Hierarchical bubble size distributions in coarsening wet liquid foams.

Coarsening of two-phase systems is crucial for the stability of dense particle packings such as alloys, foams, emulsions, or supersaturated solutions. Mean field theories predict an asymptotic scaling state with a broad particle size distribution. Aqueous foams are good model systems for investigations of coarsening-induced structures, because the continuous liquid as well as the dispersed gas phases are uniform and isotropic. We present coarsening experiments on wet foams, with liquid fractions up to their unjamming point and beyond, that are performed under microgravity to avoid gravitational drainage. As time elapses, a self-similar regime is reached where the normalized bubble size distribution is invariant. Unexpectedly, the distribution features an excess of small roaming bubbles, mobile within the network of jammed larger bubbles. These roaming bubbles are reminiscent of rattlers in granular materials (grains not subjected to contact forces). We identify a critical liquid fraction [Formula: see text], above which the bubble assembly unjams and the two bubble populations merge into a single narrow distribution of bubbly liquids. Unexpectedly, [Formula: see text] is larger than the random close packing fraction of the foam [Formula: see text]. This is because, between [Formula: see text] and [Formula: see text], the large bubbles remain connected due to a weak adhesion between bubbles. We present models that identify the physical mechanisms explaining our observations. We propose a new comprehensive view of the coarsening phenomenon in wet foams. Our results should be applicable to other phase-separating systems and they may also help to control the elaboration of solid foams with hierarchical structures.

Comparison of Methods Used to Investigate Coalescence in Emulsions.

We present a study of moderately stable dilute emulsions. These emulsions are models for water contaminated by traces of oil encountered in many water treatment situations. The purification of water and the elimination of oil rely on the emulsion stability. Despite actively being studied, the topic of emulsion stability is still far from being fully understood. In particular, it is still unclear whether experimental methods accessing different length scales lead to the same conclusions. In the study presented in this paper, we have used different methods to characterize the emulsions, such as centrifugation and simple bottle tests, as well as investigations of the collision of single macroscopic oil drops at an oil-water interface. We studied different emulsions containing added polymer or surfactant. In the case of added polymer, centrifugation and single drop experiments led to opposite trends in stability when the polymer concentration is varied. In the case of added surfactant, both centrifugation and single drop experiments show a maximum stability when the surfactant concentration is increased, whereas bottle tests show a monotonous increase in stability. We propose tentative interpretations of these unexpected observations. The apparent contradictions are due to the fact that different methods require different drop sizes or different drop concentrations. The puzzling decrease in emulsion stability at a higher surfactant concentration observed with some methods, however, remains unclear. This coalescence study illustrates the fact that different results can be obtained when different experimental methods are used. It is therefore advisable not to rely on a single method, especially in the case of emulsions of limited stability for reasons explained in the paper.

Recent Advances on Emulsion and Foam Stability.

In this perspective paper, we highlight the numerous open problems in the topic of stability of emulsions and foams, focusing on the simplest case of dispersions stabilized by surfactants. There are three main destabilization processes, gravity induced evolution, Ostwald ripening, and drops or bubble coalescence, which are analyzed separately. The discussion is restricted to the case of Newtonian fluids, deprived of microstructure, except for the presence of micelles. Thanks to continuing efforts and recent breakthroughs, we show that the understanding of emulsion and foam stability is progressing. Many problems are still open, however, and much work remains to be done along the lines outlined in the paper.

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 ϕ between 15 and 50% were investigated to study the transition between bubble growth laws previously reported near the dry limit ϕ → 0 and the dilute limit ϕ → 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 ϕ*. At liquid fractions beyond this transition, neighboring bubbles are no longer all in contact, like at a jamming transition. Remarkably ϕ* is significantly larger than the random close packing volume fraction of the bubbles ϕrcp which was determined independently. We attribute the differences between ϕ* and ϕrcp to a weakly adhesive bubble interaction that we have studied in complementary ground-based experiments.

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.

Mechanical Properties of DPPC-POPE Mixed Langmuir Monolayers.

The mechanical properties of lipid monolayers and their responses to shear and compression stresses play an important role in processes such as breathing and eye blinking. We studied the mechanical properties of Langmuir monolayers of a model mixture, composed of an unsaturated lipid, 1-palmitoyl-2-oleoyl-sn-glycero-phosphoethanolamine (POPE), and a saturated lipid, 1,2-dipalmitoyl-sn-glycero-phosphocholine (DPPC). We performed isothermal compressions and sinusoidal shear deformations of these mixed monolayers. Also, the different phases were observed with Brewster angle microscopy. We found that the mechanical behavior is affected by the miscibility of both lipids. In the two-phase region, the compression elastic modulus increases with the amount of the LC phase but does not follow the predictions of a simple effective medium model. The discrepancies arise from the fact that, upon compression, the domains grow at a rate faster than the compression rate but not fast enough to reach thermodynamic equilibrium. Before reaching the LC phase, domain percolation is observed and compression and shear moduli become equal to those of the pure LC phase. Most of the monolayers behave as viscoelastic fluids at the frequencies investigated. A minimum in the compression modulus and shear viscosity was observed for mixtures close to equimolar composition, with the minimum being accompanied by a change in domain shapes.

Interfacial Dynamics and Its Relations with ?Negative? Surface Viscosities Measured at Water?Air Interfaces Covered with a Cationic Surfactant.

We studied the dynamics of a cationic surfactant monolayer, Gemini 12-2-12, at the air?water interface for surfactant aqueous solutions at concentrations below the critical micelle concentration. We present surface rheology experiments performed in a Langmuir trough by the oscillatory barrier technique. From these, we found negative surface viscosities at certain frequencies. We demonstrate that this unphysical result is a consequence of an unconsidered surfactant dynamics within the interfacial region. By surface pressure relaxation experiments, after a sudden modification of the interfacial area and by dynamic surface tension and surface potential measurements, several relaxation phenomena and relaxation times were identified. We found that surfactant adsorption and desorption processes are asymmetric: the characteristic times and the number of processes involved in the mechanisms of adsorption and desorption are different. This asymmetry invalidates the usual data analysis procedure that leads to the negative viscosities. Similar mechanisms could be at the origin of the negative viscosities reported in other systems, a possibility that remains to be explored.

Measurement of film permeability in 2D foams.

The coarsening of quasi-2D wet foams is well described theoretically by the model of Schimming and Durian, that takes into account the diffusion through the Plateau borders and the vertices in a rigorous manner. In this article, we describe an experimental study of coarsening in which the foam film permeability is measured in such quasi-2D wet foams. We first performed a full characterization of the structure of the studied foams. Then we measured the coarsening rates. It appears that, in these foams, the film thicknesses are still too small for the Plateau borders and the vertices to contribute, but the surface Plateau borders lead to a smaller coarsening rate compared to dry foams. This rate increases with capillary pressure and follows well the prediction of the model. We demonstrate the importance of working in controlled pressure conditions during permeability measurements. Indeed, permeability depends on film thickness itself depending on capillary pressure.

Instability of Emulsions Made with Surfactant-Oil-Water Systems at Optimum Formulation with Ultralow Interfacial Tension.

We have studied emulsions made with two- and three-phase oil-water-surfactant systems in which one of the phases is a microemulsion, the other phases being water or/and oil excess phases. Such systems have been extensively studied in the 1970-1980s for applications in enhanced oil recovery. It was found at that time that the emulsions became very unstable in the three-phase systems, but so far few explanations have been proposed. In the most complete one, Kabalnov and colleagues related the emulsion stability to the probability of hole nucleation in the liquid film separating two nearby emulsion drops and associated this probability to the curvature elastic energy of the surfactant layer covering drop surfaces. We propose a different explanation, linked to another type of interfacial elastic energy, associated with compression of the surfactant layers. As found long ago, the three-phase systems are found near optimum formulation (hydrophile lipophile difference, HLD = 0), where the interfacial tension exhibits a deep minimum. The determination of interfacial elastic properties in low interfacial tension systems is not straightforward. In our present work, we used a spinning drop tensiometer with an oscillating rotation velocity. We show that the interfacial compression elastic modulus and viscosity also exhibit a minimum at optimum formulation. We propose that this minimum is related to the acceleration of the surfactant exchanges between the interface, oil and water, near the optimum formulation. Furthermore, we find that the surfactant partitions close to equally between oil and water at the optimum, as in earlier studies. The interfacial tension gradients that slow the thinning of liquid films between drops are reduced by surfactant exchanges between drops and the interface, which are fast whatever the type of drop, oil or water; film thinning is therefore very rapid, and emulsions are almost as unstable as in the absence of surfactant.

Foamed emulsion drainage: flow and trapping of drops.

Foamed emulsions are ubiquitous in our daily life but the ageing of such systems is still poorly understood. In this study we investigate foam drainage and measure the evolution of the gas, liquid and oil volume fractions inside the foam. We evidence three regimes of ageing. During an initial period of fast drainage, both bubbles and drops are very mobile. As the foam stabilises drainage proceeds leading to a gradual decrease of the liquid fraction and slowing down of drainage. Clusters of oil drops are less sheared, their dynamic viscosity increases and drainage slows down even further, until the drops become blocked. At this point the oil fraction starts to increase in the continuous phase. The foam ageing leads to an increase of the capillary pressure until the oil acts as an antifoaming agent and the foam collapses.

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.

On the stability of foams made with surfactant bilayer phases.

The stability of foams made with sponge phases (L3 phases) and lamellar phases (L(α) phases), both containing surfactant bilayers, has been investigated. The extreme stability of foams made with lamellar phases seems essentially due to the high viscosity of the foaming solution, which slows down gravity drainage. Moreover, the foams start draining only when the buoyancy stress overcomes the yield stress of the L(α) phase. The bubble growth associated with gas transfer is unusual: it follows a power law with an exponent smaller than those corresponding to Ostwald ripening (wet foams) and to coarsening (dry foams). The foams made with sponge phases are in turn very unstable, even less stable than pure surfactant foams made with glycerol solutions having the same viscosity. The fact that the surfactant bilayers in the sponge phase have a negative Gaussian curvature could facilitate bubble coalescence.

Interfacial Assembly of Surfactant-Decorated Nanoparticles: On the Rheological Description of a Colloidal 2D Glass.

We address the rheology of assemblies of surfactant-decorated silica nanoparticles irreversibly adsorbed at the gas/liquid interface. Positively charged surfactant molecules (such as CTAB) bind to silica nanoparticle surfaces, and the resulting particle-surfactant complexes adsorb at gas/liquid interfaces. The surfactant molecules control the wettability of such decorated nanoparticles and their adsorption. The interparticle forces can be tuned by changing the surfactant concentration Cs. Increasing Cs, in addition to a decrease of the particles wettability, leads to an increase of the area fraction of particles at the interface. Oscillatory shear measurements (strain- and frequency-sweep) have been performed. Here, we explore the effect of the surfactant concentration Cs. At high enough Cs, the interface is highly packed, and an overall solidlike response is observed, with 2D glass properties.

Precipitating Sodium Dodecyl Sulfate to Create Ultrastable and Stimulable Foams.

Ultrastable foams are made very simply by adding salt (NaCl or KCl) to sodium dodecyl sulfate. The addition of high concentrations of salt leads to the precipitation of the surfactant on the bubble surfaces and as crystals in the interstices between the bubbles. As a consequence, the ageing of the foams is stopped to make them stable indefinitely, or until they are heated above the melting temperature of the crystals. The use of KCl is shown to be much more effective than that of NaCl because potassium dodecyl sulfate has a higher melting temperature and faster rates of crystallization. The crystalline structures have been investigated inside the foam using small angle neutron scattering. The larger lattice spacing of the crystals formed with NaCl in comparison with KCl has been evidenced. These simple temperature stimulable foams could have many potential applications.

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.

Foams stabilised by mixtures of nanoparticles and oppositely charged surfactants: relationship between bubble shrinkage and foam coarsening.

We have studied foams stabilised by surfactant-decorated nanoparticles adsorbed at the bubble surfaces. We show that the controlled compression of a single bubble allows one to understand the coarsening behavior of these foams. When bubbles are compressed, the particles become tightly packed in the surface layer. They lose their mobility, and the interface becomes solid-like when the jammed state is reached. Further compression leads to interfacial buckling characterised by crumpled surfaces. We find that the surface concentration of particles at which the jamming and the buckling transitions occur are independent of the surfactant concentration. This is a surprising feature. It suggests that the surfactants are mandatory to help the particles adsorb at the interface and that they change the equilibrium surface concentration of the decorated particles. But they do not affect the surface properties once the particles are adsorbed. We measured the compression elastic modulus of the surface in the jammed state and found it to be compatible with the Gibbs condition for which the spontaneous dissolution of bubbles is arrested. Due to this effect, the coarsening process of a foam composed of many close-packed bubbles occurs in two steps. In the first step, coarsening is slow and coalescence of the bigger bubbles is observed. In the second step, a number of very small bubbles remains, which exhibit crumpled surfaces and are stable over long times. This suggests that foam coarsening is arrested once the smallest bubbles become fully covered after the initial shrinking step.

Shear rheology of lipid monolayers and insights on membrane fluidity.

The concept of membrane fluidity usually refers to a high molecular mobility inside the lipid bilayer which enables lateral diffusion of embedded proteins. Fluids have the ability to flow under an applied shear stress whereas solids resist shear deformations. Biological membranes require both properties for their function: high lateral fluidity and structural rigidity. Consequently, an adequate account must include, in addition to viscosity, the possibility for a nonzero shear modulus. This knowledge is still lacking as measurements of membrane shear properties have remained incomplete so far. In the present contribution we report a surface shear rheology study of different lipid monolayers that model distinct biologically relevant situations. The results evidence a large variety of mechanical behavior under lateral shear flow.

Adsorption, organization, and rheology of catanionic layers at the air/water interface.

We have investigated the adsorption and organization at the air/water interface of catanionic molecules released from a dispersion of solid-like catanionic vesicles composed of myristic acid and cetyl trimethylammonium chloride at the 2:1 ratio. These vesicles were shown recently to be promising foam stabilizers. Using Brewster angle microscopy, we observed the formation of a catanionic monolayer at the air/water interface composed of liquid-condensed domains in a liquid-expanded matrix. Further adsorption of catanionic molecules forced them to pack, thereby forming a very dense monolayer that prevented further vesicle rupture by avoiding contact of the vesicles with air. Moreover, confocal fluorescence microscopy revealed the presence of layers of intact vesicles that were progressively creaming toward this catanionic monolayer; the surface tension of the vesicle dispersion remained constant upon creaming. The catanionic monolayer behaved as a soft glassy material, an amorphous solid with time- and temperature-dependent properties. Using interfacial oscillatory rheology, we found that the monolayer relaxed mechanical stresses in seconds and melted at a temperature very close to the melting transition temperature of the vesicle bilayers. These results have potential application in the design of smart foams that have temperature-tunable stability.

Shear and compression rheology of Langmuir monolayers of natural ceramides: solid character and plasticity.

The present work addresses the fundamental question of membrane elasticity of ceramide layers with a special focus on the plastic regime. The compression and shear viscoelasticity of egg-ceramide Langmuir monolayers were investigated using oscillatory surface rheology in the linear regime and beyond. High compression and shear moduli were measured at room temperature-a clear signature for a solid behavior. At deformations larger than one per mill, egg-ceramide monolayers display plastic features characterized by a decrease of the storage modulus followed by a viscous regime typical of fluid lipids. This behavior is accompanied by a marked decrease of the loss modulus with increasing stress above a yield point. The results permit to univocally classify ceramide monolayers as 2D solids able to undergo plastic deformations, at the difference of typical fluid lipid monolayers. These unusual features are likely to have consequences in the mechanical behavior of ceramide-rich emplacements in biological membranes.

Plate coating: influence of concentrated surfactants on the film thickness.

We present a large range of experimental data concerning the influence of surfactants on the well-known Landau-Levich-Derjaguin experiment where a liquid film is generated by pulling a plate out of a bath. The thickness h of the film was measured as a function of the pulling velocity V for different kinds of surfactants (C(12)E(6), which is a nonionic surfactant, and DeTAB and DTAB, which are ionic) and at various concentrations near and above the critical micellar concentration (cmc). We report the thickening factor α = h/h(LLD), where h(LLD) is the film thickness obtained without a surfactant effect, i.e., as for a pure fluid but with the same viscosity and surface tension as the surfactant solution, over a wide range of capillary numbers (Ca = ηV/γ, with η being the surfactant solution viscosity and γ its surface tension) and identify three regimes: (i) at small Ca α is large due to confinement and surface elasticity (or Marangoni) effects, (ii) for increasing Ca there is an intermediate regime where α decreases as Ca increases, and (iii) at larger (but still small) Ca α is slightly higher than unity due to surface viscosity effects. In the case of nonionic surfactants, the second regime begins at a fixed Ca, independent of the surfactant concentration, while for ionic surfactants the transition depends on the concentration, which we suggest is probably due to the existence of an electrostatic barrier to surface adsorption. Control of the physical chemistry at the interface allowed us to elucidate the nature of the three regimes in terms of surface rheological properties.