A model for foam formation, stability, and breakdown in glass-melting furnaces

A dynamic model for describing the build-up and breakdown of a glass-melt foam is presented. The foam height is determined by the gas flux to the glass-melt surface and the drainage rate of the liquid lamellae between the gas bubbles. The drainage rate is determined by the average gas bubble radius and the physical properties of the glass melt: density, viscosity, surface tension, and interfacial mobility. Neither the assumption of a fully mobile nor the assumption of a fully immobile glass-melt interface describe the observed foam formation on glass melts adequately. The glass-melt interface appears partially mobile due to the presence of surface active species, e.g., sodium sulfate and silanol groups. The partial mobility can be represented by a single, glass-melt composition specific parameter psi. The value of psi can be estimated from gas bubble lifetime experiments under furnace conditions. With this parameter, laboratory experiments of foam build-up and breakdown in a glass melt are adequately described, qualitatively and quantitatively by a set of ordinary differential equations. An approximate explicit relationship for the prediction of the steady-state foam height is derived from the fundamental model.     

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.     

Physicochemical control of foam properties

This article summarizes our recent understanding on how various essential foam properties could be controlled (viz. modified in a desired way) using appropriate surfactants, polymers, particles and their mixtures as foaming agents. In particular, we consider the effects of these agents on the foaminess of solutions and suspensions (foam volume and bubble size after foaming); foam stability to liquid drainage, bubble coalescence and bubble Ostwald ripening; foam rheological properties and bubble size in sheared foams. We discuss multiple, often non-trivial links between these foam properties and, on this basis, we summarize the mechanisms that allow one to use appropriate foaming agents for controlling these properties. The specific roles of the surface adsorption layers and of the bulk properties of the foaming solutions are clearly separated. Multiple examples are given, and some open questions are discussed. Where appropriate, similarities with the emulsions are noticed.     

Atomic Force Microscopy Study of the Adhesion of Saccharomyces cerevisiae

The influence of the liquid properties and the operating variables on the intrinsic volumetric flow rate, q(0), of the droplets at the liquid-atmosphere interface in nonfoaming adsorptive bubble separation and that, W(f0), of the liquid in foam at the liquid-foam interface in foam separation was studied to estimate the enrichment ratio of surface-active substance in the two techniques. Each intrinsic flow rate was determined by the extrapolation method, which the authors proposed previously, and was mainly influenced by superficial gas velocity, liquid viscosity, and surface tension. Although the changes in the surface tension and the liquid viscosity were small, they greatly affected the intrinsic flow rates for both the droplets and the liquid in foam. The experimental results were applied to a dimensional analysis. Dimensionless volumetric flow rates, q(0)/Q and W(f0)/Q, were successfully correlated with a dimensionless number (Ohnesorge number, Z=&mgr;(L)/(rho(L)sigmad(b))(0.5)). q(0)/Q=6.66 Z(1.46) and W(f0)/Q=2.53Z(0.533) were obtained for the nonfoaming and the foaming regions within errors of 30 and 35%, respectively. The enrichment ratio of surface-active substance in the droplets and the liquid in foam to the bulk liquid was derived by using these correlations for the nonfoaming and the foaming regions, respectively. A good agreement of the experimental enrichment ratio and the calculated ones was obtained by using the correlations for nonfoaming and foaming. Copyright 2001 Academic Press.     

Effect of counterions on surface and foaming properties of dodecyl sulfate

The influence of counterions of surfactant on interfacial properties is studied by measuring foamability, foam stability, equilibrium and dynamic surface tension, and surface viscosity. The surfactant chosen is anionic dodecyl sulfate with various counterions, Li(+), Na(+), Cs(+), and Mg(++). Surface tension measurements show a decrease in the following order: LiDS > NaDS > CsDS > Mg(DS)(2). Foamability done using shaking method shows similar order as surface tension, i.e., LiDS > NaDS > CsDS > Mg(DS)(2). This has been explained in terms of the differences in micellar stability and diffusion of monomers. This is further confirmed by our dynamic surface tension results, which show the same order as equilibrium surface tension (i.e., LiDS > NaDS > CsDS > Mg(DS)(2)) at low bubble frequencies but the order is LiDS > NaDS = Mg(DS)(2) > CsDS at high bubble frequencies. Foam stability measurements were done at concentrations below and above cmc to elucidate the role of micelles. It was found that there is no significant change in foam stability when counterions are changed for surfactant concentration values below the cmc, but at concentration above cmc the foam stability of CsDS and Mg(DS)(2) are much greater than LiDS and NaDS indicating presence of stable micelles are essential to high foam stabilities. Surface viscosity measurements correlated well with the foam stability trends and gave the following order LiDS < NaDS < CsDS < Mg(DS)(2), indicating that the molecules of CsDS and Mg(DS)(2) are tightly packed at the air/water interface.     

A proposed mechanism for detergent-assisted foam fractionation of lysozyme and cellulase restored with β-cyclodextrin

Foam fractionation by itself cannot effectively concentrate hydrophilic proteins such as lysozyme and cellulase. However, the addition of a detergent to a protein solution can increase the foam volume, and thus, the performance of the foam fractionation process. In this article, we propose a possible protein concentration mechanism of this detergent-assisted foam fractionation: A detergent binds to an oppositely charged protein, followed by the detergent-protein complex being adsorbed onto a bubble during aeration. The formation of this complex is inferred by a decrease in surface tension of the detergent-protein solution. The surface tension of a solution with the complex is lower than the surface tension of a protein or a detergent solution alone. The detergent can then be stripped from the adsorbed protein, such as cellulase, by an artificial chaperone such as beta-cyclodextrin. Stripping the detergent from the protein allows the protein to return to its original conformation and to potentially retain all of its original activity following the foam fractionation process. Low-cost alternatives to beta-cyclodextrin such as corn dextrin were tested experimentally to restore the protein activity through detergent stripping, but without success.     

Interfacial tension measurements at the interface between two highly immiscible electrolyte solutions: the trapped air bubble method

A dynamic method for the measurement of interfacial tension at a liquid–liquid interface under controlled interfacial potential difference is described. The interface was formed as a drop suspended at the tip of a liquid filled glass micro-syringe into which a trapped air bubble of known volume had been introduced. Changes in volume of the air bubble allow changes in the surface tension to be calculated. Application to measurement of the variation in interfacial tension with cyclic variation in interfacial potential difference (‘cyclic volttensiometry’) is demonstrated.     

Dynamics of foams of ethoxylated ionic surfactant in the presence of micelles and multivalent ions

Foams produced from surfactant solutions containing micelles of the anionic surfactant sodium polyoxyethylene-2 sulfate and counterions of different valence (aluminium, calcium or sodium) are investigated. For this purpose an experimental setup consisting of a glass column and units for detection of pressure, flow and frequency is constructed. Blowing gas bubbles in the surfactant solution at a constant gas pressure produces the foam. Simultaneous monitoring of the bubble volume and frequency relates the foam growth rate to the dynamic surface tension of the surfactant solution. The foam growth rate plotted versus the gas flow rate exhibits a break point at about 80 mL/min, attributed to the transition from regime of bubbles (at lower flow rates - monodisperse foam) to jet regime (at higher flow rates - polydisperse foam). Due to the high surfactant concentration, the foam is stable and its height is linearly increasing with the time. Two types of experiments are carried out. (i) At a constant counterion concentration and variable surfactant concentration, the rate of foam growth increases initially with increasing of the surfactant concentration reaching a plateau at higher concentrations. The foams of pure surfactant grow always slower than the foams with added aluminium ions. (ii) At a constant surfactant concentration and variable counterion concentration, the rate of foam growth exhibits a maximum. It corresponds to number of aggregated surfactant monomers nearly equal to the number of charges provided by the counterions, for example when one aluminium ion binds three surfactant monomers in a micelle. The point of maximum coincides with the transition from small spherical micelles to large cylindrical ones. This transition affects also the micelle lifetime, which is related to the ability of releasing monomers by a micelle in order to supply the bubble surface with surfactant. In support to this hypothesis, the maximum foam growth is found corresponding to lower dynamic surface tension allowing the generation of a large number smaller in size bubbles. The results for the foam growth agree in some extent with the data from independent measurements on the liquid drainage from wet foams.     

A Study of Dynamic Interfacial Properties as Related to Foaming Properties of Sodium 2,5-dialkyl Benzene Sulfonates

In this article, foaming properties and dynamic interfacial properties of a series of sodium 2,5-dialkyl benzene sulfonates in aqueous solutions were carried out to elucidate the relationship between foaming properties and dynamic interfacial properties. The properties of foams generated from bubbling air through different surfactant solutions were measured using a modified Bikerman device. The dynamic surface tension and surface dilational elasticity were obtained from an image analysis technique based on the oscillating bubble method. The surfactants molecular adsorption at the air/water interface was introduced with Rosen empirical equation and the rate of adsorption was determined from measurements of the dynamic surface tension. The surfactant with the longest alkyl chain shows the lowest dynamic surface activity, which lead to the lowest foam volume. The short ortho straight alkyl chain has little effect on the arrangement of molecules at the interface and the foam stability changes a little with the changing of the ortho alkyl chain length. The foam stability is correlated with both the higher surface dilational elasticity and the larger surface monolayer strength.     

Wet foams: Formation,properties and mechanism of stability

Overall picture of phenomena occuring during formation and existence of the wet foams is presented. Properties and mechanism of stability are discussed on the example of the wet foams obtained from solutions of two homologous series of surface active substances; the fatty acids and n-alkanols. In general three physical processes which contribute to foam stability can be distinguished: drainage of liquid out of the foam, coalescence and/or rupture of bubbles, and disproportionation (which may be called Ostwald ripening or gas diffusion from one bubble to another). Dynamic and non-equilibrium character of the wet foams is stressed.Motion of a bubble through the solution causes disequilibration of the surface concentration alongside the bubble surface. The surface concentration on the upstream part of the bubble is much smaller than the equilibrium concentration. Thus, the bubbles arrive at the solution surface with non-equilibrium surface concentration, and these actual non-equilibrium surface coverages determine possibility of formation and properties of the foams.Solution content ϕ in the volume of wet foam is high (of an order 307.), while in top foam layer it is much smaller (ϕ≅5%) . It shows that rupture of the wet foam takes place practically only in the top layer of bubbles and durability of these top foam films determine stability and volume of the whole foam column. On the basis of measurements of liquid content ϕ and lifetimes of bubbles in the top foam layer it was estimated that thicknesses of rupture of these top films were of an order of a few micrometers. At such thicknesses the force of disjoining pressure do not attain yet any meaningful value.Influence of kinetics of adsorption, frequency of external disturbances, surface activity of the solute and lifetime of the foam films on magnitude of the surface elasticity forces induced in the systems studied is discussed. It is shown that stability of the wet foams can be explained in terms of the effective elasticity farces, i.e. the surface elasticity forces which are induced at an actual non-equilibrium surface coverage. There is agreement between the courses of the dependences of the foamability parameter (retention time, rt) and the effective elasticity forces as a function of the number n of carbon atoms in the fatty acid and n-alkanol molecule. This shows that the effective elasticity forces are decisive parameter in formation and stability of the wet foams. It also explains why the foamability of a substance with a stronger surface activity can be lower than that of a substance with a weaker surface activity. The foamability, especially under dynamic conditions, cannot simply be correlated with the surface activity.     

评价表面活性剂溶液泡沫性能的方法—真球气泡法北大核心CSCD

通过真球气泡法测定了不同价数和浓度的无机盐体系下十二烷基硫酸钠(SDS)表面活性剂溶液的表面张力和表面扩展黏度;通过Ross-Miles法测定了相应同一溶液的发泡力和泡沫稳定性;结果表明:SDS溶液的表面张力值随着各种无机盐浓度的增加而减小至不变,此时的无机盐浓度作为相对浓度100%来考察时,发现临界胶束浓度(CMC)值与添加盐的种类无关,只随无机盐的相对浓度的增加而减少;即CMC值随着无机盐的相对浓度的增加从不含无机盐时的8.3 mmol/L均收敛至最小值3.0 mmol/L;表面张力值和对应的发泡力值呈负线性关系,由此推断表面张力值可以评价发泡力;表面扩展黏度值和对应的泡沫稳定性值呈正线性关系,由此推断表面扩展黏度可以评价泡沫稳定性;无机盐种类对SDS表面活性剂发泡力和泡沫稳定性的影响力随阳离子价数(Na^(+)、Cu^(2+)、Fe^(3+))增加而增加。     

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.     

Control of Ostwald ripening by using surfactants with high surface modulus

We describe results from systematic measurements of the rate of bubble Ostwald ripening in foams with air volume fraction of 90%. Several surfactant systems, with high and low surface modulus, were used to clarify the effect of the surfactant adsorption layer on the gas permeability across the foam films. In one series of experiments, glycerol was added to the foaming solutions to clarify how changes in the composition of the aqueous phase affect the rate of bubble coarsening. The experimental results are interpreted by a new theoretical model, which allowed us to determine the overall gas permeability of the foam films in the systems studied, and to decompose the film permeability into contributions coming from the surfactant adsorption layers and from the aqueous core of the films. For verification of the theoretical model, the gas permeability determined from the experiments with bulk foams are compared with values, determined in an independent set of measurements with the diminishing bubble method (single bubble attached at large air-water interface) and reasonably good agreement between the results obtained by the two methods is found. The analysis of the experimental data showed that the rate of bubble Ostwald ripening in the studied foams depends on (1) type of used surfactant-surfactants with high surface modulus lead to much slower rate of Ostwald ripening, which is explained by the reduced gas permeability of the adsorption layers in these systems; (2) presence of glycerol which reduces the gas solubility and diffusivity in the aqueous core of the foam film (without affecting the permeability of the adsorption layers), thus also leading to slower Ostwald ripening. Direct measurements showed that the foam films in the studied systems had very similar thicknesses, thus ruling out the possible explanation that the observed differences in the Ostwald ripening are due to different film thicknesses. Experiments with the Langmuir trough were used to demonstrate that the possible differences in the surface tensions of the shrinking and expanding bubbles in a given foam are too small to strongly affect the rate of Ostwald ripening in the specific systems studied here, despite the fact that some of the surfactant solutions have rather high surface modulus. The main reason for the latter observation is that the rate of surface deformation of the coarsening bubbles is extremely low, on the order of 10(-4) s(-1), so that the relaxation of the surface tension (though also slow for the high surface modulus systems) is still able to reduce the surface tension variations down to several mN/m. Thus, we conclude that the main reason for the reduced rate of bubble Ostwald ripening in the systems with high surface modulus is the low solubility and diffusivity of the gas molecules in the respective condensed adsorption layers (which have solid rather than fluid molecular packing).     

Effect of equilibrium and dynamic surface activity of surfactant on foam transport in porous medium

An apparatus containing a visual porous medium plate model and digital video recorder was employed to investigate the transportation of foam stabilized by sodium polyoxyethylene alkylether sulfate (AES), sodium dodecyl benzene sulfonate (SDBS) and TritonX-100 in porous medium. The results showed that transfiguration and fracture were the main transport manners for foam in the porous medium at high gas and liquid transfusion rate. The increase in probability of transfiguration in foam transport process corresponded to the higher flow impedance. A simple U-shape device was designed to investigate the rigidity of surfactant layer at the gas/liquid interface, and the equilibrium surface tension was assigned to be the key parameter which manifests the rigidity of surfactant interface layer. The dynamic surface tension of different surfactant system has also been measured, and the parameters gotten by Rosen model might be the measurement of dynamic elasticity of surfactant interface layer. There is consanguineous relation between the equilibrium surface activity or dynamic activity of the surfactants and the transport of the foam in the porous medium.     

Adsorption of Water-Soluble Proteins onto Bubbles in Continuous Foam Separation

The mechanism of water-soluble protein enrichment in continuous foam separation was studied. The liquid flow rate and the protein concentration in the foam phase were measured at various heights from the interface between the bulk liquid and foam layer, and the intrinsic values at the interface were estimated by the extrapolation method to determine the accurate adsorption density on the bubble surface. Ovalbumin (OA) and hemoglobin (HB) were used as the soluble proteins. The solution pH values were varied from 3.5 to 6.0 for OA and from 6.0 to 8.0 for HB. The experimental isotherms for OA and HB were compared to the Langmuir isotherm, and the two adsorption parameters of the equilibrium constant, K, and the saturated density, gamma, at each pH were determined. Both gamma values obtained for OA and HB showed maxima at their isoelectric point (pH 4.6 for OA and pH 6.8 for HB). Assuming that OA and HB molecules are spherical in shape and are adsorbed on the bubble surface in a close-packed structure at saturation, the calculated diameters for OA and HB molecules were quite similar to the literature values. The variation in gamma for both OA and HB is discussed qualitatively in relation to the net charge of the protein molecule. Copyright 2000 Academic Press.     

Measurement of bubble size distribution in protein foam fractionation column using capillary probe with photoelectric sensors

Bubble size is a key variable for predicting the ability to separate and concentrate proteins in a foam fraction ation process. It is used to characterize not only the bubble-specific interfacial a rea but also coalescence of bubbles in the foam phase. This article describes the development of a photoelectric method for measuring the bubble size distribution in both bubble and foam columns for concentrating proteins. The method uses a vacuum to withdraw a stream of gas-liquid dispersion from the bubble or foam column through a capillary tube with a funnel-shaped inlet. The resulting sample bubble cylinders are detected, and their lengths are calculated by using two pairs of infrared photoelectric sensors that are connected with a high-speed data acquisition system controlled by a microcomputer. The bubble size distributions in the bubble column 12 and 1 cm below the interface and in the foam phase 1 cm above the interface are obtained in a continuous foam fractionation process for concentrating ovalbumin. The effects of certain operating conditions such as the feed protein concentration, superficial gas velocity, liquid flow rate, and solution pH are investigated. The results may prove to be helpful in understanding the mechanisms controlling the foam fractionation of proteins.     

Structuring bubbles and foams in gelatine solutions within a circular microchannel device

A flow-focusing device with circular cross-section to produce monodispersed air bubbles and foams in several gelatine solutions is presented. Four flow regimes were studied by varying the gas pressure: dripping, bi-disperse bubbly, bubbly and foam flows. Bubble formation at the flow-focusing exit is discussed in detail and compared with that in rectangular microchannels. The bubble volume was shown to depend on the viscosity of the gelatine solution but not on the surface tension. For the bubbly flow, the frequency of bubble formation in this geometry was similar to that found in rectangular microchannels. For the foam flow the frequency was independent of the pressure. Study in the outlet microchannel for the bubbly and foam flows showed that the gas flow followed a power law with the applied pressure. Finally, the viscous resistance was measured and a pressure drop law was determined for each regime.     

Nonequilibrium bubbles in a flowing langmuir monolayer

We investigate the nonequilibrium behavior of two-dimensional gas bubbles in Langmuir monolayers. A cavitation bubble is induced in liquid expanded phase by locally heating a Langmuir monolayer with an IR-laser. At low IR-laser power the cavitation bubble is immersed in quiescent liquid expanded monolayer. At higher IR-laser power thermo capillary flow around the laser-induced cavitation bubble sets in. The thermo capillary flow is caused by a temperature dependence of the gas/liquid line tension. The slope of the line tension with temperature is determined by measuring the thermo capillary flow velocity. Thermodynamically stable satellite bubbles are generated by increasing the surface area of the monolayer. Those satellite bubbles collide with the cavitation bubble. Upon collision the satellite bubbles either coalesce with the cavitation bubble or slide past the cavitation bubble. Moreover we show that the satellite bubbles can also be produced by the emission from the laser-induced cavitation bubbles.     

Dynamics of positronium bubble growth in liquid media and the energy dissipation problem

The dynamics of positronium bubble growth and dissipative energy loss accompanying this process were considered in the hydrodynamic approximation for liquid media with strongly differing values of the surface tension and viscosity. The driving force of the growth of the positronium bubble is repulsive exchange interaction between the electron inherent in the positronium atom and electrons of surrounding molecules. Intermolecular attraction (Laplace pressure) and viscous media retard bubble growth. In liquid helium and glycerol, the Ps formation time is comparable to or even longer than the parapositronium lifetime. Dissipative energy losses accompanying the bubble growth are substantially higher than the surface energy of the equilibrium bubble.Translated from Khimiya Vysokikh Energii, Vol. 39, No. 1, 2005, pp. 44–51.Original Russian Text Copyright © 2005 by Mikhin, Stepanov, Byakov.     

Model for Plateau border drainage of power-law fluid with mobile interface and its application to foam drainage

A model for drainage of a power-law fluid through a Plateau border is proposed which accounts for the actual Plateau border geometry and interfacial mobility. The non-dimensionalized Navier-Stokes equations have been solved using finite element method to obtain the contours of velocity within the Plateau border cross section and average Plateau border velocity in terms of dimensionless inverse surface viscosity and power-law rheological parameters. The velocity coefficient, the correction for the average velocity through a Plateau border of actual geometry compared to that for a simplified circular geometry of the same area of cross section, was expressed as a function of dimensionless inverse surface viscosity and flow behavior index of the power-law fluid. The results of this improved model for Plateau border drainage were then incorporated in a previously developed foam drainage model [G. Narsimhan, J. Food Eng. 14 (1991) 139] to predict the evolution of liquid holdup profiles in a standing foam. Foam drainage was found to be slower for actual Plateau border cross section compared to circular geometry and faster for higher interfacial mobility and larger bubble size. Evolution of liquid holdup profiles in a standing foam formed by whipping and stabilized by 0.1% beta-lactoglobulin in the presence of xanthan gum when subjected to 16g and 45g centrifugal force fields was measured using magnetic resonance imaging for different xanthan gum concentrations. Drainage resulted in the formation of a separate liquid layer at the bottom at longer times. Measured bubble size, surface shear viscosity of beta-lactoglobulin solutions and literature values of power-law parameters of xanthan gum solution were employed in the current model to predict the evolution of liquid holdup profile which compared well with the experimental data. Newtonian model for foam drainage for zero shear viscosity underpredicted drainage rates and did not agree with the experimental data.