fraction has decreased sufficiently during liquid drainage. Unlike in foams with larger bubbles, the liquid fraction at which the foam destabilizes is surprisingly high. In order to interpret this observation we propose that film rupture occurs during reorganization events (T1) induced by bubble coarsening, which is particularly rapid in the case of small bubbles. New films are therefore formed rapidly and if their thickness is too small, they cannot be sufficiently covered by surfactant and they break. Using literature data for the duration of T1 events and the thickness of the new films, we show that this mechanism is consistent with the behavior of the foams studied.

A critical review of the growth, drainage and collapse of foams

This review focuses on the current knowledge regarding (i) the mechanisms governing foamability and foam stability, and (ii) models for the foam column kinetics. Although different length scales of foam structure, such as air-water interface and liquid film, have been studied to elucidate the mechanisms that control the foamability and foam stability, many questions remain unanswered. It is due to the collective effects of different mechanisms involved and the complicated structures of foam sub-structures such as foam films, Plateau borders and nodes, and foam networks like soft porous materials. The current knowledge of the effects of solid particles on liquid film stability and foam drainage is also discussed to highlight gaps in our present level of understanding foam systems with solid particles. We also critically review and summarize the models that describe macroscopic foam behaviors, such as equilibrium foam height, foam growth and collapse, within the context of the mechanisms involved.

Coalescence preference in densely packed microbubbles

A bubble merged from two parent bubbles with different size tends to be placed closer to the larger parent. This phenomenon is known as the coalescence preference. Here we demonstrate that the coalescence preference can be blocked inside a densely packed cluster of bubbles. We utilized high-speed high-resolution X-ray microscopy to clearly visualize individual coalescence events inside densely packed microbubbles with a local packing fraction of ~40%. The surface energy release theory predicts an exponent of 5 in a relation between the relative coalescence position and the parent size ratio, whereas our observation for coalescence in densely packed microbubbles shows a different exponent of 2. We believe that this result would be important to understand the reality of coalescence dynamics in a variety of packing situations of soft matter.

Effect of Gas Permeability and Solubility on Foam

We perform a study on the influence of gas permeability and solubility on the drainage and stability of foam stabilized with an anionic surfactant. Our study compares the foam stability for four pure gases and two gas mixtures while previous works only compared two pure gases. Drainage and foam-volume-decay rates are calculated from the experimental data and analysed. We find good agreement with existing theory as the foam stability is strongly influenced by the properties of the gas phase, in particular its solubility in the aqueous phase (measured by Henry’s solubility constant, kH) and permeability (measured by foam-film permeability coefficient, K). The foam volume decreases considerably with increasing K. Moreover, we observe that foams are more stable when a less soluble gas is added to a more soluble gas. Our analysis confirms theories linking drainage, stability, and coarsening rate. Finally, we introduce a new formulation for the foaming index that considers gas solubility and permeability.

The role of the hydrophobic phase in the unique rheological properties of saponin adsorption layers

Saponins are a diverse class of natural, plant derived surfactants, with peculiar molecular structure consisting of a hydrophobic scaffold and one or several hydrophilic oligosaccharide chains. Saponins have strong surface activity and are used as natural emulsifiers and foaming agents in food and beverage, pharmaceutical, ore processing, and other industries. Many saponins form adsorption layers at the air-water interface with extremely high surface elasticity and viscosity. The molecular origin of the observed unique interfacial visco-elasticity of saponin adsorption layers is of great interest from both scientific and application viewpoints. In the current study we demonstrate that the hydrophobic phase in contact with water has a very strong effect on the interfacial properties of saponins and that the interfacial elasticity and viscosity of the saponin adsorption layers decrease in the order: air > hexadecane ≫ tricaprylin. The molecular mechanisms behind these trends are analyzed and discussed in the context of the general structure of the surfactant adsorption layers at various nonpolar phase-water interfaces.

Oil repartition in a foam film architecture

The propagation and distribution of oil inside the aqueous network of a foam is investigated in the case where oil can invade the foam without breaking it. The oil is injected into an elementary foam architecture of nine foam films and four vertices obtained by plunging a cubic frame in a foaming solution. The frame is then deformed to trigger a film switching (topological rearrangement named T1) and oil redistribution through this process is reported. Depending on the relative ratio of injected oil and water, different behaviours are observed. For small amounts of oil, a globule is trapped in one single node whereas for large oil volumes, it invades the four nodes of the foam film assembly. In both these cases, a T1 process does not change the oil distribution. However, for intermediate volumes, oil initially trapped in one node is able to propagate to the neighbouring nodes after the T1 process. This important observation shows that topological rearrangements, which naturally occur in foams when they evolve with time or when they flow, do affect the distribution of the third phase that they carry. These different regimes are captured by simple modeling based on the capillary pressure balance inside the foam network. Moreover, in the large-oil-volume limit, a transient situation is evidenced where an oil film is trapped within the freshly formed water film. This oil film modifies the dynamics of the T1 process and can be stable for up to a few minutes. We expect this mechanism to have consequences on the rheological properties of oil-laden foams. Film rupture dynamics is also experimentally captured.

Coalescence of dry foam under water injection

When a small volume of pure water - typically a drop - is injected within an aqueous foam, it locally triggers the rupture of foam films, thus opening an empty cavity in the foam's bulk. We consider the final shape of this cavity and we quantify its volume as a function of the volume of injected water, the diameter of the bubbles and the liquid fraction of the foam. We provide quantitative understanding to explain how and when this cavity appears. We epitomize the dilution of surfactants at the water-air interfaces as the main cause lying behind the coalescence process. We identify a new coalescence regime for which a critical surfactant concentration rules the stability of the foam.

Comparison between generations of foams and single vertical films--single and mixed surfactant systems

The purpose of this article is to compare experiments carried out with single vertical foam films and with foams. We focus on the generation of films and foams and measure (i) the quantity of water entrained and (ii) the stability of the systems. The surfactants we used are C12E6, β-C12G2 and their 1 : 1 mixture because those systems are very well characterised in the literature and are known to stabilise foams with very different properties. We show that the quantity of water uptake in foams and single vertical films scales in the same way with the velocity of generation. However, the different surfactant solutions have different foamabilities, whereas the films they stabilise have exactly the same thickness. Moreover, the foamability of a C12E6 solution is much lower than that of a β-C12G2 solution or of a solution of the 1 : 1 mixture. This is due to the rapid rupture of the C12E6 foam films during foam generation. Surprisingly, the isolated films have exactly the same lifetime for all the surfactant solutions. We conclude that, though drawing a correlation between films and foams is tempting, the results obtained do not allow correlating of film and foam stability during the generation process. The only difference we observed between the single films stabilised by the different solutions is the stability of their respective black films. We thus suggest that the stability of black films during foam generation plays an important role which should be explored further in future work.

Capture-induced transition in foamy suspensions

We investigate the drainage behaviour of foamy granular suspensions. Results reveal large fluctuations in the drainage velocity as bubble size, particle size and gas volume fraction are varied for a given particle volume fraction. Particle capture is proved to control the overall drainage behaviour through the parameter λ, which compares the particle size to the size of passage through constrictions within the foam pore space. λ highlights a sharp transition: for λ < 1 particles are free to drain with the liquid, which involves the shear of the suspension in foam interstices, for λ > 1 particles are trapped and the resulting drainage velocity is strongly reduced. A phenomenological model is proposed to describe this behaviour.

A study of generation and rupture of soap films

What are the lifetime and maximum length of a soap film pulled at a velocity V out of a bath of soapy solution? This is the question we explore in this article by performing systematic film rupture experiments. We show that the lifetime and maximal length of the films are fairly reproducible and controlled only by hydrodynamics. For surfactants with high surface elastic modulus, we argue that the rupture is triggered by the expansion of a thinning zone at the top of the film. The length ltz of this zone expands with time at a velocity equal to V/2, which can be obtained by a balance between gravity and viscous forces. The film lifetime is then found to decrease with the pulling velocity V, which implies that the surface tension gradient along the film increases with V. This surface tension gradient is found to be surprisingly small. Finally, the lifetime of films stabilised by solutions with small surface elastic modulus turns out to be much shorter than the ones for films with rigid interfaces.

Microgravity studies of aqueous wet foams

Foams and foaming pose important questions and problems for both fundamental research and practical applications. Despite the fact that foams have been extensively studied, many aspects of foam physics and chemistry still remain unclear. Experiments on foams performed under microgravity can be extended far beyond their counterpart where gravity is fully present (i.e. most experiments on Earth). They allow, in particular, observation of the wet foams obtained during the foaming process; on Earth, foams at this stage evolve too quickly due to gravity drainage and cannot be studied. This paper reviews the existing studies of foams under microgravity, which include studies in parabolic flights, in sounding rockets and in the International Space Station.

Extension of a suspended soap film: a homogeneous dilatation followed by new film extraction

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 negligible dilatational moduli. We predict this complex behavior using a model based on Frankel's theory and on interface rigidification induced by confinement.

Size segregation in sheared two-dimensional polydisperse foam

We report experiments on simple shear of a monolayer of bidisperse and polydisperse bubbles in a Couette device. The bubbles segregate according to their sizes, with larger ones in the middle of the gap and smaller ones closer to the walls, when the shear rate and the bubble size ratio are each above a threshold. The spatial distribution of the larger bubbles becomes flatter across the gap as its area fraction increases. To explain these observations, we adapt a model for monodisperse emulsions that predicts the spatial distribution of droplets as an outcome of the competition between migration away from the walls and shear-induced diffusion. The dense packing of bubbles in our foam intensifies bubble-bubble interaction, which manifests itself both in lateral migration due to wall repulsion and in collision-induced diffusion. After accounting for this difference via an effective capillary number based on the deformation of the bubbles, the model predicts the observed bubble distributions accurately.