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.     

旋流气浮中气泡-颗粒碰撞效率影响因素理论分析

在旋流气浮接触区碰撞模型基础上,通过理论计算考察了物性、运行和结构参数对分散相颗粒/油滴与气泡碰撞效率的影响. 结果表明,物性参数中的分散相粒径与密度、运行参数中气泡直径与切向速度和结构参数中等效旋流直径对碰撞效率影响较大. 在旋流气浮工艺中,碰撞效率随分散相粒径增大而增大,但随气泡直径和分散相颗粒/油滴密度增大而减小;分散相粒径小于0.02 mm时,碰撞效率随切向速度增大而减小、随等效旋流直径增大而增大;分散相颗粒/油滴大于0.02 mm时,碰撞效率随切向速度增大而增大、随等效旋流直径增大而减小. 旋流气浮去除的主要是油滴大于0.02 mm的非溶解性油,因此,设备紧凑可提高气泡与分散相颗粒的碰撞效率,达到高效分离目的.     

Demonstration of a minimum in the recovery of nanoparticles by flotation: Theory and experiment

The flotation of nano- and submicron particles does not follow the conventional collection theory based on the interception and collision mechanisms, which predicts extremely low collection efficiency for particles smaller than 10-μm. Brownian diffusion and colloidal forces strongly influence the collection of such particles by air bubbles in flotation. In this paper, a theoretical model is presented for predicting the collection efficiency of nanoparticles. The theory incorporates mass transfer by Brownian diffusion, microhydrodynamics of particles in the vicinity of a slip surface of rising air bubbles, and colloidal interactions that come into effect at small separation distances. The governing equation was solved numerically using the Crank-Nicolson method with variable step size. A finite difference scheme with mesh refinement in the vicinity of the air bubble surface was used to discretise the stiff partial differential equation for the particle concentration. The mesh refinement produced correct numerical solutions without oscillation in the particle concentration distribution, which otherwise occurred due to the stiffness of the differential equation and coarseness of the numerical mesh. Predictions from the model were compared with experimental results obtained with a small laboratory column cell, in which colloidal silica particles with diameters in the range were floated using fine bubbles of typical average diameter . The particle concentration in the pulp was about 1% by weight. Cetyltrimethyl ammonium bromide and Dowfroth 250 were used as the flotation collector and frother, respectively. Both the theory and experiment show significant effect of the electrical double-layer and non-DLVO hydrophobic attractive forces on the collection of nanoparticles by air bubbles. The theoretical and experimental results show the collection efficiency to have a minimum at a particle size in the order of . With larger particles, the interception and collision mechanisms predominate, while the diffusion and colloidal forces control the collection of particles with a size smaller than the transition size.     

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.     

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.     

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].     

Flotation behaviour of fine particles with respect to contact angle

The flotation behaviour of methylated quartz particles of different size, but within the size range from 0.2 to 50 μm, and varying contact angle, was probed in a mechanical flotation cell. Results suggest that particles of a given size need to possess a minimum critical contact angle (θ_crit) for flotation to occur. This behaviour is shown not to be solely dependent on fine particles having lower collision efficiency with bubbles, but rather due to a combination of low collision efficiency and particles not having enough kinetic energy at collision with bubbles to form the three phase line of contact and initiate the attachment process. In the particle size range investigated, the critical contact angle increases with a decrease in particle size.     

声波信号多尺度分解与固体颗粒质量流率的测定

利用声发射检测技术，根据不同速度的颗粒撞击壁面产生不同能量的声发射信号，结合小波分析，建立了单粒径颗粒质量流率预测模型，该模型可以定量描述颗粒质量流率随特征频段的声发射信号能量与表观气速的变化规律。以空气-聚乙烯颗粒体系为例，分别考察了0.84、0.59、0.42、0.21 mm 4种线性低密度聚乙烯颗粒，在表观气速为4.62～6.35 m·s-1条件下的声发射信号。在考察的气速范围内，在0～500 kHz频率范围内对声发射信号做7尺度的小波分解，发现特征频段的声发射信号能量与表观气速平方之比和固体颗粒的质量流率呈线性关系。同时，基于单粒径颗粒质量流率预测模型，根据混合颗粒声发射能量为各单一粒径颗粒声发射能量的线性叠加，得到混合颗粒的质量流率预测模型，模型的计算值与称重法获得的质量流率相比，平均相对误差为4.15%，表明声发射检测技术能便捷、快速、准确、环保地实现循环管内颗粒质量流率的在线检测。     

多效旋风分离器性能的实验研究

多效旋风分离器通过采用2级螺旋管预分离含尘气体、螺旋形顶盖板导流、筒体中心稳流锥稳流和吸气回流系统防止粉尘返混等措施,解决了在旋风流场中分离微米及亚微米级颗粒的难题。文中通过实验研究了直径为0.25 m的多效旋风分离器的压降、分离效率和进口风速的关系,实验物料粒径范围为0.1—23μm,平均粒径为7.59μm。结果表明:在10—14 m/s入口风速时,对0.1—3μm颗粒的分离效率大于90%,对大于5μm颗粒的分离效率接近100%,压降在500—1 000 Pa。风速大于16 m/s时,对0.1—2μm颗粒的分离效率大于75%。     

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.     

Picobubble Enhanced Fine Coal Flotation

Abstract

Froth flotation is widely used in the coal industry to clean ?28 mesh fine coal. A successful recovery of particles by flotation depends on efficient particle‐bubble collision and attachment with minimal subsequent particle detachment from bubble. Flotation is effective in a narrow size range beyond which the flotation efficiency drops drastically. It is now known that the low flotation recovery of particles in the finest size fractions is mainly due to a low probability of bubble‐particle collision while the main reason for poor coarse particle flotation recovery is the high probability of detachment. A fundamental analysis has shown that use of picobubbles can significantly improve the flotation recovery of particles in a wide range of size by increasing the probability of collision and attachment and reducing the probability of detachment.

A specially designed column with a picobubble generator has been developed for enhanced recovery of fine coal particles. Picobubbles were produced based on the hydrodynamic cavitation principle. They are characterized by a size distribution that is mostly below 1 µm and adhere preferentially to the hydrophobic surfaces. The presence of picobubbles increases the probability of collision and attachment and decreases the probability of detachment, thus enhancing flotation recovery. Experimental results with the Coalberg seam coal in West Virginia, U.S.A. have shown that the use of picobubbles in a 2″ column flotation increased fine coal recovery by 10–30%, depending on the feed rate, collector dosage, and other flotation conditions. Picobubbles also acted as a secondary collector and reduced the collector dosage by one third to one half.     

Enhanced graphite recovery by optimising flotation energy input

This experimental work on graphite flotation investigated the effect of energy input on flotation performance of three particle size fractions. Results obtained from flotation tests indicated that the required energy input rate increases with the decreasing particle size. The maximum graphite recovery of coarse particles was obtained at 121 J/min, while the optimum recovery of fine particles was obtained at 330 J/min. However, the demand of energy for each coarse particle is slightly higher than that of the fine particle in collision process. Numerical analysis showed that the streamlines have little effect on the trajectories of coarse particles, which can significantly contribute to a higher recovery of coarse particles in comparison with fine particles at the same energy input rate.     

Prediction for particle removal efficiency of a reverse jet scrubber

Numerical computation was conducted to predict the collection performance of a reverse jet scrubber for polydisperse particles. The particle size distribution of polydisperse particles was represented by a lognormal function, and the continuous evolution of the particle size distribution in a reverse jet scrubber is taken into account with the first three moment equations. Numerical results were compared with the analytic results using average relative velocity in all zones and experimental results.

In a reverse jet scrubber, the impaction is the main particle collection mechanism because of high relative velocity and short collection time. The particle collection by impaction increases with an increase in particle size, and geometric mean diameter and geometric standard deviation decrease as time goes on. High droplet velocity and gas velocity increase the particle collection efficiency, and the small droplet size also increases the collection efficiency because smaller droplet size provides broader surface area. The packing density is a factor affecting particle collection efficiency in a scrubbing process. The dense packing density also provides large surface area and leads to high collection efficiency.     

Simultaneous effect of particle size and solid concentration on the hydrodynamics of slurry bubble column reactors

The simultaneous effect of particle size and concentration on the total gas holdup of slurry bubble column reactors was investigated in this work. The total gas holdup was measured for air–water–glass beads systems. Three solid concentrations and three particle diameters were used. It was found that increasing particle size at high constant concentration decreases gas holdup. Moreover, increasing solid concentration decreases gas holdup and this decreasing effect is higher for larger particles. Also, solid particles have two effects on hydrodynamics, namely, changing the viscosity and density of the liquid phase as well as hindering the bubbles from rising within the column by the collision phenomenon. Therefore, a novel correcting factor was introduced to correct the gas holdup. The hindering factor considers both the collision efficiency affected by the particle size as well as the solid concentration. A novel correlation was developed to predict the experimental data of the three-phase gas holdup.     

Experimental testing of the hydrodynamic collision model of fine particle flotation

Flotation rates of glass beads and of latex particles have been measured as a function of particle size using very small bubbles. With glass beads the observed rate versus size relationship agreed quite well with the prediction of a simple hydrodynamic collision model, but that found with latex particles did not. It is suggested that electrical forces may have to be taken into account when the particles have a significant zeta potential. With both types of particle, the relationship between flotation rates measured at two different bubble sizes is consistent with the model's predictions.     

Attrition characteristics of alumina catalyst for fluidized bed incinerator

Attrition characteristics of alumina catalyst for catalytic incineration have been studied in a fluidized bed cold mode combustor (F10 cm, 160 cm height). The particle size and density of alumina catalyst were 1.4-1.7 mm and 1.13 g/cm3. As operating variables, excess gas velocity (U-U_mf) and bed weight (W_b) were selected. The experimental results show that attrition rate of alumina catalyst increased with excess gas velocity and bed weight due to intensive rubbing and collision caused by bubble coalescence. The size of the entrained particles collected in cyclone ranges over 0.5 to 100 mm, and the mean size for number base increases with an increase of excess gas velocity.     

Flotation of blue-green algae using methylated egg ovalbumin

The removal of blue-green algae by dispersed gas flotation was conducted. Methylated ovalbumin (MeOA) was used as frother and flocculant, which is a biodegradable substance. The continuous flotation experiments were conducted at different feed mass flow rate of the blue-green algae cells and MeOA. The operating variables were the mass flow rate of blue-green algae cell and MeOA, the initial concentration of the cells and MeOA, and superficial gas velocity. The results showed that the mass flow rate of MeOA was the most dominant variable affected by the removal efficiency and that the removal efficiency achieved ca. 0.85 when a ratio of the mass flow rate of MeOA and that of the cells was over 0.3. A proposed flotation model considering the adsorptions of MeOA to the cells, MeOA to bubble surface and the cells bearing with MeOA to bubble surface was applied to explain the experimental removal efficiency. The experimental and the calculated removal efficiency were within error 19%, indicating that the proposed model was valid fundamentally.     

Study of Oil Removal Kinetics using Cyclone-Static Microbubble Flotation Column

The cyclonic-static microbubble flotation column (FCSMC) has dual effects including the cyclonic separation and airflotation separation with advantages in the oily wastewater treatment field such as the small lower limit of the effective separation size, short separation time, large handling capacity, and low operating cost, especially the polymer-flooding oily wastewater treatment aspect. In this paper, the cyclonic separation function mechanism of the FCSMC was investigated. In addition, several operating parameters which impact oil removal efficiency and kinetics constants such as circulating pressure, the superficial gas velocity and the frother consumption were also investigated. The mathematical model relationship between the separation kinetics constants and the factors including circulating pressure, gas superficial velocity, and the average bubble diameter was established. Based on the strength by steps, the physical separation model of the cyclonic-static microbubble was also established.     

下行床弧面气固快速分离器内颗粒运动

采用二维相位多普勒颗粒分析仪(PDPA)对下行床弧面气固快速分离器内颗粒相的流动进行了定量测量，得到了分离器内颗粒运动向量图、体积通量分布和粒径分布. 颗粒通过气固惯性的差别、弧面、挡板的碰撞导向和浓缩作用实现气固分离. 弧面附近颗粒体积通量有较宽的分布，但主要集中在靠近弧面处，对分离有利. 在横向气相曳力和湍流扩散的作用下，在弧面附近小颗粒向外围扩散，粒度分布逐渐形成双峰特征. 减小喷嘴宽度，可以减弱颗粒向外围扩散的程度，提高分离效率.     

Flotation efficiency of activated sludge flocs using population balance model in dissolved air flotation

The activated sludge process is one of the most frequently used processes for biological wastewater treatment. Conventional gravity sedimentation (CGS), which is widely used as a secondary clarifier in activated sludge processes, has a routine problem due to floating tendency, called bulking, caused by filamentous microorganisms. Dissolved air flotation (DAF) has been applied as potential alternative to CGS as a secondary clarifier. A series of experiments were performed to measure physico-chemical characteristics and removal efficiency of activated sludge flocs. The removal efficiency of flocs corresponding in lag and exponential growth phases was lower, while that of flocs both in stationary and endogenous phases considerably increased. The rise velocity of floc/bubble agglomerates was calculated by using a population balance (PB) model explaining the distribution of floc/bubble agglomerates. The experimental results of flotation efficiency showed a similar tendency with the results predicted by PB model for the rise velocity and distribution of floc/bubble agglomerates. It was found from our study that the DAF process was very effective as a secondary clarifier in the activated sludge process.