Bubble particle heterocoagulation under turbulent conditions

An analytical model that enables the calculation of the flotation rate constant of particles as a function of particle size with, as input parameters, measurable particle, bubble, and hydrodynamic quantities has been derived. This model includes the frequency of collisions between particles and bubbles as well as their efficiencies of collision, attachment, and stability. The generalized Sutherland equation collision model and the modified Dobby-Finch attachment model developed previously for potential flow conditions were used to calculate the efficiencies of particle-bubble collision and attachment, respectively. The bubble-particle stability efficiency model includes the various forces acting between the bubble and the attached particle, and we demonstrate that it depends mainly on the relative magnitude of particle contact angle and turbulent dissipation energy. The flotation rate constants calculated with these models produced the characteristic shape of the flotation rate constant versus particle size curve, with a maximum appearing at intermediate particle size. The low flotation rate constants of fine and coarse particles result from their low efficiency of collision and low efficiencies of attachment and stability with gas bubbles, respectively. The flotation rate constants calculated with these models were compared with the experimental flotation rate constants of methylated quartz particles with diameters between 8 and 80 micro m interacting with gas bubbles under turbulent conditions in a Rushton flotation cell. Agreement between theory and experiment is satisfactory.     

Effect of droplet size of the emulsified kerosene on the floatation of amorphous graphite

The micro-floatation of an amorphous graphite sample was conducted using a Hallimond tube with various droplet sizes of emulsified kerosene as collector. The results showed that the experimental recovery of the sample and the kinetic constants (both k and ?_∞) obtained from the four kinetics models all increased with the decrease of the droplet size. These may be attributed to the fact that the smaller and greater the specific surface area of the droplets, the more easy it is for them to collide with, adhere to, and spread on the sample particles, and then render the particles more hydrophobic. The stronger hydrophobic of particles was better beneficial to the adhesion probability and force between them and the bubbles, which made more amorphous graphite particles floated in the floatation process. In addition, the extended Derjaguin–Landau–Verwey–Overbeek (DLVO) theory was applied to study the interaction between the sample particles and the emulsified kerosene droplets. The results indicated that the hydrophobic attractions played a dominant role in the combined effect of collision and attachment between the sample particles and the droplets.     

Alkali chloride cluster ion dissociation examined by the kinetic method: heterolytic bond dissociation energies,effective temperatures,and entropic effects

Branching ratios have been measured as a function of collision energy for the dissociation of mass-selected chloride-bound salt cluster ions, [Rb-³⁵Cl-M_i]⁺, where M_i = Na, K, Cs. The extended version of the kinetic method was used to determine the heterolytic bond dissociation energy (HBDE) of Rb-Cl. The measured value of 480.8 ± 8.5 kJ/mol, obtained under single collision conditions, agrees with the HBDE value (482.0 ± 8.0 kJ/mol), calculated from a thermochemical cycle. The observed effective temperature of the collisionally activated salt clusters increases with laboratory-frame collision energy under both single- and multiple-collision conditions. Remarkably, the effective temperatures under multiple collision conditions are lower than those recorded under single-collision conditions at the same collision energy, a consequence of the inability of the triatomic ions to store significant amounts of internal energy. Laboratory-frame kinetic energy to internal energy transfer (T→V) efficiencies range from 3.8 to 13.5%. For a given cluster ion, the T→V efficiency decreases with increasing collision energy. Many features of the experimental results are accounted for using MassKinetics modeling (Drahos and Vékey, J. Mass Spectrom. 2001, 36, 237).     

Microgravity laser-photophoresis of high density microparticles in water

Laser-photophoresis is a new technique, which can be used to characterize and separate microparticles in liquids. The photophoretic migration of high density solid particles in water has been observed experimentally for the first time by experiments under microgravity conditions. The photophoretic velocity was measured under microgravity conditions, in order to minimize the effects of density difference and convection. Furthermore, by using an optical cylindrical cell, we could observe the precise photophoretic velocities without the wall-induced drag effect. The apparatus consisted of a cw Nd:YAG laser (532 nm), a microscope, a CCD system, and a remote controlled sample stage and was set in a capsule which was used for a free-fall experiment. All the experimental operations were made externally by using a personal computer. The photophoretic velocities for the particles of carbon, stainless steel, gold plated nickel, and polystyrene in water were determined under microgravity. It was found that the photophoretic efficiencies of the photo-absorbing carbon particles and the photo-reflecting metal particles were much larger than those of transparent particles. The order of magnitude of the observed photophoretic efficiency was carbon>stainless steel>gold plated nickel>polystyrene. The photophoretic efficiencies were compared with those calculated by a Mie scattering theory. It was proved that the Mie scattering theory was useful for the prediction of the photophoretic efficiency of various kinds of particles in water.     

Electrostatic attraction between a hydrophilic solid and a bubble

The contact between fine hydrophilic α-Al(2)O(3) particles and nitrogen bubbles was studied as a function of solution composition in single bubble capture experiments, where the bubble collection efficiency was measured. The surface charges of both bubble and particle were controlled by varying the electrolyte concentration and pH of the solution. In all experiments the bubbles were negatively charged while the α-Al(2)O(3) particles were either negatively (above pH of the isoelectric point, pH(IEP)) or positively (below pH(IEP)) charged. The collection efficiency was found to be strongly influenced by the surface charge of the particles. The maximum collection efficiency occurred when the bubble and particle were oppositely charged (at low pH values) and at low salt concentration, i.e. when a long range attractive electrostatic interaction is present. In the case where both bubble and particle were of the same charge, the collection efficiency was near to zero within experimental error and was not influenced by either salt concentration or pH. This is the first experimental proof of the concept of 'contactless flotation', first proposed by Derjaguin and Dukhin in 1960, with far reaching implications from minerals processing to biology.     

Dynamic aspects of small bubble and hydrophilic solid encounters

The capture of solid particles suspended in aqueous solution by rising gas bubbles involves hydrodynamic and physicochemical processes that are central to colloid science. Of the collision, attachment and aggregate stability aspects to the bubble-particle interaction, the crucial attachment process is least understood. This is especially true of hydrophilic solids. We review the current literature regarding each component of the bubble-particle attachment process, from the free-rise of a small, clean single bubble, to the collision, film drainage and interactions which dominate the attachment rate. There is a particular focus on recent studies which employ single, very small bubbles as analysis probes, enabling the dynamic bubble-hydrophilic particle interaction to be investigated, avoiding complications which arise from fluid inertia, deformation of the liquid-vapour interface and the possibility of surfactant contamination.     

用直接数值模拟对移动颗粒层除尘的研究及实验对比

利用气固两相流数值模拟计算模型，分别采用不同粒径的移动颗粒层过滤除尘器，对不同粒径粉尘颗粒的碰撞次数进行统计，并对移动床除尘中过滤介质尺寸与粉尘粒径尺寸之间的相互选择性进行了初步研究。模拟计算了在同一风速下碰撞次数与粉尘粒径以及移动层颗粒径之间的关系。计算统计的结果与实验结果对比发现，二者存在定性上的一致。结果表明，在移动床过滤除尘器中不同粒径的过滤层对不同粒径尘粒具有明显的选择性。     

Bubble colloidal AFM probes formed from ultrasonically generated bubbles

Here we introduce a simple and effective experimental approach to measuring the interaction forces between two small bubbles (approximately 80-140 microm) in aqueous solution during controlled collisions on the scale of micrometers to nanometers. The colloidal probe technique using atomic force microscopy (AFM) was extended to measure interaction forces between a cantilever-attached bubble and surface-attached bubbles of various sizes. By using an ultrasonic source, we generated numerous small bubbles on a mildly hydrophobic surface of a glass slide. A single bubble picked up with a strongly hydrophobized V-shaped cantilever was used as the colloidal probe. Sample force measurements were used to evaluate the pure water bubble cleanliness and the general consistency of the measurements.     

An improved collision efficiency model for particle aggregation

A generalized geometric model is presented which describes the collision efficiency factor of aggregation (the probability of a binary particle or aggregate collision resulting in adhesion) for systems comprised of two oppositely charged species. Application of the general model to specific systems requires calculation of the area of each species available for collision with a second species. This is in contrast to previous models developed for polymer-particle flocculation that are based on the fractional surface coverage of adsorbed polymer. The difference between these approaches is suggested as an explanation for previously observed discrepancies between theory and observation. In the current work the specific case of oppositely charged nondeformable spherical particles (heteroaggregation) is quantitatively addressed. The optimum concentration of oppositely charged particles for rapid aggregation (maximum collision efficiency) as a function of relative particle size is calculated and an excellent correlation is found with data taken from literature.     

Hydrodynamic boundary layer at a rising air bubble and entrapment of fine solids: Gravity effects on particle–bubble interactions

A model study of the dynamic interactions of fine non-neutrally buoyant solids with background boundary layer (BL) flow on rising bubbles is developed. The aim is to clarify the specific role of the gravity effects. The approach is based on the acquisition of asymptotic equations about the disturbed flow field in the particle vicinity and accounts for both viscous deformation and sedimentation effects. It is established that two particle density regions are of major interest. In Region I the coupling of hydrodynamic and gravity effects results in granulometric separation of the solids. In Region II the role of particle sedimentation dominates over the purely hydrodynamic interactions. As a result, the lighter the particles are, and the smaller their sizes are, the more important is the granulometric effect inside the BL. For high-density fines and larger bubbles, the gravity effects couple with the BL flow. The particle capture results in significant amplification of the collision chances. The obtained results are expected to refine the approach to recovery of fine species from ground materials in conventional flotation and should be taken into account in the assessment of the overall capture efficiency for fine particles in microflotation and separation processes.     

Electrochromatographic behavior of silica monolithic capillaries of different skeleton sizes synthesized with a simplified and shortened sol-gel procedure

Silica monolithic capillaries (SMCs) were synthesized by a sol-gel process. First, a simplification of the synthesis was proposed by replacing the calcination and the drying steps which can have tremendous effects on chromatographic and physical properties, by a single water or methanol 2 h washing step. The efficiency of such a washing step was demonstrated and the comparison of the chromatographic and electrochromatographic properties between calcined and washed SMCs has shown that such a modification did not impair retention, efficiency, and stability of the monolith. This simplified procedure was carried out to synthesize SMCs with two different skeleton sizes. These capillaries were evaluated in electrochromatography and present high efficiencies (H = 5 microm) at least equal to the best ones reported in the literature. Furthermore, the influence of the skeleton size on the EOF of the second kind (EOF-2) was investigated with unmodified SMCs used under various experimental conditions including electrical field strength and buffer concentration. The ionic strength of the mobile phase and the applied electrical field that enable this EOF-2 were related to the size of the skeleton which was tuned by the synthesis conditions.     

Ion-neutral potential models in atmospheric pressure ion mobility time-of-flight mass spectrometry IM(tof)MS

The ion mobilities and their respective masses of several classes of amines (primary, secondary, and tertiary) were measured by electrospray ionization atmospheric pressure ion mobility time-of-flight mass spectrometry IM(tof)MS. The experimental data obtained were comparatively analyzed by the one-temperature kinetic theory of Chapman-Enskog. Several theoretical models were used to estimate the collision cross-sections; they include the rigid-sphere, polarization-limit, 12-6-4, and 12-4 potential models.These models were investigated to represent the interaction potentials contained within the collision integral that occurs between the polyatomic ions and the neutral drift gas molecules. The effectiveness of these collision cross-section models on predicting the mobility of these amine ions was explored. Moreover, the effects of drift gas selectivity on the reduced-mass term and in the collision cross-section term was examined. Use of a series of drift gases, namely, helium, neon, argon, nitrogen, and carbon dioxide, made it possible to distinguish between mass effects and polarizability effects. It was found that the modified 12-4 potential that compensates for the center of charge not being at the same location as the centers of mass showed improved agreement over the other collision cross-section models with respect to experimental data.     

Influence of very small bubbles on particle/bubble heterocoagulation

Very small bubbles which partially coat the surface of particles influence whether or not heterocoagulation between a particle and a bubble occurs. The electrostatic and van der Waals forces of interaction between particles and bubbles were calculated as a function of electrolyte concentration, particle size, and the size and distributions of these very small bubbles present on the particle surface. The height of the surface force barrier was compared with the hydrodynamic pressing force under conditions of flotation. The presence of these very small bubbles has a profound effect on the interaction between particles and bubbles and, in particular, strongly decreases the critical particle radius for heterocoagulation.     

Aggregation of Charged Particles under Electrophoresis or Gravity at Arbitrary Péclet Numbers

Collision efficiencies are considered for colloidal suspensions of solid spheres moving in a viscous fluid under the influence of electrophoresis or gravity, Brownian motion, and electrostatic and van der Waals forces. The results are compared to those for convection (electrophoresis or gravity) and diffusion (Brownian motion) acting independently. The collision efficiency increases by many orders of magnitude over that predicted by simply adding diffusive and convective efficiencies in a specific parameter regime. This regime occurs when there is a large energy barrier in the interparticle potential, causing a stable region of parameter space if there is no diffusion. Brownian motion alone will only cause small amounts of aggregation under these conditions. However, for electric fields or buoyancy effects which are only slightly too weak to allow particles to overcome the potential barrier, the addition of weak Brownian motion to a system with convection can cause significant numbers of particles to overcome the energy barrier and aggregate. Copyright 2000 Academic Press.     

Ion sampling effects under conditions of total solvent consumption

The motivation of this work was to study some of the properties of nanoelectrospray operation under conditions where the entire sprayed liquid is vaporized and inhaled into the vacuum system. Under these conditions the desolvation requirements, sampling efficiency, concentration versus mass sensitivity, and molar response characteristics of various compounds were studied. The combined efficiency of ion production from solution and transfer into the vacuum system, referred to as sampling efficiency, is presented under various inlet conditions including different flow rates, solution compositions, and compound types. Under ideal solvent conditions the results for favorable compounds show sampling efficiencies of 70-85% at flows in the range of 50-500 nL/min. Efficiencies were lower for aqueous samples and compounds of different structures gave different molar response factors under these high sampling efficiency conditions. The relative molar response factors are presented in terms of those observed with higher flow rate sources which operate at significantly lower sampling efficiencies. In all cases, operating in this flow regime, the ion count rate was directly proportional to the absolute mass of analyte molecules entering the source. The experimental source used to carry out these studies included gas nebulization to stabilize the electrospray process, a heated laminar flow chamber to enhance desolvation and ion production, and various atmosphere-to-vacuum aperture diameters to maximize ion transfer.     

Capillary electrochromatography with macroporous particles.

The performance of macro-porous particles in capillary electrochromatography is studied. Three reversed-phase stationary phases with pore diameters between 500 A and 4000 A have been tested for separation efficiency and mobile phase velocity. With these stationary phases, a large portion of the total flow appears to be through the pores of particles, thereby increasing the separation efficiency through a further decrease of the flow inhomogeneity and through enhancement of the mass transfer kinetics. The effects of pore size and mobile phase composition on the plate height and mobile phase velocity have been studied. With increasing buffer concentrations and larger pore diameters, higher mobile phase velocities and higher separation efficiencies have been obtained. Columns packed with 7 microns particles containing pores with a diameter of 4000 A generated up to 430,000 theoretical plates/m for retained compounds. Reduced plate heights as low as 0.34 have been observed, clearly demonstrating that a significant portion of the flow is through the pores. For the particles containing 4000 A pores no minimum was observed in the H-u plot up to linear velocities of 3.3 mm/s, suggesting that the separation efficiency is dominated by axial diffusion. On relatively long (72 cm) columns, efficiencies of up to 230,000 theoretical plates/column have been obtained under non-optimal running conditions. On short (8.3 cm) columns fast separations could be performed with approximately 15,000 theoretical plates generated in less than 30 s.     

Multi-parameter investigation of tandem mass spectrometry in a linear ion trap using response surface modelling

The feasibility of experimental design in combination with subsequent response surface modelling was illustrated for the prediction and interpretation of tandem mass spectrometric (MS/MS) fragmentation data using a linear quadrupole ion trap under various experimental conditions. The instrumental parameters included were (i) the pressure of the collision gas, (ii) the collision energy, (iii) the fill time of the linear ion trap and (iv) the scan rate. The spectral intensity and width of five fragment ions of the doubly charged neuro-active peptide bombesin were used for evaluation, and all experiments were performed so as to resemble the results obtained from a liquid chromatographic peak. The reported results show how fairly simple mathematical tools can be utilized successfully to describe fundamental mechanisms associated with multiple collisional activation and collision-induced dissociation processes without an extensively controlled experimental environment. Most beneficial, using the suggested approach, is the ability to study interaction (synergistic) effects between various parameters. As was realized from the results, many interaction effects are indeed significant. For example, the effect on the signal intensity of different collision gas pressure settings is strongly dependent on the settings of the other parameters. The described approach can easily be adopted for optimization purposes of any MS/MS experiment.     

Buoyancy-driven coalescence of spherical drops covered with incompressible surfactant at arbitrary Péclet number

Collision efficiencies are determined for two surfactant-covered spherical drops in the limits of nearly uniform surface coverage and bulk insolubility for Brownian and/or gravitational motion as a function of drop-size ratio, drop-to-medium viscosity ratio, and retardation parameter. For two equal-sized drops in Brownian motion in the limit of small viscosity ratio, the calculated collision efficiencies agree well with earlier results for bubbles. While the two-sphere relative mobility functions for motion parallel to the drops' line of centers tend to the same values in the limits of infinite viscosity ratio and infinite retardation parameter, the asymmetric mobility functions do not, because the coefficients for the rotational term in Lamb's singular solution are independent of the presence of surfactant. The complex dependence of the transverse mobility functions on the viscosity ratio and retardation parameter makes it possible for the gravitational collision efficiency to increase slightly with viscosity ratio at fixed size ratio and retardation parameter of O(10(3)) or larger. Typical hydrosols are also studied in gravitational motion at arbitrary Péclet number, showing the combined influence of Brownian and gravitational motion.     

On the collision efficiency approach to flocculation

The collision efficiency approach to flocculation is analyzed on the basis of a model describing the probability of aggregation by polymer bridging. The model allows for the effect of the randomness of distribution of polymer over particles as well as the effect of simultaneous coagulation and weak flocculation. It is argued that the collision efficiency approach is applicable to a rather limited range of experimental systems and provides a qualitative understanding rather than a quantitative theory of the relationship between flocculation and adsorption.     

A review of induction and attachment times of wetting thin films between air bubbles and particles and its relevance in the separation of particles by flotation

Bubble-particle attachment in water is critical to the separation of particles by flotation which is widely used in the recovery of valuable minerals, the deinking of wastepaper, the water treatment and the oil recovery from tar sands. It involves the thinning and rupture of wetting thin films, and the expansion and relaxation of the gas-liquid-solid contact lines. The time scale of the first two processes is referred to as the induction time, whereas the time scale of the attachment involving all the processes is called the attachment time. This paper reviews the experimental studies into the induction and attachment times between minerals and air bubbles, and between oil droplets and air bubbles. It also focuses on the experimental investigations and mathematical modelling of elementary processes of the wetting film thinning and rupture, and the three-phase contact line expansion relevant to flotation. It was confirmed that the time parameters, obtained by various authors, are sensitive enough to show changes in both flotation surface chemistry and physical properties of solid surfaces of pure minerals. These findings should be extended to other systems. It is proposed that measurements of the bubble-particle attachment can be used to interpret changes in flotation behaviour or, in conjunction with other factors, such as particle size and gas dispersion, to predict flotation performance.