Foam–wall friction: Effect of air volume fraction for tangentially immobile bubble surface

Decontamination of Spores on Model Stainless-Steel Surface by Using Foams Based on Alkyl Polyglucosides

In the food industry, the surfaces of processing equipment are considered to be major factors in the risk of food contamination. The cleaning process of solid surfaces is essential, but it requires a significant amount of water and chemicals. Herein, we report the use of foam flows based on alkyl polyglucosides (APGs) to remove spores of Bacillus subtilis on stainless-steel surfaces as the model-contaminated surface. Sodium dodecyl sulfate (SDS) was also studied as an anionic surfactant. Foams were characterized during flows by measuring the foam stability and the bubble size. The efficiency of spores' removal was assessed by enumerations. We showed that foams based on APGs could remove efficiently the spores from the surfaces, but slightly less than foams based on SDS due to an effect of SDS itself on spores removal. The destabilization of the foams at the end of the process and the recovery of surfactant solutions were also evaluated by using filtration. Following a life cycle assessment (LCA) approach, we evaluated the impact of the foam flow on the global environmental footprint of the process. We showed significant environmental impact benefits with a reduction in water and energy consumption for foam cleaning. APGs are a good choice as surfactants as they decrease further the environmental impacts.

Collapse of a hemicatenoid bounded by a solid wall: instability and dynamics driven by surface Plateau border friction

The collapse of a catenoidal soap film when the rings supporting it are moved beyond a critical separation is a classic problem in interface motion in which there is a balance between surface tension and the inertia of the surrounding air, with film viscosity playing only a minor role. Recently [Goldstein et al., Phys. Rev. E, 2021, 104, 035105], we introduced a variant of this problem in which the catenoid is bisected by a glass plate located in a plane of symmetry perpendicular to the rings, producing two identical hemicatenoids, each with a surface Plateau border (SPB) on the glass plate. Beyond the critical ring separation, the hemicatenoids collapse in a manner qualitatively similar to the bulk problem, but their motion is governed by the frictional forces arising from viscous dissipation in the SPBs. We present numerical studies of a model that includes classical laws in which the frictional force f_v for SPB motion on wet surfaces is of the form f_v ∼ Caⁿ, where Ca is the capillary number. Our experimental data on the temporal evolution of this process confirms the expected value n = 2/3 for mobile surfactants and stress-free interfaces. This study can help explain the fragmentation of bubbles inside very confined geometries such as porous materials or microfluidic devices.

Friction Dynamics of Foams under Nonlinear Motion

Foams are viscoelastic soft materials with complex mechanical properties. Here, we evaluated the friction dynamics of foams between acrylic plates using a sinusoidal motion friction evaluation system and we found some interesting characteristics under accelerated conditions. On a typical solid surface, a symmetrical friction profile, in which static and kinetic frictions are observed, is obtained under reciprocating nonlinear motion. Meanwhile, significant lubricant effects and velocity-dependent friction profiles without static friction were observed in foams. The friction force in foams increased in proportion to the power of velocity, with a power index of <1. These characteristic and dynamic phenomena in foams were observed in this study. They had been caused by the formation of a thick lubricant film and various dissipative modes including surfactant diffusion, viscous dissipation, and wall slip of bubbles. Moreover, the addition of a thickener increased the friction force and the delay time of friction response and improved the foam durability against normal force and shear. These findings are useful for understanding dynamic phenomena in soft materials.

Capillary pressure, osmotic pressure and bubble contact areas in foams

The capillary pressure of foams and emulsions is the difference between the average pressure in the dispersed phase and the pressure in the continuous phase. The pressure difference between individual bubbles or drops and the continuous phase is due to interfacial tension, and governs the thickness of films that separate neighbouring particles. Princen and Derjaguin presented an analytic relation, validated for ordered monodisperse foams with face-centered cubic (fcc) structure, that links the capillary pressure to osmotic pressure; they conjectured that it also held for disordered polydisperse foams that are encountered more frequently in nature and applications. Their conjecture is widely accepted. We derive their relation from first principles, and use known empirical expressions for the osmotic pressure to obtain analytic predictions for the capillary pressure and the average bubble contact area in a foam over the full range of liquid fractions. These results are validated using Surface Evolver simulations and previous experimental data. They also apply to emulsions.

Foam-in-vein: A review of rheological properties and characterization methods for optimization of sclerosing foams

Varicose veins are chronic venous defects that affect >20% of the population in developed countries. Among potential treatments, sclerotherapy is one of the most commonly used. It involves endovenous injection of a surfactant solution (or foam) in varicose veins, inducing damage to the endothelial layer and subsequent vessel sclerosis. Treatments have proven to be effective in the short-term, however recurrence is reported at rates of up to 64% 5-year post-treatment. Thus, once diagnosed with varicosities there is a high probability of a permanently reduced quality of life. Recently, foam sclerotherapy has become increasingly popular over its liquid counterpart, since foams can treat larger and longer varicosities more effectively, they can be imaged using ultrasound, and require lower amounts of sclerosing agent. In order to minimize recurrence rates however, an investigation of current treatment methods should lead to more effective and long-lasting effects. The literature is populated with studies aimed at characterizing the fundamental physics of aqueous foams; nevertheless, there is a significant need for appropriate product development platforms. Despite successfully capturing the microstructural evolution of aqueous foams, the complexity of current models renders them inadequate for pharmaceutical development. This review article will focus on the physics of foams and the attempts at optimizing them for sclerotherapy. This takes the form of a discussion of the most recent numerical and experimental models, as well as an overview of clinically relevant parameters. This holistic approach could contribute to better foam characterization methods that patients may eventually derive long term benefit from.

Foam-driven fracture

In hydraulic fracturing, water is injected at high pressure to crack shale formations. More sustainable techniques use aqueous foams as injection fluids to reduce the water use and wastewater treatment of conventional hydrofractures. However, the physical mechanism of foam fracturing remains poorly understood, and this lack of understanding extends to other applications of compressible foams such as fire-fighting, energy storage, and enhanced oil recovery. Here we show that the injection of foam is much different from the injection of incompressible fluids and results in striking dynamics of fracture propagation that are tied to the compressibility of the foam. An understanding of bubble-scale dynamics is used to develop a model for macroscopic, compressible flow of the foam, from which a scaling law for the fracture length as a function of time is identified and exhibits excellent agreement with our experimental results.

Wall Slip of Soft-Jammed Systems: A Generic Simple Shear Process

From well-controlled long creep tests, we show that the residual apparent yield stress observed with soft-jammed systems along smooth surfaces is an artifact due to edge effects. By removing these effects, we can determine the stress solely associated with steady-state wall slip below the material yield stress. This stress is found to vary linearly with the slip velocity for a wide range of materials whatever the structure, the interaction types between the elements and with the wall, and the concentration. Thus, wall slip results from the laminar flow of some given free liquid volume remaining between the (rough) jammed structure formed by the elements and the smooth wall. This phenomenon may be described by the simple shear flow in a Newtonian liquid layer of uniform thickness. For various systems, this equivalent thickness varies in a narrow range (35±15  nm).

Wall slipping behavior of foam with nanoparticle-armored bubbles and its flow resistance factor in cracks

In this work, wall slipping behavior of foam with nanoparticle-armored bubbles was first studied in a capillary tube and the novel multiphase foam was characterized by a slipping law. A crack model with a cuboid geometry was then used to compare with the foam slipping results from the capillary tube and also to evaluate the flow resistance factor of the foam. The results showed that the slipping friction force F FR in the capillary tube significantly increased by addition of modified SiO2 nanoparticles, and an appropriate power law exponents by fitting F FR vs. Capillary number, Ca, was 1/2. The modified nanoparticles at the surface were bridged together and formed a dense particle "armor" surrounding the bubble, and the interconnected structures of the "armor" with strong steric integrity made the surface solid-like, which was in agreement with the slip regime associated with rigid surface. Moreover, as confirmed by 3D microscopy, the roughness of the bubble surface increased with nanoparticle concentration, which in turn increased the slipping friction force. Compared with pure SDBS foam, SDBS/SiO2 foam shows excellent stability and high flow resistance in visual crack. The resistance factor of SiO2/SDBS foam increased as the wall surface roughness increased in core cracks.

Surfactant- and Aqueous-Foam-Driven Oil Extraction from Micropatterned Surfaces

Liquid-infused surfaces are rough or patterned surfaces in which a lubricating fluid, such as oil, is infused, which exhibits various original properties (omniphobicity, biofouling, drag reduction). An outer flow in a confined geometry can entrain the oil trapped between the pattern of the surfaces by shearing the oil-water interface and cause the loss of the omniphobic properties of the interface. Starting from the theoretical analysis of Wexler et al. (Shear-driven failure of liquid-infused surfaces. Phys. Rev. Lett. 2015, 114, 168301), where a pure aqueous solution is the outer phase, we extend the predictions by introducing an extraction efficiency parameter α and by accounting for new dynamical effects induced by surfactants and aqueous foams. For surfactant solutions, decreasing the oil-water interfacial tension (γ_ow) not only enhances oil extraction as expected but also modifies the dynamics of the receding oil-water interface through the variations of the receding contact angle (θ) with the capillary number (Ca), which is the ratio between the viscous and the capillary forces at the oil-water interface. For aqueous foams, the extraction dynamics are also influenced by the foam flow: oil is sheared by the thin film between the bubbles and the lubricating layer, which imposes a stronger interfacial shear compared to pure aqueous solutions. In both surfactant and foam cases, the experimental observations show the existence of nonuniform extraction dynamics related to the surfactant-induced instability of a two-fluid shear flow.

Droplets in Microchannels: Dynamical Properties of the Lubrication Film

We study the motion of droplets in a confined, micrometric geometry, by focusing on the lubrication film between a droplet and a wall. When capillary forces dominate, the lubrication film thickness evolves nonlinearly with the capillary number due to the viscous dissipation between the meniscus and the wall. However, this film may become thin enough (tens of nanometers) that intermolecular forces come into play and affect classical scalings. Our experiments yield highly resolved topographies of the shape of the interface and allow us to bring new insights into droplet dynamics in microfluidics. We report the novel characterization of two dynamical regimes as the capillary number increases: (i) at low capillary numbers, the film thickness is constant and set by the disjoining pressure, while (ii) above a critical capillary number, the interface behavior is well described by a viscous scenario. At a high surfactant concentration, structural effects lead to the formation of patterns on the interface, which can be used to trace the interface velocity, that yield direct confirmation of the boundary condition in the viscous regime.

Linear and non-linear wall friction of wet foams

We study the wall slip of aqueous foams with a high liquid content. We use a set-up where, driven by buoyancy, a foam creeps along an inclined smooth solid wall which is immersed in the foaming solution. This configuration allows the force driving the bubble motion and the bubble confinement in the vicinity of the wall to be tuned independently. First, we consider bubble monolayers with small Bond number Bo < 1 and measure the relation between the friction force F and the bubble velocity V. For bubbles which are so small that they are almost spherical, the friction law F ∝ V is Stokes-like. The analysis shows that the minimal thickness of the lubricating contact between the bubble and the wall is governed by DLVO long-range forces. Our results are the first evidence of this predicted linear friction regime for creeping bubbles. Due to buoyancy, large bubbles flatten against the wall. In this case, dissipation arises because of viscous flow in the dynamic meniscus between the contact film and the spherical part of the bubble. It leads to a non-linear Bretherton-like friction law F ∝ V(2/3), as expected for slipping bubbles with mobile liquid-gas interfaces. The Stokes-like friction dominates for capillary numbers Ca larger than the crossover value Ca* ∼ Bo(3/2). The overall friction force can be expressed as the sum of these two contributions. On this basis, we then study 3D foams close to the jamming transition with osmotic pressures Π small compared to the capillary pressure Pc. We measure the wall shear stress τ as a function of the capillary number, and we evidence two friction regimes that are consistent with those found for the monolayer. Similarly to this latter case, the total shear stress can be expressed as the sum of the Stokes-like friction term τ ∝ Ca and the Bretherton-like one τ ∝ Ca(2/3). However, for a 3D foam, the crossover at a capillary number Ca** between both regimes is governed by the ratio of the osmotic pressure to the capillary pressure, such that Ca** ∼ (Π/Pc)(3/2).

Bubbles and foams in microfluidics

Microfluidics offers great tools to produce highly-controlled dispersions of gas into liquid, from isolated bubbles to organized microfoams. Potential technological applications are manifold, from novel materials to scaffolds for tissue engineering or enhanced oil recovery. More fundamentally, microfluidics makes it possible to investigate the physics of complex systems such as foams at scales where the capillary forces become dominant, in model experiments involving few well-controlled parameters. In this context, this review does not have the ambition to detail in a comprehensive manner all the techniques and applications involving bubbles and foams in microfluidics. Rather, it focuses on particular consequences of working at the microscale, under confinement, and hopes to provide insight into the physics of such systems. The first part of this work focuses on bubbles, and more precisely on (i) bubble generation, where the confinement can suppress capillary instabilities while inertial effects may play a role, and (ii) bubble dynamics, paying special attention to the lubrication film between bubble and wall and the influence of confinement. The second part addresses the formation and dynamics of microfoams, emphasizing structural differences from macroscopic foams and the influence of the confinement.

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.

Convective heat transfer in foams under laminar flow in pipes and tube bundles

The present study reports experimental data and scaling analysis for forced convection of foams and microfoams in laminar flow in circular and rectangular tubes as well as in tube bundles. Foams and microfoams are pseudoplastic (shear thinning) two-phase fluids consisting of tightly packed bubbles with diameters ranging from tens of microns to a few millimeters. They have found applications in separation processes, soil remediation, oil recovery, water treatment, food processes, as well as in fire fighting and in heat exchangers. First, aqueous solutions of surfactant Tween 20 with different concentrations were used to generate microfoams with various porosity, bubble size distribution, and rheological behavior. These different microfoams were flowed in uniformly heated circular tubes of different diameter instrumented with thermocouples. A wide range of heat fluxes and flow rates were explored. Experimental data were compared with analytical and semi-empirical expressions derived and validated for single-phase power-law fluids. These correlations were extended to two-phase foams by defining the Reynolds number based on the effective viscosity and density of microfoams. However, the local Nusselt and Prandtl numbers were defined based on the specific heat and thermal conductivity of water. Indeed, the heated wall was continuously in contact with a film of water controlling convective heat transfer to the microfoams. Overall, good agreement between experimental results and model predictions was obtained for all experimental conditions considered. Finally, the same approach was shown to be also valid for experimental data reported in the literature for laminar forced convection of microfoams in rectangular minichannels and of macrofoams across aligned and staggered tube bundles with constant wall heat flux.

Solubility limits and phase diagrams for fatty acids in anionic (SLES) and zwitterionic (CAPB) micellar surfactant solutions

The limiting solubility of fatty acids in micellar solutions of the anionic surfactant sodium laurylethersulfate (SLES) and the zwitterionic surfactant cocamidopropyl betaine (CAPB) is experimentally determined. Saturated straight-chain fatty acids with n=10, 12, 14, 16, and 18 carbon atoms were investigated at working temperatures of 25, 30, 35, and 40°C. The rise of the fatty acid molar fraction in the micelles is accompanied by an increase in the equilibrium concentration of acid monomers in the aqueous phase. Theoretically, the solubility limit is explained with the precipitation of fatty acid crystallites when the monomer concentration reaches the solubility limit of the acid in pure water. In agreement with theory, the experiment shows that the solubility limit is proportional to the surfactant concentration. For ideal mixtures, the plot of the log of solubility limit vs. the chainlength, n, must be a straight line, which is fulfilled for n=14, 16, and 18. For the fatty acids of shorter chains, n=10 and 12, a deviation from linearity is observed, which is interpreted as non-ideal mixing due to a mismatch between the chainlengths of the surfactant and acid. The data analysis yields the solubilization energy and the interaction parameter for the fatty acid molecules in surfactant micelles. By using the determined parameter values, phase diagrams of the investigated mixed solutions are constructed. The four inter-domain boundary lines intersect in a quadruple point, whose coordinates have been determined. The results can be applied for the interpretation and prediction of the solubility, and phase behavior of medium- and long-chain fatty acids and other amphiphiles that are solubilizable in micellar surfactant solutions, as well as for determining the critical micellization concentration (CMC) of the respective mixed solution.

Effect of disjoining pressure on terminal velocity of a bubble sliding along an inclined wall

The influence of salt concentration on the terminal velocities of gravity-driven single bubbles sliding along an inclined glass wall has been investigated, in an effort to establish whether surface forces acting between the wall and the bubble influence the latter's mobility. A simple sliding bubble apparatus was employed to measure the terminal velocities of air bubbles with radii ranging from 0.3 to 1.5 mm sliding along the interior wall of an inclined Pyrex glass cylinder with inclination angles between 0.6 and 40.1°. Experiments were performed in pure water, 10 mM and 100 mM KCl solutions. We compared our experimental results with a theory by Hodges et al. which considers hydrodynamic forces only, and with a theory developed by two of us which considers surface forces to play a significant role. Our experimental results demonstrate that the terminal velocity of the bubble not only varies with the angle of inclination and the bubble size but also with the salt concentration, particularly at low inclination angles of ∼1-5°, indicating that double-layer forces between the bubble and the wall influence the sliding behavior. This is the first demonstration that terminal velocities of sliding bubbles are affected by disjoining pressure.

Droplet deformation under confined Poiseuille flow

The flow behavior of droplet-based liquid-liquid systems, such as emulsions, polymer blends, and foodstuff, which are ubiquitous in everyday life, has attracted scientific interest in different disciplines. In this review, we focus on the pressure-driven confined flow behavior of isolated droplets in circular and rectangular cross-section channels, which are valuable model geometries to gain insight into more complex flow conditions found in industrial applications. The effect of the relevant nondimensional parameters governing droplet deformation and breakup, such as viscosity ratio, capillary number, and ratio of droplet to tube radius, is presented both for axisymmetric and off-axis droplets, including cross-stream migration. The role of surfactants is also discussed. Ongoing research directions include the field of microfluidics techniques, where confined flow geometries can be exploited to manipulate droplets with a variety of possible applications.

A systematic and quantitative study of the link between foam slipping and interfacial viscoelasticity

Aqueous foams are often used under various flow regimes, and one of the biggest challenges is to create predictive models of their complex rheological properties. Previous theoretical and experimental studies have qualitatively characterized the wall slip of foams. We focus on this phenomenon in a 1D geometry, studying the friction force to move a train of foam films in a narrow channel. We perform, and correlate, 1D experiments and interfacial measurements of surface elasticity. We adapt existing models to correctly analyze and interpret 1D data, allowing for comparison with 3D foam slip results. Different mixtures of surfactants allow us to quantify the influence of interfacial properties. In particular, we show for 1D experiments that already with a low elasticity, of order 1 mN m(-1), we leave the regime where the interface can be considered as fluid, to enter a regime where dissipation depends only marginally on surface elasticity.

Flow in linearly sheared two-dimensional foams: From bubble to bulk scale

We probe the flow of two-dimensional (2D) foams, consisting of a monolayer of bubbles sandwiched between a liquid bath and glass plate, as a function of driving rate, packing fraction, and degree of disorder. First, we find that bidisperse, disordered foams exhibit strongly rate-dependent and inhomogeneous (shear-banded) velocity profiles, while monodisperse ordered foams are also shear banded but essentially rate independent. Second, we adapt a simple model [E. Janiaud, D. Weaire, and S. Hutzler, Phys. Rev. Lett. 97, 038302 (2006)] based on balancing the averaged drag forces between the bubbles and the top plate F[over ]_{bw} and the averaged bubble-bubble drag forces F[over ]_{bb} by assuming that F[over ]_{bw} approximately v;{2/3} and F[over ]_{bb} approximately ( partial differential_{y}v);{beta} , where v and ( partial differential_{y}v) denote average bubble velocities and gradients. This model captures the observed rate-dependent flows for beta approximately 0.36 , and the rate independent flows for beta approximately 0.67 . Third, we perform independent rheological measurements of F[over ]_{bw} and F[over ]_{bb} , both for ordered and disordered systems, and find these to be fully consistent with the forms assumed in the simple model. Disorder thus leads to a modified effective exponent beta . Fourth, we vary the packing fraction phi of the foam over a substantial range and find that the flow profiles become increasingly shear banded when the foam is made wetter. Surprisingly, the model describes flow profiles and rate dependence over the whole range of packing fractions with the same power-law exponents-only a dimensionless number k that measures the ratio of the prefactors of the viscous drag laws is seen to vary with packing fraction. We find that k approximately (phi-phi_{c});{-1} , where phi_{c} approximately 0.84 corresponds to the 2D jamming density, and suggest that this scaling follows from the geometry of the deformed facets between bubbles in contact. Overall, our work shows that the presence of disorder qualitatively changes the effective bubble-bubble drag forces and suggests a route to rationalize aspects of the ubiquitous Herschel-Bulkley (power-law) rheology observed in a wide range of disordered materials.

Microfluidic crystals: dynamic interplay between rearrangement waves and flow

Microfluidic crystals are assemblies of miniature bubbles or drops flowing in channels. We explore here the flow of these crystals, when submitted to a given driving pressure. The flow velocity is linked to the finite number of elements in the channel width, and presents discontinuities when the crystal structure changes. At the transition from one structure to the other original dynamic features appear. The flow can self-regulate itself on a fixed velocity whatever the driving pressure, or, on the contrary, can spontaneously pulsate. All these features are predicted by simply considering the crystal's energy and friction, and looking at the propagation of structure rearrangements. We anticipate these results to improve the control over the structure of dense two-phase flows in microfluidic systems.

Surfactant mixtures for control of bubble surface mobility in foam studies

A new class of surfactant mixtures is described, which is particularly suitable for studies related to foam dynamics, such as studies of foam rheology, liquid drainage from foams and foam films, and bubble coarsening and rearrangement. These mixtures contain an anionic surfactant, a zwitterionic surfactant, and fatty acids (e.g., myristic or lauric) of low concentration. Solutions of these surfactant mixtures exhibit Newtonian behavior, and their viscosity could be varied by using glycerol. Most importantly, the dynamic surface properties of these solutions, such as their surface dilatational modulus, strongly depend on the presence and on the chain-length of fatty acid(s). Illustrative results are shown to demonstrate the dependence of solution properties on the composition of the surfactant mixture, and the resulting effects on foam rheological properties, foam film drainage, and bubble Ostwald ripening. The observed high surface modulus in the presence of fatty acids is explained with the formation of a surface condensed phase of fatty acid molecules in the surfactant adsorption layer.

Structure of liquid films of an ordered foam confined in a narrow channel

A bamboo foam is the simplest case of an ordered foam confined in a narrow channel. It is made of a regular film distribution, arranged perpendicularly to the channel. Our work consists of studying the structural properties of several films taken in a drained foam. X-ray experiments highlighted the equality of the equilibrium thickness for each film within a foam. The same thickness was found as by measurements of disjoining pressure isotherms, proving as well that films of a bamboo foam behave like isolated ones. The refinement of X-ray data by a simple model of specular reflectivity showed a significant variation of the electronic distribution of the surfactant layer for a common black film forwarding from one equilibrium state to another. A discussion on the organization of the surfactant molecules to the gas/liquid interface and film is proposed.

Yield drag in a two-dimensional foam flow around a circular obstacle: effect of liquid fraction

We study the two-dimensional flow of foams around a circular obstacle within a long channel. In experiments, we confine the foam between liquid and glass surfaces. In simulations, we use a deterministic software, the Surface Evolver, for bubble details and a stochastic one, the extended Potts model, for statistics. We adopt a coherent definition of liquid fraction for all studied systems. We vary it in both experiments and simulations, and determine the yield drag of the foam, that is, the force exerted on the obstacle by the foam flowing at very low velocity. We find that the yield drag is linear over a large range of the ratio of obstacle to bubble size, and is independent of the channel width over a large range. Decreasing the liquid fraction, however, strongly increases the yield drag; we discuss and interpret this dependence.

Viscous froth lens

Microscale models of foam structure traditionally incorporate a balance between bubble pressures and surface tension forces associated with curvature of bubble films. In particular, models for flowing foam microrheology have assumed this balance is maintained under the action of some externally imposed motion. Recently, however, a dynamic model for foam structure has been proposed, the viscous froth model, which balances the net effect of bubble pressures and surface tension to viscous dissipation forces: this permits the description of fast-flowing foam. This contribution examines the behavior of the viscous froth model when applied to a paradigm problem with a particularly simple geometry: namely, a two-dimensional bubble "lens." The lens consists of a channel partly filled by a bubble (known as the "lens bubble") which contacts one channel wall. An additional film (known as the "spanning film") connects to this bubble spanning the distance from the opposite channel wall. This simple structure can be set in motion and deformed out of equilibrium by applying a pressure across the spanning film: a rich dynamical behavior results. Solutions for the lens structure steadily propagating along the channel can be computed by the viscous froth model. Perturbation solutions are obtained in the limit of a lens structure with weak applied pressures, while numerical solutions are available for higher pressures. These steadily propagating solutions suggest that small lenses move faster than large ones, while both small and large lens bubbles are quite resistant to deformation, at least for weak applied back pressures. As the applied back pressure grows, the structure with the small lens bubble remains relatively stiff, while that with the large lens bubble becomes much more compliant. However, with even further increases in the applied back pressure, a critical pressure appears to exist for which the steady-state structure loses stability and unsteady-state numerical simulations show it breaks up by route of a topological transformation.

Periodic microfluidic bubbling oscillator: insight into the stability of two-phase microflows

This Letter describes a periodically oscillating foam flow in a microfluidic device. For constant input parameters, both the produced bubble volume and the flow rate vary over a factor of two. We make explicit the link between the foam topology alternance and flow rate changes, and construct a retroaction model where bubbles still present downstream determine the volume of new bubbles, in agreement with experiment. This gives insight into the various parameters important to maintain monodispersity and at the same time shows a method to achieve controlled polydispersity.

The response of 2D foams to continuous applied shear in a Couette rheometer

The continuum model that has reproduced the experimental observation of exponential shear localisation for straight-edge boundary conditions is adapted to the case of circular geometry. Essentially the same effect is found. However, the scenario of possible velocity profiles is much richer. Our calculations elucidate many recent experiments qualitatively and suggest further extensions of them. Various limits are analysed. In particular, the localisation length vanishes as the inner-boundary velocity tends to zero.

Physical chemistry in foam drainage and coarsening

This review covers recent advances in the study of foam drainage and coarsening, focusing especially on the effective role of the foam chemical components on those aging processes. The determination of the relevant parameters controlling foam drainage and coarsening today remains a major issue: are the physical parameters (like bubble size and liquid fraction) sufficient to define a foam and to predict its evolution, or do the chemical components also matter? And if these foam components are important, one has to determine by which mechanisms, and which microscopic parameters involved in these mechanisms are eventually crucial. I report here recent experimental results, shedding light on these issues. It allows us to summarize how the surfactant, the liquid bulk properties, and the gas modify or not the drainage and coarsening features. The coupling between drainage and coarsening is also discussed, as well as the role of the experimental conditions (sample height, shape or foam uniformity).