On the Modulus of Transverse Elasticity of Thin Foam Films

The theory of transverse elasticity of thin foam films is formulated under the conditions when the action of Gibbs elasticity is excluded. The theory predicts the presence of maxima of the modulus of transverse elasticity and film thickness near the critical micellization concentration as functions of the content of surfactant at a given disjoining pressure. Theoretical conclusions are confirmed experimentally by measuring film thickness at various heights of equilibrium foam column.     

In situ investigations on organic foam films using neutron and synchrotron radiation

We report on small-angle neutron scattering (SANS) and X-ray scattering (SAXS) investigations of foam films stabilized by sodium dodecyl sulfate. Previous measurements on dry foams (Axelos, M. A. V.; Boue, B. Langmuir 2003, 19, 6598) have shown the presence of spikes in the two-dimensional scattering data which suggest that the incident beam is reflected on some film surfaces. The latter interpretation is confirmed by new neutron studies performed on ordered ("bamboo") foams which allow selection of single films. In the first case, we show that the spikes of the scattered intensity can be obtained by reflection on two parts of the foam, namely, the films and the Plateau borders. With synchrotron radiation, first observations of distinct interference fringes have allowed an accurate determination of the film thickness. A comparison with X-ray and neutron data is made, opening a general discussion about the capabilities of small-angle scattering techniques for studying the microscopic properties of foam films.     

Extremes of some foam properties and elasticity of thin foam films near the critical micelle concentration

The elasticity of open and closed thin foam films is analyzed. The elasticity modulus of a closed film is shown to be additive with respect to contributions from Gibbs elasticity and disjoining pressure. A detailed expression for the film elasticity modulus explains the pronounced maxima of foaminess and foam stability near the critical micelle concentration observed earlier in many experiments. A theory of transversal elasticity of thin foam films is formulated under conditions excluding the action of Gibbs elasticity. Near the critical micelle concentration, the theory predicts maxima of the transversal elasticity modulus and of the films thickness as functions of concentration at a given disjoining pressure. The prediction has been verified experimentally by measuring the film thickness in equilibrium foam as a function of height.     

Decay of standing foams: drainage,coalescence and collapse

A summary of recent theoretical work on the decay of foams is presented. In a series of papers, we have proposed models for the drainage, coalescence and collapse of foams with time. Each of our papers dealt with a different aspect of foam decay and involved several assumptions. The fundamental equations, the assumptions involved and the results obtained are discussed in detail and presented within a unified framework.Film drainage is modeled using the Reynolds equation for flow between parallel circular disks and film rupture is assumed to occur when the film thickness falls below a certain critical thickness which corresponds to the maximum disjoining pressure. Fluid flow in the Plateau border channels is modeled using a Hagen-Poiseuille type flow in ducts with triangular cross-section.The foam is assumed to be composed of pentagonal dodecahedral bubbles and global conservation equations for the liquid, the gas and the surfactant are solved to obtain information about the state of the decaying foam as a function of time. Homogeneous foams produced by mixing and foams produced by bubbling (pneumatic foams) are considered. It is shown that a draining foam eventually arrives at a mechanical equilibrium when the opposing forces due to gravity and the Plateau-border suction gradient balance each other. The properties of the foam in this equilibrium state can be predicted from the surfactant and salt concentration in the foaming solution, the density of the liquid and the bubble radius.For homogeneous foams, it is possible to have conditions under which there is no drainage of liquid from the foam. There are three possible scenarios at equilibrium: separation of a single phase (separation of the continuous phase liquid by drainage or separation of the dispersed phase gas via collapse), separation of both phases (drainage and collapse occurs) or no phase separation (neither drainage nor collapse occurs). It is shown that the phase behavior depends on a single dimensionless group which is a measure of the relative magnitudes of the gravitational and capillary forces. A generalized phase diagram is presented which can be used to determine the phase behavior.For pneumatic foams, the effects of various system parameters such as the superficial gas velocity, the bubble size and the surfactant and salt concentrations on the rate of foam collapse and the evolution of liquid fraction profile are discussed. The steady state height attained by pneumatic foams when collapse occurs during generation is also evaluated.Bubble coalescence is assumed to occur due to the non-uniformity in the sizes of the films which constitute the faces of the polyhedral bubbles. This leads to a non-uniformity of film-drainage rates and hence of film thicknesses within any volume element in the foam. Smaller films drain faster and rupture earlier, causing the bubbles containing them to coalesce. This leads to a bubble size distribution in the foam, with the bubbles being larger in regions where greater coalescence has occurred.The formation of very stable Newton black films at high salt and surfactant concentrations is also explained.     

Change of Surface Structure upon Foam Film Formation

The charge distribution and coverage with surfactant molecules at foam film surfaces plays an important role in determining foam film structure and stability. This work uses the concentration depth profiling technique neutral impact collision ion scattering spectroscopy to experimentally observe the charge distribution in a foam film for the first time. The charge distribution at the surface of a foam film and the surface of the corresponding bulk liquid were measured for a cationic surfactant solution and the surface excess as well as the electric potential were determined. Describing the internal pressure of foam films by using the electrochemical potential is introduced as a new concept. The foam film can be seen to have a more negative surface charge compared to the bulk liquid surface due to re‐arranging of the surfactant molecules. It is discussed how the change in surface excess and electric potential change the electrochemical potential and the stability of the foam film.     

Foam films stabilized by dodecyl maltoside. 1. Film thickness and free energy of film formation

Foam films stabilized by a sugar-based nonionic surfactant, beta-dodecyl maltoside, are investigated. The film thickness and the film contact angle (which is formed at the transition between the film and the bulk solution) are measured as a function of NaCl concentration, surfactant concentration, and temperature. The film thickness measurements provide information about the balance of the surface forces in the film whereas the contact angle measurements provide information about the specific film interaction free energy. The use of the glass ring cell and the thin film pressure balance methods enables studies under a large variety of conditions. Thick foam films are formed at low electrolyte concentration. The film thickness decreases (respectively the absolute value of the interaction film free energy increases) with the increase of the electrolyte concentration according to the classical DLVO theory. This indicates the existence of a repulsive double layer electrostatic component of the disjoining pressure. An electrostatic double layer potential of 16 mV was calculated from the data. A decrease of the film thickness on increase of the surfactant concentration in the solution is observed. The results are interpreted on the basis of the assumption that the surface double layer potential originates in the adsorption of hydroxyl ions at the film surfaces. These ions are expelled from the surface at higher surfactant concentration.     

Charge reversal at the air/water interface as inferred from the thickness of foam films

Experiments are reported with foam films from aqueous solutions with increasing concentration of a cationic surfactant. A correlation is established between the foam film thickness and the possible variation of diffuse electric layer potential at the air/water interface from a negative value in absence of surfactant to positive values at higher surfactant concentrations. It is concluded that a charge reversal at the air/water interface is expected to occur under increasing concentration of cationic surfactants in aqueous solutions.     

Disruption of viscoelastic beta-lactoglobulin surface layers at the air-water interface by nonionic polymeric surfactants

Nonequilibrium interfacial layers formed by competitive adsorption of beta-lactoglobulin and the nonionic triblock copolymer PEO99-PPO65-PEO99 (F127) to the air-water interface were investigated in order to explain the influence of polymeric surfactants on protein film surface rheology and foam stability. Surface dilatational and shear rheological methods, surface tension measurements, dynamic thin-film measurements, diffusion measurements (from fluorescence recovery after photo bleaching), and determinations of foam stability were used as methods. The high surface viscoelasticity, both the shear and dilatational, of the protein films was significantly reduced by coadsorption of polymeric surfactant. The drainage rate of single thin films, in the presence of beta-lactoglobulin, increased with the amount of added F127, but equilibrium F127 films were found to be thicker than beta-lactoglobulin films, even at low concentration of the polymeric surfactant. It is concluded that the effect of the nonionic triblock copolymer on the interfacial rheology of beta-lactoglobulin layers is similar to that of low molecular weight surfactants. They differ however in that F127 increases the thickness of thin liquid films. In addition, the significant destabilizing effect of low molecular weight surfactants on protein foams is not found in the investigated system. This is explained as due to long-range steric forces starting to stabilize the foam films at low concentrations of F127.     

A mathematical model for an expanding foam

A theoretical and numerical model is presented for the shape evolution of the thin liquid films separating the gas bubbles in a foam. The motion is due to capillary action, surface tension gradients, and the overall expansion of the foam. The expansion is the result of the increase in gas content with time. Process modeling is accomplished via the solution of three coupled partial differential equations. Two time scales are included in the model: a process time and a drying or curing time. It is demonstrated that the amount of surfactant is the dominant control mechanism for the final film thickness. If sufficient surfactant is present, the films will be shown to dilate uniformly in space. A number of known features of expanding foams are reproduced by the model.     

Foam films stabilized with alpha olefin sulfonate (AOS)

Alpha olefin sulfonate (AOS) surfactants have shown outstanding detergency, lower adsorption on porous rocks, high compatibility with hard water and good wetting and foaming properties. These properties make AOS an excellent candidate for foam applications in enhanced oil recovery. This paper summarizes the basic properties of foam films stabilized by an AOS surfactant. The foam film thickness and contact angle between the film and its meniscus were measured as a function of NaCl and AOS concentrations. The critical AOS concentration for formation of stable films was obtained. The critical NaCl concentration for formation of stable Newton black films was found. The dependence of the film thickness on the NaCl concentration was compared to the same dependence of the contact angle experiments. With increasing NaCl concentration the film thickness decreases gradually while the contact angle (and, respectively the free energy of film formation) increases, in accordance with the classical DLVO theory.The surface tension isotherms of the AOS solutions were measured at different NaCl concentrations. They coincide on a single curve when plotted as a function of mean ionic activity product. Our data imply that the adsorption of AOS is independent of NaCl concentration at a given mean ionic activity.     

Phase diagrams of nonionic foam films: construction by means of disjoining pressure versus thickness curves

The thickness h of foam films can be measured as a function of the disjoining pressure Pi using a thin film pressure balance. Experimental Pi-h curves of foam films stabilized with nonionic surfactants measured at various concentrations resemble the p-V(m) isotherms of real gases measured at various temperatures (p is the pressure and V(m) is the molar volume of the gas). This observation led us to adopt the van der Waals approach for describing real gases to thin foam films, where the thickness h takes the role of V(m) and the disjoining pressure Pi replaces the ordinary pressure p. Our analysis results in a phase diagram for a thin foam film with spinodal, binodal as well as a critical point. The thicker common black film corresponds to the gas phase and the compact Newton black film for which the two surfaces are in direct contact corresponds to the dense liquid. We show that the tuning parameter for the phase behavior of the film is the surface charge density, which means that Pi-h curves should not be referred to as isotherms. In addition to the equilibrium properties the driving force for the phase transition from a common black film to a Newton black film or vice versa is calculated. We discuss how this transition can be controlled experimentally.     

Computer simulation studies of Newton black films

We study via molecular dynamics simulations thin films (Newton black films, NBF) consisting of water coated with sodium dodecyl sulfate (SDS) surfactants. We analyze in detail the film properties (distribution of particles, pair correlation functions, roughness of the film, tilt angle of the hydrocarbon chain, electron density profiles, and mobility of water molecules) as a function of water content in the film core (i.e., film thickness, H). Our simulations indicate that water is part of the bilayer structure as solvation water. We estimate that around 2.25 water molecules per surfactant are part of this solvation structure. The structural analysis of the NBF shows that the headgroups exhibit a high degree of in-plane ordering. We find evidence for the existence of cavities in the monolayer, where only water is present. The basic structure of the monolayer is conserved down to water contents of the order of 4 water molecules per surfactant (H approximately equal to 11 A). The computed monolayer roughness for the present model is 2.5 A, in good agreement with the experimental data. We find that the roughness is very sensitive to the details of the interatomic potentials. Water mobility calculations emphasize the sluggish dynamics of very thin NBF. Diffusion coefficients of water in the lateral direction strongly decrease with film thickness. We find that the typical mean squared displacement of water in the direction normal to the bilayer is between 9 and 80 A2. Overall, our results indicate that the equilibrium SDS Newton black films studied in the X-ray experiments contain from 2 to 4 water molecules per surfactant.     

Molecular simulations of surface forces and film rupture in oil/water/surfactant systems

We use dissipative particle dynamics (DPD) and molecular models to simulate interacting oil/water/surfactant interfaces. The system comprises sections of two emulsion droplets separated by a film. The film is in equilibrium with a continuous phase, in analogy with the surface force apparatus. This is achieved by combining DPD with a Monte Carlo scheme to simulate a muVT ensemble. The setup enables the computation of surface forces as a function of the distance between the two interfaces, as well as the detection of film rupture. We studied monolayers of nonionic model surfactants at different densities and compared oil-water-oil and water-oil-water emulsion films. Between surfactant monolayers facing each other tails-on (water-oil-water films), we observed repulsive forces due to the steric interaction between overlapping hydrophobic tails. The repulsion increases with surfactant density. Conversely, no such repulsion is observed between surfactant monolayers facing each other heads-on. Instead, the film ruptures, the monolayers merge, and a channel forms between the two droplet phases. Film rupture can also be induced in the water-oil-water films by forcing the interfaces together. The separation at rupture increases for oil-water-oil films and decreases for water-oil-water films when the surfactant density increases. The results are in qualitative agreement with existing theories of emulsion stability in creams, in particular with the channel nucleation theory based on the natural curvature of surfactants.     

Hydrodynamics of thin liquid films effect of the surfactant on the rate of thinning

Summary A theory of the effect of the surfactant on the rate of thinning of foam films is presented. The formulae obtained for the separately treated cases of low and high concentrations cover the whole concentration range. The effect of both bulk and surface diffusion is taken into consideration and it is demonstrated that the relative importance of the latter increases with the decrease of the film thickness. The role of the surface diffusion for the stability of foam films is discussed. It is shown that films stabilized with soluble surfactants never strictly obey Reynolds'eq. [19] so that the actual velocity of thinning can be substantially higher than that calculated by the quoted equation.     

Properties of foam films stabilized with tetraethylammonium perfluorooctane-sulfonate

Properties of single foam films prepared with tetraethylammonium perfluorooctane-sulfonate (TAPOS) were studied. Film thickness was measured as a function of NH₄Cl concentration in the film forming solution. The dependence of the film disjoining pressure versus the film thickness (disjoining pressure isotherms) and the mean lifetime of the films were studied. The dependence of the film thickness on the electrolyte concentration showed the presence of an electrostatic double layer at the film surfaces. The electrostatic double layer component of the disjoining pressure was screened at a NH₄Cl concentration higher than 0.2 M where Newton black films (NBFs) of 6 nm thickness were formed. These films are bilayers of amphiphile molecules and contain almost no free water. The disjoining pressure isotherms of the foam films formed with 0.001 M TAPOS were measured at two different NH₄Cl concentrations (0.005 and 0.0005 M). The Deryaguin-Landau-Verwey-Overbeek (DLVO) theory describes well the isotherms with an electrostatic double layer potential of ∼140 mV. The mean lifetime, a measure of the stability of the NBFs, was measured depending on surfactant concentrations. The observation of NBF was possible above a minimum TAPOS concentration of 9.4 × 10⁻⁵ M. Above this concentration, the lifetime increases exponentially. The dependence of the film lifetime on surfactant concentration is explained by the theory for NBF-rupture by nucleation mechanism of formation of microscopic holes.     

Phase diagrams of nonionic foam films: new interpretation of disjoining pressure vs thickness curves

Recently we constructed phase diagrams for thin foam films stabilized by a nonionic surfactant. The idea was born by synopsis of various disjoining pressure (pi) versus thickness (h) curves of foam films resembling p-Vm isotherms of real gases. The new concept of interpreting the pi-h curves of foam films in terms of phase diagrams allows us to describe experimental observations much more precisely. Three logical consequences will be discussed here to illustrate the strength of this approach. First, the observation is explained that common black films (CBF) rupture or form a Newton black film (NBF) within a certain pressure range rather than at a defined pressure. Both observations can be rationalized by invoking a nucleation process of holes or of the thinner NBF, respectively, in close analogy to the vapor to liquid condensation. Second, the question whether the CBF to NBF transition is discrete or continuous is answered by analyzing under which conditions the supercritical state of a foam film can be reached. Third, the evidence of corresponding states is discussed.     

Rupture of draining foam films due to random pressure fluctuations

A generalized formalism for the rupture of a draining foam film due to imposed random pressure fluctuations, modeled as a Gaussian white noise, is presented in which the flow inside the film is decomposed into a flow due to film drainage and a flow due to imposed perturbation. The evolution of the amplitude of perturbation is described by a stochastic differential equation. The rupture time distribution is calculated from the sample paths of perturbation amplitude as the time for this amplitude to equal one-half the film thickness and is calculated for different amplitudes of imposed perturbations, film thicknesses, electrostatic interactions, viscosities, and interfacial mobilities. The probability of film rupture is high for thicker films, especially at smaller times, as a result of faster growth of perturbations in a thick film due to a smaller disjoining pressure gradient. Larger viscosity, larger surface viscosity, higher Marangoni number, and smaller imposed pressure fluctuation result in slower growth of perturbation of a draining film, thus leading to larger rupture time. It is shown that a composite rupture time distribution combining short time simulation results with equilibrium distribution is a good approximation.     

Effect of gas type on foam film permeability and its implications for foam flow in porous media

The aim of this paper is to provide a perspective on the effect of gas type on the permeability of foam films stabilized by different types of surfactant and to present a critical overview of the tracer gas experiments, which is the common approach to determine the trapped fraction of foam in porous media. In these experiments some part of the gas is replaced by a "tracer gas" during the steady-state stage of the experiments and trapped fraction of foam is determined by fitting the effluent data to a capacitance mass-transfer model. We present the experimental results on the measurement of the gas permeability of foam films stabilized with five surfactants (non-ionic, anionic and cationic) and different salt concentrations. The salt concentrations assure formation of either common black (CBF) or Newton black films (NBF). The experiments are performed with different single gasses. The permeability of the CBF is in general higher than that of the NBF. This behavior is explained by the higher density of the surfactant molecules in the NBF compared to that of CBF. It is also observed that the permeability coefficient, K(cm/s), of CBF and NBF for non-ionic and cationic surfactants are similar and K is insensitive to film thickness. Compared to anionic surfactants, the films made by the non-ionic surfactant have much lower permeability while the films made by the cationic surfactant have larger permeability. This conclusion is valid for all gasses. For all types of surfactant the gas permeability of foam film is largely dependent on the dissolution of gas in the surfactant solution and increases with increasing gas solubility in the bulk liquid. The measured values of K are consistent with rapid diffusion of tracer gasses through trapped gas adjacent to flowing gas in porous media, and difficulties in interpreting the results of tracer-foam experiments with conventional capacitance models. The implications of the results for foam flow in porous media and factors leading to difficulties in the modeling of trapped fraction of foam are discussed in detail. To avoid complications in the interpretation of the results, the best tracer would be one with a permeability close to the permeability of the gas in the foam. This puts a lower limit on the effective diffusion coefficient for tracer in an experiment.     

FTIR-ATR spectroscopic determination of the distribution of surfactants in latex films

FTIR-ATR (Fourier Transform Infra-Red-Attenuated Total Reflection) has been used to analyze the surface composition of coalesced acrylic latex films. The behavior of two anionic surfactants has been characterized. It has been found that surfactant distribution depends on the nature of the surfactant. A comparison between the normalized absorbance in transmission and in reflection has shown an enrichment of surfactants at the surfaces of films with a coalescence time of 3 days. The surfactant concentration at the film-air interface is higher than at the film substrate interface. A concentration gradient exists through the film thickness. In addition, the incompatible surfactant migrates towards the interface as coalescence proceeds.