The influence of the capillary pressure in nanobubbles on their attachment to particles during froth flotation: Part IV. Spreading nanobubbles as natural fractals

The specific property of nanobubbles with spontaneous spreading over the solid hydrophobic particle substrate adhered to them, which is caused by a high capillary gas pressure in nanobubbles (P _c > 10⁶ N/m²), is considered. The computational principle of bubble spreading curves is considered and parameter X characterizing the intensity is introduced. Dependence X(a) (a is the bubble base diameter) is presented by a bimodal curve, which confirms that the nanobubble spreading is energetically provided by two sequentially acting independent sources. The first source is conditioned by the reduction (approximately by 11%) of the nanobubble curvilinear surface area at the initial spreading stage, and the second source is conditioned by the work of gas expansion caused by the drop of P _c when the bubble is spreading. Parameter X is characterized by a considerably larger slope of dependence X(a) at the first spreading stage compared to the second one. It now turned out that the revealed property, which determines the efficiency of industrial flotation processes in past, finds prospects for application again after its recognition. Since it manifests itself in a limited range of bubble sizes, it is proposed to attribute it to the proper or natural fractal by analogy with the Brownian motion, which manifests itself in a definite range of particle sizes. The influence of the surface activity of flotation reagents on the shape of bubble spreading curves is shown.     

Water model study on inclusion removal from liquid steel by bubble flotation under turbulent conditions

Abstract

Inclusion removal from liquid steel by bubble flotation under turbulent conditions is analysed using a water model. Turbulence is realised by impeller stirring in a water containing vessel. First, the effects of variables such as filter pore size, gas flowrate, NaCl concentration, and stirring intensity on bubble size are investigated. Second, particle removal by bubble flotation is studied using the water containing vessel system. The results indicate that particle removal rate by bubble flotation is controlled by non-first order kinetics. The factors affecting the particle removal rate constant k ₁ are discussed and a final empirical equation is derived as follows: -dc/dt = k ₁ c^1·3665 and k ₁ = A(d _p/d _B)^2·65?0·104 Q _g^1·630, where c is particle number density, t is time, A is a constant parameter, d _p and d _B are the particle and bubble diameter respectively, ? is the turbulent energy dissipation rate, and Q _g is the gas flowrate.     

Influence of capillary pressure in bubbles on their attachment to particles during froth flotation: Part two

The calculation of the energy possibility of the transfer of spherical bubble A into adhered bubble M or the A → M transition (AMT) shows how large the influence of the capillary pressure (P _c) on the results of calculation is and how, as bubbles A and M diminish and P _c in them increases, the range of the possible variation of P _cM in bubble M abruptly narrows. The influence of P _cM on the energy barrier on the path to the adherence of the bubble to a hydrophilic surface drops almost to zero, but the preference to the adherence of the bubbles to a hydrophobic surface is retained, although the difference noticeably decreases compared with large bubbles. The data of the practice of the first processes of froth flotation by microbubbles are the confirming experimental base of the results of this precision calculation. A decrease in wetting angle θ _M to 0.02° and the beginning increase in the spreading coefficient of the adhered bubble over the substrate particle apparently also promotes the adherence process in practice.     

Investigation into the froth flotation and selection of reagents on the basis of the mechanism of their action report 2. A comparison of flotation properties of millimeter,micrometer, and nanometer bubbles based on equations of capillary physics (Part Two)

The influence of the capillary pressure P _ca of gas in microbubbles on bubble spread over a substrate (particle) after adhesion is considered (for bubbles ranging in size from 2 mm to 20 nm). The dimensionless parameter K _a characterizes the microbubble spread with decrease in the bubble form factor β by no more than 0.000001 of its initial value. There is a clear symbatic relation between P _ca and K _a. The microbubble begins to spread when it measures 200 μm; its motion increases markedly as it becomes smaller. With decrease in bubble size, the rock and slurry particles adhering to its surface are removed. Of course, this enhances the foam quality.     

Fluid flow and inclusion removal in continuous casting tundish

Three-dimensional fluid flow in continuous casting tundishes with and without flow control devices is first studied. The results indicate that flow control devices are effective to control the strong stirring energy within the inlet zone, and other zones are with much uniform streamline. By dividing tundish into two zones with different inclusion removal mechanisms the inclusion removal is calculated. Three modes of inclusion removal from molten steel in the tundish, i.e., flotation to the free surface, collision and coalescence of inclusions to form larger ones, and adhesion to the lining solid surfaces, are taken into account. The Brownian collision, Stokes collision, and turbulent collision are examined and discussed. The suitable coagulation coefficient is discussed, and a value of 0.18 is derived. Calculation results indicate that, besides flotation, collision of inclusion and adhesion to the lining solid surfaces are also important ways for inclusion removal from molten steel in tundish especially for the smaller inclusions. The flotation removal holds 49.5 pct, and the adhesion removal holds 29.5 pct for the tundish with flow control devices; the collision effect is reflected in improving flotation and adhesion. Finally, industrial experiment data are used to verify the inclusion removal model.     

浮选过程中颗粒--气泡黏附作用机理及研究进展

系统分析总结了浮选过程中颗粒与气泡的黏附概率模型、EDLVO理论、颗粒-气泡集合体的受力分析、影响因素分析和颗粒-气泡黏附的研究进展.基于接触时间、感应时间的方法和能量势垒的方法,分别从动力学和热力学的角度分析总结了黏附概率模型,并从动力学和热力学的角度解释了颗粒大小、气泡大小、颗粒疏水性、颗粒表面粗糙度和溶液pH对黏附概率的影响,对静态环境和湍流环境中颗粒-气泡集合体进行了受力分析,颗粒和气泡的黏附力有毛细作用力、液体静压力和浮力,静态环境中的脱附力只有重力,但是湍流环境中的脱附力还包括振荡力和离心力.很多研究学者利用先进的仪器和检测手段对颗粒-气泡的黏附做了大量的研究,取得了大量研究成果.颗粒-气泡黏附作用过程相当复杂,试验研究时简化了作用条件,目前理论不能满意解释黏附过程,需要结合实际进行更深层次、更全面的研究.      

Hydrodynamics of Bubble-Mineral Particle Collisions

Abstract

This chapter surveys the hydrodynamic interactions between particles and bubbles in flotation. Some new approximate equations are given for collision efficiency. It is shown that collision processes of particles with bubbles are less effective than sliding processes because of their short duration and the strong deformation of the bubble at the collision point. Methods are suggested to estimate collision and sliding times. During contact between a particle and a bubble, the just forming thin liquid film must drain off and rupture. Therefore, possible ways of calculating film drainage time are discussed. Furthermore, possible experimental methods to determine these quantities are briefly described and recent experimental results presented.     

粒度大小对赤铁矿和石英浮选分离的影响

通过浮选试验、DLVO理论计算、聚焦光束反射测量（FBRM）等研究了油酸钠浮选体系下粒度大小对赤铁矿和石英浮选分离的影响。人工混合矿浮选试验表明,窄粒级粗粒或中等粒级的赤铁矿?石英混合矿（CH&CQ和MH&CQ）的浮选效果较好,其中CH&CQ和MH&CQ的分选效率分别为85.49%和84.26%,明显高于全粒级混合矿（RH&RQ）的分选效率74.94%;但窄粒级的细粒赤铁矿?石英混合矿（FH&FQ）的浮选效果则较差,其分选效率只有54.98%。浮选动力学试验表明,赤铁矿的浮选速率和回收率不仅与赤铁矿的粒度有关,还受石英粒度的影响,细粒脉石矿物石英会降低赤铁矿的浮选速率和回收率。DLVO理论计算表明,当矿浆pH值为9.0时,石英与赤铁矿颗粒间的相互作用力为斥力,此时细粒石英很难“罩盖”在赤铁矿表面并通过这种“直接作用”的方式抑制赤铁矿浮选,这也与聚焦光束反射测量（FBRM）的测定结果基本一致;颗粒?气泡碰撞分析表明,在浮选过程中细粒石英可能通过“边界层效应”的方式跟随气泡升浮（夹带作用）,影响赤铁矿颗粒与气泡间的碰撞及黏附,从而降低了赤铁矿的浮选速率和回收率。      

Flotation Kinetics

Abstract

The physical variables that influence the rate of flotation are examined. The probabilistic model of flotation is used to establish the effect of the particle si2e and density, bubble size and agitation on the rate of flotation

In quiescent flotation, it appears that the flotation rate is limited by the particle-bubble collision and subsequent attachment of the particle to the bubble. For fine (<20 μm) or low density particles the remedy for low recovery rates would be to either use small bubbles of the order of 100 μm, or to use moderate to high agitation with larger bubbles

In the usual turbulent conditions, the limit is set by the destruction of the bubble-particle aggregates. Broadly speaking, the same parameters favour both attachment and detachment so that the ultimate flotation rate is a compromise between these two competing mechanisms

The bounds which define the best agitation level and bubble size to use are strong functions of the particle size and density. This results in conflicting requirements for the optimum flotation of the fine and the coarse particles. Best conditions for the flotation of each are indicated.     

Mineralization kinetics of air bubbles allowing for the particle detachment and time of buoying of aggregates

The joint consideration of subprocesses of particle capture and detachment, and buoying of aggregates in the periodic nonfrothing flotation conditions shows that the mineral load formed on a separate part for its buoying time (τ_m). This load is a part of the equilibrium mineral load, which can be attained under the infinite mineralization time. It is proposed to characterize the composition and attainment rate of the mineral load by two dimensionless parameters, which depend on intensities of subprocesses. The sort parameter of particles (B) has been uniquely determined by the ratio of the detachment intensity to the capture intensity, while the dimensionless time (D) is determined by the ratio of the particle capture and detachment rate to the buoying velocity of the air bubble. The mineralization kinetic equation by many bubbles is derived in the exponential form similarly to the first-order Beloglazov equation. Intensities of capture and detachment subprocesses in the mineralization rate constant (K_m) determine the magnitude of recovery by a separate bubble (ε_bm) for time τ_m, while the air consumption determines the summary recovery ε.     

Interactions between a Small Bubble and a Greater Solid Particle during the Flotation Process

ABSTRACT

The interaction between bubbles and solid particles is an important mechanism in many industrial processes and flotation is a significant component of the most utilized applications. While flotation of mineral ores deals with fine particles and larger bubbles, the aim of this review is to focus on the opposite case; the interaction between smaller bubbles and larger particles encountered mostly in plastic flotation. Plastic flotation seems to be one of the appropriate methods for separating plastics, which is necessitated by increasing plastic consumption and the growing need to recycle. The first part of the article focuses on the problem of the collision of a bubble with a particle, both spherical and planar. The collision efficiency is discussed. The second part is devoted to the problem of liquid film rupture and the creation of the three-phase contact line. The third and final part focuses on the problem of the three-phase line expansion and the effect of surfactants on the resulting bubble stability.     

Thermodynamic and Kinetic Flotation Criteria

Abstract

Flotation thermodynamics and notation kinetics are discussed and compared with chemical thermodynamics and chemical kinetics. While chemical thermodynamics can predict whether a reaction will take place under a given set of conditions (temperature and pressure), and can also predict the direction in which the equilibrium will be shifted in response to variation in these parameters, flotation thermodynamics can predict how likely it is for the mineral particle and gas bubble to attach in a moment of their collision. While thermodynamics can predict the probability of particle-to-bubble attachment, it cannot predict the rate of this process, for the energy barrier, G_attach, opposing particle-to-bubble attachment, is not interrelated with the free energy change accompanying the attachment

The thermodynamic (Δ G < 0) and kinetic (τ_i; < τ_c c) flotation criteria are examined by a study of the effect of frothers on flotation. Various hypotheses that explain how the frother can affect flotation rate are discussed with emphasis on unsolved problems.     

Mathematical Model for Growth and Removal of Inclusions in Molten Steel under Gas‐stirring Conditions

A three‐dimensional mathematical model has been developed to predict growth and removal of inclusions during gas stirring through eccentric tuyeres in a ladle. In the model, the efficiency of inclusion removal is investigated under three different collision mechanisms: Brownian, turbulent and Stokes collision. The Importance of the three approaches of wall adhesion, Stokes flotation and bubble adhesion on inclusion removal is analysed and the efficiency of inclusion removal through three types of tuyeres in central, eccentric and multi‐tuyere form is studied. The results indicate that inclusion growth resulting from turbulent collision is most important and the effect of Stokes collision is remarkable with increased inclusion size, while inclusion growth resulting from Brownian collision is negligible. Removal by Stokes flotation is the main mechanism for large inclusions, while inclusion removal by wall adhesion is negligible. The smaller the bubbles are, the higher the efficiency of inclusion removal is. The type of tuyere arrangement has a great effect on inclusion removal. Inclusion removal in a 135t ladle with one eccentric tuyere is more efficient than in a ladle with central tuyere or multi‐tuyere design.     

Effect of capillary pressure in nanobubbles on their adhesion to particles under foam flotation. Part 3

The energy possibility of the transition of free bubbles A to adherent bubbles M, or the A → M (TAM) transition, is calculated on substrates with different wetting abilities: extremely hydrophilic (Φ), extremely hydrophobic (Γ), and with incomplete wetting ability (H _x ), where x is the substrate surface fraction covered by a monolayer of collector molecules). Calculations of TAM for bubbles with a diameter (d _e ) of 2 mm to 20 nm on Φ, Γ, and H _x substrates showed that the change in specific energy (ΔG/V) in a bubble in the case of TAM depends on the value of d _e , substrate wetting ability, and surface area of its contact with the bubble. According to the results of studies, high capillary pressure (P _c) in nanobubbles M promotes their instantaneous spreading over the substrate. Herewith, P _c decreases considerably. The adhesion and spreading processes occur as a single process, irreversibly, one-way, and fast, because they are not complicated by counterprocesses. Upon a decrease in equatorial diameter d _e and wetting ability of the substrate, the decrease in G/V reaches several million J/m³. The actual simultaneity of the processes of bubble adhesion and spreading is illustrated by microphotographs of larger bubbles with a luminescent apolar reagent eliminating the effect of wetting hysteresis that is easily overcome in nanobubbles in the case of high P _c values.     

An investigation of the flotation mechanism in the aerosol column flotation machine

It is shown that the induction time decreases as the temperature decreases if there is air bubble adhesion to hydrophobic and hydrophilic particles; if there isn’t, the time decreases where hydrophobic particles stick to one another and increases in the case of adhesion of hydrophilic particles. The established difference in the stability of wetting and symmetric films that depend on temperature can be explained by the fact that hydrophobic forces (involving those acting from a “hydrophobic” bubble) have a larger action radius of action than the forces of hydrophilicrepulsion. The revealed mechanisms allowed the development of a new flotation technique, namely, flotation with a steam-air mixture. The essence of this technique is that only a surface layer of the bubble, where the effect of structural forces is localized (rather than the entire slurry volume) is heated due to steam condensation. The efficiency of this technique is shown by the example of flotation concentration of minerals of different origins.     

Modeling of inclusion removal in a tundish

Mathematical models have been developed to predict the removal of alumina inclusions from molten steel in a continuous casting tundish, including the effects of turbulent collisions, reoxidation, flotation, and removal on the inclusion size distribution. The trajectories of inclusion particles are tracked through the three-dimensional (3-D) flow distribution, which was calculated with the K-ɛ turbulence model and includes thermal buoyancy forces based on the coupled temperature distribution. The predicted distributions are most consistent with measurements if reoxidation is assumed to increase the number of small inclusions, collision agglomeration is accounted for, and inclusion removal rates are based on particle trajectories tracked through a nonisothermal 3-D flow pattern, including Stokes flotation based on a cluster density of 5000 kg/m³ and random motion due to turbulence. Steel samples should be taken from as deep as possible in the tundish near the outlet and at several residence times after the ladle is opened, in order to best measure the Al₂O₃ concentration entering the submerged entry nozzle to the mold. Inclusion removal rates vary greatly with size and with the presence of a protective slag cover to prevent reoxidation. The random motion of inclusions due to turbulence improves the relatively slow flotation of small inclusions to the top surface flux layer. However, it also promotes collisions, which slow down the relatively fast net removal rates of large inclusions. For the conditions modeled, the flow pattern reaches steady state soon after a new ladle opens, but the temperature and inclusion distributions continue to evolve even after 1.3 residence times. The removal of inclusions does not appear to depend on the tundish aspect ratio for the conditions and assumptions modeled. It is hoped that this work will inspire future measurements and the development of more comprehensive models of inclusion removal. These validated models should serve as powerful quantitative tools to predict and optimize inclusion removal during molten steel processing, leading to higher quality steel.     

Bubble-solid attachment as a function of bubble surface tension

Abstract

The time-dependent surface tension exhibited by alkaline dodecylamine acetate solutions has been exploited to demonstrate the effect of bubble surface tension on bubble-solid attachment. With decreasing surface tension, a decrease in the tenacity of bubble-solid attachment was noted for a variety of solids (magnetite, hematite, quartz, glass and teflon). This is an example of bubble armouring. Captive bubble experiments showed the effect more noticeably than bubble pick-up tests.

The concept of γ_c, a critical surface tension of wetting for the solid, is introduced to characterize the hydrophobic/hydrophilic transition recorded with decreasing surface tension. A difference in γ_c for quartz and magnetite in amine solution was exploited in a differential float employing methanol to control the surface tension of the bubble.

Résumé

On a utilisé la tension superficielle des solutions alcalines D'acétate de dodécylamine, qui varie avec le temps, pour démontrer comment la tension superficielle des ces bulles influence l'adhésion bulles-solide. Lorsque la tension superficielle décroit, on observe une diminution de l'adhesion pour plusieurs différents solides (magnétite, hématite, quartz, verre et teflon). C'est un exemple de recouvrement total par bulles (bubble-armouring). Ce phénomène est démontré plus clairement dans les expériences avec des bulles captives que dans les expériences d'accumulation des bulles.

On introduit le concept de γ_c, qui represente la tension superficielle critique de mouillage d'un solide pour caractériser la transition hydrophobique/hydrophyllique observée lors de la decroissance de la tension superficielle. On exploite la diffénence entre les valeurs de γ_c, du quartz et de lamagnetite pour regler la tension superficielle de la bulle dans une flottation différentielle utilisant du méthanol.     

Electrochemical synthesis of an iridium powder with a large specific surface area

The synthesis of iridium powder in a molten NaCl–KCl medium at 700°C is carried out for the first time. The influence of the ratio of the cathode to the anode current density (i _c/i _a) on the structure and the morphology of the iridium powder is investigated. Single-phase and polycrystalline iridium powders with a specific surface of 16.8 m²/g are produced. The phase composition and the surface texture of the deposits are studied. The specific surface and the particle size of iridium powders as functions of the ratio i _c/i _a are analyzed.     

Investigation of froth flotation and selection of reagents on the basis of the mechanism of their effect: Report 1. Substantiation of the selected methods for investigation of the process

Three strengthening components of the particle-bubble contact that emerges under the effect of appearance of the external detachment force f in the dynamic conditions of froth flotation are considered. These are the flexure of the bubble surface at the contact perimeter, the increase in the contact angle θ, and the local increase in the surface tension σ on the bubble surface near the perimeter of its contact with the detached particle. Using the equations of capillary physics and experiments, three possible mechanisms of flexure of the bubble surface (which are caused by the effect of gravitation and reagents, namely, classical, hysteresis, and capillary mechanisms) are revealed. The necessary properties of reagents, which promote such flexure under the effect of f, are established. These are their ability to selective hydrophobization of the particle surface and to the local increase in the surface tension σ on the stretched bubble surface. Two groups of simple methods are recommended to investigate the process and to select reagents which model the process of froth flotation: (i) to evaluate the ability of reagents to vary the wettability of the particle surface—flotation experiments in frothing and nonfrothing apparatuses and to measure detachment forces, the time of adherence of the bubbles to the particles, and contact angles; (ii) methods for recording the relaxation curves and evaluating frothing properties (for reagents acting preferentially on the bubble surface). The effect of the capillary pressure of the gas in variously sized bubbles on the value of detachment forces of the particles from them, as well as the invariance of these forces of σ during slow detachment, are shown.