Experimental and theoretical investigation of CO2 and air bubble rising velocity through kerosene and distilled water in bubble column

This paper concerns with developing of parameters which influence terminal velocities of air and CO₂ bubbles in distilled water and kerosene pools. The objective of this study is to validate and correct the formulas that were developed by previous investigators for prediction of terminal velocities. The investigation revealed that the terminal velocity of a single rigid spherical bubble in Newtonian fluids can be developed by balancing of mechanical forces acting on the bubble. However, for large bubbles, because of deforming of the bubble which is a result of interfacial tension, the effect of surface tension should be considered in the terminal velocity prediction formula. By using PSO algorithm and plotting experimental data of terminal velocity against the size of gas bubbles, the suitable equation for each of systems was chosen. Results showed that Jamialahmadi model is more practical for terminal velocity prediction. Jamialahmadi model requires a modification to be utilized for air-kerosene, CO₂-kerosene, air- distilled water and CO₂-distilled water systems. The developed PSO algorithm model is accurate for prediction of experimental data with an average R² value of 0.9722.     

The detachment of particles from coalescing bubble pairs

This paper is concerned with the detachment of particles from coalescing bubble pairs. Two bubbles were generated at adjacent capillaries and coated with hydrophobic glass particles of mean diameter 66 μm. The bubbles were then positioned next to each other until the thin liquid film between them ruptured. The particles that dropped from the bubble surface during the coalescence process were collected and measured. The coalescence process was very vigorous and observations showed that particles detached from the bubble surfaces as a result of the oscillations caused by coalescence. The attached particles themselves and, to some extent the presence of the surfactant had a damping affect on the bubble oscillation, which played a decisive role on the particle detachment phenomena. The behaviour of particles on the surfaces of the bubbles during coalescence was described, and implications of results for the flotation process were discussed.     

A theoretical study on surfactant adsorption kinetics: effect of bubble shape on dynamic surface tension

A planar or spherical fluid-liquid interface was commonly assumed on studying the surfactant adsorption kinetics for a pendant bubble in surfactant solutions. However, the shape of a pendant bubble deviates from a sphere unless the bubble's capillary constant is close to zero. Up to date, the literature has no report about the shape effect on the relaxation of surface tension due to the shape difference between a pendant bubble and a sphere. The dynamic surface tension (DST), based on the actual shape of a pendant bubble with a needle, of the diffusion-controlled process is simulated using a time-dependent finite element method in this work. The shape effect and the existence of a needle on DST are investigated. This numerical simulation resolves also the time-dependent bulk surfactant concentration. The depth of solution needed to satisfy the classical Ward-Tordai infinite-solution assumption was also studied. For a diffusion-controlled adsorption process, bubble shape and needle size are two major factors affecting the DST. The existence of a needle accelerates the bulk diffusion for a small bubble; however, the shape of a large pendant bubble decelerates the bulk diffusion. An example using this method on the DST data of C12E4 is illustrated at the end of this work.     

Dynamics of mixed protein–surfactant layers adsorbed at the water/air and water/oil interface

Drop and bubble shape tensiometry experiments are performed at the water/air and water/hexane interfaces in order to get more information about the differences in the adsorption layer structure of mixed protein/surfactant systems. For mixtures of β-lactoglobulin and sodium dodecyl sulphate the adsorption at the water/air interface is essentially a competitive process between protein/surfactant complexes and free surfactant molecules, while the water/oil interface is essentially covered by the complexes.     

Deuterium N.M.R. of the n-octyl-β-D-glucopyranoside-solvent liquid-crystalline systems

Deuterium quadrupolar splittings were measured as a function of concentration and temperature for deuteriated water, benzene-d₆, toluene-d₈ and acetonitrile-d₃, dissolved in n-octyl-β-D-glucopyranoside (OG). The splittings and temperature dependence are larger for the apolar solvents. Water forms rather rigid structures with OG as indicated by its large linewidths. OG can accommodate both water and benzene (or toluene) together and the results for such systems are also reported. Some additional results for the hydroxyl deuteriated OG and for a system containing a lower homologue of OG are reported.     

Bubble Motion in Aqueous Surfactant Solutions

This paper presents the results of numerical simulations of the unsteady motion of a single bubble that is released or injected into water. The governing equations are solved with a finite difference method using an adaptive boundary-fitted coordinate system. Results are shown for bubbles in the size range 0.72 to 1.5 mm. The effects of surfactants on the motion and shape of the bubble are investigated. When the surfactant concentration is sufficiently small, the bubble attains a maximum velocity before slowing down to its steady-state velocity. Although the steady-state velocity is nearly independent of surfactant concentration, the maximum velocity can be comparable to steady-state velocity in pure water. This behavior is observed even when the bubble is allowed to equilibrate prior to releasing it. The formation of an immobilized surfactant cap is observed soon after the bubble is released. The effect of the injection velocity on the bubble velocity profile is investigated. The effects of the sorption rate constants and the bulk surfactant concentration on the behavior of the bubble are investigated. The feasibility of using experimental measurements and simulations of unsteady bubble velocities to estimate sorption rate constants is discussed. Copyright 2000 Academic Press.     

Force of a gas bubble on a foreign particle in front of a freezing interface

We monitored the formation and development of a single gas bubble on the surface of a spherical particle of size 1.676 mm under unidirectional freezing and thawing (4.6-5.0 microm/s) and for the first time quantitatively estimated the force exerted on this particle by measuring the deformation of an attached elastic stick. The bubble would nucleate and grow on the particle surface closest to the ice front, while the force curve for a freezing-thawing cycle presented a hysteresis characteristic. This force was much greater than in the case without a bubble, and hence it dominated the engulfment process in the present freezing tests. The bubble force increased with increasing bubble size and was shown to be mainly attributable to the elastic force by the deformed bubble shape. Comments were made on the need to incorporate the role of bubbles in predicting the critical velocity to freeze a suspension with high dissolved gas content.     

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.     

Comments on "Bubble motion in aqueous surfactant solutions"

The numerical simulations of bubble motion in dilute surfactant solutions reported previously by two of the authors contained a serious numerical inaccuracy. In agreement with experiments, single bubbles released from rest were predicted to reach a maximum speed before slowing to a terminal speed. However, subsequent experiments demonstrated that, in the simulations, the bubbles reached their terminal speed too quickly. The source of the discrepancy is an inaccuracy associated with the numerical algorithm used to solve the surfactant transport equation on the bubble surface. After correcting the problem, the simulations agree much better with the experiments.     

Adsorption kinetics of some carotenoids at the oil/water interface

The kinetic analysis of the adsorption of two carotenoids (i.e., ethyl ester of β-apo-8′-carotenoic acid and β-carotene, all trans-isomers) from n-hexane solutions at the oil/water interface is presented for several carotenoid concentrations in the oil phase. A new kinetic approach is developed and it addresses the diffusion adsorption associated with a reversible interfacial reaction, which describes the reorientation of surfactant molecules between two conformations. This approach leads to a general analytical expression that contains four physical parameters and describes with high accuracy the experimental dynamic interfacial tensions for the two carotenoids, which independently adsorb from n-hexane phase to the n-hexane/water interface. The calculations give the characteristic times for the carotenoid adsorption at the oil/water interface in terms of diffusion relaxation and kinetic relaxation times. The results explain the long time effects on the adsorption of these carotenoids at the oil/water interface. The data are in substantial agreement with the molecular structure of these carotenoids and with the earlier data recorded for cholesterol adsorption at the n-heptane/water interface. Based on these findings, we propose a molecular mechanism for the interfacial transformation of carotenoid molecules at a hydrophobic/hydrophilic interface.     

Counterion Nature and Alkylammonium Halide Adsorption Thermodynamics

Two surfactants were synthesized by reacting hydrogen halides (hydrogen chloride and hydrogen bromide) with 1-dodecylamine. The resultant cationic surfactants, 1-dodecylammonium chloride (DDAC) and 1-dodecylammonium bromide (DDAB), were characterized by NMR spectrometry and FTIR spectroscopy and data related to their adsorption at the fluid liquid/gas interface were obtained employing bubble surface tensiometry, in pure water and in HCl 0.1 M. Data did not fit well to Langmuir isotherm but Frumkin isotherm did adequately describe to process of adsorption. Adsorption isotherms, as well as data related to critical micelle concentration, CMC, indicated that in HCl 0.1 M, the presence of electrolytes and a common ion to DDAC decreased chloride solvation, changing surface packing and adsorption profile for this surfactant.     

Gas Holdups of Small and Large Bubbles in a Large-scale Bubble Column with Elevated Pressure

Gas holdups of large bubbles and small bubbles were measured by means of dynamic gas disengagement approach in the pressured bubble column with a diameter of 0. 3 m and a height of 6.6 m. The effects of su-perficial gas velocity, liquid surface tension, liquid viscosity and system pressure on gas holdups of small bub-bles and large bubbles were investigated. The holdup of large bubbles increases and the holdup of small bub-bles decreases with an increase of liquid viscosity. Meanwhile, the holdup of large bubbles decreases with in-creasing the system pressure. A correlation for the holdup of small bubbles was obtained from the experimen-tal data.     

Investigation into the Formation of Bubbles in Capillary Electrochromatography

The formation of bubbles in capillary electrochromatography (CEC) is well documented: possible origins include Joule heating and variations in EOF velocity on passing from the stationary phase through the frit and into the open tube. Methods for the prevention of bubble formation are discussed which are confirmed by experimental results. Using frit lengths varying from 1 mm to 6 mm it is shown how frit length is directly related to the likelihood of bubble formation and how this is affected by applied voltage. It is shown that the change in applied voltage across a capillary affects the formation of bubbles and also that rebonding octadecylsilane (ODS) onto the silica frit after formation of the frit can minimize the formation of bubbles and how this effects the chromatography. A method is also described for increasing the robustness of silica capillaries using a column coupler along with modifications made to conventional capillary electrophoresis equipment to cater for CEC.     

Viscometric study of the sodium hyaluronate-sodium chloride-alkyl-(n)-ammonium surfactant system

Viscosity and rheological properties of the system sodium hyaluronate (NaHA)-NaCl-alkyl-(n)-ammonium surfactant were studied. The system with monomeric (n=1) surfactant dodecyltrimethylammonium bromide DTAB separated into two phases below the 200 mM NaCl concentration. At high NaCl concentration (>0.3 M), the hyaluronate–surfactant interaction is screened. At low NaCl concentration (0.2 M), the hyaluronate–surfactant interaction appears at higher concentration of micelles. In the system with dimeric surfactant (n=2) alkanediyl-,ω-bis(dimethyldodecylammonium bromide) referred to as 12-s-12, the hyaluronate–surfactant interaction was observed at low surfactant concentration, opposite to the case of NaHA-NaCl-monomeric surfactant. In certain range of surfactant concentration, viscosity of the system can be fairly good described by the empirical Jones–Dole equation. However, the fit fails at high surfactant concentration. From the rheological measurements follows that NaHA aqueous solution shows non-Newtonian behaviour. When adding NaCl and shearing, viscosity increases as a result of affecting the ion atmosphere which surrounds micelles, by shearing. The same effect was observed in the system NaHA-NaCl-ammonium surfactant (both monomeric and dimeric). The hyaluronate–surfactant interaction is assumed at low shearing. The influence of surfactant structure on viscosity at the same NaCl concentration shows that the increasing value of the carbon number in spacer of dimeric surfactant increases viscosity and stretches the hyaluronate coils.     

Adsorption of heavy metal ions from aqueous solution by polyrhodanine-encapsulated magnetic nanoparticles

The influence of salt concentration on the terminal velocities of gravity-driven single bubbles sliding along an inclined glass wall has been investigated, in an effort to establish whether surface forces acting between the wall and the bubble influence the latter's mobility. A simple sliding bubble apparatus was employed to measure the terminal velocities of air bubbles with radii ranging from 0.3 to 1.5 mm sliding along the interior wall of an inclined Pyrex glass cylinder with inclination angles between 0.6 and 40.1°. Experiments were performed in pure water, 10 mM and 100 mM KCl solutions. We compared our experimental results with a theory by Hodges et al. which considers hydrodynamic forces only, and with a theory developed by two of us which considers surface forces to play a significant role. Our experimental results demonstrate that the terminal velocity of the bubble not only varies with the angle of inclination and the bubble size but also with the salt concentration, particularly at low inclination angles of ～1-5°, indicating that double-layer forces between the bubble and the wall influence the sliding behavior. This is the first demonstration that terminal velocities of sliding bubbles are affected by disjoining pressure.     

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.     

Coalescence of bubbles covered by particles

The interaction between two bubbles coated with glass particles in the presence of a cationic surfactant (cetyltrimethylammonium bromide, CTAB) was studied experimentally. The time taken for two bubbles to coalesce was determined as a function of the fractional coverage of the surface by particles. The results suggested that the coalescence time increases with the bubble surface coverage. Interestingly, it was found that although the particles did not have any physical role in film rupture at low surface coverage, they still added resistance to film drainage. For particle-loaded bubbles, the initial resistance was due to the lateral capillary interactions between particles on the interface, which hold the particles firmly together. The coalescence dynamics of bubbles was also observed to be affected by the presence of attached particles.     

Dynamics of surfactant sorption at the air/water interface: continuous-flow tensiometry

Dynamic interfacial tensiometry, gauged by axisymmetric drop shape analysis of static drops or bubbles, provides useful information on surfactant adsorption kinetics. However, the traditional pendant-drop methodology is not readily amenable to the study of desorption kinetics. Thus, the question of sorption reversibility is difficult to assess by this technique. We extend classical pendant/sessile drop dynamic tensiometry by immersing a sessile bubble in a continuously mixed optical cell. Ideal-mixed conditions are established by stirring and by constant flow through the cell. Aqueous surface-active-agent solutions are either supplied to the cell (loading) or removed from the cell by flushing with water (washout), thereby allowing study of both adsorption and desorption kinetics. Well-mixed conditions and elimination of any mass transfer resistance permit direct identification of sorption kinetic barriers to and from the external aqueous phase with time constants longer than the optical-cell residence time. The monodisperse nonionic surfactant ethoxy dodecyl alcohol (C(12)E(5)), along with cationic cetyltrimethyl ammonium bromide (CTAB) in the presence of added salt, adsorbs and desorbs instantaneously at the air/water interface. In these cases, the experimentally observed dynamic-tension curves follow the local-equilibrium model precisely for both loading and washout. Accordingly, these surfactants below their critical micelle concentrations (CMC) exhibit no detectable sorption-activation barriers on time scales of order a min. However, the sorption dynamics of dilute CTAB in the absence of electrolyte is markedly different from that in the presence of KBr. Here CTAB desorption occurs at local equilibrium, but the adsorption rate is kinetically limited, most likely due to an electrostatic barrier arising as the charged surfactant accumulates at the interface. The commercial, polydisperse nonionic surfactant ethoxy nonylphenol (NP9) loads in good agreement with local-equilibrium theory but shows deviation from the theoretical washout curve, presumably due to slow desorption of solubilized but otherwise water insoluble components. The polymeric nonionic triblock copolymer Pluronic exhibits almost complete irreversible adsorption at the air/water interface over a molecular-weight range from 3 to 14 kDa. Similar irreversible dynamic behavior is observed for adsorption/desorption of the protein bovine serum albumin (BSA) from dilute aqueous solutions at the air/water interface. The new continuous-flow tensiometer (CFT) is a simple, yet powerful, tool to investigate sorption dynamics at fluid/fluid interfaces, especially for larger molecular weight surface-active agents that exhibit significant hindrance to desorption.     

Dynamic Surface Tension and Adsorption Mechanism of Surfactant Benzyltrimethylammonium Bromide at the Air/Water Interface

The air‐solution equilibrium tension, γ_c and dynamic surface tension, γ_t, of aqueous solutions of a novel ionic surfactant benzyltrimethylammonium bromide (BTAB) were measured by Wilhelmy method and Maximum bubble pressure method (MBPM), respectively. Adsorption equilibrium and mechanism of BTAB at the air‐solution interface were studied. The CMC was determined to be 0.11 mol/L. The results show that at the start, the adsorption process is controlled by a diffusion step. Toward the end, it changes to a mixed kinetic‐diffusion controlled mechanism with the adsorption activation energy of about 11.0 KJ/mol. Effects of temperature, inorganic salts, and alcohols on adsorption kinetics also are discussed.     

Bubble shapes and orientations in low Re simple shear flow

We present measurements of shape and orientation of air bubbles in a viscous Newtonian fluid deformed by simple shear. The apparatus is a variation of the "parallel band" device developed by G. I. Taylor. Previous experimental studies on low viscosity ratio, low Reynolds number (Re < 1) bubble deformation have focussed on either small or large deformations (mostly small deformation) and have only qualitatively examined the orientation of bubbles except for small deformations. Our data set spans both the theoretical small deformation and high deformation limits. With these data we confirm theoretical relationships and assess the range of capillary numbers (Ca) over which theoretical relationships for shape and orientation of bubbles are appropriate. We also examine the geometry of deformed bubbles as they relax to a spherical shape once shear stresses are removed. Our data indicate that for extremely small Reynolds numbers and viscosity ratios, the small deformation theoretical relationship first developed by Taylor, is a good approximation for Ca<0.5. The large deformation results for both shape and bubble orientation derived by Hinch and Acrivos agree with our data for Ca>1 and Ca>0.5, respectively.