Determination of the collision frequency between bubbles and particles in flotation

Collision efficiency for a spherical bubble rising in a uniform concentration of small non-inertial particles is studied by direct numerical simulations (DNS). The Stokes number of the particles is negligibly small so that the particle trajectories follow the streamlines. The effect of the bubble interface contamination is studied for the flow surrounding the bubble using the spherical cap model. Numerical results are obtained for a wide range of bubble Reynolds number (based on bubble diameter d_b) ranging from 0.01 to 1000 and for different angles of contamination ranging from 0^° to 180^°. The collision efficiency is found to be increased with the Reynolds number and significantly decreased with the level of contamination. Correlations of the numerical results are proposed for efficiencies versus d_p/d_b (d_p being the particle diameter), bubble Reynolds number and interface contamination degree. For clean (respectively, fully contaminated) spherical bubbles, the efficiency evolves as d_p/d_b (respectively (d_p/d_b)²) whatever the bubble Reynolds number and the particle size. For partially contaminated bubbles, efficiency can be scaled with d_p/d_b or (d_p/d_b)² depending on both the level of contamination and the particle size.     

A new experimental method for determining particle capture efficiency in flotation

A single bubble experiment has been developed for the determination of the capture efficiency of particles by bubbles in flotation under well-controlled hydrodynamics and physico-chemical conditions. In a glass column, small single bubbles (d_b=0.22−1.16 mm) are produced in pure water and then rise at their terminal velocity through a suspension consisting of spherical glass particles where bubble–particle capture takes place. The capture efficiency E_capt is calculated as the ratio of the number of particles captured by one bubble to the number of particles present in the volume swept out by this bubble. Images recorded at high optical magnification show that particles slip on the interface, then adhere to air bubbles individually or as aggregates and cover the rear part of bubble surface. The bubble's effective density and interface contamination level are increased by captured particles. As a result, bubble's rising velocity U_b is reduced along the experimental device. By establishing the relationship between capture efficiency E_capt, bubble rise velocity U_b and bubble clean angle θ_clean, a new approach to measure particle–bubble capture efficiency is proposed. This new experimental technique is applied to provide a new set of data for capture efficiency in the case of bubbles with a clean interface. E_capt is found to grow as d_b decreases and d_p increases, within the range between 0.02 and 0.20, which is in the order of magnitude of experimental results of Ralston and Dukhin (1999) as well as of numerical results of Sarrot et al. (2005). These data are favorably compared to numerical modeling of collision efficiency.     

Yoon-Luttrell collision and attachment models analysis in flotation and their application on general flotation kinetic model

We theoretically used the models of Yoon and Luttrell for collision and attachment efficiencies to show the effect of fluid flow condition, the effect of bubble size and velocity and particle surface hydrophobicity in flotation system, and in order to demonstrate the effect of particle density on the attachment behavior we incorporate the correct expression for the maximum collision angle developed by Dukhin collision model in the Yoon-Luttrell attachment efficiency applied for two minerals species such as the quartz and chalcopyrite. Then we used the expression of the analytical model that enables the calculation of the flotation rate constant of particles derived by Pyke et al., developed under turbulent condition and with including the efficiency of collision using the generalized Sutherland equation (GSE), the attachment efficiency using modified Dobby-Finch model, and stability of bubble-particle aggregate includes the various forces acting between the bubble and the attached particle. Some results are obtained revealing the positive inertial effect for the quartz and galena particles under defined flotation data conditions by incorporating in the flotation rate constant mentioned above, the collision and attachment efficiency models of Yoon-Luttrell developed for potential flow condition with assuming that the bubble surface is completely mobile and the particle inertia is ignored. The results show also the influence of the increasing of the bubble velocity to determine the particle size range between the models considering the inertial effect and those who ignored the particle Inertia.     

A study of the bubble properties in the column flotation system

The bubble properties in the column flotation system are deeply affected by the bubble-generator type, frother dosage, and superficial gas velocity. This study is to determine the bubble-generator type, which effectively produces micro-bubbles to affect the flotation efficiency. Characteristics for two types of bubble generators like the in-line mixer and sparger are examined by bubble properties such as bubble diameter, holdup and bubble velocity. Micro bubbles generated from an in-line mixer result in the increase of the bubble rising velocity and gas holdup. Bubbles produced at the in-line mixer were more effective for operating the flotation system than that of the sparger. It means that the in-line mixer bubble generator is more effective than a sparger in designing or operating the column flotation system.     

CFD-based multiscale modelling of bubble-particle collision efficiency in a turbulent flotation cell

In this paper, bubble-particle collision efficiency in a turbulent flow is investigated from a multiscale modelling viewpoint. An integrated CFD-based scheme for the prediction of turbulent bubble-particle collision efficiency is developed. As part of this scheme, the effect of turbulence and the bubble wall effect on bubble-particle collision efficiency are systematically studied using a 3D low turbulent Reynolds number shear-stress-transport turbulence model. Example simulations and comparisons are carried out to illustrate the methodology. The method can also be applied to non-Newtonian slurries.     

Particle–bubble interaction and attachment in flotation

Flotation is an important unit operation in the minerals industry, among others. Current state-of-the-art flotation modelling combines computational fluid dynamics (CFD) with user-defined algorithms based on the “induction time” concept to describe selective bubble–particle attachment and separation of hydrophobic and hydrophilic particles.We have undertaken experimental studies permitting direct observation of particle–bubble interaction and attachment at the microscale to provide empirical data for comparison with new theoretical predictions.Observations were made on a model system in which 150 μm glass particles were dropped onto a captive 1.3 mm air bubble formed in water within a glass cell. The interactions were recorded on high-speed digital video, permitting direct estimation of relevant parameters such as the approach velocity, and the duration of particle sliding over the bubble surface. A new experimental configuration has allowed the particle path toward, around, and away from the bubble to be totally unimpeded.Particle trajectories show a significant deviation at separations much larger than their own diameter; such deviations are due to the hydrodynamics. Comparisons with theoretical predictions indicate that the bubble surface exhibited mobility intermediate between “full slip” and “no slip”. Theoretical predictions for an immobile bubble surface were practically symmetrical about the bubble's equator, while asymmetry was apparent in the theoretical predictions for a mobile bubble surface. However, the strongest asymmetries were seen in the observed particle trajectories and speeds.Particles dropping more centrally were seen to slide over the surface of the bubble. In several cases the sliding particle ‘jumped in’ toward the bubble, which is interpreted as the precise moment of attachment. This provides for a direct estimate of the threshold duration to achieve attachment, i.e. “induction time”. Among the events observed were rotation of the particle upon jumping in, and particle jump-in below the bubble's equator. Explanations are proposed in terms of particle properties and flow phenomena.     

On the structure of collision and detachment frequencies in flotation models

New explicit analytical expressions are obtained for both the collision frequency and the bubble/particle detachment frequency which enter flotation separation models. The expression for the collision frequency takes into account both the particle settling velocity and the bubble rise velocity while that for the detachment frequency is motivated by analogous results for floc disruption in a turbulent flow field. In all the cases considered, it is shown that the inclusion of the particle settling velocity increases the collision frequency by a factor of approximately 1.5 and that the most significant factor affecting the collision frequency is the bubble radius.     

Bubble size distribution in cyclonic zone of a novel flotation column

In order to investigate bubble size distribution (BSD) in the cyclonic flotation column, a series of tests were conducted to study flow velocity distribution (FVD) and BSD by using the method of particle image velocimetry (PIV). Foaming performance of the n-octyl alcohol is more applicable than both of n-butyl alcohol and terpenic oil. At different circulation volume conditions, BSD range lies in 0–800 μm, and a large number of tiny bubbles (<90 μm) are generated. Besides, the curve presents a normal distribution in 90–180 μm. With the increase in circulation volume, bubble size decreases. BSD determined by cyclonic flow effect plays a crucial role on bubble mineralization with fine particle in cyclonic zone of the flotation column.     

Experimental determination of particles capture efficiency in flotation

A single bubble experiment is developed for the determination of the capture efficiency by rising bubbles in a uniform concentration of small inertialess glass particles under carefully controlled hydrodynamics and physico-chemical conditions. Air bubbles (0.35-1.3 mm in diameter) rise and reach their terminal velocity in clean water before passing through a suspension of particles (15- in size), where capture takes place. After passing through another zone containing pure water to remove particles trapped in their wake, bubbles release captured particles at the surface from where the particles are collected and counted. A capture efficiency is then calculated as the ratio of the number of particles captured by one rising bubble to the number of particles present in the volume swept out by this bubble. Capture efficiencies range between 10^-3 and 5×10^-1 and are in the order of magnitude of the experimental results presented by Ralston and Dukhin [1999. The interaction between particles and bubbles. Colloids and Surfaces A: Physicochemical and Engineering Aspects 151, 3-14] as well as of numerical results for collision efficiency presented by Sarrot et al. [2005. Determination of the collision frequency between bubbles and particles in flotation. Chemical Engineering Sciene 60 (22), 6107-6117].     

Influence of particle concentration on initial collection efficiency and surface coverage in porous media filtration

Four sizes (0.095, 0.53, 1.0 and 2.01 μm) of polystyrene latex particles were used to prepare monodispersed suspensions at three different ionic strengths (10³,10^-2.5 and 10^-2 M KCl). Filtration experiments were conducted using those suspensions in a filter column with glass beads as porous medium. The filter bed depth and the filtration velocity were kept at 5 cm and 1 m/h, respectively. When suspensions with equal mass concentrations (0.2 mg/L) or equal surface area concentrations (0.12 cm²/mL) were filtered through the system, the largest particles exhibited higher initial single collector efficiency, ⪯. The difference between the ? of largest particles and the smaller particles was prominent for suspensions with equal surface area concentrations at higher ionic strengths. The collision efficiency,α of those particles exhibits higher values at higher ionic strengths. Both at equal mass concentration and equal surface area concentration,α is only slightly dependent on particle sizes when compared to its dependence on ionic strength. Further, it was found that the specific surface coverage was similar for 0.095 μm, 0.53 μm and 1.0 μm particles during the transient stage of filtration at any ionic strength when the surface area concentrations of those suspension were equal.     

Effect of particle size and freezing conditions on freeze-casted scaffold

Freeze casting is one of the emerging and novel manufacturing routes to fabricate porous scaffolds for various applications including orthopedic implants, drug delivery, energy storing devices etc. Thus, it becomes important to understand this process in a deeper sense. Present work was focused to study the effect/influence of basic parameters, particle sizes, and freezing conditions on the mechanical properties and microstructures of porous scaffold fabricated by freeze casting. β-tricalcium phosphate (β-TCP) and hydroxyapatite (HAp) powder with particle sizes of 10?μm and 20?nm were used. Prepared slurries were freeze casted at constant freezing temperature (5?°C) and constant freezing rate (1.86?°C/min) to study the effect of freezing conditions on mechanical and microstructural properties of the porous scaffold. It was observed that porous scaffold fabricated by nanoparticles has given better porosity (63.22–76.16%), than scaffold fabricated by microparticles (13–43.05%) at given solid loading of both freezing conditions. Although, the range of pore size of the scaffold fabricated by nanoparticles (CFR: 2.60–0.84?μm; CFT: 1.66–0.46?μm) was lower than that of scaffold fabricated by microparticles (CFR: 9.45–4.83?μm; CFT: 4.72–2.84?μm). The compressive strength of scaffolds prepared by nanoparticles was in the range of trabecular bone. Moreover, the results of present work will pave the way for the fabrication of porous scaffold with desired pore size and porosity for various implants, energy, and drug delivery applications.     

Effect of spatial inhomogeneity and temporal fluctuation of particle distributions on interparticle collision rate in particulate flows

Direct measurements on the interparticle collision processes in a vertical gas-particle two-phase flow were conducted using high-speed flow visualization and PTV techniques. The commonly-used theoretical model for interparticle collision rate, which was derived from the analogy with kinetic theory of gases, was evaluated by the experimental data. It was shown that the theoretical model markedly overestimated the interparticle collision rate in gas-particle flows. This overestimation was analyzed to be caused by the discrepancies between the model assumptions and the actual particulate flows. One of the most significant factors was the inhomogeneity and fluctuation of particle distributions, which was a general characteristic in actual particulate flows but neglected in the model. The quantitative scales of the inhomogeneity and fluctuation of particle distributions were analyzed by the coefficient of variation and introduced into the interparticle collision rate expression to modify the theoretical model. The estimations by the modified collision rate model agreed well with the experimental data. The modified model was proved to be valid for the analyses of interparticle collisions in actual particulate flows.     

填料在充填浮选柱中的应用及研究

介绍了化工填料在浮选柱的应用及研究情况,探讨了填料在浮选柱中所起的作用,说明了今后的研究方法及方向。     

粒径对云南海口胶磷矿浮选的影响

矿物颗粒尺寸是影响矿物浮选的重要因素。通过对球磨后的海口胶磷矿进行粒度分析及分粒级浮选实验,了解粒径对胶磷矿浮选结果的影响。结果表明,MgO含量高的矿物易被磨细,在磨矿过程中有向细粒级富集的趋势;而含P_2O_5较多的矿物则相对难磨,在磨矿过程中在粗粒级得到相对富集;通过对比不分粒级比分粒级更有利于胶磷矿浮选。     

Direct measurement of entrainment in large flotation cells

A key response variable to describe the metallurgical performance in a flotation cell is the concentrate grade. The mineral feed characteristics and conditioning determine the grade of the particles attached directly to the surfaces of the bubbles by true flotation, while the operating conditions, such as gas rate, bubble size, froth depth and others, determine the amount of gangue recovered by entrainment, which finally decreases the concentrate grade.In this paper, the recovery of liquid and solids by entrainment was evaluated by direct measurement of the fraction of liquid and solids reported to the concentrate in a 130 m³ mechanical flotation cell.The liquid and solids entrainment, per size classes (+ 150; − 150 + 45; − 45 µm), was measured by the radioactive tracer technique. The procedure consisted of introducing a tracer impulse at the cell feed entrance. The tracer time response was monitored on-line at the concentrate overflow and at the tailings discharge. Also, in order to obtain the quantitative distribution of the feed, samples were taken periodically from the concentrate and tailings streams, for a period of 4 residence times, during the tracer tests. This allowed the quantification of the mass of tracer reporting to both streams.Experimental results confirmed that solids entrainment with the froth was strongly dependent on particle size, and that the entrainment factor (EF = solid/water recovery ratio) was similar to that reported for smaller size cells under similar operations conditions.     

Measurement of coal particle size and shape with concentrated coal-water mixtures

The behavior of concentrated coal-water mixtures having narrow particle size ssfractions of coal was investigated. The pulverized coal was fractionated into six distinct particle size ranges, i.e. -70+80, -80+120, -120+140,-140+200, -200+400 and -400 mesh sizes by using a series of sieves. Settling rates were determined as functions of solids concentration for suspensions in water of coal particles to establish the measurement of particle size and shape factor and to assess concentration effect upon the observed hindered settling rates. The settling rates were modelled using the Richardson-Zaki model with the exponent n variable to account for the nonspherical shape of the coal particles. The data was also correlated with the Michaels-Bolger model which explicitly account for the excess water which is dragged down along with the particles undergoing sedimentation. In addition, coal particles and suspensions were characterized by coal analysis, heating value, solid heat capacity and thermal conductivity, densities, maximum packing concentrations and pore size distributions.     

Effect of the particle size on the viscoelastic properties of filled polyethylene

Composites of surface treated and non-treated colloidal calcium carbonate and high-density polyethylene with different filler loading were prepared. Their viscoelastic properties were studied by dynamic strain sweep and small-amplitude oscillatory shear, and compared to those of the corresponding composites of micron-sized calcite. The specific surface area of the filler enormously increases as the average particle diameter becomes smaller than 600 nm, leading to a strong tendency to agglomeration (soft flocks) and aggregation (hard clusters that need attrition to be disintegrated). In nanocomposites, more and stronger filler clusters are formed than in microcomposites due to the large contact area between the particles. The clusters have different shapes and maximum packing than the nearly spherical primary particles, thus enhance the moduli and viscosity of the composites. The obtained results indicate that the higher moduli and viscosity of the nanocomposites is not a direct consequence of the particle size but is due to the presence of more agglomerates and aggregates. Clusters that are local structures and do not represent a space-filling filler network enhance the moduli in the low frequency region more than at high frequencies and increase the storage more than the loss modulus. The presence of strong local structures in the nanocomposites leads to weak log moduli-log frequency dependence in the low frequency (terminal) region. Polymer adsorption on the particles' surface results in a transient filler-polymer network and slow dynamics of the bound polymer, which contribute to the moduli of the complex fluid. The sum of all these factors leads to gradual increase in moduli and to a shift of the crossover frequency to lower values. Above a certain filler volume fraction, the composite responds as a viscoelastic solid (storage modulus>loss modulus over the whole frequency range and both moduli are frequency independent in the terminal zone of the log-log plot).     

充填浮选柱分选胶磷矿的工艺研究

充填浮选柱是一个复杂的气液固三相体系。本文考查了用充填浮选柱分选胶磷矿的主要操作参数的影响，讨论了Ｐ２Ｏ５的品位的沿柱高的分布，证实了充填浮选柱具有优良的分选性能，并为寻求缩短胶磷矿浮选工艺流程的途径提供了依据。     

Implications of particle size to transient stage of deep bed filtration

This study was aimed at investigating the effect of particle size, mostly in the submicron range, on break-through stage of filtration. Latex beads, with diameters ranging from 0.46- to 2.967-μm were filtered through filter grains of diameters 0.1-, 0.175- and 0.45-mm. Experimental conditions were chosen so as to obtain breakthrough curves. The experimental results showed that the initial efficiency follows the pattern reported by previous experimental and theoretical studies, i.e., lower efficiency for 0.825-μm particles which fall in the range of critical size. However, the particle removal during the transient stage increased with an increase in particle size for the range of sizes studied. This pattern is qualitatively confirmed by the theoretical predictions of Vigneswaran and Chang (1986) model. This study also provides experimental verification of the effect of the ratio of particle size and grain size at different stages of filtration.     

Regrinding sulphide minerals — Breakage mechanisms in milling and their influence on surface properties and flotation behaviour

Changes in surface properties with grinding and regrinding play a key role in mineral flotation performance. Different particle breakage mechanisms in grinding mills may change the mineral surface properties in different ways, possibly leading to different mineral floatabilities depending upon the predominant breakage mechanism. The Magotteaux Mill^® and IsaMill were selected as representations of a tumbling and a stirred mill, respectively. The latter has a greater contribution to particle size reduction from the abrasion mechanism than the former which also has contributions from impact breakage.Mineral recovery decreased with size reduction through stirred mill regrinding (i.e., the IsaMill) employing ceramic media from 90%, achieved before regrinding (d₈₀ 80 μm regrind feed), to 71, 58, 20 and 5% achieved after regrinding to d₈₀ values of 60, 40, 20 and 10 μm, respectively. A similar trend of decreasing recovery was also observed with regrinding in the tumbling mill (i.e., Magotteaux Mill^®). Changes in mineral flotation behaviour were investigated with respect to (i) particle size, (ii) increase in surface area, and (iii) surface contamination with size reduction in the two different mills. The flotation of pyrrhotite with additional reagents illustrated that the total change in recovery through regrinding results mainly from the increase in surface area of the pyrrhotite afforded by size reduction. The effects of the predominating particle breakage mechanism on the change of mineral surface properties were studied through regrinding in the two different mills. In particular it was observed that the hydrophobicity/floatability of the coarse particles decreased to a greater extent with stirred mill regrinding than with tumbling mill regrinding at coarser regrind product sizes (d₈₀ 70 and 60 μm) presumably due to the greater contribution of the abrasion mechanism to size reduction afforded by the stirred mill. It was also observed that the difference in recovery for the same regrind product size from the two different mills decreased when approaching finer regrind sizes, which indicated that the particle breakage mechanisms of the different mills for fine regrind product size were not as influential as for coarse regrind product sizes.