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.     

Effect of Xanthan Gum on the Performance of Aqueous Film-Forming Foam

Solution properties of aqueous film-forming foam (AFFF) formulations containing different xanthan gum contents were investigated first by varying the mass fraction of xanthan gum in the range of 0.1–0.5%. Foam properties and fire-extinguishing performance of the AFFF formulations were then evaluated. Results indicated that xanthan gum content slightly affected surface tension of foam solutions. However, xanthan gum significantly affected viscosity of AFFF concentrates. Foaming of the AFFF formulations was hardly affected by xanthan gum, but foam stability of the compounds was obviously enhanced with the addition of xanthan gum. Optimal xanthan gum content was determined as 0.3%, which resulted in the shortest 90% control time and fire extinguishment time. Burnback time of foams increased with the addition of xanthan gum because of the enhanced foam stability.     

Effects of denaturation on soy protein-xanthan interactions: comparison of a whipping-rheological and a bubbling method

The effect of xanthan on foam formation and on physical mechanisms of destabilization involved in the breakdown of foams made from native and denatured soy protein at neutral pH was studied by a bubbling and a whipping-rheological method. Parameters describing foam formation and destabilization by liquid drainage and disproportionation obtained by the two methods showed that the addition of xanthan was accompanied by delayed rates of drainage and disproportionation and reduced foam height decay (collapse). Drainage showed the largest reduction, mainly because of the increased bulk viscosity. In the absence of xanthan, protein denaturation enhanced foam formation and stability against drainage and disproportionation, but increased the collapse of foams. In the presence of xanthan, differences in foam formation and drainage/disproportionation stability between native and denatured soy protein were greatly reduced. However, differences in foam collapse were greatly enhanced. The increased stability of foams in the presence of xanthan could not be explained purely in terms of increased aqueous phase viscosity. More specific interactions of xanthan and soy proteins at the air-water interface influencing the surface rheology, and the protein composition and aggregation, are involved.     

Maximum disjoining pressure in protein stabilized concentrated oil-in-water emulsions

A model for the prediction of the equilibrium profile of film thickness and continuous phase liquid holdup profile in a concentrated oil-in-water (O/W) emulsion is proposed. This model is employed to infer the maximum disjoining pressure in a concentrated corn oil-in-water emulsion stabilized by bovine serum albumin (BSA) from the experimental measurements of different proportions of oil, polyhedral O/W foam, and aqueous layers at different centrifugal accelerations. The inferred maximum disjoining pressures were found to be higher at higher concentrations of BSA, lower ionic strengths as well as at pH values farther away from pI. The predicted variations of disjoining pressure with film thickness for a concentrated O/W emulsion stabilized by BSA exhibited two maxima due to steric and electrostatic interactions, respectively. The experimental maximum disjoining pressures for toluene-in-water emulsion stabilized by BSA were found to be about two to three times the predicted maxima due to steric interactions but were two to three orders of magnitude higher than the maxima due to electrostatic interactions, thus indicating that steric interaction is the dominant stabilizing mechanism. The discrepancy between the experimental and predicted maximum disjoining pressures is believed to be mainly due to lack of information with regard to the thickness of the adsorbed protein layer at the oil—water interface.     

Influence of polymers on dust-related foam properties of sodium dodecyl benzene sulfonate with Foamscan

Foamability, liquid holdup, and foam appearance are key factors that determine dust control efficiencies. As the foam production method of the FoamScan instrument is similar to foaming device used for dust control, and its measurement means can satisfy the requirements of precise measuring, the FoamScan technology is adopted to explore the influence of xanthan gum (XG) and partial hydrolytic polyacrylamide (HPAM) on dust-related foam properties of sodium dodecyl benzene sulfonate (SDBS). It was found that with the increase of the polymer mass fraction, the liquid volume in the foam gradually increased. Additionally, the foaming time t₂₀₀ of the foaming agent decreased at first, then remained almost constant for both polymers, which indicated that the foamability and liquid holdup were enhanced by the addition of polymers into SDBS. In addition, the efficiencies of XG are higher than that of HPAM. The image analysis using the CSA software revealed that the mean radius formed by XG was smaller than that by HPAM and the number of bubbles was larger with XG than with HPAM. Thus, the XG foam has more area to contact with dust and could control dust better. The highly branched molecular structure and hydrogen bonds formed by XG played important roles in dust-related foam properties.     

On the Origin of Foam Stability: Understanding from Viscoelasticity of Foaming Solutions and Liquid Films

The foam stability (drainage half-life) of α-olefin sulfonate (AOS) with partially hydrolyzed polyacrylamide (HPAM) or xanthan gum (XG) solution was evaluated by the Warring Blender method. With the increase of polymer (HPAM or XG) concentration, foam stability of the surfactant–polymer complexes increased, and the drainage half-life of AOS-XG foam was higher than that of AOS-HPAM foam at the same polymer and surfactant concentration. With the addition of polymer (HPAM or XG), the viscoelasticity of bulk solution and the liquid film were enhanced. The viscoelasticity of AOS-XG bulk solution and liquid film were both higher than that of AOS-HPAM counterparts.      

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.     

Drainage of aqueous film-forming foam stabilized by different foam stabilizers

The present study focuses on the drainage property of aqueous film-forming foam stabilized by different types and concentrations of foam stabilizers. Aqueous film-forming foam (AFFF) formulation concentrates are prepared based on the main components of fluorocarbon surfactant, hydrocarbon surfactant, and organic solvents. Carboxymethylcellulose sodium (CS), xanthan gum (XG), and lauryl alcohol (LA) are selected as foam stabilizers of the AFFF. Surface tension, viscosity, and foamability tests of the AFFF solutions are conducted to evaluate the effect of foam stabilizers on the properties of AFFF solutions. Particularly, an apparatus is established based on the law of connected vessel in order to obtain the instantaneous mass of liquids drained from foams. The drainage features of the AFFFs containing different foam stabilizers are analyzed and compared with each other. The results indicate that AFFF drainage is significantly affected by the type and the concentration of foam stabilizers. The addition of CS and XG to AFFF results in a deceleration of foam drainage, while foam drainage is accelerated by the addition of LA. The variations of surface tension, viscosity, and liquid fraction of foams are the main reasons for the varying foam drainage rate. This study provides a direct connection between chemical components and fundamental properties of AFFF.     

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.     

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.     

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.     

Experimental Study on Stability and Improving Sweep Efficiency with Microfoam in Heterogeneous Porous Media

In this paper, we attempted to prepare microfoam by using a sandpack filled with glass beads with co-flowing gas and foaming solution, the microfoam stability and effectiveness in improving profile control capacity at micromodel and pore media were evaluated by micromodel tests and double-core experiments. The results of micromodel tests showed that microfoam stability was increased with increasing xanthan gum concentration due to a higher solution viscosity and viscoelasticity of liquid film. The xanthan gum-stabilized microfoam had a longer propagation distance through the low permeable region of heterogeneous micromodel at time of breakthrough than common microfoam, the optimum performance of microfoam for fluid diversion was multiple bubble trapping and mobilization rather than lamella division. According to the results of double-core experiments, the microfoam could plug the high permeability sandpack and improve the sweep efficiency in the low permeability sandpack, which could improve the water injection profile of porous media effectively. The increase in profile control effects had a good correspondence with the increase of xanthan gum concentration. The presented results were useful in understanding and designing microfoam injection in reservoirs for enhanced oil recovery.     

The zeta-potential of the endogenous particles of a wine of Champagne in relation to the foaming behaviour

It was shown that the endogenous particles of the champagnes influence the lifetime, and not the maximum expansion of their evanescent foam (Food Hydrocolloids (1999) 12, 217-226). Actually, champagnes are electrolytic solutions with pH 3 and ionic strength equal to 0.02 mol/l in which bentonites, diatomites, and yeast cells are the more numerous colloids and particles present. In this context, we have investigated the electrophoretic properties of these particles to determine whether they can electrostatically interact with the foam bubbles. Results are that in model alcoholic solutions of proteins at same pH and ionic strength as the champagne, the zeta-potential was not vanishing whereas it dropped down to zero in wines. The zeta-potential of the particles does not vanish either when they are suspended in nanofiltered wines on molecular weight cut-off membrane (porosity=200-300 Da) or when the wines are basified upon addition of sodium hydroxide. This particular behaviour was tentatively assigned to the adsorption of some endogenous organic cationic ions on the particle surfaces, which screened out their electrostatic charge. The possible candidates are discussed.     

Effect of protein aggregates on foaming properties of β-lactoglobulin

Our paper aims at determining the respective part of protein aggregates and non-aggregated proteins in the foam formation and stability of β-lactoglobulin. We report results on fractal aggregates formed at neutral pH and strong ionic strength (aggregates size from 30 to 190 nm). Pure aggregates and mixtures of non-aggregated/aggregated proteins at varying ratios were used. The capacity of aggregates to form and stabilize foams has been studied in relation with their ability to absorb at air/water interfaces. Our results show that protein aggregates are not able by themselves to improve the foaming properties but participate to a better foam stabilization in the presence of non-aggregated proteins. Non-aggregated proteins appear to be necessary to produce stable foams. We have shown that the amount and the size of aggregates had an influence on the drainage rate.     

Restoration of protein foam stability through electrostatic propylene glycol alginate-mediated protein–protein interactions

The action of propylene glycol alginate in the enhancement of foam stability of a destabilised Tween 20/bovine serum albumin mixed system was evaluated. A significant increase in the foam stability was observed in the presence of low concentrations of propylene glycol alginate. A pseudo-plateau level of foam stability was obtained in the presence of approximately 0.8 μg/ml propylene glycol alginate in the solution used to form the foam. Foam stability enhancement due to bulk viscosity changes and surface effects were elucidated. The increase in foam stability was investigated by reference to the properties of thin liquid films and the macroscopic interface of test solutions. Propylene glycol alginate was found to slow the rate of thin film drainage, increase the equilibrium thickness of the films, slow the lateral diffusion of a fluorescent probe molecule located in the adsorbed layer and increase the elasticity of the interface. Data are consistent with propylene glycol alginate-induced crosslinking of protein in the adsorbed layer. This polysaccharide presents a means for controlling protein foam stability.     

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.     

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.     

Batch foam fractionation of kudzu (Pueraria lobata) vine retting solution

The aqueous protein solution from kudzu(Pueraria lobata) vine retting broth, without the addition of other surfactants, was foam-fractionated in a vertical tubular column with multiple sampling ports. Time-varying trajectories of the total protein levels were determined to describe the protein behavior at six positions along the 1-m column. The lowest two trajectories of this batch process represented a loss of proteins from the bulk liquid and tended to merge and decay together in time; the other trajectories displayed a gain in proteins in the foam phase. These upper column port protein concentration trajectories generally increased in time up to 45 min, followed by a decrease, reflecting the removal of proteins from the column ports. The foam became dryer as it passed up the column to the top port. The protein concentration was about 5–8×higher in the top port foam than in the initial bulk solution, mainly as a result of liquid drainage from the foam along the column axis. This concentration increase in the collected foam was dependent on the initial pH of the bulk solution. The mol-wt profile of the proteins in the concentrated foam effluent was determined by one-dimensional gel electrophoresis. An analysis of the gel electropherograms indicated that the most abundant proteins could be cellulases and pectinases.