Computational validation of the Generalized Sutherland Equation for bubble–particle encounter efficiency in flotation

Bubble–particle encounter during flotation is governed by liquid flow relative to the rising bubble, which is a function of the adsorbed frothers, collectors, and other surfactants and surface contaminants. Due to surface contamination, the bubble surface in flotation has been considered as immobile (rigid). However, surface contamination can be swept to the backside of the rising bubble due to the relative liquid flow, leaving the front surface of the rising bubble mobile with a non-zero tangential component of the liquid velocity. The bubble with a mobile surface was considered by Sutherland who applied the potential flow condition and analyzed the bubble–particle encounter using a simplified particle motion equation without inertia. The Sutherland model was found to over-predict the encounter efficiency and has been improved by incorporating inertial forces which are amplified at the mobile surface with a non-zero tangential velocity component of the liquid phase. An analytical solution was obtained for the encounter efficiency using approximate equations and is called the Generalized Sutherland Equation (GSE). In this paper, the bubble–particle encounter interaction with the potential flow condition has been analyzed by solving the full motion equation for the particle employing a numerical computational approach. The GSE model was compared with the exact numerical results for the encounter efficiency. The comparison only shows good agreement between the GSE prediction and the numerical data for ultrafine particles (< 10 μm in diameter), the inertial forces of which are vanishingly small. For non-ultrafine particles, a significant deviation of the GSE model from the numerical data has been observed. Details of the numerical methodology and solutions for the (collision) angle of tangency and encounter efficiency are described.     

Particle size distribution analysis of sand-sized particles by laser diffraction: an experimental investigation of instrument sensitivity and the effects of particle shape

Laser diffraction is now widely used for particle size distribution analysis of sediments and soils. The technique can be very precise, and offers advantages of speed and cost over many other methods when used to analyse mixtures of sand, silt and clay. This study presents the results of an experimental investigation that examined the sensitivity of the Beckman-Coulter LS230 instrument to mixtures of different grain populations and differences in particle shape. The instrument was found to have high sensitivity to coarse particles in a finer matrix (detection threshold 1–2%), but much lower sensitivity to finer particles in a coarser mixture (detection threshold 12–17%). Experiments using near-spherical ballotini showed that laser analysis provides very similar values to dry sieving for the mean, median and mode, but for a range of natural sand samples values for the mean, median and mode were offset by 8–21%, with an average of ca 15%, compared with sieving. Analysis using a Beckman-Coulter RapidVUE instrument, which provides both size and shape information, provided support for the hypothesis that the differences between laser analysis and sieving are partly attributable to the effects of particle shape. However, an additional factor is the way in which the laser software interprets the optical diffraction data. The software predicts a high degree of log-normality in the size distribution, such that highly skewed, truncated or bimodal samples are poorly represented. Experiments using sieved fractions of ballotini indicated that, even with near-perfectly spherical particles, the particle size distribution predicted by the laser software includes a relatively large percentage of particles outside the sieve class limits.     

ToF-SIMS-derived hydrophobicity in DTP flotation of chalcopyrite: Contact angle distributions in flotation streams

Particle hydrophobicity has been derived from Time of Flight Secondary Ion Mass Spectrometry (ToF-SIMS) measurements and its impact on the flotation behaviour of chalcopyrite investigated. Batch flotation tests were performed using a dithiophosphate-type of collector in different concentrations. Three flotation regimes were studied using particle size ranges of 20–38 μm, 75–105 μm and 150–210 μm. The individual particle contact angle, and hence, the distribution of contact angles of chalcopyrite within feed, concentrate and tail flotation samples has been determined using ToF-SIMS secondary ions. The effects of particle size and hydrophobicity on the flotation behaviour have been investigated using this new approach. The hydrodynamic effects of the particle size were highlighted by the different distributions of contact angles obtained for each concentrate size fraction, with fine and coarse sizes requiring higher average contact angles to float. This effect was overtaken by hydrophobicity when a high collector concentration was used. The broad distribution of contact angles observed in all samples, i.e. heterogeneity in hydrophobicity, has significant consequences for interpreting flotation behaviour. The methodology of analysis conducted in this study was applied to real ore and can be used as a quantitative, diagnostic tool for examining surface chemical factors affecting hydrophobicity. This new technique has promise and may advance the understanding of mechanisms, which may lead to better control strategies for improving flotation performance. Furthermore, any mineral–collector system can be targeted, provided appropriate calibration is performed.     

Precipitation of dodecyl amine in KCl–NaCl saturated brine and attachment of amine particles to KCl and NaCl surfaces

Long-chain amines, used in potash ore flotation as collectors, are insoluble in NaCl–KCl saturated brine. In commercial applications, these amines are melted at 70–90 °C, dispersed in acidic solution of hydrochloric or acetic acids, and such emulsions are then introduced to the flotation pulp.To model the commercial potash ore flotation process, dodecyl amine, used in this study, was melted at 70 °C, dispersed in hydrochloric acid aqueous solution and was added to a KCl–NaCl saturated brine at room temperature. This results in the precipitation of the amine. The present study summarizes the influence of the conditions on the particle size and morphology of the precipitating amine particles. Methyl isobutyl carbinol (MIBC), common frother in flotation processes, was shown to affect amine dispersion when added into a hot amine emulsion prior to mixing with a saturated brine. This study demonstrates that the precipitating amine particles are selectively abstracted by KCl particles, but not by NaCl particles.     

Discrete element modeling of crushable sands considering realistic particle shape effect

This study proposed a novel approach for generating crushable agglomerates with realistic particle shapes in discrete element modeling (DEM). The morphologies of sand particles were obtained by X-ray micro-computed tomography scanning and image processing. Based on the particle surface reconstructed by spherical harmonic analysis, the crushable agglomerates with realistic particle shapes can be generated in DEM simulations. The results of single particle crushing tests showed that particle shapes significantly influence the fracture patterns and crushing strengths of sand particles. Furthermore, two one-dimensional compression tests were conducted to investigate the particle shape effect on micro- and macro-mechanical behaviors of crushable sands.     

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.     

Dissolved air flotation (DAF) of fine quartz particles using an amine as collector

Experimental studies concerning the dissolved air flotation (DAF) of fine (d_p < 100 μm) quartz particles, using two different flotation cells (setups), are presented. Pure and well characterised quartz samples were treated with a commercial amine as collector prior to flotation and bubbles were characterised by the LTM-BSizer technique. Bubble size distribution showed 71% (by volume) and 94% (by number) of the bubbles having sizes (d_b) lower than 100 μm (i.e. microbubbles). The Sauter and arithmetic mean diameters were 79 μm and 56 μm, respectively, for the bubbles generated at 300 kPa (gauge) saturation pressure (after 30 minute saturation time). Quartz particle size distribution (obtained by laser diffraction) showed a volume-moment diameter of 13 μm. The Rosin–Rammler–Bennett, Gates–Gaudin–Schumann and log-normal distribution functions were well fitted (R² > 0.96) to the bubble size distribution and quartz particle size distribution data. Values of total quartz recovery ranging from 6% to 53% (by mass) were obtained for the DAF experiments under different collector concentrations (up to 2 mg g^− 1), with an optimal collector concentration found at 1 mg g^− 1. These results are significant considering that 27% (by volume) of the quartz particles are ultrafine (d_p < 5 μm), demonstrating the widely-known efficiency of DAF to remove small particles when applied in the field of water and wastewater treatment. The true flotation behaviour, as a function of particle diameter (d_p), exhibits a local minimum when particles are approximately 3–5 μm in size. The results contribute to the discussion in the literature about the existence of such a minimum, which is generally interpreted as a change in the mechanism of particle collection from convection (collision) to diffusion at lower particle sizes.     

抗转动对颗粒材料组构特性的影响研究

颗粒材料大多由不规则形状的颗粒组成,如砂土、谷物等,抵抗转动是不规则形状颗粒的固有特性。已有研究表明,颗粒抗转动特性对其宏观力学特性有显著影响。因此,在颗粒材料的细观数值模拟中或采用非圆颗粒,或在圆颗粒离散元模拟中采用考虑抗转动的接触模型。采用有限元-离散元耦合方法（FDEM）和离散元方法（DEM）分别对椭球形状颗粒和具有抗转动能力的圆球颗粒进行三轴剪切数值模拟,指出了采用抗转动接触模型考虑颗粒形状影响的局限性,并基于颗粒的局部排布结构揭示了形状影响的细观来源。峰值内摩擦角和剪胀均随着转动摩擦系数和形状偏离圆球程度而单调增加,但颗粒形状对它们的影响呈现出明显的收敛趋势。细观组构分析也表明,虽然颗粒形状和转动摩擦都能显著增强组构各向异性,但是组构各向异性的演化模式有明显的区别。造成以上结果的差异在于其抵抗转动的影响机制不同。转动摩擦是通过限制颗粒转动,增强了颗粒间的稳定承载能力,而非圆颗粒是通过咬合作用形成稳定的局部排列结构。由于椭球颗粒腹部比端部能够传递更大的接触力,颗粒受剪切后发生转动,颗粒长轴倾向于正交大主应力方向,呈现交错排列,颗粒间相互锁定。     

Isopropylxanthate ions uptake by modified natural zeolite and removal by dissolved air flotation

This work describes a laboratory study concerning the adsorption of isopropylxanthate ions onto modified zeolites particles. The separation of the loaded carrier and their removal, from aqueous solutions, was conducted by flocculation followed by dissolved air flotation, DAF. The zeolite employed was a natural sample (approximately 48% clinoptilolite and 30% mordenite) which was previously treated with sodium ions (activation) and modified with copper ions (Cu–Z) before the xanthate ions uptake. Adsorption capacities (q_m) for Cu–Z were 0.34 meq g^− 1 for the powdered form, and 1.12 meq g^− 1 for the floc form. The adsorption capacity for the floc form appears to involve an enhanced electrostatic adsorption due to the positive sites on the floc surface. In all cases, the isopropylxanthate concentration in the treated water was found to be negligible (< 0.04 mg L^{− 1}). The flotation technique showed to be a fast process, requires a low recycle ratio (20%) in air saturated water, and the treated water ended up with a very low residual turbidity (6.8 NTU). It is believed that this adsorption–flotation technique, here named adsorptive particulate flotation, using activated and modified natural zeolite has a high potential as an alternative for pollutants removal (copper and isopropylxanthate ions) from waste mining effluents.     

Studying the effect of non‐spherical micro‐particles on Hoek–Brown strength parameter mi using numerical true triaxial compressive tests

The strength parameter m_i in the Hoek–Brown strength criterion is empirical and was developed by trial and error. To better understand the fundamental relationship between m_i and the physical characteristics of intact rock, this paper presents a systematic study of m_i by representing intact rock as a densely packed cemented particle material and simulating its mechanical behavior using particle flow modeling. Specifically, the three‐dimensional particle flow code (PFC3D) was used to conduct numerical true triaxial compression tests on intact rock and to investigate the effect of non‐spherical micro‐particle parameters on m_i. To generate numerical intact rock specimens containing non‐spherical micro‐particles, a new genesis process was proposed, and a specific loop algorithm was used based on the efficiency of the process and the acceptability of generated specimens. Four main parameters—number, aspect ratio, size, and shape—of non‐spherical micro‐particles were studied, and the results indicated that they all have great effect on m_i. The strength parameter m_i increases when the number, aspect ratio, or size is larger or the shape becomes more irregular, mainly as a result of the higher level of interlocking between particles. This confirms the observations from engineering experience and laboratory experiments. To simulate the right strength parameter m_i, it is important to use appropriate non‐spherical micro‐particles by controlling these four parameters. This is further demonstrated by the simulation of two widely studied rocks, Lac du Bonnet granite and Carrara marble. Copyright © 2014 John Wiley & Sons, Ltd.     

Phospholipid ester-linked fatty acids composition of size-fractionated particles at the top ocean surface

Surface microlayer and subsurface water samples were collected at an oligotrophic Mediterranean site during a diel cycle. The composition of phospholipid ester-linked fatty acids (PLFA) was determined in size-fractionated particles (0.2–0.7 μm; 0.7–200 μm) in order to characterize the major contributors of organic matter to different size fractions. GF/F-retained particles (0.7–200 μm) from the surface microlayer were consistently enriched in PLFA relative to the underlying water. Molecular markers revealed a substantial difference in biological assemblages in both particle sizes. The larger particles were dominated by dinoflagellates, cyanobacteria, microzooplankton and attached bacteria, whereas particles filtered through GF/F and collected on 0.2 μm porosity Durapore filters (0.2–0.7 μm) were mostly bacteria and heterotrophic flagellates. Bacterial PLFA associated with 0.7–200 μm particles were more abundant than those in the 0.2–0.7 μm particles. Specific markers in the branched series appeared more representative of bacteria of smaller particle size.     

Effects of Particle Size and Chain Length on Flotation and Adsorption of Quaternary Ammonium Salts onto Kaolinite

Effects of particle size and chain length on flotation of quaternary ammonium salts (QAS) onto kaolinite have been investigated by mico-flotation tests. The two kinds of quaternary ammonium salts [RN(CH3)3] with different chain lengths, dodecyltrimethylammonium chloride (DTAC) and cetyltrimethylammonium chloride (CTAC) were used as collectors for kaolinite in different particle size fractions (0.075–0.01 mm, 0.045–0.075 mm, 0–0.045 mm). The anomalous flotation behavior of kaolinite have been further explained based on crystal structure considerations by adsorption tests and molecular dynamics (MD) simulation. The results show that the flotation recovery of kaolinite in all different particle size fractions decreases with an increase in pH when DTAC and CTAC are used as collectors. As the concentration of collectors increases, the flotation recovery increases. The longer the carbon chain of QAS is, the higher the recoveries of coarse kaolinite (0.075–0.01 mm and 0.045–0.075 mm) are. But the flotation recovery of the finest kaolinite (0–0.045 mm) decreases with chain lengths of QAS collectors increasing, which is consistent with the flotation results of unsifted kaolinite (0–0.075 mm). It is explained by the froth stability related to the residual concentration of QAS collector. In lower residual concentration, the froth stability becomes worse. Within the range of flotation collector concentration, it's easy of CTAC to be completely adsorbed by kaolinite in the particle size fraction (0–0.045 mm), which led to lower flotation recovery. Moreover, it is interesting that the particle size of kaolinite is coarser, the flotation recovery is higher. The anomalous flotation behavior of kaolinite is rationalized based on crystal structure considerations. The results of MD simulations show that the (001) kaolinite surface has the strongest interaction with DTAC, compared with the (001), (010) and (110) surfaces. On the other hand, when particle size of kaolinite is altered, the number of basal planes and edge planes is changed. It is observed that the finer kaolinite particles size become, the greater relative surface area of edges is, and the more the number of edges is. It means that fine kaolinite particles have more edges to adsorb less cationic colletors than that of coarse kaolinite particles, which is responsible for the poorer floatability of fine kaolinite.     

Fractal distribution of particle size in carbonate cataclastic rocks from the core of a regional strike-slip fault zone

We present particle size data from 31 samples of carbonate cataclastic rocks collected across the 26 m thick fault core of the Mattinata Fault in the foreland of the Southern Apennines, Italy. Particle size distributions of incoherent samples were determined by a sieving-and-weighting technique. The number of weight-equivalent spherical particles by size is well fitted by a power-law function on a log–log space. Fractal dimensions (D) of particle size distributions are in the 2.091–2.932 range and cluster around the value of 2.5. High D-values pertain to gouge in shear bands reworking the bulk cataclastic rocks of the fault core. Low D-values characterise immature cataclastic breccias. Intermediate D-values are typical of the bulk fault core. Analysis of the ratio between corresponding equivalent particle numbers from differently evolved cataclastic rocks indicates that the development of particle size distributions with D>2.6–2.7 occurred by a preferential relative increase of fine particles rather than a selective decrement of coarse particles. This preferentially occurred in shear bands where intense comminution enhanced by slip localisation progressed by rolling of coarse particles whose consequent smoothing produced a large number of fine particles. Our data suggest that during the progression of cataclasis, the fragmentation mode changed from the Allègre et al.'s [Nature 297 (1982) 47] “pillar of strength” mechanism in the early evolutionary stages, to the Sammis et al.'s [Pure and Applied Geophysics 125 (1987) 777] “constrained comminution” mechanism in the subsequent stages of cataclasis. Eventually, localised shear bands developed mainly by abrasion of coarse particles.     

Investigation of mechanism of ultrasound on coal flotation

Coal flotation studies were carried out in ultrasonically assisted flotation cells. Representative hard coal slime samples from Prosper-Haniel Coal Preparation Plant located in Bottrop, Ruhr Region of Germany were used for this purpose. A Wemco type flotation cell was fitted with transducers and tests were carried out at variable frequency and power. The reagent for coal flotation was Ekofol-440 with variable dosages during conventional and ultrasonic flotation experiments. The results showed that ultrasonic coal flotation yields more combustible recovery and lower ash values in concentrates than conventional flotation by using similar reagent dosages. These results are explained on the basis of efficient surface cleaning of the coal particles.     

Surface chemical analysis in coal preparation research: complementary information from XPS and ToF-SIMS

The application of X-ray photoelectron spectroscopy (XPS) to coal surface characterisation for preparation research is described. Progress towards the acquisition of complementary surface chemical information by time-of-flight secondary ion mass spectrometry (ToF-SIMS) is also discussed. Surface-based beneficiation techniques such as flotation are assuming greater importance as the proportion of fines in raw coal increases due to the proliferation of high capacity mining methods. A necessary condition for the floatability of a coal particle is adequate hydrophobicity, and the degree of hydrophobicity of the flotation concentrate is one factor influencing the ease with which its dewatering can be affected. The hydrophobicity of a coal is very difficult to measure directly because of microporosity, and it is often necessary to deduce the degree of hydrophobicity from a knowledge of the surface chemistry. XPS is able to provide sufficient analytical data to allow relative levels of hydrophobicity to be estimated. In principle, ToF-SIMS should be able to supply additional information enabling refinement of such estimates; however, there are insufficient data at present to allow the ionic fragments detected to be related to specific functional groups at the coal surface.     

The destabilization of froth by solids. I. The mechanism of film rupture

The interactions of several particles of different shapes and degrees of hydrophobicity with an artificially thinned film of water were recorded by means of high-speed cinematography. On bridging a film, a particle causes it to rupture only when the two three-phase boundary lines are forced to migrate to the same point on the particle. A contact angle on the particle of θ > 90° is normally required before this migration will occur, but particles that have special shapes can rupture films even when θ < 90°. A liquid film has to be thinned to half the diameter of a particle or less before it can be ruptured by the particle.     

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.     

Effects of surfactant adsorption and surface forces on thinning and rupture of foam liquid films

The properties of thin liquid films (TLF) are of paramount significance for colloidal disperse systems, and a number of industrial processes, including froth flotation. In flotation, the bubble–particle attachment is controlled by the thinning and rupture of the intervening liquid film between an air bubble and a mineral particle. The froth evolution and its transient stability are also a function of the drainage and rupture of liquid films between air bubbles. Surface-active substances (surfactants) are used as flotation reagents to control the behavior of the liquid films. This paper presents a review of our research in the area of surfactant adsorption, surface forces and liquid films. It mainly focuses on the validation, application and extension of the Stefan–Reynolds theory on the liquid drainage. The extension of the Stefan–Reynolds theory comprises surface forces (disjoining pressure), surface tension variation, caused by the adsorption and diffusion of surfactants. Both the experimental and theoretical results are mostly related to the free (foam) films formed between two bubbles but can be principally extended to emulsion films between two oil drops and wetting films between an air bubble and a solid surface.     

The effect of thermal treatment on the flotation of chrysocolla

Flotation studies using a Hallimond tube have been carried out on purified samples of chrysocolla. The results confirm that by heating the sample to 550°C, flotation of the sulphidized sample with amyl xanthate is considerably improved. Flotation with sodium dodecyl sulphate is also considerably higher. The recovery with cationic collectors is not modified by the thermal treatment.Electrophoretic mobility measurements and flotation studies using benzene instead of air for the collection of the particles suggest that the increase in flotation after thermal treatment is a consequence of (1) an increase in the solubility of copper ions and their adsorption on to the surface of the particles, and (2) an increase of the intrinsic hydrophobicity of the particles due to condensation of some of the free silanol groups on their surface.     

Organization of amphiphiles, Part VIII: Role of polyoxyethylated alkylphenols in optimizing the beneficiation of hydrophilic mineral

The floatability of silica has been determined by adsorbing various concentrations of a series of polyoxyethylated nonyl and octyl alkyl phenols of varying oxyethylene units (10–40 units) to investigate the role of adsorbed layer. It is seen that the floatability of silica increases with increase in concentration till a maximum of  90% in premicellar region and then decrease to minimum of 40–45% in all cases in spite of the significant differences in adsorption densities. Zeta potential measurement reveals that a thin oxyethylene layer is formed at silica–water interface masking silica surface (Pramila K. Misra, P. Somasundaran, J. Surf. Deterg., Vol. 7, 2004, 373). This layer with oxyethylene units lying on silica surface and alkyl chain dangling to the bulk solution provides the same extent of hydrophobicity. The decrease in flotation recovery has been attributed to increase in the solvent hydrophobicity due to formation of premicellar aggregates and micelles.