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.     

Effect of alcohol and polyglycol ether frothers on foam stability,bubble size and coal flotation

The frothers of alcohol family (MIBC and Alpha-terpineol) were compared with polyglycol ethers (DF-1012) in terms of two phase characterization parameters like foamability, foam stability, surface activity and bubble size distribution. In this research, fundamental two phase frother characterization parameters were linked with three phase coal flotation behavior.     

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.     

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.     

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.     

Effect of particle size distribution on the bio-cementation of coarse aggregates

The effect of grain size distribution on the unconfined compressive strength (UCS) of bio-cemented granular columns is examined. Fine and coarse aggregates were mixed in various percentages to obtain five different grain size distributions. A four-phase percolation strategy was adopted where a bacterial suspension and a cementation solution (urea and calcium chloride) were percolated sequentially. The results show that a gap-graded particle size distribution can improve the UCS of bio-cemented coarser granular materials. A maximum UCS of approximately 575 kPa was achieved with a particle size distribution containing 75% coarse aggregate and 25% fine aggregate. Furthermore, the minimum UCS obtained has applications where mitigation of excessive bulging of stone/sand columns, and possible slumping that might occur during their installation, is needed. The finding also implies that the amount of biochemical treatments can be reduced by adding fine aggregate to coarse aggregate resulting in effective bio-cementation within the pore matrix of the coarse aggregate column as it could substantially reduce the cost associated with bio-cementation process. Scanning electron microscopy results confirm that adding fine aggregate to coarse aggregate provides more bridging contacts (connected by calcium carbonate precipitation) between coarse aggregate particles, and hence, the maximum UCS achieved was not necessarily associated with the maximum calcium carbonate precipitation.     

Dependence of flotation rate on particle size and fractional mineral content

Specific rates of flotation, K, as a function of particle size, d, and fractional mineral content, W, were measured for a quartz-hematite ore in a continuous flotation system using hydroxamate collector. The resulting K-d-W surface is explained in terms of flotation mechanisms and results of previous investigators. A K-d-W relationship will be of value to flotation models.     

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.     

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.     

Criterion of vehicle stability in floodwaters based on theoretical and experimental studies

Vehicles parking on streets or roads can cause various hazards to people and property when they are swept away by urban floods. It is therefore appropriate to investigate the criterion of vehicle stability for such flood conditions, especially for different scenarios and where the criterion of vehicle stability is usually represented by the incipient velocity for the vehicle. In the current study, different forces acting on a partially submerged vehicle are outlined, together with the corresponding expressions of these forces, and a mechanics-based formula of incipient velocity is given for partially submerged vehicles under different orientation angles. About 200 runs of flume experiments were conducted to obtain the conditions of water depth and corresponding velocity at the threshold of vehicle instability for three orientation angles, using two types of die-cast model vehicles at two model scales. Experimental data obtained from the large-scale model vehicles were then used to determine two parameters in the derived formula. Finally, incipient velocities for three vehicle orientation angles were estimated using two different approaches, including predictions using the scale ratios from the small-scale model vehicles and computations based on derived formula using the prototype vehicle parameters. These critical conditions for the prototype conditions, based on the scale ratios, compared well with the calculations obtained using the derived formula, which guaranteed the predicative accuracy of the formula. In addition, the effect of different ground slopes on the vehicle incipient motion was also investigated, using similar experiments and based on the theory of similarity, which indicated that the incipient velocity for a small passenger vehicle on a ground slope of 1:50 was about 25 % lower than the value on a flat ground for an incoming depth of 0.25 m.     

超高排土场的粒径分级及其边坡稳定性分析研究

明显的粒径分级是超高排土场区别于土质边坡的最重要特征。针对西源岭413台阶排土场,结合开发的HHC-CA模型和现场散体粒径分布情况的调查,建立了考虑超高排土场粒径分级特征的边坡模型。在此模型的基础上,借助FLAC3D软件分析了现状边坡和各种堆排模式下的边坡稳定性。结果表明:西源岭413台阶排土场现状边坡上部位移矢量表现为下沉,其下沉方向与坡面保持同向,中部位移矢量表现为剪切,下部位移矢量略有反抬升的趋势。其边坡破坏模式为顶部平台拉裂,中部以圆弧形剪出;此排土场的现状边坡处于暂时性稳定阶段。而采用全覆盖式多台阶排土的边坡上部位移矢量表现为下沉,在排土场底部过渡到水平方向;破坏模式为顶部平台拉裂,下部以圆弧形剪出。仅考虑堆积散体的材料强度对排土场稳定性影响时,超高排土场的粒径分级有利于排土场边坡的稳定。     

Perxanthates — A new factor in the theory and practice of flotation

A compound with a UV absorption maximum at 348 nm was observed in Mount Isa copper flotation plant solution. This spectrum was similar to that of the product of reaction of xanthate and peroxide in dilute, alkaline aqueous solution. The compound was termed perxanthate (more correctly “O”-alkyl dithiomonoperoxycarbonate).A new compound, ammonium sec-butyl perxanthate (C₄H₉ OCSSO·NH₄), was prepared by reacting potassium sec-butyl xanthate and hydrogen peroxide in dilute alkaline solution, acidifying, extracting into iso-octane, and precipitating with anhydrous ammonia. Solutions of this compound were compared with solutions containing the Mount Isa compound. Each compound was found to have the same UV absorption spectrum in a given solvent (alkaline aqueous, acid aqueous, chloroform, iso-octane, iso-amyl alcohol, and n-butyl acetate), but the spectra were different in different solvents (especially in alkaline and acid aqueous solutions). Both compounds could be extracted from acid, but not alkaline, aqueous solutions by organic solvents, and both had similar IR and mass spectra.It was concluded that the perxanthate in plant solution resulted from reaction of xanthate with peroxide derived from reduction of oxygen during flotation. This lends credence to the electrochemical theory of flotation and has some important theoretical and practical implications.     

Particle loss and volume change on dissolution: experimental results and analysis of particle size and amount effects

Soil particles may be lost through dissolution, degradation or erosion. Regardless of the process of loss, there follows a change in soil structure both in terms of phase composition and grading. In this paper, the influence of size and amount of particle loss on phase composition at two stresses is investigated. The tests are performed on sand–salt mixtures, loaded in a modified permeation oedometer and subsequently dissolved. Changes in overall volume and void ratio are presented. Two significant observations about the volumetric consequences of particle loss can be made. First, overall volume changes are directly related to the amount of dissolved particles and to a lesser extent, the size of particle lost. Second, particle loss leads to an increase in void ratio; the magnitude of the increase is related to the amount of dissolved particles but appears not to be sensitive to either the size of particle lost or the pre-dissolution void ratio. Based on the observed response and a dissolution-induced void change parameter, the influence of different mechanisms of volume change is discussed. Tests were performed at two different vertical stresses with no discernible influence on void ratio change.     

A theoretical and experimental study on the behaviour of lignosulfonate-treated sandy silt

The effectiveness of an environmentally friendly stabilising agent for soil, namely, lignosulfonate was examined through a series of laboratory tests. A simple bounding surface plasticity model was developed to capture the bonding effects induced by lignosulfonate. One of the appealing aspects of the model is that it can incorporate the mechanical behaviour of the bonded soil during shearing, including the brittle and ductile failure modes. Validity of the model was verified by experimental results of lignosulfonate-treated soils under different stress path conditions. The mechanical behaviour of chemically treated soil was adequately captured by the model.     

Fe-Mg cordierite stability in high-grade pelitic rocks based on experimental,theoretical, and natural observations

Stability relations of Fe-Mg cordierite with K feldspar have been determined for conditions of muscovite-quartz instability, applicable to highgrade metamorphism of pelitic rocks. Fe cordierite, K feldspar, and water break down to Fe biotite, sillimanite, and quartz at pressures above a line through 640 ° C, 2kbar and 710 ° C, 2.7 kbar. A P-X diagram for the Fe-Mg analogue of this reaction at 675 ° C is consistent with a naturally occuring cordierite-biotite K _D value of 0.53 if Al content of biotite and cordierite water of hydration are taken into account.At higher temperatures Fe cordierite breaks down alone to almandine, sillimanite, quartz and water at pressures above a line through 650 ° C, 3.41 kbar and 760 ° C, 2.9 kbar. For the Fe-Mg reaction, P-X data up to 4 kbar may be extrapolated with use of natural K _D values increasing toward one with increasing temperatures.Lines of constant cordierite composition for the two reactions intersect in an Fe-Mg univariant reaction of sillimanite-biotite-quartz to cordieritealmandine-K feldspar-water which is metastable relative to melt at = P _tot Reduced water pressure and impurities in the garnet and K feldspar greatly reduce the temperature of this reaction so that it becomes a reasonable reaction for upper amphibolite and granulite facies conditions.The results demonstrate that (1) cordierite may be used as a geobarometer if temperature and approximate can be estimated, (2) almandine low in Mn and Ca does not participate in cordierite reactions where muscovite is present, and (3) the reaction which forms cordierite, almandine, and K feldspar is a possible melt-forming reaction which, under reduced , occurs about 50 ° C above the muscovite melting reaction.     

Counting error in petrographic point-count analysis: A theoretical and experimental study

The binomial model, commonly used to estimate counting error in point-count analysis, misestimates this error when the observation points on a grid are positively or negatively correlated. A model, called the cell model, is proposed as an alternative to the binomial model for use in studies, especially with coarse-grained rocks, in which such correlation is known or thought to exist. In the new model the thin section is conceptually partitioned into a number of cells (six is recommended), and the assumption is made that the proportions in the individual cells are statistically independent and that their variance does not differ from cell to cell. Empirical relations obtained from a suite of 200 thin sections of limestones are in reasonable support of the prediction that large particle size adversely affects counting error estimates based on the binomial model.