Liquid drainage through aqueous foam: study of the flow on the bubble scale

Impact of Eco-Friendly Drilling Additives on Foaming Properties for Sustainable Underbalanced Foam Drilling Applications

Underbalanced foam drilling stands out as a drilling technique acclaimed for its capacity to enhance safety and efficiency in operations. Utilizing foams as drilling fluids offers several benefits over traditional methods, including lower density, diminished formation damage, and augmented borehole stability. However, the persistent challenge of sustaining foam stability in demanding conditions, particularly amid elevated water salinity and alkaline environments, remains a critical issue. Current literature lacks comprehensive insights into foam stability under such specific circumstances, raising concerns about the practicality of numerous reported foaming agents in field applications. This study aims to fill this knowledge void to align with industry standards. With a heightened focus on sustainability due to mounting environmental considerations, the research explores the use of an eco-friendly surfactant, ammonium alcohol ether sulfate (AAES). Additionally, the investigation delves into the impact of environmentally friendly drilling additives-polyanionic cellulose (PAC), carboxymethyl cellulose (CMC), and starch-on the stability of bulk foam under mildly alkaline conditions. Employing a dynamic foam analyzer, diverse foam properties of AAES foams were assessed, encompassing stability, foamability, and bubble structure. The results demonstrated that the optimal concentrations of the tested additives, in the order of PAC > CMC > starch, significantly prolonged the half-life of the AAES foam bubbles. The introduction of PAC and CMC additives elevated the viscosity of AAES foaming solutions, enhancing the liquid retention within the foam structure. In contrast, starch addition exerted no influence on the solution viscosity and did not impede liquid drainage, although it did reduce bubble coalescence. Furthermore, the PAC- and CMC-based AAES foams manifested as considerably wetter foams with a rounded bubble structure, while the starch-based AAES foam exhibited a dry foam characterized by a distinct polyhedral bubble structure. These findings offer valuable insights into the potential application of the AAES surfactant in foam drilling, showcasing its efficacy in improving foam stability and contributing to the evolution of eco-friendly drilling practices.

Impact of Pressure and Temperature on Foam Behavior for Enhanced Underbalanced Drilling Operations

Foam, a versatile underbalanced drilling fluid, shows potential for improving the drilling efficiency and reducing formation damage. However, the existing literature lacks insight into foam behavior under high-pH drilling conditions. This study introduces a novel approach using synthesized seawater, replacing the conventional use of freshwater on-site for the foaming system's liquid base. This approach is in line with sustainability objectives and offers novel perspectives on foam stability under high-pH conditions. Experiments, conducted with a high-pressure, high-temperature (HPHT) foam analyzer, investigate how pressure and temperature affect foam properties. The biodegradable foaming agent ammonium alcohol ether sulfate (AAES) is employed. Results demonstrate that the pressure significantly impacts foam stability. Increasing pressure enhances stability, reducing decay rates and promoting uniform bubble sizes, especially at lower temperatures. This highlights foam's capacity to withstand high-pressure conditions. Conversely, the temperature plays a substantial role in foam decay, particularly at elevated temperatures (75 and 90 °C). Decreased liquid viscosity accelerates the liquid drainage and foam decay. While pressure mainly influences the AAES foam stability at temperatures up to 50 °C, temperature becomes the dominant factor at higher temperatures. Temperature's impact on foamability is minimal under constant pressure, maintaining consistent gas volume for maximum foam height. However, foam stability is sensitive to temperature variations, with increasing temperature leading to a more significant bubble size increase gradient. These findings stress the importance of considering temperature effects in foam drilling, particularly in deep and high-temperature environments. AAES foam exhibits stability at lower temperatures, making it suitable for surface and intermediate drilling. Understanding temperature-induced changes in foam structure and bubble size is essential for optimizing performance in high-temperature and deep drilling scenarios.

Plant polyphenol surfactant construction with strong surface activity and chelation properties as efficient decontamination of UO22+ on cotton fabric

Chemically synthesized surfactants have promising applications in the treatment of uranium, however, their hazardous environmental effects, non-biodegradability, and numerous drawbacks prevent them from being widely used in practice. Herein, we successfully synthesized a green chelating and foaming integrated surfactant (BTBS) by Mannich reaction and acylation of bayberry tannin for the effective removal of UO22+ from aqueous environments or solid surfaces. The as-prepared surfactant was systematically characterized by FT-IR, showing that the hydrophobic groups were successfully grafted onto tannin. The modified material showed better foaming and emulsifying properties, which proved this method could improve the amphiphilicity of tannin. Moreover, for the first time, a foam fractionation method in conjunction with a tannin-based surfactant was applied for UO22+ removal from water. This surfactant was used as a co-surfactant and could readily remove 90 % of UO22+ (20 mg L-1) from water. The removal of UO22+ could be completed in a short time (30 min), and the maximum adsorption capacity was determined as 175.9 mg g-1. This surfactant can also be used for efficient decontamination of uranium-contaminated cotton cloth with a high removal rate of 94.55 %. In addition, the mechanism studies show that the adsorption of BTBS for UO22+ can be mainly attributed to a chelating mechanism between UO22+ and the adjacent phenolic hydroxyls. The novel biomass-derived BTBS with advantages such as high capture capacity, environmental friendliness, and cost-effectiveness suggests that it plays an important role in the remediation of radionuclide pollution.

Physical Insight into the Conditions Required in the Solid-Phase Molecular Self-Assembly of SDS Revealed by Coarse-Grained Molecular Dynamics Simulation

Molecular self-assembled materials have attracted considerable interest in recent years. As part of the efforts to overcome the shortcoming that the solution-based methods were hardly applicable in preparing bulk macroscopic molecular self-assemblies, Yan [ CCS Chem. 2020, 2, 98-106] developed a strategy of solid-phase molecular self-assembly (SPMSA) that allows scaling up the generation of massive supramolecular films. It is highly desired to understand the physical insight into the SPMSA at a molecular level. Here, in combination with the experimental study, we report molecular dynamics (MD) simulations on the SPMSA of the surfactant sodium dodecyl sulfate (SDS) using a coarse-grained method with the Martini force field model. The MD simulations clearly manifest that a small amount of water is required to endow the SDS molecules with sufficient mobility to self-assemble, and the smaller size of the preassembled SDS particles favors their further fusion into mesophases by reducing the total surface Gibbs free energy, while the smaller interparticle distance decreases the time for the particle fusion. The simulation results agree well with the conditions required in the experiment, confirming that SMPSA is a free-energy-favored process leading to bulk self-assembled materials.

A flow velocity dependence of dynamic surface tension in Plateau borders of foam

HYPOTHESIS

Liquid drainage through foams is a multiscale process, that primarily occurs through channels known as Plateau borders (PBs). Recent experimental studies of isolated PBs have observed variations in channel surface tension, γ, with liquid flow rate, Q, for systems containing soluble low molecular weight surfactant (LMWS). The current study proposes that the dynamic surface tension (DST) could be responsible for this effect, where the residence time of surfactant molecules in the PB is similar to the time required for their adsorption to the channel interface.

EXPERIMENTS

Profile geometries of isolated 'ideal' PB's were created in a bespoke experimental setup at controlled forced liquid flow rates. Average surfactant residence times, τ_Res, were calculated for solutions of Sodium dodecylsulfate (SDS), Tween 20 (T20) and Tween 80 (T80), and used to calculate corresponding average DST values in discrete regions of measured PB profiles. DST values were combined with microscale drainage theory to assess the potential physical implications on liquid flow.

FINDINGS

Significant variations in the magnitude of γ were calculated based on surfactant characteristics, where only the rapid adsorption of SDS was sufficient to produce DST values approaching equilibrium. These findings seriously question assumptions of near equilibrium surface tension in LMWS foam systems above their critical micelle concentration (CMC). Furthermore, the presence of surface tension gradients identified using this discrete approach, highlights the need to further refine the current theory to a continuous approach incorporating Marangoni effects.

Different strategies of foam stabilization in the use of foam as a fracturing fluid

An attractive alternative to mitigate the adverse effects of conventional water-based fluids on the efficiency of hydraulic fracturing is to inject foam-based fracking fluids into reservoirs. The efficiency of foaming fluids in subsurface applications largely depends on the stability and transportation of foam bubbles in harsh environments with high temperature, pressure and salinity, all of which inevitably lead to poor foam properties and thus limit fracturing efficiency. The aim of this paper is to elaborate popular strategies of foam stabilization under reservoir conditions. Specifically, this review first discusses three major mechanisms governing foam decay and summarizes recent progress in research on these phenomena. Since surfactants, polymers, nanoparticles and their composites are popular options for foam stabilization, their stabilizing effects, especially the synergies in composites, are also reviewed. In addition to reporting experimental results, the paper also reports recent advances in interfacial properties via molecular dynamical simulation, which provide new insights into gas/liquid interfacial properties under the influence of surfactants at molecular scale. The results of both experiments and simulations indicate that foam additives play an essential role in foam stability and the synergic effects of surfactants and nanoparticles exhibit more favorable performance.

Foam drainage placed on a thin porous layer

Drainage of foams placed on porous substrates has only recently been theoretically investigated (O. Arjmandi-Tash, N. Kovalchuk, A. Trybala, V. Starov, Foam Drainage Placed on a Porous Substrate, Soft Matter, 2015, 11(18), 3643-3652), where an equation describing foam drainage (with non-slip boundary conditions on the liquid-air interfaces) was combined with that of imbibition of liquid into the thick porous substrate. Foam-based applications have been used as a method of drug delivery, which is a recent and promising area of research related to application of medicinal products onto the skin or hair, which are both thin porous layers. A theory of foam drainage (taking into account surface viscosity) placed on a completely wettable thin porous layer is developed: the rate of foam drainage and imbibition inside the porous layer and other characteristics of the process are predicted. The "effective slip" caused by the surface viscosity increased a movement of the top boundary of the foam. The theoretical predictions are compared with experimental observations of foam drainage placed on thin porous layers. The comparison showed a reasonable agreement between the theoretical predictions and experimental observations. One of the phenomena during foam application is the possibility of a build-up of a free liquid layer on the foam/porous layer interface, which can be very useful for applications. Three different regimes of spreading/imbibition process have been predicted. Conditions and durations of free liquid layer formation have been theoretically predicted and compared with experimental observations.

Removal of trace hexavalent chromium from aqueous solutions by ion foam fractionation

Ion foam fractionation is a green and cost-effective technology where separation of molecules exploits the difference in surface affinity. In this work, a batch ion foam fractionation system was designed and optimized for the separation of trace hexavalent chromium (Cr(VI)) from aqueous solutions. The effect of surfactant head groups (collectors) on the adsorption dynamics was analyzed. Cetyl trimethyl ammonium bromide (CTAB), a cationic surfactant showed high efficiency for the removal of Cr(VI) from aqueous solutions. An experimental investigation of the effect of different operational parameters on the separation characteristics is presented. The recovery of Cr(VI) increased with the increase in CTAB/Cr(VI) molar ratio and reached a maximum of 92.5% at optimum operating conditions. However, with CTAB concentrations close to the critical micelle concentration (CMC) wet foams were produced resulting in high liquid hold-up and poor enrichment ratio. The presence of Cr(VI) at the gas-liquid interface significantly improved the drainage characteristics of the foam decreasing the liquid hold-up. Further, a three-stage ion foam fractionation unit was developed with Cr(VI) removal efficiency of more than 99%. The concentration of Cr(VI) in the residue after the three-stage operation was less than 0.02 mg/L which is below the USEPA recommended standards for drinking water.

Measuring the impact of channel length on liquid flow through an ideal Plateau border and node system

The phenomenon of foam drainage is a complex multi-scale process that unites molecular level interactions with bulk foam characteristics. Foam drainage is primarily governed by the flow of liquid in the channels and junctions that form between bubbles, which are known as Plateau borders (PBs) and nodes respectively. Existing theoretical work predicts the surface rheology of the PB and node air-liquid interface to influence liquid flow rates; however, direct experimental observations of this phenomenon remain scarce. This study recognises the clear need for a reproducible, accurate and standardised approach to directly studying liquid flow at the scale of a theoretically 'ideal' PB-node architecture. Measurements of PB geometric profiles and their apparent surface shear viscosities, μs, were made for an aqueous solution of Sodium Dodecyl Sulphate (SDS) at varying PB lengths, l1, and liquid flow rates in the range 10 μl min-1 ≤ Q ≤ 200 μl min-1. Geometric profiles displayed previously unobserved transitions between PB relaxation and expansion towards the node, with expansion dominating under conditions approaching conventional foam drainage. Average values of μs in the PB relaxation regions showed virtually inviscid behaviour, with magnitudes of 10-8 g s-1 < μs < 10-4 g s-1 for l1 in the range 27.5 mm ⪆ l1 ⪆ 8.0 mm. Decreasing magnitudes of μs and degrees of shear thinning were observed with increasing l1. This was attributed to a compressibility of the interface that was limited by an SDS concentration dependence on l1. Numerical evaluation predicted the appearance of Marangoni forces that scaled strongly with liquid shear rates, and could therefore have been responsible for the apparent shear thinning behaviour.

A review of aqueous foam in microscale

In recent years, significant progress has been achieved in the study of aqueous foams. Having said this, a better understanding of foam physics requires a deeper and profound study of foam elements. This paper reviews the studies in the microscale of aqueous foams. The elements of aqueous foams are interior Plateau borders, exterior Plateau borders, nodes, and films. Furthermore, these elements' contribution to the drainage of foam and hydraulic resistance are studied. The Marangoni phenomena that can happen in aqueous foams are listed as Marangoni recirculation in the transition region, Marangoni-driven flow from Plateau border towards the film in the foam fractionation process, and Marangoni flow caused by exposure of foam containing photosurfactants under UV. Then, the flow analysis of combined elements of foam such as PB-film along with Marangoni flow and PB-node are studied. Next, we contrast the behavior of foams in different conditions. These various conditions can be perturbation in the foam structure caused by injected water droplets or waves or using a non-Newtonian fluid to make the foam. Further review is about the effect of oil droplets and particles on the characteristics of foam such as drainage, stability and interfacial mobility.

Effect of Surface Dilatational Modulus on Foam Flow in a Porous Medium

In order to clarify the role of surface dilatational property in foam flow in a porous medium, three systems were prepared: a system with low surface dilatational modulus and high surface tension, a system with low surface dilatational modulus and low surface tension, and a system with high surface dilatational modulus and low surface tension. By measuring the lamella number and pressure drop across the porous medium, it has been found that differing from flow in a capillary tube, a system with high surface dilatational modulus could achieve a high pressure drop in a porous medium. The conclusion drawn as to the reason is that bubbles with smaller diameter resulting from a structure induced breakup and high dilatational modulus are the main reasons. Flow experiments at 40°C also demonstrate the effect of surface dilatational modulus on the pressure drop.

Foam drainage placed on a porous substrate

A model for drainage/imbibition of a foam placed on the top of a porous substrate is presented. The equation of liquid imbibition into the porous substrate is coupled with a foam drainage equation at the foam/porous substrate interface. The deduced dimensionless equations are solved using a finite element method. It was found that the kinetics of foam drainage/imbibition depends on three dimensionless numbers and the initial liquid volume fraction. The result shows that there are three different regimes of the process. Each regime starts after initial rapid decrease of a liquid volume fraction at the foam/porous substrate interface: (i) rapid imbibition: the liquid volume fraction inside the foam at the foam/porous substrate interface remains constant close to a final liquid volume fraction; (ii) intermediate imbibition: the liquid volume fraction at the interface with the porous substrate experiences a peak point and imbibition into the porous substrate is slower as compared with the drainage; (iii) slow imbibition: the liquid volume fraction at the foam/porous substrate interface increases to a maximum limiting value and a free liquid layer is formed between the foam and the porous substrate. However, the free liquid layer disappears after some time. The transition points between these three different drainage/imbibition regimes were delineated by introducing two dimensionless numbers.

Foam clogging

To what extent are aqueous foams prone to clogging? Foam permeability is measured as a function of particulate loading (trapped hydrophilic particles) under conditions where the particle to bubble size ratio is allowed to increase when the number of particles per bubble is fixed. In addition to experiments performed on the foam scale, we investigated experimentally and numerically the hydrodynamic resistance of a single foam node loaded with one particle. It is shown that, with respect to solid porous media, aqueous foams clog more efficiently due to two reasons: (i) the deformation of interfaces allows for larger particles to be incorporated within the interstitial network and (ii) the interfacial mobility contributes to lowering of the reduced permeability.

Soft nanofluidic transport in a soap film

We investigate experimentally the electrokinetic properties of soft nanofluidic channels that consist in soap films with nanometric thickness, covered with charged surfactants. Both the electric and fluidic responses of the system are measured under an applied voltage drop along the film. The electric field is shown to induce an electro-osmotic hydrodynamic flow in the film. However, in contrast to systems confined between solid surfaces, the soft nature of the nanochannel results furthermore in a thickening of the film. This effect accordingly increases the total electro-osmotic flow rate, which behaves nonlinearly with the applied electric field. This behavior is rationalized in terms of an analogy with a Landau-Levich film withdrawn from a reservoir, with the driving velocity identified here with the electro-osmotic one.

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.

How topological rearrangements and liquid fraction control liquid foam stability

The stability of foam is investigated experimentally through coalescence events. Instability (coalescence) occurs when the system is submitted to external perturbations (T1) and when the liquid amount in the film network is below a critical value. Microscopically, transient thick films are observed during film rearrangements. Film rupture, with coalescence and eventual collapse of the foam, occurs when the available local liquid amount is too small for transient films to be formed. Similar experiments and results are shown in the two-bubble case.

Shear induced drainage in foamy yield-stress fluids

Shear induced drainage of a foamy yield-stress fluid is investigated using MRI techniques. Whereas the yield stress of the interstitial fluid stabilizes the system at rest, a fast drainage is observed when a horizontal shear is imposed. It is shown that the sheared interstitial material behaves as a viscous fluid in the direction of gravity, the effective viscosity of which is controlled by shear in transient foam films between bubbles. Results provided for several bubble sizes are not captured by the R2 scaling classically observed for foams. Furthermore, foam films are found to be responsible for the unexpected arrest of drainage, thus trapping irreversibly a significant amount of interstitial liquid.

Recirculation model for liquid flow in foam channels

Although extensively studied in the past, drainage of aqueous foams still offers major unaddressed issues. Among them, the behaviour of foam films during drainage has great significance as the thickness of the films is known to control the Ostwald ripening in foams, which in turn impacts liquid drainage. We propose a model relating the films' behavior to the liquid flow in foam channels. It is assumed that Marangoni-driven recirculation counterflows take place in the transitional region between the foam channel and the adjoining films, and the Gibbs elasticity is therefore introduced as a relevant parameter. The velocity of these counterflows is found to be proportional to the liquid velocity in the channel. The resulting channel permeability is determined and it is shown that Marangoni stresses do not contribute to rigidify the channel's surfaces, in strong contrast with the drainage of horizontal thin liquid films. New experimental data are provided and support the proposed model.

Foam drainage in the presence of nanoparticle-surfactant mixtures

The drainage of SiO(2) nanoparticle-cationic surfactant (TTAB) mixtures through calibrated aqueous foams had been studied by combining several approaches on both the macroscopic and the local scale. Macroscopic measurements reveal a strong stabilizing effect arising for nanoparticle concentrations as low as 2 wt % mainly because of a drainage kinetic slow-down dependent on the nanoparticle concentration. We show that the variation of the viscous parameters (bulk viscosity, interfacial viscosity, or both) in the classical theoretical models of foam drainage, mainly developed for aqueous surfactant solutions, does not enable fitting experimental data obtained via steady- or free-drainage strategies for [SiO(2)] > or = 2 wt %. In contrast, the quantitative analysis of the data obtained from front propagation velocities has revealed a drainage regime transition from a node-dominated regime toward a Plateau-border-dominated regime upon nanoparticle concentration increase. Observations performed at the Plateau border scale brought to light the drainage kinetic slow-down process by evidencing that the presence of insoluble aggregates induces traffic jamming and even cork formation for silica concentrations above 2 wt %. Considering these observations, a simple mechanism of aggregate growth and cork formation is proposed. Finally, we analyze the discrepancy between experiments (steady- and free-drainage methods) and theory by pointing out that the hypothesis relative to the foam structure that is usually assumed for both the liquid fraction calculation and the determination via conductivity measurements is strongly modified when large insoluble aggregates are present in the system. In this view, the method based on the liquid fraction determination through the measurement of the front propagation velocity seems to be the most suitable for studying the drainage of colloidal dispersion because of the lower dependence of this approach toward hypothesis on the local geometry of the foam continuous phase.

Permeability of aqueous foams

We perform forced-drainage experiments in aqueous foams and compare the results with data available in the literature. We show that all the data can be accurately compared together if the dimensionless permeability of the foam is plotted as a function of liquid fraction. Using this set of coordinates highlights the fact that a large part of the published experimental results corresponds to relatively wet foams (epsilon approximately 0.1). Yet, most of the foam drainage models are based on geometrical considerations only valid for dry foams. We therefore discuss the range of validity of the different models in the literature and their comparison to experimental data. We propose extensions of these models considering the geometry of foam in the relatively wet-foam limit. We eventually show that if the foam geometry is correctly described, forced drainage experiments can be understood using a unique parameter --the Boussinesq number.

Specific surface area model for foam permeability

Liquid foams were recognized early to be porous materials, as liquid flowed between the gas bubbles. Drainage theories have been established, and foam permeability has been modeled from the microscopic description of the equivalent pores geometry, emphasizing similarities with their solid counterparts. But to what extent can the theoretical work devoted to the permeability of solid porous materials be useful to liquid foams? In this article, the applicability of the Carman-Kozeny model on foam is investigated. We performed measurements of the permeability of foams with nonmobile surfactants, and we show that, in introducing an equivalent specific surface area for the foam, the model accurately describes the experimental data over two orders of magnitude for the foam liquid fraction, without any additional parameters. Finally, it is shown that this model includes the previous permeability models derived for foams in the dry foams limit.

Breakup of bubbles and drops in steadily sheared foams and concentrated emulsions

This experimental study is focused on the process of bubble breakup in steadily sheared foams, at constant shear rate or constant shear stress. Two different types of surfactants were used and glycerol was added to the aqueous phase, to check how the bubble breakup depends on the surface modulus and on bulk viscosity of the foaming solutions. The experiments show that bubble breakup in foams occurs above a well defined critical dimensionless stress, tau[over]CR identical with(tauCRR/sigma) approximately 0.40, which is independent of surfactant used, solution viscosity, and bubble volume fraction (varied between 92 and 98%). Here tauCR is the dimensional shear stress, above which a bubble with radius R and surface tension sigma would break in sheared foam. The value of the critical stress experimentally found by us tau[over]CR approximately 0.40, is about two orders of magnitude lower than the critical stress for breakup of single bubbles in sheared Newtonian liquids, tau[over]CR approximately 25. This large difference in the critical stress is explained by the strong interaction between neighboring bubbles in densely populated foams, which facilitates bubble subdivision into smaller bubbles. A strong effect of bubble polydispersity on the kinetics of bubble breakup (at similar mean bubble size) was observed and explained. Experiments were also performed with hexadecane-in-water emulsions of drop volume fraction 83%<or=Phi<or=95% to study drop breakup in concentrated emulsions. Qualitatively similar behavior was observed to that of foams, with the critical dimensionless stress for drop breakup being lower, tau[over]CR approximately 0.15, and practically independent of the drop volume fraction and viscosity ratio (varied between 0.01 and 1). This critical stress is by several times lower than the critical stress for breakage of single drops in sheared Newtonian fluids at comparable viscosity ratio, which evidences for facilitated drop subdivision in concentrated emulsions. To explain the measured low values of the critical stress, a different type of capillary instability of the breaking bubbles and drops in concentrated foams and emulsions is proposed and discussed.

Aqueous foam drainage characterized by terahertz spectroscopy

Aqueous foam drainage has been studied using terahertz (THz) spectroscopy. Water is highly absorbing of THz radiation, allowing drainage to be determined based on water content at respective foam height. These drainage profiles were validated using a model constructed from published equations and tailored to this specific study. In addition, a slow-draining foam was scanned to produce a two-dimensional foam image.

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.

Theoretical model of viscous friction inside steadily sheared foams and concentrated emulsions

In a recent Letter [N. D. Denkov, Phys. Rev. Lett. 100, 138301 (2008)] we calculated theoretically the macroscopic viscous stress of steadily sheared foam or emulsion from the energy dissipated inside the transient planar films, formed between neighboring bubbles or drops in the shear flow. The model predicts that the viscous stress in these systems should be proportional to Ca 1/2, where Ca is a capillary number and n=1/2 is the power-law index. In the current paper we explain our model in detail and develop it further in several aspects: First, we extend the model to account for the effects of viscous friction in the curved meniscus regions, surrounding the planar films, on the dynamics of film formation and on the total viscous stress. Second, we consider the effects of surface forces (electrostatic, van der Waals, etc.) acting between the surfaces of the neighboring bubbles or drops and show that these forces could be important in emulsions, due to the relatively small thickness of emulsion films (often comparable to the range of action of surface forces). In contrast, the surface forces are usually negligible in steadily sheared foams, because the dynamic foam films are thicker than the extent of surface forces, except for foams containing micrometer-sized bubbles and/or at very low shear rates. Third, additional consideration is made for bubbles or drops exhibiting high surface viscosity, for which we demonstrate an additional contribution to the macroscopic viscous stress, created by the surface dissipation of energy. The new upgraded model predicts that the energy dissipation at the bubble or drop surface leads to power-law index n<1/2 , whereas the contribution of the surface forces leads to n>1/2 , which explains the rich variety of foam or emulsion behaviors observed upon steady shear. Various comparisons are made between model predictions and experimental results for both foams and emulsions, and very good agreement is found.

Gas and liquid transport in steady-state aqueous foam

Experiments are performed on the transport of gas and liquid in a column of aqueous foam maintained in steady state by a constant gas flux at the bottom. We measure vertical profiles of the bubble velocities, the bubble radii, and the liquid fraction, for four different gas fluxes. In steady state the bubbles move upwards with constant speed equal to the measured gas flux, which accounts for all transport of gas. The bubbles also coarsen by gas diffusion at a rate that depends on liquid fraction. Away from the bottom, the Plateau border radii are constant. Therefore capillary effects are negligible and the steady-state liquid-fraction profile is set chiefly by the balance of viscous forces and gravity. The flow within the Plateau borders may be modeled with a no-slip boundary condition for our system. These findings provide a simple description of steady-state foams via the coarsening and drainage equations, which can be combined and solved analytically for bubble radius and liquid-fraction profiles.

Remarks on the shear viscosity of surfaces stabilised with soluble surfactants

A survey is made of previously reported values of the surface shear viscosity of sodium dodecyl sulphate solution which reveals inconsistencies. The origin of these inconsistencies is thought to be due to the fact that, because SDS is a soluble surfactant, the surface deformation rate is governed by a three-dimensional sublayer adjacent to the surface and is therefore inherently experiment-dependent. Because of this, only an apparent surface shear viscosity that is specific to a particular experiment can be measured. However, for an insoluble surfactant, an intrinsic two-dimensional surface viscosity can be clearly defined. Some methods of measuring an apparent surface shear viscosity assume that the surface shear viscosity is the only surface property that determines the drainage rate from foam or individual Plateau borders but there is experimental evidence to show that other surface properties may be significant.

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).