Application of Statistical Analysis on the Bubble Surface Area Flux in a Column Flotation Cell

Flotation is a widely used separation process with applications from mineral separation to de-inking of recycled paper, waste water treatment, and solid remediation. In flotation column, bubble surface area flux (S_b) has been reported to describe the gas dispersion properties, and it has a strong correlation with the flotation rate constant. No information is available regarding S_b for coal flotation in column cell. This paper describes the effects of hydrodynamic parameters on S_b by means of a 2³ factorial experimental design in designed flotation column using coal slurry. The results showed that S_b increased with increasing superficial gas velocity and frother concentration, but decreased with increasing solid concentration. The main and interaction effects of operating parameters on S_b were evaluated using Yates’ analysis. The statistical model was developed to predict S_b in column flotation cell using experimental data. This paper also presents the development of the statistical model and the validation using a number of additional data sets. There is a good agreement between experimental results and predicted results from the developed model.     

低阶煤可浮性及浮选速率模型研究

针对低阶煤浮选困难的问题,采用煤质分析和筛分试验研究了低阶煤的可浮性。在此基础上进行了低阶煤浮选速度试验,并利用试验结果对低阶煤的浮选速率模型进行曲线拟合,经过MATLAB数值计算建立了最终的浮选速率模型。煤泥可浮性试验表明:低阶煤中挥发分、水分和O含量较高,亲水性强,可浮性很差。浮选速度试验表明,随着浮选时间的增加,精煤产率逐渐升高,尾煤产率逐渐降低,当精煤灰分为11.50%时,精煤产率仅为34.46%,尾煤产率高达65.54%,尾煤灰分仅为19.95%;2种浮选速率模型中,一级矩形分布模型计算误差较小,且相关系数平方R2更接近1,达到了很高的拟合精度,因此一级矩形分布模型是低阶煤最合适的浮选速率模型。     

Experimental studies and numerical model validation of overflowing 2D foam to test flotation cell crowder designs

A computational fluid dynamics model of froth motion has been developed to assess different flotation cell designs. This work presents an implementation of the model in a 2D case, to compare the simulated bubble velocity distribution and streamlines to an experimental foaming system. The model uses finite elements to solve Laplace's equation for a potential function from which the foam velocity can be obtained. It requires the air recovery, or the amount of air that overflows a flotation cell as unburst bubbles, as an input parameter to calculate the foam velocity distribution and bubble streamlines. The air recovery was obtained by image analysis from a vertical, overflowing monolayer of foam (2D) created in a Hele-Shaw column, which mimicked important flowing properties of flotation froths such as coalescence. Inserts were included in the foam column to represent potential crowder designs for industrial flotation cells. Three different designs were chosen to compare the effect of insert depth and shape, including rectangles and a triangle. The effect of the insert design on the overflowing foam is obvious from visual assessment of the bubble streamlines and velocity distribution, which were closely agreed by both the experiment and model.     

Gas‐Liquid Mass Transfer Approach applied to the Modeling of Flotation in a Bubble Column

A kinetic model developed to describe flotation in a bubble column is presented. This model, developed on the basis of the theory of mass transfer in gas‐liquid flows, makes explicit in its formulation the effect of the superficial saturation of bubbles on the kinetics of flotation. The model is applied to the simulation of flotation column experiments for which the classical first‐order models, commonly used in flotation modeling, are insufficient to represent the flotation kinetics. The results of the simulations obtained under different hypotheses of simplification and compared to experimental data show that the model succeeds in representing the flotation kinetics in these cases.     

Flotation of blue-green algae using methylated egg ovalbumin

The removal of blue-green algae by dispersed gas flotation was conducted. Methylated ovalbumin (MeOA) was used as frother and flocculant, which is a biodegradable substance. The continuous flotation experiments were conducted at different feed mass flow rate of the blue-green algae cells and MeOA. The operating variables were the mass flow rate of blue-green algae cell and MeOA, the initial concentration of the cells and MeOA, and superficial gas velocity. The results showed that the mass flow rate of MeOA was the most dominant variable affected by the removal efficiency and that the removal efficiency achieved ca. 0.85 when a ratio of the mass flow rate of MeOA and that of the cells was over 0.3. A proposed flotation model considering the adsorptions of MeOA to the cells, MeOA to bubble surface and the cells bearing with MeOA to bubble surface was applied to explain the experimental removal efficiency. The experimental and the calculated removal efficiency were within error 19%, indicating that the proposed model was valid fundamentally.     

浮选机模型三维构造的研究

运用3DS－MAX软件,建立一个以造型函数库为核心,构造浮选机构件模型的方法和过程,模拟浮选机的工作原理。     

A Study of Kinetics on Induced-Air Flotation for Oil-Water Separation

Abstract

Induced-air flotation makes use of the centrifugal force of a high-speed backspin impeller through which gas is introduced at the top and liquid at the bottom. The gas and liquid become fully intermingled and, after passing through a disperser outside the impeller, form a multitude of gas bubbles, thus completing the flotation separation process of a liquid-solid or liquid-liquid heterogeneous separation process of a liquid-solid or liquid-liquid heterogeneous system. The flotation machine used for treating oily sewage generally belongs to the four-cell series. Its good points are that the machine has a high removal efficiency for oil separation, shortens retention time, and has great treatment capacity. The device has been widely used in treating oily sewage in recent years (1, 2). In order to provide a basis for establishing a method of design computation and for screening appropriate chemicals, this study was initiated to gain an understanding of the variables controlling the induced-air flotation process for oil-water separation. An experimental device for simulating tests has been developed. In order to analyze its mechanism, a kinetic model of oil-water separation has been put forward. By the use of the experimental result, correlative equations, which can estimate the parameters of the model, have been obtained.     

Modeling and simulation of separation process in flotation system

In order to design a flotation circuit to remove ink and contaminants from slushed old corrugated container (OCC) pulp suspension, a model based on mass balance was developed. The model is a five fractional model, which handles mass flow rate of ink, fiber, fines, filler and dichloromethane (DCM) extractives. A detailed method of calculating the deinking selectivity of a material from experimental data, described in terms of reject ratio, is presented. Three flotation deinking systems were simulated. In a single stage flotation system, increasing the number of flotation cells improved cleanness of the accept pulp suspension while it decreased yield at the same time. Yield can be increased by adding a second stage and by introducing the accept flow of the second stage into the feed flow of the first stage. However, the cleanness of the accept pulp was deteriorated. It was shown that yield can be increased without compensating the cleanness of the accept pulp by utilizing the accept pulp from the second stage for another paper machine line instead of sending back to the feed flow of the first stage.     

CFD SIMULATION ON INFLUENCE OF SUPERFICIAL GAS VELOCITY,COLUMN SIZE,SPARGER ARRANGEMENT,AND TAPER ANGLE ON HYDRODYNAMICS OF THE COLUMN FLOTATION CELL

The use of flotation columns in the mineral processing industry has experienced a remarkable growth over the years. The detailed hydrodynamics study of a column flotation cell demands the solution of mass, momentum, phase-transfer, and turbulence quantities. Simulations have been carried out to examine the influence of superficial air velocity, column size, column taper angle, and sparger arrangement on hydrodynamics of the column flotation cell. A commercial CFD software package (ANSYS CFX 10.0) has been used to predict the complex unsteady air-water flow. The k-ε turbulence model for shear-induced turbulence, Sato's eddy viscosity model for bubble-induced turbulence, and the effect of interfacial momentum transfer terms (lift force, wall force) were considered. Present findings suggest use of low height-to-diameter ratio, low airflow rate, small column taper angle, and uniformly distributed sparger to achieve good separation in a column flotation cell.     

Convective-dispersive gangue transport in flotation froth

The transport of gangue through flotation froth has been described by solving the convection-diffusion equation. Gangue recovery is predicted to be proportional to liquid recovery, which is consistent with experimental observation. In addition, it is seen that the dependency of gangue recovery upon particle size is due to processes within the pulp phase rather than the froth, insofar as the transport of particles in a given froth is approximately independent of size. The importance of maintenance of positive bias in column flotation, previously stressed by other workers, is reinforced. This model utilises a simplified representation of the froth and, as a consequence, it does not necessarily give accurate gangue recovery estimates for practical flotation processes. However, the convective-diffusive model does illuminate the physical processes behind gangue recovery in the concentrate which will aid the development of automatic control strategies.     

浮选数模及计算机模拟在选矿试验中的应用

可浮性k值的分布密度函数f(x)是常数k_m和k_p所唯一确定的г分布。概率微元f(k)dk的实验室闭路浮选可以用马尔科夫随机过程来描述,所导出的中矿浮选动力学模型是一组无穷递减等差数列。模型参数用回归法确定。只要进行一些较简单的试验,即可用按本模型编的程序在计算机上进行多种模拟试验。经实际验证模拟结果与试验结果吻合较好。     

A mechanistic model of the gas film dynamics during the electrochemical discharge phenomenon

A model for the prediction of the current–voltage characteristics of a two electrodes cell incorporating the dynamics of the gas film formed during the electrochemical discharge phenomenon is developed. In its mean-field version, the model presents good qualitative agreement but overestimates the hysteresis effect and predicts too large current densities for the cell operation once the gas film is formed. An improved stochastic model, which assumes gas film departures from the electrode surface according to a Poisson process, addresses these issues and gives significantly better predictions. Two relations are presented which allow estimating the mean gas film detachment time and its variance from the experimental study of the hysteresis in the forward and reverse scan of a two electrode cell operated at high current densities.     

Demonstration of a minimum in the recovery of nanoparticles by flotation: Theory and experiment

The flotation of nano- and submicron particles does not follow the conventional collection theory based on the interception and collision mechanisms, which predicts extremely low collection efficiency for particles smaller than 10-μm. Brownian diffusion and colloidal forces strongly influence the collection of such particles by air bubbles in flotation. In this paper, a theoretical model is presented for predicting the collection efficiency of nanoparticles. The theory incorporates mass transfer by Brownian diffusion, microhydrodynamics of particles in the vicinity of a slip surface of rising air bubbles, and colloidal interactions that come into effect at small separation distances. The governing equation was solved numerically using the Crank-Nicolson method with variable step size. A finite difference scheme with mesh refinement in the vicinity of the air bubble surface was used to discretise the stiff partial differential equation for the particle concentration. The mesh refinement produced correct numerical solutions without oscillation in the particle concentration distribution, which otherwise occurred due to the stiffness of the differential equation and coarseness of the numerical mesh. Predictions from the model were compared with experimental results obtained with a small laboratory column cell, in which colloidal silica particles with diameters in the range were floated using fine bubbles of typical average diameter . The particle concentration in the pulp was about 1% by weight. Cetyltrimethyl ammonium bromide and Dowfroth 250 were used as the flotation collector and frother, respectively. Both the theory and experiment show significant effect of the electrical double-layer and non-DLVO hydrophobic attractive forces on the collection of nanoparticles by air bubbles. The theoretical and experimental results show the collection efficiency to have a minimum at a particle size in the order of . With larger particles, the interception and collision mechanisms predominate, while the diffusion and colloidal forces control the collection of particles with a size smaller than the transition size.     

鞣酸体系下黄铜矿与黄铁矿浮选动力学分析

在铜硫硫化矿浮选实践中,一般通过添加大量的浮选药剂强压强拉以实现硫化铜和硫化铁矿物的浮选分离。利用铜硫硫化矿物在浮选药剂体系下浮选速率的差异,可以实现其清洁浮选分离。本文通过分批次刮泡浮选试验研究了鞣酸体系下黄铜矿及黄铁矿浮选行为和浮选动力学特性,计算了黄铜矿、黄铁矿在鞣酸体系下的浮选速率常数。研究结果表明,鞣酸能有效地抑制黄铁矿的浮选,而对黄铜矿的抑制作用较弱。在鞣酸体系下,黄铜矿的浮选速率明显大于黄铁矿的浮选速率,黄铜矿的平均浮选速率常数为0.80,而黄铁矿的平均浮选速率常数只有0.31。通过数学方法拟合了两种矿物在鞣酸体系下的浮选动力学模型,拟合结果表明,黄铜矿和黄铁矿浮选动力学均适用于改进的分速一级模型。     

Mathematical model of particle-bubble flotation complex motion in vibration flotation

A mathematical model of bubble-mineral particle flotation complex motion in an oscillating liquid was constructed. The qualitative dependence of the motion direction and vibration amplitude of the flotation complex on the reduced density of the latter was shown. The results were compared to experimental data.     

Measurement of the thermal diffusivity and specific heat capacity of polyethylene foams using the transient plane source technique

Thermal diffusivity and specific heat at constant pressure of a collection of crosslinked closed cell polyethylene foams have been measured at room temperature using the transient plane source (TPS) method. A theoretical model to predict the thermal diffusivity has been proposed. The predictions of this model are in good agreement with the observed experimental trends. The theoretical model predicts a dependence of the thermal diffusivity on the density and other foam characteristics such as carbon black content and cell size. Copyright © 2004 Society of Chemical Industry     

Interaction Free Energy Studies on Floe Foam Flotation

Abstract

The Gouy-Chapman theory of the electric double layer is applied to the calculation of interaction free energy of a charged surface film and a solid surface of opposite charge immersed in a solution of electrolyte. The interaction energies calculated with a constant surface charge density model and a constant surface potential model are compared. A constant surface charge density model for floe foam flotation is found to result in less effective binding energy than the constant surface potential model. The constant surface potential model can be found to account for the decrease in efficiency of floe foam flotation which is observed experimentally when ionic strength is increased. However, studying the binding energy at various ionic strengths with the constant surface charge density model gives results that are contradictory to the experimental results. We can thus conclude that the floe foam flotation system is better analyzed with a constant surface potential model.     

Modeling volume changes due to lithium intercalation in a carbon fiber

Two different approaches were used to model the insertion of lithium ions into a single carbon particle fiber under potentiodynamic control. In the first approach, volume changes in the particle due to lithium intercalation/deintercalation were neglected (NVCP model) while in the second approach the volume changes were included (VCP model). Modeling discrimination techniques were used to determine the statistical significance of the different models when fitting experimental cyclic voltammetry data. It was found that the VCP model is a better fit of the experimental cyclic voltammetry data than the NVCP model. The VCP model predicts significant changes in the radius of the particle due to lithium intercalation/deintercalation. It is recommended to extend the application of the VCP model to a complete lithium ion cell. Incorporation of volume changes into the model along with the formation of the SEI layer may be the key to understanding and predicting capacity fade in a lithium ion battery during cycling.     

Enrichment of Silica Sand Ore by Cyclojet Flotation Cell

Cyclojet flotation is an alternative technique of jet flotation. It essentially has a mechanism for bubble formation with pulp jet spouting from the apex of hydrocyclone. The size of the bubbles formed with pulp jet in the cyclojet cell is very small, and the quantity of bubbles produced also limits its potential to produce high bubble-particle collision. This is particularly efficient in beneficiation of fine-grained ores. In this study, the performance of the cyclojet flotation cell was tested for removing iron-oxides from silica sand ore. Whether it can be used as an alternative to conventional mechanical cells was studied. The findings obtained from the cyclojet cell were compared with findings obtained from the conventional cell. It was seen that the cyclojet cell produced slightly better results than the conventional cell. Under the best conditions, while the cyclojet cell reduced the iron-oxide content in silica sand from 0.41% to 0.08%, the conventional cell reduced it to 0.10%. While iron removal efficiency was 80.49% for the cyclojet flotation, it was calculated as 75.61% for the conventional cell. These findings showed that cyclojet flotation can be used as an alternative method to conventional flotation for the removal of iron oxides from silica sand.