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.

Lifetime of vertical giant soap films: role of the relative humidity and film dimensions.

We consider the lifetime of rectangular vertical soap films and we explore the influence of relative humidity and both dimensions on the stability of large soap films, reaching heights of up to 1.2 m. Using an automated rupture detection system, we achieve a robust statistical measurement of their lifetimes and we also measure the film thinning dynamics. We demonstrate that drainage has a negligible impact on the film stability as opposed to evaporation. To do so, we compare the measured lifetimes with predictions from the Boulogne & Dollet model, originally designed to describe the convective evaporation of hydrogels. Interestingly, we show that this model can predict a maximum film lifetime for all sizes.

Role of surfactants in electron cryo-microscopy film preparation.

Single-particle electron cryo-microscopy (cryo-EM) has become an effective and straightforward approach to determine the structure of membrane proteins. However, obtaining cryo-EM grids of sufficient quality for high-resolution structural analysis remains a major bottleneck. One of the difficulties arises from the presence of detergents, which often leads to a lack of control of the ice thickness. Amphipathic polymers such as amphipols (APols) are detergent substitutes, which have proven to be valuable tools for cryo-EM studies. In this work, we investigate the physico-chemical behavior of APol- and detergent-containing solutions and show a correlation with the properties of vitreous thin films in cryo-EM grids. This study provides new insight on the potential of APols, allowing a better control of ice thickness while limiting protein adsorption at the air-water interface, as shown with the full-length mouse serotonin 5-HT3A receptor whose structure has been solved in APol. These findings may speed up the process of grid optimization to obtain high-resolution structures of membrane proteins.

Evaporation-Induced Temperature Gradient in a Foam Column.

Various parameters affect foam stability: surface and bulk rheology of the solution, gravitational drainage, mechanical vibrations, bubble gas composition, and also evaporation. Evaporation is often considered through the prism of liquid loss but also induces a cooling effect due to the enthalpy of vaporization. In this study, we combine a theoretical and experimental approach to explore the temperature field in a foam column evaporating from the top. We show that a measurable temperature profile exists in this geometry, with temperatures at the interface lower than the environmental temperature by a few degrees. We demonstrate that the temperature profile is the result of a balance between the enthalpy of vaporization and heat fluxes originating from the thermal conduction of foam and air and thermal radiation. For small foam thicknesses compared to the radius, we found that the temperature gradient is established over the foam thickness, while for large aspect ratios, the gradient spans over a length scale comparable to the tube radius.

Dynamics of bubbles spontaneously entering into a tube.

When an open tube of small diameter touches a bubble of a larger diameter, the bubble spontaneously shrinks and pushes a soap film into the tube. We characterize the dynamics for different bubble sizes and number of soap films in the tube. We rationalize this observation from a mechanical force balance involving the Laplace pressure of the bubble and the viscous force from the advancing soap lamellae in the tube. We propose a numerical resolution of this model, and an analytical solution in an asymptotic regime. These predictions are then compared to the experiments. The emptying duration is primarily affected by the initial bubble to tube diameter ratio and by the number of soap films in the tube.

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.

Measurement of the Temperature Decrease in Evaporating Soap Films.

Recent advances have demonstrated that evaporation can play a significant role on soap film stability, which is a key concern in many industrial areas but also for children playing with bubbles. Thus, evaporation leads to a film thinning but also to a film cooling, which has been overlooked for soapy objects. Here, we study the temperature variation of an evaporating soap film for different values of relative humidity and glycerol concentrations. We evidence that the temperature of soap films can decrease after their creation up to 8 °C. We propose a model describing the temperature drop of soap films after their formation that is in quantitative agreement with our experiments. We emphasize that this cooling effect is significant and must be carefully considered in future studies on the dynamics of soap films.

The impact of physical-chemistry on film thinning in surface bubbles.

In this paper, we investigate the thinning dynamics of evaporating surfactant-stabilised surface bubbles by considering the role of physical-chemistry of solutions used in a liquid bath. We study the impact of the surfactant concentration below and above the cmc (critical micelle concentration) and the role of ambient humidity. First, in a humidity-saturated atmosphere, we show that if the initial thickness depends on the surfactant concentration and is limited by the surface elasticity, the drainage dynamics are very well described from the capillary and gravity contributions. These dynamics are independent of the surfactant concentration. Second, our study reveals that the physical-chemistry impacts the thinning dynamics through evaporation. We include in the model the additional contribution due to evaporation, which shows a good description of the experimental data below the cmc. Above the cmc, although this model is unsatisfactory at short times, the dynamics at long times is correctly rendered and we establish that the increase of the surfactant concentration decreases the impact of evaporation. Finally, the addition of a hygroscopic compound, glycerol, can be also rationalized by our model. We demonstrate that glycerol decreases the bubble thinning rate at ambient humidity, thus increasing their stability.

An optimized recipe for making giant bubbles.

Large bubbles are primarily used in physics laboratories to study 2D turbulence, surface wavers, and fundamental properties of soap systems. Outside of physics, blowing large bubbles is also a part of many performances and shows. Both the scientific and artistic communities usually want to get reasonably stable foam films. The purpose of this article is to propose the main physical ingredients needed for an effective recipe to make stable films and bubbles. We propose controlled experiments to measure both the ease of generating a bubble, and its stability in different stabilizing solutions, which we choose by adding the ingredients contained in a bubble artist's recipe one by one. Our main findings are that (i) the surfactant concentration must not be too high, (ii) the solution must contain long flexible polymer chains to allow for easy bubble generation and (iii) the addition of glycerol provides improved bubble stability by preventing evaporation. Finally, we propose an efficient recipe, which takes into account these considerations.

Blowing big bubbles.

Although street artists have the know-how to blow bubbles over one meter in length, the bubble width is typically determined by the size of the hoop, or wand they use. In this article we explore a regime in which, by blowing gently downwards, we generate bubbles with radii up to ten times larger than the wand. We observe the big bubbles at lowest air speeds, analogous to the dripping mode observed in droplet formation. We also explore the impact of the surfactant chosen to stabilize the bubbles. We are able to create bubbles of comparable size using either Fairy liquid, a commercially available detergent often used by street artists, or sodium dodecyl sulfate (SDS) solutions. The bubbles obtained from Fairy liquid detach from the wand and are stable for several seconds, however those from SDS tend to burst just before detachment.

A new setup for giant soap films characterization.

Artists, using empirical knowledge, manage to generate and play with giant soap films and bubbles. Until now, scientific studies of soap films generated at a controlled velocity and without any feeding from the top, studied films of a few square centimeters. The present work aims to present a new setup to generate and characterize giant soap films (2 m [Formula: see text] 0.7 m). Our setup is enclosed in a humidity-controlled box of 2.2 m high, 1 m long, and 0.75 m large. Soap films are entrained by a fishing line withdrawn out of a bubbling solution at various velocities. We measure the maximum height of the generated soap films, as well as their lifetime, thanks to automatic detection. This is allowed by light-sensitive resistors collecting the light reflected on the soap films and ensures robust statistical measurements. In the meantime, thickness measurements are performed with a UV-VIS-spectrometer, allowing us to map the soap film's thickness over time.

The Life of a Surface Bubble.

Surface bubbles are present in many industrial processes and in nature, as well as in carbonated beverages. They have motivated many theoretical, numerical and experimental works. This paper presents the current knowledge on the physics of surface bubbles lifetime and shows the diversity of mechanisms at play that depend on the properties of the bath, the interfaces and the ambient air. In particular, we explore the role of drainage and evaporation on film thinning. We highlight the existence of two different scenarios depending on whether the cap film ruptures at large or small thickness compared to the thickness at which van der Waals interaction come in to play.

Roughness-Induced Friction on Liquid Foams.

Complex liquids flow is known to be drastically affected by the roughness condition at the interfaces. We combined stresses measurements and observations of the flow during the motion of different rough surfaces in dry liquid foams. We visually show that three distinct friction regimes exist: slippage, stick-slip motion, and anchored soap films. Our stress measurements are validated for slippage and anchored regimes based on existing models, and we propose a leverage rule to describe the stresses during the stick-slip regime. We find that the occurrence of the stick-slip or anchored regimes is controlled by the roughness factor, defined as the ratio between the size of the surface asperities and the radius of curvature of the Plateau borders.

Stability of big surface bubbles: impact of evaporation and bubble size.

Surface bubbles have attracted much interest in the past few decades. In this article, we aim to explore the lifetime and thinning dynamics of centimetric surface bubbles. We study the impact of the bubble size as well as that of the atmospheric humidity through a careful control and systematic variation of the relative humidity in the measuring chamber. We first address the question of the drainage under saturated water vapor conditions and show that a model including both capillary and gravity driven drainage provides the best prediction for this process. Additionally, unprecedented statistics on the bubble lifetimes confirm experimentally that this parameter is set by evaporation to leading order. We make use of a model based on the overall thinning dynamics of the thin film and assume a rupture thickness of the order 10-100 nm to obtain a good representation of these data. For experiments conducted far from saturation, the convective evaporation of the bath is shown to dominate the overall mass loss in the cap film due to evaporation.

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.

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.

Influence of Evaporation on Soap Film Rupture.

Although soap films are prone to evaporate due to their large surface to volume ratio, the effect of evaporation on macroscopic film features has often been disregarded in the literature. In this work, we experimentally investigate the influence of environmental humidity on soap film stability. An original experiment allows to measure both the maximum length of a film pulled at constant velocity and its thinning dynamics in a controlled atmosphere for various values of the relative humidity [Formula: see text]. At first order, the environmental humidity seems to have almost no impact on most of the film thinning dynamics. However, we find that the film length at rupture increases continuously with [Formula: see text]. To rationalize our observations, we propose that film bursting occurs when the thinning due to evaporation becomes comparable to the thinning due to liquid drainage. This rupture criterion turns out to be in reasonable agreement with an estimation of the evaporation rate in our experiment.

Drainage in a rising foam.

Rising foams created by continuously blowing gas into a surfactant solution are widely used in many technical processes, such as flotation. The prediction of the liquid fraction profile in such flowing foams is of particular importance since this parameter controls the stability and the rheology of the final product. Using drift flux analysis and recently developed semi-empirical expressions for foam permeability and osmotic pressure, we build a model predicting the liquid fraction profile as a function of height. The theoretical profiles are very different if the interfaces are considered as mobile or rigid, but all of our experimental profiles are described by the model with mobile interfaces. Even the systems with dodecanol are well known to behave as rigid in forced drainage experiments. This is because in rising foams the liquid fraction profile is fixed by the flux at the bottom of the foam. Here the foam is wet with higher permeability and the interfaces are not in equilibrium. These results demonstrate once again that it is not only the surfactant system that controls the mobility of the interface, but also the hydrodynamic problem under consideration. For example liquid flow through the foam during generation or in forced drainage is intrinsically different.

Life and death of not so "bare" bubbles.

In this paper, we investigate how the drainage and rupture of surfactant-stabilised bubbles floating at the surface of a liquid pool depend on the concentration of surface-active molecules in water. Drainage measurements at the apex of bubbles indicate that the flow profile is increasingly plug-like as the surfactant concentration is decreased from several times the critical micellar concentration (cmc) to just below the cmc. High-speed observations of bubble bursting reveal that the position at which a hole nucleates in the bubble cap also depends on the surfactant concentration. On average, the rupture is initiated close to the bubble foot for low concentrations (

Investigating the role of a poorly soluble surfactant in a thermally driven 2D microfoam.

Foam drainage dynamics is known to be strongly affected by the nature of the surfactants stabilising the liquid/gas interface. In the present work, we consider a 2D microfoam stabilized by both soluble (sodium dodecylsulfate) and poorly soluble (dodecanol) surfactants. The drainage dynamics is driven by a thermocapillary Marangoni stress at the liquid/gas interface [V. Miralles et al., Phys. Rev. Lett., 2014, 112, 238302] and the presence of dodecanol at the interface induces interface stress acting against the applied thermocapillary stress, which slows down the drainage dynamics. We define a damping parameter that we measure as a function of the geometrical characteristics of the foam. We compare it with predictions based on the interface rheological properties of the solution.