The dynamics of a bubble ensemble in a cavitation field

A system of equations was obtained to describe the dynamics of bubbles in a cavitation cloud taking into account the interaction of pulsating bubbles involved in translational motion. The kinetics of cavitation bubble concentration changes, changes in the compressibility of the liquid, and phase transitions within a cavitation bubble and in the neighboring volume of the liquid were taken into account. The role played by bubble deformation in a cavitation cloud was considered. The Bernoulli pressure effect was shown to be negligible. The interaction of cavitation bubbles was a substantial factor that strongly influenced the dynamics of bubbles. It was suggested that there was at least one more mechanism that reduced sonoluminescence intensity from the multiple-bubble cavitation field, namely, a fairly high efficiency of sonoluminescence quenching could additionally be related to the arrival of a cumulative liquid stream at the central cavitation bubble region, where the concentration of active species was high. The dynamics of bubbles in the cavitation field is not only related to the expansion and compression of cavitation bubbles in the acoustic field, but also governed to a great extent by their interaction, translational motion, deformation, and the influence of cumulative streams penetrating the bubbles.     

Modification of ilmenite surface chemistry for enhancing surfactants adsorption and bubble attachment

In this study, microwave irradiation is used to modify ilmenite surface chemistry to enhance the adsorption of surfactants and the air bubble attachment. The results indicate that microwave irradiation can increase ilmenite flotation recovery by 20%. A positron emission particle tracking technique is used to study the dynamic behaviour of ilmenite particles in a Denver cell. The data shows that the poor flotation recovery of ilmenite is not only due to the reduce probability of ilmenite being captured by air bubbles, but also the short residence time of the particles remaining in the froth phase. The ilmenite particles can be frequently captured by air bubbles, but dropped to the bulk liquid from the froth phase, normally over 15 s. Microwave irradiation changes the ilmenite flow pattern in the Denver cell. The average time of ilmenite remaining in froth phase is increased from 11.5 to 29.1 s.     

Rise of liquids and bubbles in angular capillary tubes

We discuss the rise of a liquid inside an angular capillary tube. It is shown that for a wetting liquid, the height of the rise is (as usually) inversely proportional to the length which characterizes the confinement. The exact laws deduced from energetic considerations are found to be in excellent agreement with the data. We then show how such tubes can be used to prevent bubbles from being trapped. The rising velocity of a bubble is finally discussed, in the particular case of a square tube.     

Nanobubble clusters of dissolved gas in aqueous solutions of electrolyte. II. Theoretical interpretation

A quantitative model of ion-stabilized gas bubbles is suggested. Charging the bubbles by the ions, which are capable of adsorption, and the screening by a cloud of counter-ions, which are less absorptable, is modeled. It is shown that, subject to the charge of bubble, two regimes of such screening can be realized. For low-charged bubbles, the screening is described in the framework of the known linearized Debye-Huckel approach, when the sign of the counter-ion cloud is preserved everywhere in the liquid, whereas at large charge this sign is changed at some distance from the bubble surface. This effect provides the mechanism for the emergence of two types of compound particles having the opposite polarity, which leads to the aggregation of such compound particles into fractal clusters. Based on experimental data, arguments in favor of the existence of the clusters composed of the ion-stabilized bubbles in aqueous electrolyte solutions are advanced. This paper provides theoretical grounds for the experimental results presented in the previous paper (part I) published in this journal.     

Dynamic surface and interfacial tensions of surfactant and polymer solutions

Dynamic surface and interfacial tensions are the most frequently measured non-equilibrium properties of adsorption layers at liquid interfaces. The review presents the theoretical basis of adsorption kinetics, taking into consideration different adsorption mechanisms, and specific experimental conditions, such as liquid flow and interfacial area changes. Analytical solutions, if available, approximations as well as numerical procedures for direct solution of the physical models are presented.Several experimental techniques are discussed frequently used in studies of the dynamic adsorption behaviour of surfactants and polymers at liquid interfaces: drop volume, maximum bubble pressure, and pendent drop technique, drop pressure tensiometry, pulsating bubble and elastic ring method. Experimental results, most of all obtained with different technique on one and the same surfactant system, are then discussed on the basis of current theories.Finally, the role of dynamic interfacial properties in several practical applications is discussed: foam and emulsion film formation and stabilisation, rising of bubbles and drops in a surfactant solution.     

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.     

Asymmetric deformation of bubble shape: cause or effect of vortex-shedding?

Two perpendicular projections of rising bubbles were observed in counter-current downstream diverging flow. Evidently, the bubbles did not enter the boundary layer at the channel wall and a plug liquid flow assumption was acceptable in our experimental equipment. This confirmed that the experiment was appropriate for simulation of bubble rises in a quiescent liquid column. Recent data obtained by a high-speed camera permitted recording over a period of 60 s. Image analysis by a tailor-made program provided a time-series of quantities related to the position, size, and shape of bubbles. In addition to determination of the aspect ratio of the equivalent oblate ellipsoid, deviation from this shape was investigated in respect of the difference between the bubble’s centre of mass and the geometrical centre of bubble projection. Autocorrelation of the data indicated that the bubble inclination oscillated harmonically with a frequency of 5–10 Hz; cross correlation showed that the horizontal shift of the centre of mass, as well as the horizontal velocity, increased with increasing bubble inclination, and the vertical shift of the centre of mass increased with an increases in the absolute value of the bubble inclination. There is no significant phase shift in the oscillation of these quantities. The bulky bottom side of the bubbles is in accordance with the model of bubble oscillation induced by instability of the equilibrium of gravity and surface tension forces. The oscillation frequency dependence on surface forces (Eötvös number) is evident, while viscosity does not play a significant role in low-viscosity liquids. Therefore, vortex-shedding is more likely to be an effect of the oscillation and not its cause.     

Flow field in a downward diverging channel and its application

The flow in a downward divergent channel turns out to be an interesting experimental setup for the observation of upward floating bubbles that appear to be levitating in view of the observer. A more detailed analysis of this flow and its characteristic parameters is necessary for better understanding of this phenomenon. The boundary layer theory was used to derive the velocity field for the experimental setup. The actual flow of a liquid in the presence of a bubble was studied experimentally by measuring the position of the bubble; the data were then statistically processed by an image analysis. Observation of the bubble positions distribution showed that it is reasonable to assume a flat velocity profile of the liquid in the channel and that the bubbles do not tend to move into the boundary layer. In our experiments, volume of the air bubbles floating in water was 200 mm and of that of bubbles floating in aqueous glycerin was 300 mm³. Thus, the experiment used in this work is suitable for reliable determination of instantaneous and average bubble rising velocities as well as of those of horizontal and vertical oscillations.     

Correlation between acoustic cavitation noise and yield enhancement of sonochemical reaction by particle addition

The mechanism of the effect of particle addition on sonochemical reaction is studied through the measurements of frequency spectrum of sound intensity for evaluating the cavitation noise and the absorbance for the liberation of iodine from an aqueous solution of KI as an index of oxidation reaction by ultrasonic irradiation in the presence or absence of alumina particles. As it is expected that both the acoustic noise and a rise in temperature in the liquid irradiated by intense ultrasound will increase with the number of collapsing bubbles, these are supposed to be the best tools for evaluating the relative number of bubbles. In the present investigation, it has been shown that the addition of particles with appropriate amount and size results in an increase in the absorbance when both the acoustic noise and the rise in the liquid temperature due to cavitation bubbles also increase. This suggests that the enhancement in the yield of sonochemical reaction by appropriate particle addition comes from an increase in the number of cavitation bubbles. The existence of particle in liquid provides a nucleation site for cavitation bubble due to its surface roughness, leading to the decrease in the cavitation threshold responsible for the increase in the number of bubbles when the liquid is irradiated by ultrasound. Thus, from the present investigation, it is clarified that the particle addition has a potential to enhance the yield in the sonochemical reaction.     

Critical Phenomena in the Clouding Behavior of Nonionic Surfactants Induced by Additives

Effects of anionic surfactants, hydrotropes, and electrolytes on the cloud point of Triton X-100 have been studied over six decades of additives concentrations. A comprehensive look at all the data reveals significant new learnings. While anionic surfactants and hydrotropes affect the cloud point of non-ionics at ultra low (monomeric) concentrations, electrolytes exhibit a minimum critical concentration above which they cast their effect. This suggests that the former work by modifying the surface charge of non-ionic micelles (i.e., by affecting the solute), whereas the latter work by modifying the properties of the bulk medium. Above their respective critical concentrations, salting-out electrolytes decrease the cloud point while salting-in electrolytes increase it, the trends being linear with additive concentration in either case. The magnitude of the effect of anionic surfactants and hydrotropes increases gradually with increasing concentration till their respective cmc's are reached and then there is a sharp rise in the cloud point. Copyright 1999 Academic Press.     

Imaging of copper oxygenation reactions in a bubble flow

Reactions of gases with liquids play a crucial role in the production of many bulk chemicals. Often, the gas is bubbled into the chosen reactor. Most of the processes at the gas–liquid interface of the bubbles and in their tails are not fully understood and warrant further investigation. For this purpose, NMR imaging or Magnetic Resonance Imaging has been applied to visualize some of the processes in the bubble tail. To generate sufficient contrast, a magnetogenic gas–liquid reaction associated with a change of magnetic state, from diamagnetic to paramagnetic, was employed. In this work, a copper(I)‐based compound was oxidized to copper(II) to exploit relaxation contrast. To match the speed of the rising bubbles to the acquisition time of the spin‐echo imaging sequence, polyethylene glycol was added to increase the viscosity of the reacting solution. Images of the oxygen ingress into a static solution as well as of oxygen bubbles rising in the solution are presented. In both cases, changes in magnetism were observed, which reported the hydrodynamic processes.     

Anomalous Capillary Pressure, Stress, and Stability of Solids-Coated Bubbles

A two-dimensional theoretical model for solids-coated, or "armored," bubbles shows how the armor can support a liquid-vapor interface of reduced or reversed curvature between the particles, giving the bubble zero or even negative capillary pressure. The inward capillary force pulling the particles into the center of the bubble are balanced by large contact forces between the particles in the armor. Thus the bubble is stabilized against dissolution of gas into surrounding liquid, which otherwise would rapidly collapse the bubble. The stresses between particles in such cases are large and could drive sintering of the particles into a rigid framework. Earlier work on solids-coated bubbles assumed that solids can freely enter or leave the bubble surface as the bubble shrinks or expands. In such a case, armored bubbles would not be stable to gas dissolution into surrounding liquid. A new free-energy analysis, however, suggests that a shrunken bubble would not spontaneously expel a solid particle from its armor to relieve stress and allow the bubble to shrink further. Implications and limitations of the theory are discussed. Copyright 1999 Academic Press.     

Acoustic emission spectra from 515 kHz cavitation in aqueous solutions containing surface-active solutes

The effect of adding surface-active solutes to water being insonated at 515 kHz has been investigated by monitoring the acoustic emission from the solutions. At low concentrations (<3 mM), sodium dodecyl sulfate causes marked changes to the acoustic emission spectrum which can be interpreted in terms of preventing bubble coalescence and declustering of bubbles within a cavitating bubble cloud. By conducting experiments in the presence of background electrolytes and also using non-ionic surfactants, the importance of electrostatic effects has been revealed. The results provide further mechanistic evidence for the interpretation of the effect of surface-active solutes on acoustic cavitation and hence on the mechanism of sonochemistry. The work will be valuable to many researchers in allowing them to optimize reaction and process conditions in sonochemical systems.     

Bubble entrainment with drops

The study reported here was undertaken because recent research on nucleate boiling has implicated vapor entrainment by drops as a mechanism for vapor bubble nucleation. The mechanism has been called secondary nucleation. The purpose of this research was to determine the behavior of entrained air bubbles when a drop of liquid strikes a liquid surface. A liquid drop striking the surface of a pool of the same liquid was found usually to entrain large numbers of small air bubbles. Some of these bubbles are frequently carried rapidly deep into the pool by a vortex ring but many can be deposited in a trail or left floating on the surface. Air bubble entrainment was observed with water and several organic liquids and some differences were noted. Drops with diameters from 200 μm to 4 mm were studied. Sometimes hundreds of bubbles were entrained some with diameters up to 100 μm. These results lend support to the secondary nucleation hypothesis and indicate further research on vapor bubble entrainment under conditions more typical of boiling would be appropriate.     

The effect of surface-active solutes on bubble coalescence in the presence of ultrasound

The sonication of an aqueous solution generates cavitation bubbles, which may coalesce and produce larger bubbles. This paper examines the effect of surface-active solutes on such bubble coalescence in an ultrasonic field. A novel capillary system has been designed to measure the change in the total volume resulting from the sonication of aqueous solutions with 515 kHz ultrasound pulses. This volume change reflects the total volume of larger gas bubbles generated by the coalescence of cavitation bubbles during the sonication process. The total volume of bubbles generated is reduced when surface-active solutes are present. We have proposed that this decrease in the total bubble volume results from the inhibition of bubble coalescence brought about by the surface-active solutes. The observed results revealed similarities with bubble coalescence data reported in the literature in the absence of ultrasound. It was found that for uncharged and zwitterionic surface-active solutes, the extent of bubble coalescence is affected by the surface activity of the solutes. The addition of 0.1 M NaCl to such solutes had no effect on the extent of bubble coalescence. Conversely, for charged surface-active solutes, the extent of bubble coalescence appears to be dominated by electrostatic effects. The addition of 0.1 M NaCl to charged surfactant solutions was observed to increase the total bubble volume close to that of the zwitterionic surfactant. This suggests the involvement of electrostatic interactions between cavitation bubbles in the presence of charged surfactants in the solution.     

Electrokinetic potentials at the gas-aqueous interface by spinning cylinder electrophoresis

The natural buoyancy of gas bubbles has hampered conventional electrokinetic methods of evaluating charge at the gas-liquid interface. In this study, bubbles are held by centripetal force at the centre of a horizontal, rotating cylinder filled completely with liquid. Migration of the bubble along the axis of the cylinder can be achieved by applying a gravity force or an electrophoretic force. An expression for the drag coefficient has been developed and used to calculate surface charge densities and electrokinetic potentials. In the presence of potassium chloride, anionic and non-ionic surfactants, the electrokinetic potentials were negative (～2–5 mV) at the air-aqueous interface. A cationic surfactant rendered the zeta potential positive. A knowledge of the air-aqueous interfacial rheology is desirable if the drag coefficient, and consequently the zeta potential, at all types of gas-liquid interfaces is to be evaluated.     

Modeling the cycles of growth and detachment of bubbles in carbonated beverages

In this paper, a model for the formation of bubbles in carbonated beverages is presented. It has previously been shown that bubbles form from cellulose fibers within such beverages and the passage of such bubbles from the fibers to the liquid surface has been modeled. A model is thus presented here that considers the process of formation, which is governed by diffusion through the fiber and bubble surfaces. The model comprises two stages, growth and detachment, and it is shown here that both play an important role. The latter process is found to occur over a much shorter time scale than the former, enabling the models to be partially decoupled. The total number of bubbles released from individual fibers over time is found to be approximated well by an exponential relationship, and the parameters in this relationship are presented for a range of different detachment angles and fiber sizes. It is found that bubble formation is promoted in narrow, long tubes, but that the time constant is solely determined by the rate of diffusion across the liquid surface. The surface tension is found to have minimal influence on the number of bubbles produced.     

The pressure drop along rectangular microchannels containing bubbles

This paper derives the difference in pressure between the beginning and the end of a rectangular microchannel through which a flowing liquid (water, with or without surfactant, and mixtures of water and glycerol) carries bubbles that contact all four walls of the channel. It uses an indirect method to derive the pressure in the channel. The pressure drop depends predominantly on the number of bubbles in the channel at both low and high concentrations of surfactant. At intermediate concentrations of surfactant, if the channel contains bubbles (of the same or different lengths), the total, aggregated length of the bubbles in the channel is the dominant contributor to the pressure drop. The difference between these two cases stems from increased flow of liquid through the "gutters"-the regions of the system bounded by the curved body of the bubble and the corners of the channel-in the presence of intermediate concentrations of surfactant. This paper presents a systematic and quantitative investigation of the influence of surfactants on the flow of fluids in microchannels containing bubbles. It derives the contributions to the overall pressure drop from three regions of the channel: (i) the slugs of liquid between the bubbles (and separated from the bubbles), in which liquid flows as though no bubbles were present; (ii) the gutters along the corners of the microchannels; and (iii) the curved caps at the ends of the bubble.     

Microstructure, morphology, and lifetime of armored bubbles exposed to surfactants

We report the behavior of particle-stabilized bubbles (armored bubbles) when exposed to various classes and concentrations of surfactants. The bubbles are nonspherical, which is a signature of the jamming of the particles on the interface, and are stable to dissolution prior to the addition of surfactant. Armored bubbles exposed to surfactants, dissolve, and exhibit distinct morphological, microstructural, and lifetime changes, which correlate with the concentration of surfactant employed. For low concentrations of surfactant, an armored bubble remains nonspherical while dissolving, whereas for concentrations close to and above the surfactant cmc a bubble reverts to a spherical shape before dissolving. We propose a microstructural interpretation, supported by our experimental observations of particle dynamics on the bubble interface, that recognizes the role of interfacial jamming and stresses in particle-stabilization and surfactant-mediated destabilization of armored bubbles.     

On the influence of the surfactant''s polar group on the local and terminal velocities of bubbles

The local and the terminal velocities, the size and the degree of bubbles’ shape deformations were determined as a function of distance from the position of the bubble formation (capillary orifice) in solutions of n-octyltrimethylammonium bromide, n-octyldimethylphosphine oxide, n-octyl-β-D-glucopyranoside and n-octanoic acid.

These surface-active compounds have different polar groups but an identical hydrocarbon chain (C8) in the molecule. The motion of the bubbles was monitored and recorded using a stroboscopic illumination, a CCD camera, and a JVC professional video. The recorded bubble images were analyzed by the image analysis software. The bubbles accelerated rapidly and their shape was deformed immediately after detachment from the capillary. The extent of the bubbles’ shape deformation (ratio of horizontal and vertical diameters) was 1.5 in distilled water and dropped rapidly down to a level of ca. 1.05–1.03 with increasing surfactant concentration. After the acceleration period the bubbles either attained a constant value of the terminal velocity (distilled water and high concentrations of the solutions), or a maximum in the velocity profiles was observed (low concentrations). The values of the terminal velocity diminished drastically with increasing concentration, from the value of 35 cm/s in water down to about 15 cm/s, while the bubble diameter decreased by ca. 10% only. The surfactant adsorption at the surface of the bubbles was evaluated and the minimum adsorption coverages required to immobilize the bubbles’ surface were determined. It was found that this minimum adsorption coverage was ca. 4% for n-octyldimethylphosphine oxide, n-octyl-β-D-glucopyranoside, n-octanoic acid and 25% for n-octyltrimethylammonium bromide. The difference in the adsorption coverage together with the surfactants’ surface activities indicate that it is mainly the adsorption kinetics of the surfactants that governs the fluidity of interfaces of the rising bubbles.