Modeling a protein foam fractionation process

A simple staged model for the protein foam fractionation process is proposed in this article. This simplified model does not detail the complex foam structure and gas-liquid hydrodynamics in the foam phase but, rather, is built on the conventional theoretical stage concept considering upward bubbles with entrained liquid and downward liquid (drainage) as counter-current flows. To simulate the protein concentration distribution in the liquid along the column by the model, the bubble size and liquid hold-up with respect to the position must be known, as well as the adsorption isotherm of the protein being considered. The model is evaluated for one stage by data from the semibatch foam fractionation of egg albumin and data from the continuous foam fractionation of bovine serum albumin. The effect of two significant variables (superficial gas velocity and feed protein concentration) on enrichment is well predicted by the model, especially for continuous operation and semibatch operation when initial concentration is high.     

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).     

Investigation on properties of aqueous foams stabilized by aliphatic alcohols and polypropylene glycol

Foams stabilized by nonionic surfactants are usually moderately stable due to high drainage rate and intense bubble coalescence and coarsening. This study aimed to investigate comparatively the foam properties of aliphatic alcohols (methyl isobutyl carbinol (MIBC) and 2-octanol) and polypropylene glycol (PPG400). Experiments were conducted using the FoamScan method at various surfactant concentrations and gas flow rates where the foam volume, liquid content of foam and foam half-life were determined. The results showed that both foamability and foam stability of surfactant solution increased with increasing gas flow rate and surfactant concentration for all tested surfactants. PPG400 was an unusually strong surfactant having the largest surface activity compared with MIBC and 2-octanol, which exhibited the maximum foaming performance and foam stability at all tested gas flow rates and concentrations. The present study suggested that foam properties depended primarily on the type of surfactant and its concentration and secondarily on the gas flow rate. In addition, properties of interface are closely related to that of foam, which is a significant point if one wants to produce foams for specific applications.     

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.     

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.     

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.     

Surface rheology and foaming properties of sodium oleate and C12(EO)6 aqueous solutions

The dynamic surface tension (DST) and the surface viscoelastic modulus of sodium oleate aqueous solutions at different concentrations were measured using an image analysis tensiometer based on the oscillating bubble technique. The diffusion coefficient of oleate moieties was calculated from DST measurements and the surface viscoelastic modulus using the Langmuir-Szyszkowski and the diffusion-controlled adsorption models. The viscoelastic moduli obtained from model calculations were compared with the corresponding experimental values. The diffusion coefficient of C(12)(EO)(6) in water and the parameters of the Langmuir-Szyszkowski adsorption isotherm were taken from the literature and used to calculate the surface viscoelastic modulus of its aqueous solutions at different concentrations. The foaming properties of both C(12)(EO)(6) and sodium oleate solutions, viz., the foam conductance and the water volume fraction in the foam, were measured using a commercial Foamscan device. Foaming experiments with C(12)(EO)(6) and sodium oleate solutions were carried out either under static conditions; i.e., the foam conductance and the water volume fraction were measured as a function of time after the generation of a fixed volume of foam, or under dynamic conditions; i.e., the foam conductance and the water volume fraction were measured during foam formation. The variations in the foam permeability as a function of surfactant concentration were related to the viscoelastic properties of the air/water interface and to the presence of micelles in the foam films. With foams in which the water volume fraction was higher than 0.05, the foam electrical conduction could be described using a simple parallel resistor model and their conductance measurements were related to the foam water volume fraction. The results related to water drainage under static conditions were used to interpret water drainage under dynamic conditions. Preliminary conjectures on the influence of foam permeability and water volume fraction on the yield of the flotation deinking process were drawn from these results.     

Experimental study of the influence of silica nanoparticles on the bulk stability of SDS-foam in the presence of oil

The influence of silica nanoparticles on the bulk stability of SDS-foam in the presence of oil was investigated in this study using KRÜSS dynamic foam analyzer. The bulk foam static stability was evaluated from half-decay time, liquid drainage, bubble size distribution, and change in total height and volume of the generated foams with respect to time. Results clearly showed that foam stability in the presence of oil mainly depends on the viscosity and density of the oil. Foam stability increased with the addition of silica nanoparticles due to the aggregation of the nanoparticles at the thin lamellae of the foam, which prevents spreading of the oil at the gas–liquid interface. Moreover, optimum foam stability was obtained with the modified nanosilica–SDS mixtures, while slower liquid drainage from the foam did not generally result in high foam stability.     

Mass transfer of volatile organic carbons through aqueous foams

A model is developed to study diffusive mass transfer of hydrocarbon vapor through a flexible foam blanket. The model accounts for the diffusion of hydrocarbon vapor through gas-phase and liquid lamellae, the combined gravity and capillary drainage from the plateau border, the thinning of foam lamellae caused by the forces of capillary suction, London-van der Waals attraction, and electrostatic double-layer repulsion, and foam collapse. Uniform bubble size is assumed, and hence, interbubble gas diffusion arising out of variation in bubble sizes alone is not incorporated into the model. A high-stability aqueous foam formulation that remains stable in the presence of oil (hexane) at foam-oil contact was developed using surfactants, stabilizers, and viscosifiers. Emission of hexane vapor through the foam was measured. The model predicts that the initially taller foam columns collapse faster. Their mass-transfer resistance is higher before the onset of collapse but not very different from that of the shorter foam columns at long times. If the solubility and diffusivity of the hexane gas in the foam liquid are unaffected, the foams with higher viscosities persist longer and provide greater diffusive mass-transfer resistance. Foam bubble size does not significantly impact the mass-transfer resistance of the foam column before the onset of foam collapse. However, the foams with smaller bubbles collapse earlier, and their ability to act as a mass-transfer barrier to the diffusing hydrocarbon vapor diminishes rapidly. The experimental results compared reasonably with the model for varying initial foam heights and bubble sizes.     

The titration of clay minerals I. Discontinuous backtitration technique combined with CEC measurements

Evolution of liquid holdup profile in a standing foam formed by whipping and stabilized by sodium caseinate in the presence of xanthan gum when subjected to 16 and 29g centrifugal force fields was measured using magnetic resonance imaging for different pH, ionic strength, protein and xanthan gum concentrations. Drainage resulted in the formation of a separate liquid layer at the bottom at longer times. Foam drainage was slowest at pH 7, lower ionic strength, higher protein and gum concentrations. Foam was found to be most stable at pH 5.1 near the isoelectric point of protein, lower ionic strength and higher protein and xanthan gum concentrations. A predicted equilibrium liquid holdup profile based on a previous model (G. Narsimhan, J. Food Eng. 14 (1991) 139) agreed well with experimental values at sufficiently long times. A proposed model for velocity of drainage of a power law fluid in a Plateau border for two different simplified geometries was incorporated in a previously developed model for foam drainage (G. Narsimhan, J. Food Eng. 14 (1991) 139) to predict the evolution of liquid holdup profiles. The model predictions for simplified circular geometry of Plateau border compared well with the experimental data of liquid holdup profiles at small times. At longer times, however, the predicted liquid holdup profile was larger than the observed, this discrepancy being due to coarsening of bubble size and decrease in foam height not accounted for in the model. A Newtonian model for foam drainage under predicted drainage rates did not agree with the experimental data.     

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.     

Foam consolidation and drainage

A theoretical model of foam as a consolidating continuum is proposed. The general model is applied to foam in a gravity settler. It is predicted that liquid drainage from foam in a gravity settler begins with a slow drainage stage. Next, a stage with faster drainage occurs where the drainage rate doubles compared to the initial stage. The experiments conducted within the framework of this work confirmed the theoretical predictions and allowed measurements of foam characteristics. Foams of three different concentrations of Pantene Pro-V Classic Care Solutions shampoo were studied, as well as the addition of polyethylene oxide (PEO) in one case. The shampoo's main foaming components are sodium lauryl sulfate and sodium laureth sulfate. It is shown to what extent foam drainage is slowed down by using higher shampoo concentrations and how it is further decreased by adding polymer (PEO).     

Influence of gas flow rate and sodium carboxymethylcellulose on foam properties of fatty alcohol sodium polyoxyethylene ether sulfate solution

Foamability, foam initial liquid volume, and bubble size of fatty alcohol sodium polyoxyethylene ether sulfate (AES) surfactant solution were studied with and without the addition of sodium carboxymethylcellulose (CMC) at different gas flow rates, using a sparging method. The generation time decreased with increasing gas flow rate. At low gas flow rates, the added CMC greatly enhanced the foamability by preventing bubble collapse. The initial liquid volume of the foam first increased rapidly, and then gradually decreased. Increasing the CMC concentration increased the initial liquid volume of the foam. The mean bubble diameter first clearly decreased, then increased slowly with increasing gas flow rate. CMC showed different effects on bubble size at high and low gas flow rates. Adsorption of CMC on AES molecules forms a network structure and improves bubble film stability, which can explain the above results. These findings provide guidelines for generating foam with excellent properties suitable for coal mine dust control by adjusting the gas flow rate and the concentration of the added water-soluble polymer.     

Effect of bubble size on foam fractionation of ovalbumin

The bubble size distribution and void fraction (ɛ _g ) (at two bulk liquid pool positions below the bulk liquid-foam interface and one lower foam phase position) in a continuous foam fractionation column containing ovalbumin were obtained using a photoelectric capillary probe. The bubble size and ɛ _g data were gathered for different operating conditions (including the changes in the superficial gas velocity and feed flow rate) at a feed solution of pH 6.5 and used to calculate the specific area, a, of the bubbles. Thus, local enrichment (ER _l ), values of ovalbumin could be estimated and compared with directly obtained experimental results. The ER _l results were also correlated with the bubble size and ɛ _g to understand better the concentration mechanisms of foam fractionation. The high ER _l in the lower foam phase was largely attributable to the abrupt increase in ɛ _g (from 0.25 to 0.75), or the a (from about 12 to 25 cm²/cm³) from the bulk liquid to the foam phase. These changes correspond with enhanced gravity drainage. With an increase in the superficial gas velocity, the bubble size increased and the a decreased in both the bulk liquid and lower foam phases, resulting in a decrease in the local experimentally determined enrichments at high superficial gas velocities. At intermediate feed flow rates, the bubble size reached the maximum. The ɛ _g and a, on the other hand, were the largest for the largest feed flow rate. The ER _l in the lower foam phase was maximized at the lowest feed flow rate. It follows, therefore, that a alone is not sufficient to determine the magnitude of the ER _l in the foam phase.     

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.     

Marangoni effects in aqueous polypropylene glycol foams

The foam behavior of three polypropylene glycols covering the molecular weight range between 192 and 725 g/mol has been examined. Static and dynamic surface tension data, as well as bubble size distribution and retention time in the foam, were incorporated into a simple model of foam stability. The latter clearly indicates that surface tension differences between the plateau border and lamellar region adjacent to the bubble surface are the dominant factor in controlling foamability, causing liquid flow in the direction opposite to liquid drainage, a process termed the Marangoni effect.     

Multiple light scattering as a probe of foams and emulsions

Light propagating in foams or emulsions is strongly scattered by the gas–liquid or liquid–liquid interfaces. This feature makes it generally impossible to directly observe the structure and dynamics deep within the bulk of such materials. However, multiple light scattering can be used as the basis of non-invasive experimental techniques that probe the average bubble size, droplet size or the dispersed volume fraction. If the sample is illuminated with a laser, the transmitted or backscattered light forms a speckled interference pattern whose temporal fluctuations reveal the dynamics of internal structural changes. Such changes can be due to coarsening, flocculation, or applied strain. We briefly recall the fundamental principles of multiple light scattering and present an overview of the experimental techniques that have been developed in recent years.     

Unusually stable liquid foams

Obtaining stable liquid foams is an important issue in view of their numerous applications. In some of these, the liquid foam in itself is of interest, in others, the liquid foam acts as a precursor for the generation of solid foam. In this short review, we will make a survey of the existing results in the area. This will include foams stabilised by surfactants, proteins and particles. The origin of the stability is related to the slowing down of coarsening, drainage or coalescence, and eventually to their arrest. The three effects are frequently coupled and in many cases, they act simultaneously and enhance one another. Drainage can be arrested if the liquid of the foam either gels or solidifies. Coalescence is slowed down by gelified foam films, and it can be arrested if the films become very thick and/or rigid. These mechanisms are thus qualitatively easy to identify, but they are less easy to model in order to obtain quantitative predictions. The slowing down of coarsening requests either very thick or small films, and its arrest was observed in cases where the surface compression modulus was large. The detail of the mechanisms at play remains unclear.     

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.     

Foam drainage

This review focuses on recent works on foam drainage + including both the advanced theoretical and experimental studies into foam drainage, standard and extended drainage theories with analytical and numerical solutions. Highlights of recent works include the effect of physico-chemical properties of the gas–liquid interface on foam drainage, and the foam-structure related properties governing the channel-and node-dominated drainage regimes. Important results obtained using the foam pressure drop technique which allows a systematic investigation of foam drainage with the constant and varying Plateau border radius are discussed. The free and forced drainage methods have also been the useful experimental techniques for revealing two important drainage regimes by the channels and the nodes. Finally, the influence of the syneresis on the foam stability and destruction is reviewed.