Soap-Film Membranes for CO2/Air Separation.

Thin liquid films are a potential game changer in the quest for efficient gas separation strategies. Such fluid membranes, which are complementary to their solid counterparts involving porous materials, can achieve complex separation by combining permeability and adsorption mechanisms in their liquid core and at their surface. In addition, unlike porous solid membranes that must be regenerated between separation steps to recover a gas-free porosity, thus preventing continuous operation, liquid membranes can be regenerated using continuous liquid flow through the fluid film. Here, building on the self-sustained mobile film technique, we propose a simple experimental setup allowing direct quantitative assessment of the gas permeability of soap films stabilized by different surfactant types. Using a simple prototypical example involving O2/N2 mixtures, the measurement principle is first presented to establish a proof of concept. As the gas solubilities and diffusivities are known, the results of such experiments can be compared with microscopic models to disentangle the liquid core and surface permeabilities from a direct macroscopic transport response of the film subjected to a gas concentration difference. The same dynamical experiments performed for air enriched in CO2 indicate that the permeability of the soap film varies with the molar fraction in the gas compartment, a feature not observed for O2/N2. These experimental findings pave the way for the design of novel separation technologies in fields and situations where porous solid membranes are of limited efficiency.

Coarsening of Foams Driven by Concentration Gradients of Gases of Different Solubilities.

The evolution of a foam driven by the transfer of two gases of different solubilities across the soap films is studied. A bamboo foam, or a train of films, is used as a model system; it is made of a poorly soluble gas and put into contact with a reservoir of a soluble gas at an initial time. The measurement of the time evolution of the volume of each bubble shows that the foam swells as it progressively incorporates the soluble gas. The dynamics is modeled from the gas fluxes across each film. The continuous limit of this model at a large number of bubbles is studied in detail: it gives an effective nonlinear diffusion equation, which fits the data very well. The corresponding diffusion constant, given by the product of the permeability of the soluble gas and the initial size of the bubbles, is shown to be the key parameter governing the coarsening dynamics of the foam.

Relation between oxidation kinetics and reactant transport in an aqueous foam.

HYPOTHESIS: Aqueous foams are expected to constitute exquisite particularly suitable reactive medium for the oxidation of metals, since the reactant H+ can be supplied through the continuous liquid phase, while the reactant O2 can be transported through the gas bubbles. EXPERIMENTS: To test this hypothesis, we investigated the oxidation of a metallic copper cylinder immersed in an aqueous foam. To study the relation between the transport of these reactants and the kinetics of the chemical reaction we use a forced drainage setup which enables us to control both the advection velocity of the H+ ions through the foam and the foam liquid fraction. FINDINGS: We find experimentally that the mass of dissolved copper presents a maximum with the drainage flow rate, and thus with the foam liquid fraction. Modeling analytically the transfer of H+ and O2 through the foams enables us to show that this non-monotonic behavior results from a competition between the advective flux of H+ ions and the unsteady diffusion of O2 through the thin liquid films which tends to be slower as the area of the thin liquid films decreases with the drainage flow rate and the liquid fraction. This study shows for the first time how to optimize the foam structure and drainage flow in reactive foams in which the reactants are present both in the liquid and gaseous phases.

Three-dimensional liquid foam flow through a hopper resolved by fast X-ray microtomography.

We probe the complex rheological behaviour of liquid foams flowing through a conical constriction. With fast X-ray tomographic microscopy we measure in situ the displacement and deformation of up to fifty thousand bubbles at any single time instance while varying systematically the foam liquid fraction, the bubble size and the flow direction - convergent vs. divergent. The large statistics and high spatio-temporal resolution allows to observe and quantify the deviations from a purely viscous flow. We indeed reveal an asymmetry between the convergent and divergent flows associated to the emergence of elastic stresses in the latter case, and enhanced as the liquid fraction is reduced. Such effect is related to the reorientation of the deformed bubbles flowing out of the constriction, from a prolate to an oblate shape in average, while they pass through the hopper waist.

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.

Protein Transport upon Advection at the Air/Water Interface: When Charge Matters.

The formation of dense protein interfacial layers at a free air-water interface is known to result from both diffusion and advection. Furthermore, protein interactions in concentrated phases are strongly dependent on their overall positive or negative net charge, which is controlled by the solution pH. As a consequence, an interesting question is whether the presence of an advection flow of water toward the interface during protein adsorption produces different kinetics and interfacial structure of the adsorbed layer, depending on the net charge of the involved proteins and, possibly, on the sign of this charge. Here we test a combination of the following parameters using ovalbumin and lysozyme as model proteins: positive or negative net charge and the presence or absence of advection flow. The formation and the organization of the interfacial layers are studied by neutron reflectivity and null-ellipsometry measurements. We show that the combined effect of a positive charge of lysozyme and ovalbumin and the presence of advection flow does induce the formation of interfacial multilayers. Conversely, negatively charged ovalbumin forms monolayers, whether advection flow is present or not. We show that an advection/diffusion model cannot correctly describe the adsorption kinetics of multilayers, even in the hypothesis of a concentration-dependent diffusion coefficient as in colloidal filtration, for instance. Still, it is clear that advection is a necessary condition for making multilayers through a mechanism that remains to be determined, which paves the way for future research.

Polyhedral Bubble Vibrations.

Underwater bubbles are extremely good acoustic resonators, but are freely evolving and dissolving. Recently it was found that bubbles can be stabilized in frames, but the influence of the frame shape is still undocumented. Here we first explore the vibration of polyhedral bubbles with a low number of faces, shaped as the five Platonic solids. Their resonance frequency is well approximated by the formula for spherical bubbles with the same volume. Then we extend these results to shapes with a larger number of faces using fullerenes, paving the way to obtain arbitrary large resonant bubbles.

Spherical oscillations of encapsulated microbubbles: Effect of shell compressibility and anisotropy.

We introduce a model that describes spherical oscillations of encapsulated microbubbles in an unbounded surrounding fluid. A Rayleigh-Plesset-like equation is derived by coupling the Navier-Stokes equation that describes fluid dynamics with the Navier equation that describes solid dynamics via the internal/external boundary conditions. While previous models were restricted to incompressible isotropic shells, the solid shell is modeled here as a compressible viscoelastic isotropic material and then generalized to an anisotropic material. The exact value of the resonance frequency is calculated analytically, and the damping constant is computed in the approximation of weak damping. A correction of the widely used Church model for incompressible shells is evidenced, and the effects of shell compressibility and anisotropy are discussed.

Impact of Fluorocarbon Gaseous Environments on the Permeability of Foam Films to Air.

A foam film, free to move and stabilized with tetradecyltrimethylammonium bromide or sodium dodecylsulfate surfactants, is deposited inside of a cylindrical tube. It separates the tube into two distinct gaseous compartments. The first compartment is filled with air, while the second one contains a mixture of air and perfluorohexane vapor (C6F14), which is a barely water-soluble fluorinated compound. This foam film thus acts as a liquid semipermeable membrane for gases equivalent to the solid semipermeable membranes conventionally used in fluid separation processes. To infer the rate of air transfer through the membrane, we measure the displacement of the mobile foam film. From this, we deduce the instantaneous permeability of the membrane. In contrast to the permeability of solid membranes, which inexorably decreases over time because they become clogged, an anticlogging effect is observed with a permeability that systematically increases over time. Because the thickness of the film is constant over time, we attribute this to the possibility of adsorbing or desorbing fluorinated gas molecules on the liquid membrane. Indeed, because the partial pressure of the fluorinated gas is high at the beginning of the experiment, the density of the adsorbed molecules is also high, which leads to a low permeability to air transfer. On the contrary, at the end of the experiment, the partial pressure in fluorinated gas and thus the density of the adsorbed molecules are low. This leads to a higher permeability and a less clogged membrane.

Ultrasound Contrast Agent Modeling: A Review.

Ultrasound is extensively used in medical imaging, being safe and inexpensive and operating in real time. Its scope of applications has been widely broadened by the use of ultrasound contrast agents (UCAs) in the form of microscopic bubbles coated by a biocompatible shell. Their increased use has motivated a large amount of research to understand and characterize their physical properties as well as their interaction with the ultrasound field and their surrounding environment. Here we review the theoretical models that have been proposed to study and predict the behavior of UCAs. We begin with a brief introduction on the development of UCAs. We then present the basics of free-gas-bubble dynamics upon which UCA modeling is based. We review extensively the linear and non-linear models for shell elasticity and viscosity and present models for non-spherical and asymmetric bubble oscillations, especially in the presence of surrounding walls or tissue. Then, higher-order effects such as microstreaming, shedding and acoustic radiation forces are considered. We conclude this review with promising directions for the modeling and development of novel agents.

Transition from Exponentially Damped to Finite-Time Arrest Liquid Oscillations Induced by Contact Line Hysteresis.

To clarify the role of wetting properties on the damping of liquid oscillations, we studied the decay of oscillations of liquid columns in a U-shaped tube with controlled surface conditions. In the presence of sliding triple lines, oscillations are strongly and nonlinearly damped, with a finite-time arrest and a dependence on initial amplitude. We reveal that contact angle hysteresis explains and quantifies this solidlike friction.

Order to Disorder Transition in a Coarsening Two-Dimensional Foam.

We quantify the spatiotemporal transformation of a monodisperse and well-ordered monolayer of bubbles, as they undergo Ostwald ripening, by tracking the size polydispersity of the bubbles and local ordering of the foam. After nuclei of disorder appear at random locations, the transition takes place through two successive phases: first, the disordered regions grow while the value of polydispersity increases slowly, then the polydispersity grows rapidly once the disordered zones begin to merge together. The transition is captured by a modified logistic model.

Self-Similar Relaxation of Confined Microfluidic Droplets.

We report an experimental study concerning the capillary relaxation of a confined liquid droplet in a microscopic channel with a rectangular cross section. The confinement leads to a droplet that is extended along the direction normal to the cross section. These droplets, found in numerous microfluidic applications, are pinched into a peanutlike shape thanks to a localized, reversible deformation of the channel. Once the channel deformation is released, the droplet relaxes back to a pluglike shape. During this relaxation, the liquid contained in the central pocket drains towards the extremities of the droplet. Modeling such viscocapillary droplet relaxation requires considering the problem as 3D due to confinement. This 3D consideration yields a scaling model incorporating dominant dissipation within the droplet menisci. As such, the self-similar droplet dynamics is fully captured.

Drying of channels by evaporation through a permeable medium.

We study the drying of isolated channels initially filled with water moulded in a water-permeable polymer (polydimethylsiloxane, PDMS) by pervaporation, when placed in a dry atmosphere. Channel drying is monitored by tracking a meniscus, separating water from air, advancing within the channels. The role of two geometrical parameters, the channel width and the PDMS thickness, is investigated experimentally. All data show that drying displays a truncated exponential dynamics. A fully predictive analytical model, in excellent agreement with the data, is proposed to explain such a dynamics, by solving water diffusion both in the PDMS layer and in the gas inside the channel. This drying process is crucial in geological or biological systems, such as rock disintegration or the drying of plant leaves after cavitation and embolism formation.

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.

Cavitation in a liquid-filled cavity surrounded by an elastic medium: Intercoupling of cavitation events in neighboring cavities.

The subject of the present theoretical study is the dynamics of a cavitation bubble in a spherical liquid-filled cavity surrounded by an infinite elastic solid. Two objectives are pursued. The first is to derive equations for the velocity and pressure fields throughout the liquid filling the cavity and equations for the stress and strain fields throughout the solid medium surrounding the cavity. This derivation is based on the results of our previous paper [A. A. Doinikov et al., Phys. Rev. E 97, 013108 (2018)10.1103/PhysRevE.97.013108], where equations for the evolution of a bubble inside a cavity were derived. The second objective is to apply the equations obtained at the first step of the study to ascertain if the cavitation process in one cavity can trigger the nucleation in a neighboring cavity. To this end, we consider a neighboring cavity in which a cavitation bubble is absent. We derive equations that describe the disturbance of the liquid pressure inside the second cavity, assuming this disturbance to be caused by the cavitation process in the first cavity. The developed theory is then used to perform numerical simulations. The results of the simulations show that the magnitude of the background negative pressure inside the second cavity increases at the second half period of the pressure disturbance, which in turn enhances the probability of nucleation in the second cavity.

Model for the growth and the oscillation of a cavitation bubble in a spherical liquid-filled cavity enclosed in an elastic medium.

Equations are derived that describe the growth and subsequent damped oscillation of a cavitation bubble in a liquid-filled cavity surrounded by an elastic solid. It is assumed that the nucleation and the growth of the bubble are caused by an initial negative pressure in the cavity. The liquid is treated as viscous and compressible. The obtained equations allow one to model, by numerical computation, the growth and the oscillation of the bubble in the cavity and the oscillation of the cavity surface. It is shown that the equilibrium radius reached by the growing bubble decreases when the absolute magnitude of the initial negative pressure decreases. It is also found that the natural frequency of the bubble oscillation increases with increasing bubble radius. This result is of special interest because in an unbounded liquid, the natural frequency of a bubble is known to behave oppositely, namely it decreases with increasing bubble radius.

Convective evaporation of vertical films.

Motivated by the evaporation of soap films, which has a significant effect on their lifetime, we performed an experimental study on the evaporation of vertical surfaces with model systems based on hydrogels. From the analogy between heat and mass transfer, we adopt a model describing the natural convection in the gas phase due to a density contrast between dry and saturated air. Our measurements show a good agreement with this model, both in terms of scaling law with the Grashof number and in terms of order of magnitude. We discuss the corrections to take into account, notably the contribution of edge effects, which have a small but visible contribution when lateral and bottom surface areas are not negligible compared to the main evaporating surface area.

Lamella Division in a Foam Flowing through a Two-Dimensional Porous Medium: A Model Fragmentation Process.

We flow a 2D foam through a model 2D porous medium and study experimentally and numerically how the bubble size distribution evolves along the medium. The dominant mechanism of bubble creation is a fragmentation process occurring when bubbles pinched against obstacles are split in two smaller bubbles. We infer the statistics of these individual and local fragmentation events from the experimental data and propose a fragmentation equation to relate that statistics to the evolution of the global size distribution. The predicted evolution shows very good agreement with direct experimental measurements of the bubble size distribution.

Blast wave attenuation in liquid foams: role of gas and evidence of an optimal bubble size.

Liquid foams are excellent systems to mitigate pressure waves such as acoustic or blast waves. The understanding of the underlying dissipation mechanisms however still remains an active matter of debate. In this paper, we investigate the attenuation of a weak blast wave by a liquid foam. The wave is produced with a shock tube and impacts a foam, with a cylindrical geometry. We measure the wave attenuation and velocity in the foam as a function of bubble size, liquid fraction, and the nature of the gas. We show that the attenuation depends on the nature of the gas and we experimentally evidence a maximum of dissipation for a given bubble size. All features are qualitatively captured by a model based on thermal dissipation in the gas.