A rational interpretation of the role of particle size in flotation

From the examination of data from detailed plant surveys and associated laboratory batch testing, the principal effects of particle size in flotation have been identified. The current state of knowledge concerning the role of this variable is discussed in terms of the evidence presented. It is concluded that the minimum degree of hydrophobicity necessary for the flotation of a particle depends upon its size and as a result, recovery-size curves are a valuable diagnostic aid to the assessment of flotation performance. Entrainment is shown to be an important contributory mechanism to the recovery of fine particles which, when coupled with a low rate of genuine flotation, can account for much of the observed behaviour of such fines. The significance of particle size and its consequences in flotation research, in plant operations and in control schemes has been under-rated. The separate conditioning or flotation or both of separate size fractions seems inevitable as ores become increasingly difficult to concentrate.     

The effect of bubble size on the rate of flotation of fine particles

Flotation experiments have been carried out in a cell in which bubbles of known size could be generated independently of the turbulence levels, which could be controlled by varying the impeller speed. The mean bubble size ranged from 75 μm to 655 μm.Results are reported for the flotation rates of fine particles, less than 50 μm diameter. The materials floated were polystyrene latex particles, quartz and zircon. These were chosen to give a wide range of specific gravity.It was found that the flotation rate was very strongly affected by the bubble size, there being an increase of up to one hundred-fold when the bubble size was reduced from 655 μm to 75 μm. Effects of particle density and impeller speed are also reported.     

New method and equations for determining attachment tenacity and particle size limit in flotation

A new method and simple, yet accurate, equations for determining the tenacity of particle attachment and the particle size limit in flotation were developed by applying the force analysis of the gravity–capillarity coupling phenomena controlling the bubble–particle stability and detachment. Approximate solutions to the Young–Laplace equation were used to develop simple equations for the tenacity of attachment of particles with diameter up to 20 mm. Simple equations for the maximum size of floatable particles were derived as explicit functions of the particle contact angle, the surface tension, the particle density and the mean centrifugal acceleration of turbulent eddies. For the typical particle size and contact angle encountered in flotation, the analysis showed that the bubble size has little effect on the tenacity of particle attachment. The prediction for the largest size of floatable particles is compared with the experimental data and signifies influence of turbulence on the particle detachment.     

Dimensionless number and approximate calculation of the upper particle size of floatability in flotation machines

Two simple approximating equations are given for the calculation of the upper particle size of floatability under the turbulent hydrodynamic conditions in a flotation machine (apparatus). They comprise solid density ?_p, fluid density ?_fl, surface tension σ, contact angle θ and a parameter depending on energy dissipation, the vortex acceleration, which we call “machine acceleration” $\text{b}{}_{\mathrm{<mtext>m</mtext>}}$. Some diagrams are shown for practical purposes. A dimensionless characteristic number analogous to the bond number is introduced in order to characterize the stability of aggregates.     

晶体及矿物颗粒大小对岩土材料力学性质的影响

岩石常见较大的晶体或者矿物颗粒,混凝土中是骨料,通过团簇模拟大颗粒的力学行为、团簇可以破裂。根据设计的相同数量、相同位置、不同半径的大颗粒数值单轴压缩试验,在虚拟试验条件下,考察了颗粒大小对材料力学响应的影响。通过分析颗粒材料的破裂形态、裂纹扩展过程、应力-应变曲线和破裂能量演化规律发现：大颗粒具有明显的增强特性,有阻止裂纹扩展的作用,破裂多绕大颗粒发展;增强幅度随颗粒半径的增加呈单增趋势,半径较小时,增强效果不明显。     

The entrainment factor in froth flotation: Model for particle size and other operating parameter effects

Accurately estimating entrainment is crucial when predicting flotation performance as it is essential for determining the concentrate grade achieved. It has been found previously that the amount of gangue entrained is proportional to the water recovery; this proportionality is referred to as the entrainment factor. Experimentally it has been found that entrainment is a strong function of particle size, as well as being dependent on other cell operating parameters such as froth depth and air rate.A simplified theoretical model for entrainment is developed which includes the effects of liquid motion and content, particle settling and particle dispersion. First, a detailed one-dimensional differential model for the entrainment factor is developed and solved numerically. Thereafter, a simplified analytical expression for the entrainment factor is produced which is a good approximation to the more detailed one-dimensional model. Both these models are shown to predict closely experimental trends for entrainment as a function of particle size and froth depth.     

The selective flotation of galena from sphalerite with special reference to the effects of particle size

The selectivity of galena flotation from a synthetic mixture with sphalerite and quartz and from a typical Broken Hill ore has been determined. It was found that the selectivity was limited by the relative flotabilities of coarse galena and sphalerite of intermediate sizes. The use of split conditioning in the preparation for flotation resulted in significant improvements in lead-zinc selectivity for both samples. By contrast the use of conventional zinc depressants in the flotation of the ore resulted in only slight changes in the behaviour of the minerals and had no discernible effect on the selectivity.     

The effect of particle shape and hydrophobicity in flotation

The effect of particle shape on the flotation process has been investigated in laboratory experiments with monosized spherical ballotini and ground ballotini. The particles were treated by partial methylation with trimethylchlorosilane to achieve varying degrees of hydrophobicity. In flotation, the process of film thinning and liquid drainage is critical in the formation of stable bubble–particle attachments and this is affected by the particle shape and surface hydrophobicity. Flotation tests with different particle sizes were conducted in a modified batch Denver cell. Predictions from a computational fluid dynamic model of the flotation cell that incorporates fundamental aspects of bubble–particle attachment were compared with data from flotation tests. Contact angles of the particles were measured using a capillary rise technique to indicate surface hydrophobicity. Ground ballotini generally has higher flotation rates than spherical ballotini; the results are consistent with effects from faster film thinning and rupture at rough surfaces and are well correlated by the sphericity index.     

Study on infiltration rate based on primary particle size distribution data in arid and semiarid region soils

Soil particle size distribution (PSD) is used to estimate some soil processes, soil moisture characteristics, and infiltration rate (IR). Prediction of infiltration rate from soil texture data requires an accurate characterization of PSD. The objective of this study was to determine more important primary particle diameters that control IR. The experiments were conducted using double-ring method with constant head of 5 cm in 15 different soils and three replications. The range of measured IR for studied soils varied from 1.6 to 30.66 cm h^?1. The results indicated that the primary PSD had a significant influence on IR. In other words, most D _n fractions had significant positive effect on the final IR. Among different fractions, D ₃₀, D ₄₀, and D ₆₀ showed higher relationships with IR than the others. These diameters are attributed to particles with diameter of 0.05, 0.08, and 0.16 mm, respectively. The results also showed that increasing the percent of sand have intensified influence on increasing the final IR. Reversely, clay and silt contents showed negative effects on final IR. Furthermore, the CaCO₃ had a meaningful effect on the IR that showed the importance of lime in arid and semiarid regions. Finally, it is revealed that the role of texture was important, especially in behavior of infiltration, runoff, and production capability.     

A new fractal modification of ultrasonic attenuation model for measuring particle size in mineral slurries

Weight percentages of different size incremental particles in a mineral slurry is integrated into the ultrasonic attenuation model to derive a relation between ultrasonic attenuation and particle sizes. However, in the inertial and scattering regimes of frequency–radius space, irregularity and aggregation of particles can results in values of ultrasonic attenuation that are significantly different from those predicted by the derived model, which is based on the assumption of separated smooth spherical particles in mineral slurries. Experimental attenuation data obtained previously from mineral slurries of iron ores particles are compared with predicted values. It is shown that there is a negligible difference between predictions and experimental data. A new modification of theoretical model for ultrasonic attenuation is derived. The theory uses ωτ_v or κR as a fractal scale. It requires an empirical determination of the difference between the fractal dimension of the measured mineral slurry and that of a hypothetical slurry of spheres with the same particle size distribution. The new fractal modification of ultrasonic attenuation model is found to enable better agreement with measured attenuation as a function concentration for irregular particles than the theoretical model. Moreover, the fractal approach is found to discriminate between the effects of particle irregularity and aggregation.     

Suspended sediment concentration and particle size distribution,and their relationship with heavy metal content

This paper aims at assessing the feasibility of suspended sediment concentration (SSC) estimation by using predictor variables of heavy metal concentration (HMC, viz., iron, chromium, zinc and nickel) transported in solution and solid. The study was conducted in the Research and Educational Forest Watershed of the Tarbiat Modares University (Kojour) which comprises an area of ca. 50000 ha. For this study, suspended sediment samples were collected from the left bank of the Kojour River twice a week, as well as during runoff events from November 2007 to June 2008. The samples were then prepared through direct digestion and finally analyzed by atomic absorption spectrophotometry (AAS). The relationship between SSC and particle size distribution (PSD) were correlated with HMC by using bivariate and multivariate regression models. Proposed models were then selected based on statistical criteria. The results showed high correlation between dissolved and particulate chromium content with efficiency coefficients beyond 77% (P < 0.001). However, a lower relationship was found between SSC and nickel content. From these results, it is clearly shown that the HMC can practically be estimated by SSC in watersheds with different accuracy and vice versa. It is also understood that heavy metal pollution can be easily managed by controlling SSC.     

Influence of shape characteristics of talc mineral on the column flotation behavior

Column flotation, which is a very effective process in mineral processing especially for easily floatable minerals, is one of the most important new developments to emerge in mineral processing technology in the last years. In this study, the flotation behavior of talc products having different particle shapes produced by different grinding mills (ball and rod mill) was determined by using column flotation process. Shape characteristics of the particles were investigated by the two dimensional measuring technique based on the particle projections obtained from the SEM microphotographs using a COREL Draw 10.0 program. The results showed that particles possessing higher elongation and flatness properties were recovered better during column flotation, whilst roundness and relative width had a negative effect on the flotation behavior of the talc mineral studied. Consequently, as the shape of the particles produced by the mill deviated from the ideal sphere, their floatability was increased.     

全风化花岗岩孔径分布-颗粒组成-矿物成分变化特征及指标相关性分析

孔径分布、颗粒组成和矿物成分是全风化花岗岩微观和结构特征的3个主要方面,也是决定其工程地质性质的关键因素。理论研究和实际工程中,常用大、中小和微孔隙、角砾、砂粒和粉粘粒、三大矿物（石英、长石和粘土矿物）含量等指标表征这3方面的特征。3方面指标在一定范围上变化幅度多大？数值间相关性及作为土结构模型组份因子,它们相对权重多大？通过对香港九龙两处边坡51件全风化花岗岩试样压汞测试、颗粒分析和X射线衍射（XRD）等微观结构特征分析,结果表明：两处边坡粗粒和细粒结构全风化花岗岩有明显区别,前者主要属于砾石土和砂砾土,部分为含砾土,大孔隙多,石英和粘土矿物多,而后者部分属含砾土,部分为细砂土和亚砂土,微孔隙多,长石多;两者长石和粘土矿物含量变化正好相反。借助于多因素关系矩阵法,对3方面共9个指标作相关分析发现,相关性较好的指标是：角砾和砂粒 (0.948);大孔隙和微孔隙(0.846);石英和长石(0.827);长石和粘土矿物 (0.747)。从土结构因子角度考虑,权重从大到小指标是：微孔隙、长石、粘土矿物、砂粒、角砾、大孔隙、中小孔隙、粉粘粒和石英。其分析结果可为该类土微观结构特征细化及分类提供依据,为其微结构力学研究提供基础材料。     

Dependence of radon exhalation on grain size of sedimentary waste

Tailings resulted from sulphuric acid leaching process of uranium from sedimentary rocks contain high concentrations of ²²⁶Ra and its daughters, the most important of which is ²²²Rn. Movement of radon gas out of the tailings is strongly influenced by the physicochemical characteristics of these tailings especially their radium content and the grain size. So, the tailing samples were size fractionated into four sizes (>?250, 250–125, 125–74 and <?74 µm). The natural radioactivity was investigated using hyper-pure germanium detector and solid-state nuclear track detectors (CR-39) for bulk size and after size fractionation. The activity concentrations of different radionuclides in size-fractionated tailing samples have been shown to be strongly dependent on the size of the particles. In the range of >?250 and <?74 µm, the activity concentrations of ²³⁰Th, ²²⁶Ra, ²¹⁴Pb, ²¹⁴Bi, ²¹⁰Pb, ²³²Th and ⁴⁰K increased throughout with decreasing particle size, while that of ²³⁸U, ²³⁴U and ²³⁵U have an opposite effect. The results revealed an inverse relationship between the radon exhalation rate and size fractionation. Also, the results showed a good correlation between radium activity concentration and radon mass exhalation rate.     

Variation of flotation rate coefficients in zinc cleaning circuits

The detailed flotation behaviour observed in industrial zinc cleaning circuits at Broken Hill differs markedly from that commonly reported for rougher and scavenger flotation. Flotation is strongly influenced by solids to liquid ratio (pulp density) and the behaviour can be described by an exponential relationship between the flotation rate coefficient and the pulp density in each cell. The dependence on pulp density is largely independent of mineral type but does depend upon particle size. The largest variation is observed for coarse particles.The observations are of considerable significance to control of circuit performance. The results of simulations incorporating the dependence of rate coefficient upon pulp density differ substantially from those obtained from conventional models which assume constant rate coefficients.     

颗粒离散元岩石模型的颗粒尺寸效应研究

颗粒尺寸是影响颗粒离散元模型宏观力学性质与计算效率的一个重要因素。为充分考虑由模型随机性导致的模拟结果的不确定性,利用统计学方法对模型的颗粒尺寸效应进行研究。整体检验结果表明：特征长度比L/R的改变对模型力学参数（峰值强度、弹性模量、泊松比及峰值应变）与破坏特征参数（黏结破裂率）的总体分布位置均有显著性影响,且各参数的变异系数会随着L/R的减小而增大。进一步的多重比较结果表明：当L/R≥125时,L/R对峰值强度、弹性模量、泊松比及峰值应变的总体分布位置均无显著影响;当L/R≥79时,相邻3个粒径水平的黏结破坏率总体分布位置无显著性差异;随着L/R的减小,模型损伤程度增加,破坏模式由整体剪切破坏转向局部损伤引起的失稳破坏,最终失去模拟岩石材料的效力。最后,综合各项力学参数的统计学检验结果、模型破坏模式及计算效率,岩石模型颗粒的特征长度比取L/R=200较为合适。