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.     

Surfactant accumulation within the top foam layer due to rupture of external foam films

The analysis of processes taking place in a steady pneumatic (dynamic) foam shows the possibility of different modes of surfactant accumulation within the top layers of bubbles due to rupture of external foam films. An increasing surfactant concentration within the top layers promotes the stabilisation of bubbles and the foam as a whole. Considering the balance of surfactant and water during the bursting of films it is possible to estimate the accumulated surfactant loss caused by a downwards flow through the Plateau borders of the subsurface bubble layer. This effect depends on the particular conditions, especially on the surfactant activity and concentration of the surfactant, water volume fraction in the foam and size of foam bubbles. The process of surfactant accumulation in the top foam bubble layer can be complicated due to the removal of part of the accumulated surfactant through transport with droplets spread out during bubble bursting.     

Bubble formation in a quiescent pool of gold nanoparticle suspension

This paper begins with an extensive review of the formation of gas bubbles, with a particular focus on the dynamics of triple lines, in a pure liquid and progresses into an experimental study of bubble formation on a micrometer-sized nozzle immersed in a quiescent pool of aqueous gold nanofluid. Unlike previous studies of triple line dynamics in a nanofluid under evaporation or boiling conditions, which are mainly caused by the solid surface modification due to particle sedimentation, this work focuses on the roles of nanoparticles suspended in the liquid phase. The experiments are conducted under a wide range of flow rates and nanoparticle concentrations, and many interesting phenomena are revealed. It is observed that nanofluids prevent the spreading of the triple line during bubble formation, i.e. the triple line is pinned somewhere around the middle of the tube wall during the rapid bubble formation stage whereas it spreads to the outer edge of the tube for pure water. A unique ‘stick-slip’ movement of the triple line is also observed for bubbles forming in nanofluids. At a given bubble volume, the radius of the contact line is found to be smaller for higher particle concentrations, but a reverse trend is found for the dynamic bubble contact angle. With the increase of particle concentration, the bubble frequency is raised and the bubble departure volume is decreased. The bubble shape is found to be in a good agreement with the prediction from Young-Laplace equation for given flow rates. The influence of nanoparticles on other detailed characteristics related to bubble growth inside, including the variation of bubble volume expansion rate, the radius of the curvature at the apex, the bubble height and bubble volume, is revealed. It is suggested that the variation of surface tensions and the resultant force balance at the triple line might be responsible for the modified dynamics of the triple line.     

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.     

An introduction to bubble dynamics

The creation, understanding and control of mesoscopic chemical objects are at the core of many areas of chemistry and physics. Their preparation depends on a variety of nucleation and aggregation processes and they are exploitable for practical purposes, including fabrication techniques. At the opposite end, are cavitation phenomena. They also originate from a nucleation event, but result in the formation of a bubble. In recent years, bubbles have ceased to be a problem and have become increasingly more attractive for medical and industrial applications. Our understanding of bubble dynamics has steadily increased and we believe that it is timely to attempt to summarize in simple terms the knowledge accumulated in this area for a chemical audience. In this introduction, we focus on the nature of bubble formation, evolution and collapse. We discuss the macroscopic models that were developed at the beginning of the 20th century and accompany them with the results of more detailed molecular dynamics simulations.     

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.     

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.     

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.     

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.     

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.     

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.     

Formation of droplets and bubbles in a microfluidic T-junction-scaling and mechanism of break-up

This article describes the process of formation of droplets and bubbles in microfluidic T-junction geometries. At low capillary numbers break-up is not dominated by shear stresses: experimental results support the assertion that the dominant contribution to the dynamics of break-up arises from the pressure drop across the emerging droplet or bubble. This pressure drop results from the high resistance to flow of the continuous (carrier) fluid in the thin films that separate the droplet from the walls of the microchannel when the droplet fills almost the entire cross-section of the channel. A simple scaling relation, based on this assertion, predicts the size of droplets and bubbles produced in the T-junctions over a range of rates of flow of the two immiscible phases, the viscosity of the continuous phase, the interfacial tension, and the geometrical dimensions of the device.     

Variation of bubble size distribution in a protein foam fractionation column measured using a capillary probe with photoelectric sensors

Bubble size is used to characterize not only bubble-specific interfacial area but also bubble coalescence in a foam column. The bubble size distributions were obtained in a continuous foam fractionation process for concentrating ovalbumin using a developed photoelectric probe. When the continuous process reached steady state, the bubble size distribution pattern remained stable. Bubble size distribution data above (+1 cm) or below (-1 cm) the bulk liquid-foam interface showed symmetry along the diameter of the column (14 cm ID). The bubble size distribution was affected by the column wall. The nearly constant protein concentration distribution across the column cross-section indicated that the bubble flow distribution approached a flat profile across the column. A log-normal bubble distribution pattern best fit the weighted range of bubbles in the column at column lengths above and below the liquid-foam interface. These observations may prove to be useful in understanding the mechanisms underlying the foam fractionation of proteins.     

A visualization system for observing plastic foaming processes under shear stress

Previous studies offered theories to explain shear-induced bubble nucleation and growth phenomena in plastic foaming processes, but empirical verification was limited due to difficulty in observing these processes in situ under an easily adjustable and uniform shear flow. This study presents a novel visualization system that successfully achieved this goal. The system allows easy control of the critical experimental parameters: applied shear strain, shear strain rate, temperature, pressure, pressure drop rate, plastic material and blowing agent. From a foaming visualization study of polystyrene, it was observed that cell nucleation rate and maximum cell density increased with the applied shear strain, which was due to the decreased local system pressure, detachment and growth of microvoids, and elongation of bubbles. This foaming visualization system provides a direct and effective way to investigate the mechanisms of bubble nucleation and growth under dynamic conditions that simulates industrial plastic foaming processes.     

纳米通道内表面浸润性对气泡的作用

运用分子动力学模拟方法研究了在质量力驱动下不同浸润性壁面纳米通道中气泡的分布及其运动状况, 提出了一种统计纳米通道中气泡运动速度的方法. 结果显示, 在亲水性壁面的纳米通道中, 气泡位于通道中间, 气泡的运动速度接近但小于通道中心流速, 在势能强度较大时, 壁面吸附的分子较多, 气泡也较大, 反之则气泡较小; 对超疏水性壁面, 气泡则位于固壁附近, 两个壁面形成对称的一对气泡, 气泡的运动速度接近但大于边缘速度. 流体总的流动速度随着流体粒子与壁面粒子作用的减弱而增大, 滑移速度则逐渐从负转变为正.     

Rheology of foams and highly concentrated emulsions

We review the state of the art in foam and highly concentrated emulsion rheology, with an emphasis on progress made over the last five years. Since the structures and physico-chemical processes relevant for foams and emulsions are closely analogous, comparing the knowledge recently gained in these two neighboring fields brings fresh insight. In this spirit, we review how the macroscopic mechanical response arises from a coupling between interfacial energy and long range molecular interactions, entropic effects, interfacial rheology, and dynamics at the droplet or bubble scale. We present experiments and models concerning elasticity, osmotic pressure, yielding and flow behavior.     

Gas-liquid mass transfer in rotating perforated-disc contactors

This paper presents a numerical model for predicting the performance of liquid-gas mass transfer in a rotating perforated-disc type contactor. The device consists of a cylindrical section situated between two 45-degree conical sections. A liquid flows downward by gravity while a stream of air moves upward by buoyancy thus forming a counter-current flow situation in the contactor. A gas dissolved in the liquid transfers into air bubbles which are sheared to a tiny size as they rise through the perforations on the rotating disc. Both laminar and turbulent flows are treated. Utilizing the velocity distribution [10,11] and bubble trajectory [12] as the basis, the interphase mass transfer performance of carbon dioxide in the water-air system is numerically determined. It is disclosed that in both laminar and turbulent flow cases, the rate of interphase mass transfer increases significantly with a reduction in bubble size. Rotational speed does not affect mass transfer in laminar flow but causes an exponential mass transfer enhancement in higher turbulent flows. There exists an optimum through-flow rate of the liquid for the best mass transfer performance depending on the initial bubble size and disc speed. Test results [9] provide a qualitative confirmation of the theory.     

The influence of the pore size, the foaming temperature and the viscosity of the continuous phase on the properties of foams produced by membrane foaming

Membrane foaming is a new method of foaming. To enlarge the knowledge about the influencing factors and to know how to vary the structure of the resulting foam, different factors were evaluated. A whey protein solution with 10% protein was foamed as a model solution by means of a tubular cross-flow filtration membrane. The pore size of the membrane was varied. The smaller the pore size, the smaller the bubbles produced. As a result, the foam firmness increases and less drainage was observed when smaller pore sizes were applied.

An important factor is that the added amount of gas must be stabilised as completely as possible in the foam. In order to achieve this, both the process and the product parameters were varied. Raising the foaming temperature increased the quantity of stabilised gas. The whey proteins then diffuse faster to the bubble surfaces and stabilise these by unfolding and networking reactions to prevent the coalescence of the bubbles.

The product parameter viscosity was found to influence the foaming result in such a way that up to a viscosity of 40 mPa s the incorporated gas bubbles are stabilised by the higher viscosity. At viscosities higher than 40 mPa s it is difficult to incorporate in the bubbles, and the foam structure becomes coarser due to increased coalescence at the pores of the membrane. The foam stability is enhanced with higher viscosities.     

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.     

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.