Role of surface elasticity in the drainage of soap films

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.

Thermal Marangoni bubbles

When air reaches the surface of a pool (or bath) of pure liquid, it does not form long-lasting bubbles, as opposed to when the bath contains surfactants. Here we describe what happens when the pool is pure (consisting of oil), yet hot. The bubbles dwelling at the surface can then live for minutes or even longer, which we interpret as a consequence of the gradients of temperature generated in this experiment. Indeed, oil is observed to be constantly drawn to the apex of the bubble, which opposes its gravitational drainage. Since their existence relies on ascending Marangoni flows, thermal bubbles are found to be dynamical in essence, which endows the oil film with remarkable stability and persistence.

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

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

Non linear elasticity of foam films made of SDS/dodecanol mixtures

Foam film elasticity plays a significant role in film drainage and film stability and is thus expected to influence foam dynamical properties. It strongly depends on the foaming solution composition and differs from the interface elasticity measured in unconfined geometries. We use a deformable frame to deform an assembly of five films and we measure the tension and extension of each film. This provides a simple and accurate determination of the film elasticity, in the linear and non-linear regimes, for a set of SDS/dodecanol mixtures, at various concentrations. We show that the non-linear elastic behavior is well reproduced by Mysel's model coupled with a Langmuir coadsorption isotherm for a large range of chemical compositions.

Effect of gravity on the orientation and detachment of cubic particles adsorbed at soap film or liquid interfaces

We investigate the interaction that occurs between a light solid cube falling under gravity and a horizontal soap film that is pinned to a circular ring. We observe in both experiments and quasi-static simulations that the final orientation of a cube that becomes entrapped by a soap film is strongly dependent on the Bond number. A cube is rotated by a soap film into one of three main orientations in a process that is driven by energy minimisation. The likelihood of observing each of these final orientations is shown to depend on the Bond number, and the most energetically favourable orientation depends on the terminal height reached by the cube. We also find a critical value for the Bond number, above which a cube is no longer supported by a soap film and detachment occurs, to be less than one.

Motion of a Brownian particle in the presence of reactive boundaries

We study the one-dimensional motion of a Brownian particle inside a confinement described by two reactive boundaries which can partially reflect or absorb the particle. Understanding the effects of such boundaries is important in physics, chemistry, and biology. We compute the probability density of the particle displacement exactly, from which we derive expressions for the survival probability and the mean absorption time as a function of the reactive coefficients. Furthermore, using the Feynman-Kac formalism, we investigate the local time profile, which is the fluctuating time spent by the particle at a given location, both till a fixed observation time and till the absorption time. Our analytical results are compared to numerical simulations, showing perfect agreement.

Adsorption of Sodium Dodecyl Sulfate at Water-Dodecane Interface in Relation to the Oil in Water Emulsion Properties

The control of the behavior of oil in water emulsions requires deeper investigations on the adsorption properties of the emulsion stabilizers at the interfaces, which are fundamental to explain the (de)stabilization mechanisms. In this work, we present an extensive study on oil-in-water emulsions stabilized by sodium dodecyl sulfate (SDS) below its critical micellar concentration. Dynamic tensiometry, dilational rheology, and electrical conductivity measurements are used to investigate the adsorption properties at the droplet interface, whereas the aging of the respective emulsions was investigated by monitoring the macroscopic thickness of the emulsion layer, by microimaging and dynamic light scattering (DLS) analysis, to get information on the drop size distribution. In addition, the droplet coalescence is investigated by a microscopy setup. The results of this multitechnique study allow deriving a coherent scenario where the adsorption properties of this ionic surfactant relate to those of the emulsion, such as, for example, the prevention of droplet coalescence and the presence of other mechanisms, such as Ostwald ripening, responsible for the emulsion aging.

Interfacial rheology of low interfacial tension systems using a new oscillating spinning drop method

When surfactants adsorb at liquid interfaces, they not only decrease the surface tension, they confer rheological properties to the interfaces. There are two types of rheological parameters associated to interfacial layers: compression and shear. The elastic response is described by a storage modulus and the dissipation by a loss modulus or equivalently a surface viscosity. Various types of instruments are available for the measurements of these coefficients, the most common being oscillating pendent drops instruments and rheometers equipped with bicones. These instruments are applicable to systems with large enough interfacial tensions, typically above a few mN/m. We use a new type of instrument based on spinning drop oscillations, allowing to extend the interfacial rheology studies to low and ultralow interfacial tension systems. We present examples of measurements with systems of high and low tension, discuss the possible artifacts and demonstrate the capability of this new technique. We emphasize that the data shown for low interfacial tensions are the first reported in the literature. The instrument is potentially interesting for instance in enhanced oil recovery or demulsification studies.

Viscoelastic Drag Forces and Crossover from No-Slip to Slip Boundary Conditions for Flow near Air-Water Interfaces

The "free" water surface is generally prone to contamination with surface impurities, be they surfactants, particles, or other surface active agents. The presence of such impurities can modify flow near such interfaces in a drastic manner. Here we show that vibrating a small sphere mounted on an atomic force microscope cantilever near a gas bubble immersed in water is an excellent probe of surface contamination. Both viscous and elastic forces are exerted by an air-water interface on the vibrating sphere even when very low doses of contaminants are present. The viscous drag forces show a crossover from no-slip to slip boundary conditions while the elastic forces show a nontrivial variation as the vibration frequency changes. We provide a simple model to rationalize these results and propose a simple way of evaluating the concentration of such surface impurities.

Simple Optical Imaging of Nanoscale Features in Free-Standing Films

Measuring thicknesses in thin films with high spatial and temporal resolution is of prime importance for understanding the structure and dynamics in thin films and membranes. In the present work, we introduce fluorescence-interferometry, a method that combines standard reflected light thin film interferometry with simultaneous fluorescence measurements. We apply this method to the thinning dynamics and phase separation in free-standing inverse phospholipid bilayer films. The measurements were carried out using a standard fluorescence microscope using multichannel imaging and yielded subnanometer resolution, which is applied to optically measure the discrete thickness variations across phase-separated membranes.

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.

Effect of polyelectrolytes on (de)stability of liquid foam films

The review addresses the influence of polyelectrolytes on the stabilisation of free-standing liquid foam films, which affects the stability of a whole macroscopic foam. Both the composition of the film surface and the stratification of the film bulk drives the drainage and the interfacial forces within a foam film. Beside synthetic polyelectrolytes also natural polyelectrolytes like cellulose, proteins and DNA are considered.

Influence of interfacial rheology on drainage from curved surfaces

Thin lubrication flows accompanying drainage from curved surfaces surround us (e.g., the drainage of the tear film on our eyes). These draining aqueous layers are normally covered with surface-active molecules that render the free surface viscoelastic. The non-Newtonian character of these surfaces fundamentally alters the dynamics of drainage. We show that increased film stability during drainage can occur as a consequence of enhanced surface rheology. Increasing the surfactant layer viscosity decreases the rate of drainage; however, this retarding influence is most pronounced when the insoluble surfactant layer has significant elasticity. We also present a simple theoretical model that offers qualitative support to our experimental findings.

Dilational surface rheology studies of n-dodecyl-β-D-maltoside, hexaoxyethylene dodecyl ether, and their 1:1 mixture

It is time to review latest activities on the dilational surface rheology of the two nonionic surfactants n-dodecyl-β-D-maltoside (β-C12G2) and hexaoxyethylene dodecyl ether (C12E6) and their 1:1 mixture as a lot of different data generated with different techniques have been published in the last years. As the data are scattered throughout different papers and were generated with different techniques, we carried out an extensive study with one technique, which we will use as reference for the discussion of different data sets. We found that the results are in most of the cases in line with already published data as regards the general trends. However, a quantitative comparison reveals differences, which may result in different interpretations of the data. In the review at hand, we summarize, compare and discuss our latest and previously published data.

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.

Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary

We derive the boundary condition for a subdiffusive particle interacting with a reactive boundary with a finite reaction rate. Molecular crowding conditions, that are found to cause subdiffusion of larger molecules in biological cells, are shown to effect long-tailed distributions with an identical exponent for both the unbinding times from the boundary to the bulk and the rebinding times from the bulk. This causes a weak ergodicity breaking: typically, an individual particle either stays bound or remains in the bulk for very long times. We discuss why this may be beneficial for in vivo gene regulation by DNA-binding proteins, whose typical concentrations are nanomolar.

Experimental study of entrainment and drainage flows in microscale soap films

The thickness of freely suspended surfactant films during vertical withdrawal and drainage is investigated using laser reflectivity. The withdrawal process conducted at capillary numbers below 10(-3) generates initial film thicknesses in the micrometer range; subsequent thinning is predominantly impelled by capillary and not gravitational forces. Under these conditions, our results show that film thinning above and below the critical micelle concentration (cmc) is well approximated by a power law function in time whose exponents, which range from -0.9 to -1.8, are inconsistent with current descriptions of capillary-viscous drainage in inextensible films which predict exponents close to -0.5. Correlations between the experimental fitting parameters illustrate important differences in film behavior across the cmc. In addition, normalization of the drainage data yields a collapse to a single functional form over 3 decades in time for a wide range of initial withdrawal rates. We demonstrate that modification of the interface boundary condition in current models to account for Marangoni stresses through an effective slip parameter yields values of the exponents and other key parameters in excellent agreement with experiment. This modification also successfully describes the withdrawal thickness below the cmc.

Effect of Lipid Phase State and Foam Film Type on the Properties of DMPG Stabilized Foams

The drainage and stability of DMPG (l -alpha-phosphatidyl-dl -glycerol dimyristoyl) foams were studied by a microconductivity method under conditions where three different foam film types could be formed-thin foam films (TFF), common black foam films (CBF), and Newton black foam films (NBF). Foaming properties were investigated at 20 and 28°C where DMPG is in the gel and liquid-crystalline states. Higher conductivity signals were observed at the higher temperature where DMPG was in the liquid-crystalline state, which is indicative of wetter or more stable foams under these conditions. This effect was observed independent of foam film type. However, for a given phase state, the type of foam films formed significantly influenced the stability and rate of drainage of the foam. Indeed, the water content of the foams, obtained under conditions for formation of different foam films, is ranked in the order TFF > CBF > NBF. When the temperature was increased to 28°C (i.e., in the liquid-crystalline state), CBF and NBF showed a slight decrease in film thickness and an increase in film lifetime and surface molecular diffusion coefficient in the adsorbed layer. It is likely that the fluidity of the interfacial layer is an important factor contributing to DMPG foam stabilization.