Amine flotation of fine quartz and glass beads

The effect of pH on the n-dodecylamine flotation of −20 μm quartz and glass beads was studied. A microflotation cell suitable for use with very fine particles was used in the flotation experimentation. The amount of agglomeration of particles at different pH values was compared using 80% passing sizes (P₈₀) estimated from size distribution data.Results obtained show that in such flotation systems agglomerates, instead of individual particles, are generally present and floated. The presence and flotation of agglomerates suggests that low recoveries in very fine particle systems may have little to do with single particle — bubble contact, but rather are related to other problems associated with such systems.     

潮湿细粒煤聚团碰撞分离的物理过程和微观力学机制

为提高分级设备的分级效率和优化分级设备,利用高速动态摄像机拍摄了自由下落的潮湿细粒煤聚团与水平金属面的碰撞过程,借助于接触力学理论和液桥理论研究了聚团碰撞分离的物理过程和力学机制。研究表明:聚团的碰撞分离因黏附颗粒重力的不同呈现出两种模式:碰撞式分离和重力-碰撞式分离;聚团的碰撞分离过程可分成聚团与壁面的碰撞、小颗粒与大颗粒的接触碰撞以及液桥的拉伸断裂3个阶段。聚团与壁面的碰撞打破了聚团内的颗粒运动速度的一致性,颗粒的分离使粒间液桥发生拉伸变形,当颗粒间的最大分离距离超过液桥的断裂距离时,湿颗粒实现分离,湿颗粒的分离需要一个最小法向分离初速。水分的增加使湿颗粒难分的主要原因是液桥难以断裂造成的。湿颗粒聚团的分离随着碰撞速度的降低、颗粒粒径的减小、水分的增加和接触颗粒数的增多而变得困难。     

Fluid dynamics based modelling of the Falcon concentrator for ultrafine particle beneficiation

Enhanced gravity separators are widely used in mineral beneficiation, as their superior gravity field enables them to separate particles within narrow classes of density and size. This study aims to shed light on the Falcon concentrator’s ability to separate particles within size and density ranges lower than usual, say 5–60 μm and 1.2–3.0 s.g. respectively. As differential particle settling is expected to be the prevailing separation mechanism under such conditions, this study presents the workings of a predictive Falcon separation model that embeds phenomenological fluid and particle flow simulation inside the Falcon’s flowing film. Adding to the novelty of modelling the Falcon concentrator using a fluid mechanics approach, one point of practical significance within this work is the derivation of the Falcon’s partition function from fluid flow simulation results.     

水力压裂裂缝内支撑剂颗粒空隙率分布的形成机制

为了解水力压裂裂缝内支撑剂颗粒空隙率的演变,采用数值模拟方法模拟了裂缝内支撑剂颗粒在不同应力下的压缩过程,通过研究裂缝内支撑剂的接触力及配位数分布揭示了其空隙率分布的形成机制。结果表明:裂缝内支撑剂颗粒空隙率自下而上呈缓减小-急减小-缓减小-急增大-缓增大的分布趋势;将其分为底层、中层和顶层3个层位,相同应力状态下,底层支撑剂间接触力最弱为应力衰减区,平均配位数最小,空隙率最大;中层支撑剂间接触力最强为应力承受区,颗粒向下传递力的能力最弱,平均配位数最大,空隙率最小;顶层颗粒向下传递能力最强为应力传递区,支撑剂间接触力较弱,平均配位数和空隙率介于应力承受区和应力衰减区之间。     

The dependency of the critical contact angle for flotation on particle size - Modelling the limits of fine particle flotation

The flotation behaviour of fine particles is studied in this work. Fine methylated quartz particles within the size range from 0.2 to 50 μm, and with varying contact angles, were floated in a mechanical flotation cell. Results indicate that particles of a given size need to possess a minimum critical contact angle, which increases in value as particle size decreases, for flotation to be initiated. As a consequence, a non-floating component exists within a given size fraction. This is interpreted as a fraction consisting of particles below the critical contact angle for flotation for that size. The critical contact angle for flotation is explained in terms of the existence of an energy barrier for bubble-particle attachment. The flotation results are interpreted by means of [Scheludko et al., 1976] and [Drelich and Miller, 1992] models for the floatability of fine particles. The experimental data compared very well with calculations using the Drelich and Miller equation, allowing extension to the prediction of the critical contact angle for flotation down to particle sizes well below the previous limits investigated, bridging the gap existing in the literature.     

Critical contact angle for coarse sphalerite flotation in a fluidised-bed separator vs. a mechanically agitated cell

This work investigates the critical contact angle for the flotation of coarse (850–1180 μm, 425–850 μm and 250–425 μm) sphalerite particles in an aerated fluidised-bed separator (HydroFloat) in comparison to a mechanically agitated flotation cell (Denver flotation cell). In this study, the surface chemistry (contact angles) of the sphalerite particles was controlled by varying collector (sodium isopropyl xanthate) addition rate and/or purging the slurry with either nitrogen (N₂) or oxygen (O₂) before flotation. The flotation performance varied in response to the change in contact angle in both the aerated fluidised-bed separator and the mechanically agitated cell. A critical contact angle threshold, below which flotation was not possible, was determined for each particle size fraction and flotation machine. The results indicate that the critical contact angle required to float coarse sphalerite particles in a mechanically agitated cell was higher than that in the fluidised-bed separator, and increased as the particle size increased. At the same particle size and similar contact angles, the recoveries obtained by the aerated fluidised-bed separator in most cases were significantly higher than those obtained with the mechanically agitated flotation cell.     

Optimization of operating parameters for coarse sphalerite flotation in the HydroFloat fluidised-bed separator

Increasing the upper size limit of coarse particle flotation has been a long-standing challenge in the minerals processing industry. The HydroFloat separator, an air-assisted fluidised-bed separator, has been used in this study to float 250–1180 μm sphalerite particles in batch flotation tests and compared to results achieved utilizing a laboratory-scale conventional Denver cell. The quiescent environment within the HydroFloat cell significantly reduces the turbulent energy dissipation within the collection zone, hence decreasing the detachment of particles from bubbles during flotation. Three operating parameters including bed-level, superficial water and gas rates have been studied, and their effect on the flotation of coarse sphalerite particles is reported. It is shown that coarse sphalerite recovery increases with increasing bed-level, superficial water and gas flow rates. However, there are thresholds for each operating parameter above which recovery starts to decrease. A comparison of recovery with a conventional Denver flotation cell indicates that the HydroFloat separator vastly outperforms the conventional flotation machine for the very coarse particles (+425 μm), and this is mainly attributable to the absence of turbulence and the minimization of a froth zone, both of which are detrimental to coarse particle flotation.     

煤矿井下气水喷雾雾化特性实验研究

为了分析煤矿井下气水喷雾雾化特性,基于自行设计的气水喷雾实验平台,采用电磁流量计、空气质量流量计及马尔文实时高速喷雾粒度分析仪对空气雾化喷嘴流量特性、雾化粒度的空间分布规律及影响因素开展了实验研究。结果表明:随着供水压力的增加,喷嘴耗气量以指数形式不断递减,而耗水量以指数形式递增;喷嘴耗气量随供气压力以指数形式递增,而喷嘴耗水量基本呈现线性递减趋势。雾滴粒径沿喷嘴轴线方向不断增大;距离喷嘴较近的纵断面上,雾滴粒径沿径向不断增大,并呈现不对称分布;位于雾流中部的纵断面上,轴线附近区域雾滴粒径沿径向不断增大,而雾流外部区域雾滴粒径呈现沿重力方向增大的趋势;在靠近雾流末端衰减区内,雾滴粒径沿重力方向不断增大。供气压力一定时,雾滴粒径随着供水压力的增加呈现先增大后减小的变化规律,且供气压力越大所对应的拐点水压越高;随着供气压力的增加,雾滴粒径不断减小,且减小幅度随供气压力增加而有所下降。     

Exploratory modelling of grinding pressure within a compressed particle bed

With increasing industry interest in high pressure roll grinding (HPGR) technology, there is a strong incentive for improved understanding of the nature of grinding pressure that exists in the interior of a compressed particle bed. This corresponds to the crushing region of the HPGR. The relationship between applied pressure (stress) to the particle bed and induced pressure (stress) within particles and at contact points between particles is of particular interest. A detailed parametric investigation is beyond the scope of this exploratory paper. However, this exploratory investigation does suggest some interesting behaviour.The compressed particle bed within an 80 mm diameter piston has been modelled using Particle Flow Code for three dimensions. PFC3D is a discrete element code. The total number of simulated particles was 1225 and 2450 for two beds of different thickness. Particle diameters were uniformly distributed between 4 and 4.5 mm. The results of the simulations show that stress intensity within the simulated particle beds and within the observed particles increased with increase of the applied stress. The intensity of the average vertical stress in the selected particles tended to be comparable with the intensity of the pressure applied to the surface of particle bed and was only occasionally higher. However, the stress at contact points between particles could be several times higher. In a real crusher, such high stress amplification at contacts will quickly decrease due to local crushing and a resultant increase the size of the contact area. Therefore, its significance is likely to be relatively small in an industrial context.The modelling results also suggest that failure within the particle bed will progress from the crushing surface towards the depth of the bed.     

Bubble–particle detachment in a turbulent vortex I: Experimental

The mechanics of the detachment of particles from bubbles in the flotation process in a turbulent environment are unclear. The traditional hypothesis assumes a bubble–particle aggregate is trapped inside an eddy of equivalent size, and the attached particles rotate at the same speed as the eddy. The rotational movement subjects the attached particles to a centrifugal force. It is theorised that particles detach when the centrifugal force is greater than the capillary force, but this hypothesis has not yet been experimentally proven.This work is an experimental study of bubble–particle detachment in a rotating eddy. A special experiment was designed to obtain a strong confined vortex, and bubble–particle aggregates were introduced into the cavity without destroying the vortex structure. This newly developed method, which provides a realistic analogue of the turbulent conditions in a flotation cell, is well suited to the study of an important sub-process of flotation in a turbulent field, namely, the stability of single bubble–particle aggregates.Particles can detach from bubbles by a number of ways, including inertial actions induced by rapid changes in direction, and disruption due to coalescence of colliding bubbles. In this paper, we focus on a particular mechanism, in which bubbles are observed to rotate in a turbulent vortex. Particles can be held on the surface of the bubble by surface tension, and the radial centripetal force induced by the rotation is sufficiently high, particles may detach. Experiments are described in which the process of particle detachment due to centrifugal movement, was captured by a high-speed video camera, and the necessary physical parameters, especially the rotational velocity of the particles, were extracted. For the first time, centrifugal movement of the particle on the bubble surface inside a vortex was observed, and the theory of detachment due to centrifugal forces in the turbulent field was experimentally proven.     

Flotation of methylated roughened glass particles and analysis of particle–bubble energy barrier

The impact of the shape and/or anisotropy of particles (in terms of surface energy, surface charge, or wetting) on their flotation separation has been receiving more attention in recent years. The effect of particle surface roughness on interactions with other surfaces or gas bubbles has rarely been studied. The objective of this study was, therefore, to prepare spherical particles of different surface roughness characteristics and test them for their response to flotation separation. Towards this aim, glass particles with a size of 106–150 μm were either acid etched or abraded to manipulate their surface roughness. The particles were also methylated using trimethylchlorosilane to enhance their hydrophobicity and interactions with air bubbles. Micro-flotation separations were then carried out with methylated smooth and roughened particles to examine the effect of particle surface nano-roughness on flotation kinetics and their corresponding recoveries. The results confirmed that the flotation rate constants of roughened particles increased consistently with increasing dimensions of surface asperities. To explain the effect of particle surface roughness on flotation, a theoretical model based on the extended-DLVO interactions was formulated and used to quantify the effect of hydrophobic asperities on particle–bubble surface interactions. The theoretical modeling results suggest, for the first time, that the size of nano-sized hydrophobic asperities distributed over spherical microscopic particles dictate the magnitude of the energetic barrier that particles need to overcome in order to attach to bubbles.     

燃煤电厂脱硫废水烟气蒸发特性流场模拟

喷雾液滴蒸发特性是实现电厂脱硫废水零排放烟气蒸发技术的关键。利用数值模拟的方法对气液两相流过程中涉及影响液滴蒸发特性的喷雾液滴平均粒径（分布特征）、传热传质等影响因素进行分析,建立喷雾液滴群烟气蒸发传热传质模型,获得了喷雾液滴群蒸发规律及运动特征。分析结果表明：模拟喷雾粒径情况下,液滴加热迅速,完全蒸发的关键控制步骤取决于液滴表面蒸汽气相组分浓度Ci,s与烟气中蒸汽气相组分浓度Ci,∞的浓度差,相同的烟气蒸发环境下,不同粒径组都呈现出初期快速蒸发和后期缓慢蒸发2个明显的阶段,在相同最大粒径范围下（最大直径100 μm）,细颗粒群（平均粒径24 μm）主体段蒸发时间最短（0.3 s达到80.1%的蒸发质量比）,粗颗粒群（平均粒径84 μm）蒸发质量比最大（0.6 s达到95%的蒸发质量比）。     

Capture of impacting particles on a confined gas–liquid interface

Film flotation is highly dependent upon how well wanted and unwanted particles are separated at the gas–liquid free surface. Single particle experiments and modelling analysis can be undertaken to determine a critical impact velocity at which the optimum separation is likely to occur. However, in commercial film flotation systems the higher loading density of the free surface can result in interactions that change the critical impact velocity. To investigate this influence, film flotation experiments have been undertaken with 4, 5 and 6 mm diameter spherical polypropylene particles with water, sucrose and surfactant (CTAB) solutions contained within vessels of varying dimensions and wettability (static contact angle). Experimentally it was observed that for a given particle diameter the critical impact velocity was found to decrease with decreasing vessel diameter, especially when the particle-to-vessel diameter ratio increased beyond about 0.2. Conversely, the critical impact velocity was found to be relatively independent of the liquid depth; but did decrease with decreasing static contact angle in the region where the vessel wall had an influence. The experimental system was also modelled using the Young–Laplace equation using both static and advancing contact angle measurements for both the particle and vessel surfaces. The model predictions were generally in good agreement with the experimental observations, including showing an increase in particle penetration depth with increasing vessel diameter and meniscus profiles, both at the particle impact point and the wall of the vessel. The predictions were improved when the advancing contact angle was used, especially for the smaller diameter vessels where there was more liquid motion. Finally, a model to determine the critical (minimum) diameter of vessel required so that the cavity profile generated by the impacting particle is unlikely to be influenced by the vessel walls is presented.     

The influence of particle shape on parameters of impact crushing

The influence of the shape of limestone particles on impact crushing parameters has been investigated by testing single particles in a high-resolution impact analyzer. The measurements conducted included the contact time and force, the transferred energy, the fragment size and shape distribution as well as the energy utilization. The particles tested were classified in seven different shape classes that ranged from spheres and cubes to plate-shaped and acicular bodies. The results show that the measured parameters are significantly influenced by the particle shape. These differences are caused by an additional orientation phase of an irregularly shaped particle prior to the main impact. Usually, the impact bar of the crusher hits one of the corners first, accelerates, rotates the particle and disintegrates a part of it occasionally.For spherical and cubical particles the contact forces and transferred energy are the highest and the contact time is the lowest. These results suggest that the mechanical design of impact crushers could be made on the basis of testing spheres or cubes, which would provide a safety factor in the design. Regarding the size distribution of the fragments, both the upper diameter and size modulus of a truncated Rosin–Rammler–Sperling–Bennet distribution are the lowest for spherical particles while no clear trend was found in respect to the distribution modulus. The comparison of the fragment shape distributions shows, except for the coarser fragments, hardly an influence of the initial particle shape on the smaller fragments. The energy utilization is the lowest with spherical and cubical bodies and rises with increased elongation and flatness of the feed particles.     

Detachment of coarse composite sphalerite particles from bubbles in flotation: Influence of xanthate collector type and concentration

The force required to detach sphalerite ore particles from air bubbles has been measured in flotation concentrates, for particles in the size range of 150–300 μm and 300–600 μm with different degrees of liberation. An electro-acoustic vibrating apparatus, that produces typical force conditions experienced in a flotation cell, was used to measure particle–bubble detachment as a function of the vibrational acceleration. Sodium isopropyl xanthate (SIPX) and potassium amyl xanthate (PAX) collectors were used in flotation, at different concentrations. At a fixed frequency of 50 Hz, the maximum vibrational amplitude at which a particle detaches from bubble was used to calculate the particle detachment force. It was shown that changes in surface hydrophobicity (contact angle), due to variations in reagent conditions have significant impact on particles detaching from bubbles. On average, detachment of particles from oscillating bubble correlated well with xanthate concentration and hydrocarbon chain length of xanthate ions. Particles (300–600 μm) with high contact angle obviously required higher force to detach from bubbles than similar particles with lower contact angle. This correlated well with the flotation response at the different reagent conditions. SEM analysis of particles after detachment showed that fully liberated particles attached to bubbles more readily and also gave higher detachment force than composite particles. Moreover larger detachment forces were observed, on average, for particles with irregular shape compared to particles with rounded shape of the same size range.     

Determination of the rate of crushing of material in drum mills

Conclusions The author determines for the kinetic-probabilistic model of particle fracture in a drum mill the probability of particles coming within the zone of impact of the crushing bodies, and the probability of fracture of these particles. On the basis of several experiments in a laboratory mill with the material being ground, the equation of the crushing rate of the particles permits prediction of the crushing rate of this material under any operating conditions of mills of different sizes. The introduction of crushing rate equation (24) and batch crushing equation (23), together with use of the functions of the material residence time distribution in the mill, will permit subsequent prediction of the continuous crushing process. Sibénergotsvetmet, Krasnoyarsk. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 2, pp. 48–55, March–April, 1980.     

DEM simulation of cake formation in sedimentation and filtration

This paper presents a DEM study of cake formation and growth in sedimentation and filtration processes with constant flow rate or pressure. The liquid flow is assumed to be one-dimensional and the motion of particles is three-dimensional. Various forces are included to determine the motion of particles, including the particle–particle contact forces, the van der Waals force and the particle–fluid interactions such as buoyancy, drag and lift forces. The effects of the material properties of particles and liquid and the operational conditions are examined. The structures of cakes are also analysed and the relationship between cake porosity and interparticle force is quantified. The microscopic analysis demonstrates that these variables affect the process and the cake structures through their effects on the gravity or cohesive force, which competes in controlling the formation of a cake.     

The dynamic behaviour of coarse particles in flotation froths. Part II: Density tracer tests

A novel flotation cell was used in which hydrophobic particles act as film breakers and sink through the froth as concentrate, while hydrophilic particles are supported by the upward flow of froth and are recovered as a top product tailings. Experimental results on density tracers showed that the behaviour of particles (within the size range tested) in the froth phase of the cell is primarily dependent on the mass of a particle. In general, the higher the mass, the steeper is the trajectory of the particle in the froth, i.e., an increase in particle mass results in an increased recovery to the concentrate. The contact angle on the particle surface has only a secondary influence on the overall particle trajectory, in that an increase in the equilibrium contact angle will result in an increased recovery. However, the particle contact angle has very little influence on the behaviour of large, high-density particles, as well as small, low-density particles.Particles will therefore only separate on the basis of contact angle as long as their mass is between an upper and lower critical value. Any particle with a mass greater than the critical value will fall through the froth irrespective of the contact angle. Similarly, the upward force component acting on a particle with mass less than the lower critical value will dominate the force balance. The particle will therefore remain supported by the froth, irrespective of the particle contact angle and bubble film rupture time. For particles within these mass limits, the effect of the contact angle increases with a decreased mass.It was further concluded that these mass limits are dependent on the operating conditions of the cell as well as the particle shape. The particle shape determines the mass to cross-sectional surface area ratio (M/A₀). Where particles therefore have the same mass, the M/A₀ ratio would govern the particle trajectory. The higher the M/A₀ ratio, the more particles would be recovered to the concentrate, while a decrease in the M/A₀ ratio would result in flatter particle trajectories in the froth, thereby increasing the probability of a particle reporting to the tailings. A mathematical model provides an understanding of the interrelationship between the various parameters.     

浅析回转窑轮带与筒体的接触问题

给出轮带与筒体两弹性圆柱体法向接触区接触压力分布规律,讨论载荷、间隙及筒体厚度对该接触副的影响,得到轮带与筒体接触磨损寿命的计算方法.