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By Vladimir Vigdergauz

"Electrochemical studies of metal sulfides in connection with their floatability are discussed. According Frumkin, sorption of electroneutral organic substances has a maximum near the potential of zero charge. This idea initiated attempts of application of electrochemical methods for the controlling of organic collector sorption and mineral flotation. The lecture reviews results of electrochemical studies of the processes taking place during sulfide flotation: redox-state of mineral surfaces and xanthate solutions, xanthate sorption and hydrophobic layer composition, surface wettability and flotation recovery of sulfide minerals. Redox-transitions of minerals, transport of ions and charging of mineral surfaces, electroreduction of dissolved oxygen and accompanying processes of oxidation of minerals and reagents-collectors, - all these matters became the subjects of detailed research. Cyclic voltammetry, rotating disk electrodes, spectro-electrochemical techniques and other modern experimental methods now routinely accompany studies of mineral processing. Relatively new electroanalytical techniques like the voltammetry of mineral particles immobilised on electrodes using polymeric binders have become extremely useful for studying weakly conductive minerals and dispersed flotation products. Full discussion of electrochemical studies of metal sulfides in relation to mineral processing must include bioelectrochemistry and electrocatalysis which open exceptional possibilities for selective leaching of gold and non-ferrous metals. At this time, the paper focuses on the sulfide flotation as a potential-dependent process; the problem of oxygen and its influence on the sulfide flotation; the electrochemical aspects of xanthate oxidation and sorption; theory of suspended electrodes as applied to the mineral slurries and experimental study of the effect of electrochemical pretreatment of flotation pulps."

Jan 1, 2014

By F. Henríquez

Traditionally, the implementation of an automated control for a ball mill has been a challenging one. First, it must be capable of processing a variable SAG mill feed while at the same time avoiding to become a process bottle neck. Second thing is, it must deliver an adequate quality product (P80) to the process downstream. Then the ball mill itself and its associated classification equipment has problems of its own: it must maintain adequate control of cyclone?s pressure, density and pump-box level with often, less manipulated variables than needed, namely, variable pump speed and the opening/closing of cyclones. Thus, it becomes a non-linear multi-variable type of process with often too multiple and contradictory control objectives to satisfy simultaneously. On top of that, to extend cyclones availability and yet, maintaining their performance, is must both for process and maintenance purposes. Trying to solve the puzzle, Minera Los Pelambres implemented a novel and successful combination of MPC (Multivariable Predictive Control) and advanced control in two of its newest ball mills, reducing considerably process variability while maintaining high throughput and keeping the process well within constraints limits. Because of their differences in processing capacity, size and topology, two different stabilizing-control strategies were developed, tested and tuned. Hence, for both control approaches their implementation process, main results, areas of applicability, limitations and their key performance indicators are discussed further. This paper also discusses the need of such advance control technologies in the mining industry, including the impact of these technologies on best practices for their implementation, operation and long term sustainability

Sep 1, 2012

By Sanja Miskovic, Manjunath Basavarajappa

In this study, a coupled CFD-DEM (Computational Fluid Dynamics-Discrete Element Method) approach is used to simulate two-phase, solid-liquid flow within the flotation cell. Turbulence plays a key role in flotation cells and level of turbulence is affected locally by the presence of particles. Turbulence in the flow is modelled using Reynolds Averaged Navier-Stokes (RANS) based k-e model. Using particle transport and spatial distribution, mixing mechanism for differed sized particles are analysed. By including the effects of particle-particle collision, particle rotation, and particle translation, as well as the volume occupied by the particles in the fluid, CFD-DEM approach can be used to accurately predict the motion of particles in the turbulent solid-liquid flows with strong coupling. Electrical resistance tomography (ERT) is used to investigate the effect of impeller size, shape, off-bottom clearance and impeller speed on mixing and suspension behaviour inside flotation cell. The effect of flotation impeller design, impeller size, and off-bottom clearance on flow hydrodynamics is investigated. In the case of moderate and high solids loading (> 10 %w/w), energy is dissipated through inter-particle interactions and four-way coupling becomes important (Derksen 2003). The main goal of this study is to understand the effect of particle size and concentration on flow dynamics at high Re in highly turbulent systems using advanced modelling and measurement techniques. Experimental measurements obtained by ERT) system allowed detailed mapping of temporal hold-up profiles of the dispersed phase. Impeller size and off-bottom clearance are found have significant effect on the particle suspension characteristics.

Jan 1, 2014

By Jorge Rubio, Gabriel Berkowitz, Fabiano Capponim, Carlos Perez Guerrero, Elves Matiolo, Denise G. Nunes

This paper describes some advances in flotation research in fines (“F” 38 to 13 µm) and ultrafines (“UF” < 13 µm) mineral recovery by two different techniques, at laboratory scale. Extender flotation and flotation with .multi-bubbles. (bubbles with a wide size distribution) of copper sulphide fines (ore feed of about 1 % Cu) were compared with a .standardised. mill laboratory procedure. Comparative evaluation was made through concentrate grade and recovery (size by size results included), .true. (bubbles-particles attachment only) flotation recoveries and process kinetics. Both techniques yielded higher metallurgical efficiencies than the mill standard but better results were obtained with the extender flotation, with emulsified diesel oil (90 gt-1). Concentrate recoveries were of the order of 85-90 % (84 % in standard conditions), 14-17 % Cu grade (15 % Cu in the standard) and 3.5-4.5 min-1 for the Klimpel rate constant (3 min-1 in the standard). Size by size and true flotation results proved that metallurgical and kinetic gains, obtained with the two techniques, might be attributed to fines and ultrafines enhancement. Data obtained are discussed in terms of physical and physico-chemical parameters related to aggregation and capture (of particles by bubbles) phenomena and the practical potential of these techniques are envisaged.

Jan 1, 2003

By John A. Rumball, Martin R. Houchin

Data from autogenous and semi-autogenous tests in a 1.67m diameter mill have been analysed in terms of a new model for rock abrasion. This model defines specific rate as the rate of production of fines (material less than 13mm) per unit mass of rock, where the term “rock” is applied to all ore pieces of ore coarser than the grate size. In most cases, an allowance for preliminary rounding and cleavage was made. A method has been developed to analyse steady-state data, using piecewise fitting to the cumulative size distributions. The model was compared to the well-established models, which are based on the population balance method. The specific rate increased for all rock sizes as the volume of 100mm balls in the mill was increased. Tests using a coarser feed and smaller balls provided further evidence that once rocks are rounded, abrasion is due to localised surface damage, caused by impacts, rather than rotational shear. An allowance for rapid rounding of jagged rocks, followed by less rapid abrasion of rounded pebbles was also tested, but the analysis was not conclusive. The average specific rate is a useful measure of the capacity of a primary mill. The effect of power intensity (kW/t of ore) was also investigated as a means of extrapolating the pilot-plant data to large production mills.

Sep 29, 2003

By Sergio Castro, Janusz Laskowski

In the flotation in highly concentrated electrolyte solutions not only ionic strength but also chemical composition, flotation pH and mineral properties play an important role. As a result an improvement or depression may be observed. A strong improvement in the floatability of hydrophobic bituminous coals and other inherently hydrophobic minerals is characteristic for the "salt flotation process", which is carried out in concentrated electrolyte solutions at natural pH and without addition of any flotation reagents. However, pH is a key factor when saline and hipersaline waters with hydrolyzing metallic ions are used as process water. In the case of flotation of Cu-Mo sulfide ores in seawater, molybdenite is strongly depressed by the Mg2+ hydrolysis products when pH is raised to depress pyrite. Process water with a high content of Mg2+ and Ca2+ ions, and this also includes seawater, have deleterious effect on the anionic flotation of industrial minerals with fatty acids. The flotation of potash ores is carried out in NaCl-KCl saturated brine (6-7 mole/L of NaCl and KCl) with the use of long-chain amines. Such a high electrolyte concentration changes dramatically the amine Krafft point making the collector insoluble in brine; its mode of action entirely differs from that in conventional flotation processes.

Jan 1, 2014

By A. M. Amdur, A. N. Matushkina, G. I. Gazaleeva

"The article highlights results of theoretical and practical studies on the enlargement of fine gold in the process of heat treatment. The object of research is refractory gold silicate-carbonate ores of Vorontsovskoe Deposit (Northern Ural), containing fine gold. For setting up experiments and analyzing the results were used the methods of applied mathematics, mathematical statistics, mathematical and physical modeling. Modeling and calculations were performed using the software package HSC Chemistry 6.0, MatLab, setting up a full factorial experiment and other modern modeling methods. Using a scanning electron microscope, the distribution of fine-dispersed ore gold particles by size was studied. It was found that gold particles smaller than 0,4 µm smoothed the vertices and edges, i.e. they are of globules with an amorphous structure. Amorphous materials are nonequilibrium phases with high thermodynamic activity. The physicochemical properties such as melting temperature, diffusion coefficients, the content of metal impurities differ from the properties of the solid phases. In the course of the research were formulated the following scientific bases of the mechanism of enlargement of the gold particles: - the movement of dispersed droplets of gold in the process of external heat to the surface of the ore particles in the pore occurs under the action of thermocapillary pressure; - after melting of the host rock occurs flotation of molten droplets by the bubbles of gases and coagulation of fine gold; - the conditions of flotation drops of gold in oxide melts; floated drops of radius R = 1-100 µm. Analysis of the equilibrium at the perimeter of wetting a drop of gold-oxide melt-gas showed that the scheme of the tension will not significantly differ from the case of solid gold, while the radius of the gas bubbles should be at least 2 times greater than the radius of drops of gold. The proposed method of predicting the results of the enrichment of the proposed scheme, including heat treatment and gravitational centrifugal concentration of crushed ore. Experimental verification of the proposed scheme in the laboratory showed a satisfactory convergence of experiment and prediction. Gold recovery in the concentrate was 33,84 against 33,7 percent forecast. The increase in overall gold recovery to a gravity concentrate after heat treatment is more than 20 %."

Jan 1, 2018

By Shuji Owada, Shinya Suzuki, Chiharu Tokoro, Daisuke Haraguchi, Sayaka Izawa

"Coprecipitation with ferrihydrite has been one of the major treatment method for As(V) removal from wastewater such as acid mine drainage. We already confirmed coprecipitation of As(V) with ferrihydrite consists of two kinds of mechanism; one is two dimensional As(V) uptake to the surface of ferrihydrite by surface complexation and another is three dimensional As(V) uptake into ferrihydrite by surface precipitation. We also already confirmed As(V) adsorption process by ferrihydrite could be quantitatively evaluated by original surface complexation model with parameter values reported by Dzombak and Morel. However, As(V) coprecipitation process couldn’t quantitatively be represented by only the original model. In this study, construction and calculation using surface precipitation model were attempted for As(V) coprecipitation treatment with ferrihydrite. In the surface precipitation model, precipitation was described by the formation of solid compound between ferrihydrite and ferric arsenate. Activity of these precipitates was determined by surface precipitation ratio of FeAsO4(s) obtained experimentally from XANES analyses. Solubility products of surface precipitation of FeAsO4(s) (Ksp_FeAsO4(suf.)) were determined by fitting to sorption densities and surface precipitation ratio in each condition. The values of Ksp_FeAsO4(suf.) were determined 10-7.7 at pH5 and 10-10.2 at pH7, respectively. Based on the obtained Ksp_FeAsO4(suf.) value, As(V) removal and isotherm were calculated for As(V) co-precipitation treatment using surface precipitation model. Good agreement between experimental and calculated values was observed. These results were suggested that the quantitative prediction of As(V) co-precipitation treatment was possible if Ksp_FeAsO4(suf.) value was estimated experimentally."

Jan 1, 2014

By Matthew Thurley

Optimisation and control of comminution, pelletization, and agglomeration processes is a complex task with large potential for gains in productivity, energy efficiency, and particle size distribution quality. One factor in realising these gains is the requirement for fully-automated online particle size distribution measurement. Moreover, online particle size distribution measurement that is based on the particles on the visible surface and can avoid or mitigate substantial errors that result from under-sizing overlapped particles and over-sizing areas of fines particles. Literature review indicates a body of substantially 2D photographic based particle size measurement systems that suffer from a large number of significant errors except in the simplest case of a monolayer of particles under good illumination with limited color variation in the material. In order to measure the visible particles on a pile there are a number of requirements including; avoiding particle delineation errors due to variation in material color and shadows, detect overlapping versus non-overlapping particles, and identify areas of fine particles as fines and not large rocks. Results are presented using a fully-automated online measurement system of crushed rock on conveyor belt using a 3D surface laser profile. The system provides continuous online measurement and results are shown on over four hours of production after the primary crusher. Size distribution results are calculated using volumetric estimation of the particles on the surface of the pile. The results show a strong capability to discriminate size variation especially in the 10% and 20% passing values. Furthermore results show that if areas of fines are misclassified as large rocks, and overlapped particles misclassified as small rocks, then a near complete loss of discrimination occurs for the P10 and P20 values which become largely constant values.

Jan 1, 2014

By Dingwu Feng, Jannie S. J. van Devente

"The effect of ultrasonication on reactions at solid/liquid interfaces was investigated in two slurry systems, i.e. gold cyanidation and geopolymerisation. The kinetics of gold extraction were significantly enhanced and the cyanide consumption was reduced in the cyanidation of a pyrite concentrate using ultrasonication, probably due to the prevention of leaching passivation, the improvement of the dissolution of the gold host sulphides and the oxidation of soluble sulphides to sulphate. The effectiveness for ultrasonication was improved with the injection of oxygen and the addition of dithiophosphate through enhancing the formation of the oxidation radicals and selectively inducing cavitation bubbles directly at the sulphide interfaces. Ultrasonically enhanced cyanidation could render currently uneconomic deposits viable for extraction by improved cavitation efficiency with the aid of surfactants.Ultrasonication increased the compressive strength of the formed geopolymers through accelerating the dissolution of the Al-Si materials, strengthening the bonds at the solid particle/gel phase interfaces, enhancing the polycondensation process and improving the formation of semi-crystalline to crystalline phases. The use of power ultrasound will yield high-performance geopolymer materials."

Jan 1, 2003

By Jan J. Cilliers, Nicolas Barbian, Esther Ventura-Medina

"Froth structure and stability are known to play an important role in determining flotation recovery and selectivity. An industrial sampling campaign was performed to develop a clearer understanding of the effect of flotation variables on froth stability and the role played by the resulting stability on flotation performance.Froth stability was estimated as the fraction of bubbles bursting on the surface of the froth through image analysis and the solids loading on the bubbles at the top surface. It was generally found that high air flowrates resulted in a drop of froth stability showed by a drop in the fraction of air overflowing and a decrease in the solids loading and simultaneously produced low copper recoveries and low concentrate grades. Deep froths only allowed a small fraction of air to overflow and consequently produced low recoveries. An increase from a standard to high frother dosage did not result in a larger fraction of air overflowing, hence producing low recoveries. Likewise, low frother addition only allows low recoveries because the resulting unstable froth cannot support itself. Low aeration was found to be preferential as it allowed high particle loading, therefore high bubble stabilisation, and low gangue entrainment, resulting in the highest flotation performance.Additional laboratory tests were performed to introduce a new stability parameter and to give a clearer understanding of the effect of flotation variables on froth stability. The results confirmed some of the observations made on the plant."

Jan 1, 2003

By Lawrence Bbosa, Aubrey Mainza, Indresan Govender

"Positron Emission Particle Tracking (PEPT) and the Discrete Element Method (DEM) are used to develop a probability based model for the power draw of a tumbling mill. Experiments are conducted using dry spherical glass bead charge in a laboratory scale tumbling mill, which is mounted with a torque transducer and tachometer to measure mill power. Particle tracking information from PEPT is used to reconstruct the motion of glass beads and infer the overall charge behavior, while DEM is employed to simulate particle motion and interaction, with collision mechanics calculated using the Hertz-Mindlin contact model. For both sets of data, the product of torque and average angular velocities in discrete cells are accumulated to obtain mill power. This method is found to be within statistical agreement with measured power for all tests. The information from both techniques is then used to develop a model for the power draw as a function of particle size, mill speed and volumetric filling. Predictions of the model match well with measured and calculated values. The model is found to predict mill power within close agreement with measurement and follows trends consistent with existing work on tumbling mill modelling."

Jan 1, 2014

By L. Weitkämper

The big challenge at present and in the future is the economization of resources. This is applied for the whole industry but particularly in fields of mineral processing. The most important resources are energy and water. The shortage and price advance of energy is worldwide noticeable whereas the shortage of water is regionally limited at present. However due to the increasing world population, associated with a rising standard of living, water will become more and more important. Studies of the Unesco from 2001 indicate that the total water consumption raised seven times since the last 100 years at a growth of population of just three times. (UNESCO-Currier, 10/2001). This trend is going to be increased. While today more than 90 % of the humanity has access to clean water, in 2050 just about 50 % will be in the same situation. These figures indicate the importance of a gentle handling with the resource water. Further more the disposal of fine products, containing most of the water, is an environmental concern and in the future the mining and processing of raw materials will become important and necessary in desert, arid or permafrost areas. In these areas just efficient dry cleaning technologies will allow an economical beneficiation or better enable the processing at all. Most of the separation technologies with high throughput rates in mineral processing are based on wet processes. This applies especially for the separation of fines. Though there are some dry technologies available for the separation of coarse materials, like pneumatic gravity separation [air jigs and air tables], magnetic separation and not least sensor based sorters. Dry separation of fines is bounded mostly on cost intensive and low throughput technologies. The pneumatic separation undergoes at present a renaissance, mainly due to the development of the all air jig by the German supplier Allmineral. This newly developed sorting device yields good results in the separation of coarse to medium size material. All these facts and figures show the potential and motivation for developing an efficient dry separation device for fines. The following article delineates the development, performance and chance of a new dry separation technology for fines.

Jan 1, 2014

By Ghislain Bournival, Seher Ata, Graeme J. Jameson

A common method to prevent bubbles from coalescing in a flotation cell is by the addition of surfactants, called frothers. The gas dispersion properties in a column were tested for solutions of 1-pentanol, tri(propylene glycol) methyl ether, and poly(propylene glycol) in the presence of sodium chloride. The dependency of surfactant on the gas holdup can be divided into regions. It seemed that for a sufficiently low concentration of surfactant, even a stronger surfactant could show a transition in gas holdup from constant/decreasing to increasing with concentration. This region, however, was not marked by a decrease in the average bubble size. In addition, PPG gave higher gas holdup values while averaging larger bubbles. On the other hand, sodium chloride mostly affected the gas holdup when the concentration was high enough to prevent bubble coalescence. Another parameter affecting the gas holdup was the superficial gas velocity. A linear dependency was found between the two under a bubbly flow regime. The current study showed that both surfactants and salt could slightly affect the influence of the superficial gas velocity on the gas holdup.

Jan 1, 2014

By Harri J. Lehto, Marja I. Oja

Empirical models used for predicting the performance of screens on the basis of capacity, cut size, water split and grade efficiency curves were evaluated. This paper reports experimental results obtained with single-deck Derrick screens. The performance of the screen was tested with limestone in a separate screen set-up, in a pilot plant and in industrial scale test runs. The results of pilot plant experiments showed that the measured water split was higher than the measured bypass. This is an indication to that water flow does not entrain the same proportion of all fine particles present in the feed which is advantageous for screening. The experimental design for the industrial test runs was made on the basis of the pilot plant tests. Suitability of the existing models has been checked and accuracy compared. The tests showed that best grade efficiency model was the Rosin-Rammler model. An empirical model for the evaluation of the model parameters as a function of pulp density of the feed and the load of the screen is suggested.

Jan 1, 2003

By Junji Shibata

In a present process to treat the tungsten carbide tool waste, the wastes are roasted in air and then an alkali leaching is carried out in an autoclave. An environmentally friendly process is required to recover rare metals (Co and W) from the wastes. The effect of mechano-chemical (MC) treatment on leaching of rare metals was investigated in this study. The solvent extraction and crystallization-stripping methods were applied to separate and recover tungsten and cobalt in the leached solutions. The MC treatment for the rare metal leaching is effective to dissolve rare metals from the wastes due to the change in crystalline structure of WC and oxidation of WC with KMnO4. Cobalt ions are extracted with D2EHPA by a cation exchange reaction. Tungsten in the leachate can be extracted by TOA (tri-octyl amine) as an extractant, because tungsten species exist as a form of anionic species in acidic solution. The rare metals in organic phase are recovered as insoluble salts such as oxalates and ammonium salts in the crystallization-stripping process. Keywords:unheated oxidation, solvent extraction, crystallization-stripping, recycling

Sep 1, 2012

By Y. J. Ferdosi

This paper presents the outcomes of the preliminary investigation focused on the potential usage of Electrochemical Impedance Spectroscopy (EIS) in minerals processing. Currently, Electrochemical Impedance Spectroscopy has been successfully employed in the characterization of multilayer structures formed as molecules adsorb on flat surfaces and is commonly used in bio-related research. Few studies have explored the application of EIS in minerals processing, particularly for mineral particles and flotation systems. In the first series of tests, the impedance response was investigated as a function of particle size, shape and hydrophobicity using model quartz particles. The particle size fractions and the shape were found to contribute to the impedance response. The more hydrophobic quartz particles resulted in a higher impedance values. Further tests involved pure sulfide minerals including chalcocite, bornite, chalcopyrite and pyrite. The AC impedance measurements were conducted as a function of collector (sodium ethyl xanthate) dosage. The AC Impedance data was modeled using the combination of reference circuits. It has been shown that adsorption of collector onto sulfide minerals surfaces results in a higher magnitude of impedance. Increasing the collector dosage resulted in an increase in AC impedance for chalcopyrite, while a decrease was observed for chalcocite. Significant variations in impedance were exhibited by bornite and pyrite with a gradual increase in collector dosage.

Sep 1, 2012

By Richter, E. Charikinya

"Mineral processing unit models require information on particulate properties such as particle size, solids flowrate and mineralogical composition to model their operations. Process models that describe the separation process can be classified based on the level of information required from the ore, i.e. the feed stream to the separating unit. The most comprehensive level of mineral processing models is the particle-based modelling approach. Particle based modelling describes a modelling approach where mineral composition, mineral liberation and textural information of particles making up the process streams is used in modelling. The advantage of this approach is that all model streams carry particle level information (size, liberation, shape). This information is obtained by applying automated mineralogy techniques such as Quantitative Evaluation of Minerals by Scanning Electron Microscopy (QEMSCAN) analysis which provide accurate and detailed information on process stream particle properties. Currently the use of liberation information in modelling and simulation is rare, due to the limited number of separation models that liberation data as input. The objective of this study is to develop a particle based model for a dry magnetic separator, where mineralogical information is used directly to simulate a dry magnetic separator operation. Magnetic separation tests were carried out on high, medium and low grade magnetite ores using a laboratory magnetic separator. Streams from the separator were sampled and sized for chemical and liberation analyses. A sized mass and elemental balance around the magnetic separator was carried out. The elemental assays of each stream were converted to mineral quantities and a sized mineral balance was done. QEMSCAN measured liberation data was reconciled to the mineral balance based on mineral quantities obtained from chemical assays. This was followed by the development of a particle based model that calculates the trajectory of a single particle based on its mineral composition and textural properties. The model was tested on experimental data and was able to predict the effect of variation in process feed stream mineralogical attributes (liberation, grade, particle size) on magnetic separation performance. Results of this study highlight the benefits of the particle based modelling approach. INTRODUCTION The extraction of mineral values from ore requires liberation of the value minerals from the gangue followed by their separation. Liberation is achieved by size reduction operations (Desmond, 2008; Fuerstenau and Abouzeid, 2002). Separation of gangue material from value mineral takes place in various mineral upgrading stages such as classification, magnetic separation and flotation. In these concentration stages value minerals are separated from gangue minerals based on the physical properties of the ore particles making up the feed such as size, liberation, volume of magnetic material and density. The success of separation is related to the liberation of the feed particles, the performance of the separation technology applied, as well as the inherent characteristics of the feed material (Leißner et al., 2013)."

Jan 1, 2018

By Lei Pan, Roe-Hoan Yoon

"Direct force measurement for bubble-particle interaction has been difficult due to bubble deformation, which makes it difficult to know the separation distances between the two macroscopic surfaces. In the present work, we have developed a method of monitoring the deformation accurately, while directly measuring the interaction forces. In effect, we can ‘see’ bubbles interacting with mineral surfaces under different hydrodynamic and chemical conditions and determine both the hydrodynamic and surface forces involved. In the present work, a high-speed camera has been used to record the optical interference fringes of a thin liquid film (TLF) of water formed on a mineral surface. The recorded fringes are then used to reconstruct the spatiotemporal profiles, from which one can determine the hydrodynamic pressure using the Reynolds lubrications theory. From the forces directly measured in the present work and the hydrodynamic pressures obtained from the fringes, we have determined the disjoining pressure. The results show that air bubbles interacting with hydrophilic surfaces form stable TLFs with zero contact angles. The TLF formed on a hydrophobic surface thins fast, form a ‘pimpled’ film, and ruptures to form a finite contact angle. The new information obtained in the present work may be useful to better understand the role of hydrodynamic and surface forces affecting bubble-particle interactions."

Jan 1, 2014

By M. Brozek

The particle settling velocity is the argument of separation in such processes as classification and enrichment in jigs. It characterizes material forwarded to the separation process and belongs to the so-called complex arguments because it is the function of particle density and size. i.e. the function of two simple arguments. The affiliation to a given subset is determined by the values of two mag-nitudes and the distribution of such argument in a sample is the function of distributions of particle density and size. The paper will present a method of determining the distribution of settling velocity in the sample of spherical particles for the turbulent particle motion in which the settling velocity is expressed by the Newton formula. Because it depends on density and size of particle which are random variable of certain distributions, the settling velocity is a random variable. Applying theorems of probability, concerning distributions of function of random variables, the authors will present general formula of probability density function of settling velocity for the turbulent motion and particularly calculate probability density function for Weibull?s forms of frequency functions of particle size and density. Distribution of settling velocity will calculate numerically and perform in graphical form.

Jan 1, 2014