Liquid drainage in single plateau borders of foam

This paper reports on an investigation of the influence of the interfacial shear viscosity on the liquid drainage in single Plateau borders of foam. The simplified Navier-Stokes equation governing the liquid flow is solved for the liquid velocity by the numerical computational method. The numerical results show significant influence of the interfacial shear viscosity on the liquid velocity in the Plateau border. Comparison of the numerical results for the average velocity over the cross-section area of the Plateau border to the available analytical solution shows that the available analytical solution underestimates the average velocity. New, simple yet accurate correlations for the dependence of the average velocity on the radius of the cross section of the Plateau border, the pressure gradient, and the interfacial shear viscosity are obtained using the asymptotic analysis and the numerical data.     

Influence of the type of foam films and the type of surfactant on foam stability

The behaviour and the life time ( _p) of different types of foam films (thin liquid films, for which DLVO-theory is valid; common black films, Newton black films) have been studied as a function of external pressure (P), applied in the Plateau-Gibbs-borders of the foam. The foam stability and the course of thep/P-dependence are determined mainly by the type of the foam films. A criterion for estimation of foam stability is proposed on the base of the obtained experimental results.     

Effect of the adsorption component of the disjoining pressure on foam film drainage

The present work is trying to explain a discrepancy between experimental observations of the drainage of foam films from aqueous solutions of sodium dodecylsulfate and the theoretical DLVO-accomplished Reynolds model. It is shown that, due to overlap of the film adsorption layers, an adsorption component of the disjoining pressure is important for the present system. The pre-exponential factor of this adsorption component was obtained by fitting to the experimental drainage curves. It corresponds to a slight repulsion, which reduces not only the thinning velocity as observed experimentally but corrects also the film equilibrium thickness.     

Some regularities of the surfactant adsorption accumulation in the foam with high capillary pressure in Platean-Gibbs borders

Summary Some regularities of the surfactant adsorption accumulation in a foam with high capillary pressure in the Plateau-Gibbs borders are investigated. The dependencies of the accumulation ratio on the surfactant adsorption, on the dispersity and the expansion factor of the foam, and on the capillary pressure are obtained theoretically. The surfactant accumulation is investigatet in a static and in a dynamic foam. The experimental data are in a good agreement with the theoretical dependencies. The accumulation ratio reaches values up to 1000–2000.

---

Zusammenfassung Es wurden die Gesetzmäßigkeiten der Adsorptionskonzentrierung von Tensiden in einem Schaum mit hohem Kapillardruck in den Plateau-Gibbsschen Grenzen untersucht. Die Abhängigkeit des Konzentrierungskoeffizienten von der Tensidadsorption, von der Dispersität und Verschäumungszahl des Schaumes und von dem Kapillardruck wurden theoretisch erhalten. Die Konzentrierung des Tensides wurde in einem statischen und in einem dynamischen Schaum untersucht. Die experimentellen Ergebnisse stimmen gut mit den theoretischen Abhängigkeiten überein. Die Konzentrierungskoeffizienten können Werte von 1000–2000 erreichen.

---

---

With 3 figures     

Film junction effect on foam drainage

Foam drainage is modelled by the flow of liquid through Plateau borders (PBs) that are the liquid channels resulting from the merging of three liquid films separating the gas bubbles. Available models generally neglect the influence of these films. Yet, within drainage conditions, experimental observations indicate a strong coupling of these films with the channels. We consider the influence of films on foam drainage through their effect on the cross-section geometry of the channels. More precisely, we assume that the Plateau border cross-section is enclosed by three circular arcs that are not always tangent but instead exhibit a non-zero contact angle θ as it has been observed experimentally. The liquid flow through the channels is studied using numerical simulations whose parameters are θ and the Boussinesq number, Bo, that reflects the surface shear viscosity of the interface. We show that, for values of Bo relevant for foam drainage conditions, a slight increase of θ results in a strong decrease of the average liquid velocity.     

Effect of double-layer repulsion on foam film drainage

This paper presents an experimental validation of new theoretical development for foam film drainage, which focuses on the role of surface forces. The drainage of microscopic foam films (with radii smaller than 100 μm) from aqueous solutions of 10⁻⁶ to 10⁻⁴ mol/L sodium dodecyl sulphate (SDS) was studied by means of an improved Scheludko micro-interferometric technique which consisted of a conventional Scheludko cell, a high-speed camera system, and the software for digital analysis Optimas used for the digitisation of the interferometric images to obtain the monochromatic light intensity. The experimental technique allowed fast processing of the interferometric data for determining the transient film thickness with high accuracy. The zeta-potential of the air–water interface was determined from the electrophoretic mobility of micro-bubbles in SDS solutions of the same concentrations. Advanced predictions for the electrical double-layer repulsion at either constant surface potential or constant surface charge were employed. Significant discrepancy between the theoretical prediction and the experimental data was obtained. The analysis showed that the adsorption layer, which is located on the film surfaces, is far away from equilibrium, while the theory assumes condition close to equilibrium. In this term the interaction between the film surfaces is affected by the dynamics of the adsorption layers during the film drainage.     

Foam drainage on the microscale I. Modeling flow through single Plateau borders

The drainage of liquid through a foam involves flow in channels, also called Plateau borders, which generally are long and slender. We model this flow by assuming the flow is unidirectional, the shear is transverse to the flow direction, and the liquid/gas interfaces are mobile and characterized by a Newtonian surface viscosity, which does not depend on the shear rate. Numerical finite difference simulations are performed, and analytical approximations for the velocity fields inside the channels and the films that separate the bubbles are given. We compare the liquid flow rates through interior channels, exterior channels (i.e., channels contacting container walls) and films. We find that when the number of exterior channels is comparable to the number of interior channels, i.e., narrow container geometries, the exterior channels can significantly affect the dynamics of the drainage process. Even for highly mobile interfaces, the films do not significantly contribute to the drainage process, unless the amount of liquid in the films is within a factor of ten of the amount of liquid in the channels.     

Effects of surfactants on wave-induced drainage of foam and emulsion films

It is well established that the plane-parallel models of foam and emulsion films underestimate the velocity of film thinning by up to several orders of magnitude and show an incorrect dependence of thinning velocity on film radius. A new theory of film thinning has been previously formulated for tangentially immobile films [12, 13], and shows that the reason for this discrepancy is the neglect of experimentally observed finite amplitude surface waves. For thin films of relatively large radii (> 1o^–2 cm), the pumping of the fluid generated by oscillations of the surface waves, provides the dominant contribution to film thinning velocity. The present hydrodynamic model includes the effects of surfactants (Marangoni-Gibbs-effect, surface viscosity and surface diffusion) and surface waves on thinning velocity. As in the case of a tangentially immobile film, it is concluded that the thinning velocity varies inversely with less than the first power of the film radius, and not with the square of the film radius, as predicted by the plane-parallel models of thin film. Also, the velocity of thinning is found to be up to several orders of magnitudes larger than that evaluated from the plane-parallel models. The influence of waves in enhancing the thinning velocity is found to be most significant for a tangentially immobile film and this effect decreases by a factor of up to 3, with a decrease in surface elasticity and surface viscosity.     

Bubble motion measurements during foam drainage and coarsening

We have studied bubble motion within a column of foam allowed to undergo free drainage. We have measured bubble motion upward with time and as a function of their initial positions. Depending on the gas used, which sets the coarsening and drainage rates, different bubble upward motion types have been identified (constant speed, acceleration or deceleration) and explained in relation with liquid downward flows. The proofs of the consistency between bubble upward motion and liquid downward flow are obtained both by comparing the bubble motion curves to the liquid drainage ones, and by comparing the time variations of the liquid fraction extracted from bubble motion to direct liquid fraction measurements by electrical conductimetry. The agreement between bubble position tracking and electrical conductivity shows in particular that it is possible to determine the drainage regime from such simple bubble motion measurements. This work also allowed us to demonstrate a special case of foam coarsening and expansion, occurring when the foam gas is less soluble than the outside one, caused by diffusion of this external gas into the foam. All these results allow us to build a picture of drainage and coarsening seen from the bubble point of view.     

Measurement of pressure distribution in the Plateau borders of fresh and aged foams

In the interpretation of foam ageing processes it is important to know the laws of fluid motion in the Plateau borders. In foams, the rate of fluid motion is determined, in principle, by the fluid viscosity, the static and dynamic surface tension, the shape of the capillaries and the pressure distribution. An attempt is made to investigate the role of these parameters experimentally. As a first step, the pressure and the pressure distribution were measured in the Plateau borders by liquid-filled manometers kept in contact with the Plateau borders through a porous plate. The pressure is always negative, and the pressure vs. time curves show maxima at the point of the start of draining. Draining starts when pressure difference drops to zero at the bottom of the foam container. After a sufficiently long time the pressure becomes equal to the hydrostatic pressure at the given level, i. e. _p=–gh, where is the density of the liquid andh is the height of the foam column measured from the bottom of the container.     

Effect of environmental humidity on static foam stability

The quality of foaming products (such as beer and shampoo) and the performance of industrial processes that harness foam (such as the froth flotation of minerals or the foam fractionation of proteins) depend upon foam stability. In this study, experiments are performed to study the effect of environmental humidity on the collapse of static foams. The dependency of the rate at which a foam collapses upon humidity is demonstrated, and we propose a hypothesis for bubble bursting due to Marangoni instability induced by nonuniform evaporation to help explain the dependency. This hypothesis is supported by direct experimental observations of the bursting process of isolated bubbles by high speed video recording and the thinning of isolated foam films under different values of humidity and temperature by microinterferometric methods.     

Effect of lidocaine on ovalbumin and egg albumin foam stability

Foam fractionation is a simple separation process that can remove and concentrate hydrophobic molecules such as proteins, surfactants, and organic wastes from an aqueous solution. Bovine serum albumin and ovalbumin have been widely used as model proteins due to their strong foaming potential and low price. Here, we study the effect of lidocaine on albumin foam, since drugs like lidocaine are known to bind with albumin. We observed that lidocaine not only enhances the amount of foam produced but also the stability of that foam as well. The foam stability was evaluated as the decay rate constant of the foam, determined from a change in height (or volume) of the foam over a given time period.     

The effect of filamentous bacteria on foam production and stability

Bacteria have been implicated in the formation of viscous brown foams that can appear suddenly on wastewater treatment plants. Three strains of the filamentous bacterium Gordonia amarae, isolated from wastewater treatment plants, were investigated to determine their effect on foam formation and stabilisation. During the exponential phase of the bacterial growth a biosurfactant was formed, causing a significant drop in the surface tension of the filtered medium and the formation of persistent foam. Foaming tests in the presence and absence of bacteria showed that bacteria increased foam persistence, most probably by reducing the drainage from the lamellae between bubbles. Experiments showed that > or =55% of the three bacterial strains partitioned into the foam produced by the biosurfactant, indicating that their surfaces were hydrophobic. The extent of partitioning was independent of the growth stage, suggesting that the cell surface hydrophobicity did not change with age, or with cell viability. This work shows that, although the G. amarae cells themselves do not cause foaming, they do produce biosurfactant, which aids foam formation, and they stabilise the foam by reducing the rate of drainage from the foam lamellae.     

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

Macroscopic properties of foams are highly dependent on the liquid volume fraction, which has motivated many studies on foam drainage in the last decade. Theoretical developments and recent experimental results have suggested that two macroscopic drainage regimes could be expected, in relation with flow transitions occurring at the microscopic level, essentially in the Plateau border channels. We have constructed a setup, the Plateau border apparatus, to study the hydrodynamics of a single Plateau border channel, focusing on the surface properties of the foaming solution. Experimental results have shown that the actual theoretical models only partially predict the dissipation of liquid flow through a Plateau border channel. The major discrepancies can be explained considering additional dissipation processes related to the properties of the interface, and to the liquid flows induced in adjoining films as the liquid flows in the channel. Evidence of the hydrodynamic coupling between the channel and the adjoining films is given in the paper.     

Studies on foam stability by the actions of hydrophobically modified polyacrylamides

Hydrophobically modified polyacrylamide (HMPAM), as a foam stabilizer, was prepared with a cationic surfomer, acrylamide and acrylic acid by free-radical polymerization in aqueous solution. The actions of HMPAM on foam stability have been investigated with the Waring blender method. The results showed the foam containing HMPAM was stabler than that contained polyacrylamide. Moreover, a linear relationship between the logarithm of the half decay time and polymer concentration was observed, and the slope reflects the polymer ability to stabilize the foam.     

Critical capillary pressure for destruction of single foam films and foam: effect of foam film size

Foams and single foam films stabilised by ionic and amphiphile polymer surfactants are studied with foam pressure drop technique (FPDT) and thin liquid film-pressure balance technique (TLF-PBT). A pressure is reached at which the single foam films rupture and the foams destruct very fast (avalanche-like). For film rupture we named this pressure—critical capillary pressure of film rupture, P_cr,film while for foam destruction, we introduced a new parameter—critical capillary pressure of foam destruction, P_cr,foam. The surfactant kind and foam film type (common thin, common black and Newton black) affect the values of both parameters. When below 20 kPa, P_cr,film and P_cr,foam are close by value, when over 20 kPa, there is a significant difference between them. The P_cr,film versus film size and P_cr,foam versus foam dispersity dependences, indicate that the film size and foam dispersity strongly affects the critical capillary pressure values. Film size distribution histograms reveal that a foam always contains films that are of a larger than the most probable size. They rupture at lower pressures, does initiating the destruction of the whole foam, which can be an explanation why higher than 20 kPa there is a difference between P_cr,film and P_cr,foam values. This parameter, P_cr,foam is considered of significant with respect to foam stability and could find use in industry.     

Influence of interfacial rheology on foam and emulsion properties

Foams and emulsions are stabilized by surfactant monolayers that adsorb at the air-water and oil-water interfaces, respectively. As a result of monolayer adsorption, the interfaces become viscoelastic. We will describe experiments showing that foaming, emulsification, foam and emulsion stability, are strongly dependent upon the value of compression elasticity and viscosity. This will include excited surface wave devices for the measurement of surface viscoelasticity and thin film videointerferometry for the study of model films between air bubbles and emulsion drops.