Bubble particle heterocoagulation under turbulent conditions

An analytical model that enables the calculation of the flotation rate constant of particles as a function of particle size with, as input parameters, measurable particle, bubble, and hydrodynamic quantities has been derived. This model includes the frequency of collisions between particles and bubbles as well as their efficiencies of collision, attachment, and stability. The generalized Sutherland equation collision model and the modified Dobby-Finch attachment model developed previously for potential flow conditions were used to calculate the efficiencies of particle-bubble collision and attachment, respectively. The bubble-particle stability efficiency model includes the various forces acting between the bubble and the attached particle, and we demonstrate that it depends mainly on the relative magnitude of particle contact angle and turbulent dissipation energy. The flotation rate constants calculated with these models produced the characteristic shape of the flotation rate constant versus particle size curve, with a maximum appearing at intermediate particle size. The low flotation rate constants of fine and coarse particles result from their low efficiency of collision and low efficiencies of attachment and stability with gas bubbles, respectively. The flotation rate constants calculated with these models were compared with the experimental flotation rate constants of methylated quartz particles with diameters between 8 and 80 micro m interacting with gas bubbles under turbulent conditions in a Rushton flotation cell. Agreement between theory and experiment is satisfactory.     

A new insight to the role of bubble properties on inertial effect in particle–bubble interaction

In this study the impact of bubble surface characterization (mobility or immobility), its diameter and velocity is investigated on inertial forces in particle–bubble collision efficiency (E_C). Three models including Sutherland (E_C-SU), Schulze (E_C-SC), and generalized Sutherland Equation (E_C-GSE) were taken into account with regard to their differences from the inertial point of view in the particle size range of 1–100?µm. Bubble diameters of 0.08, 0.12, and 0.15?cm and bubble velocities of 10, 20 and 30?cm/s were selected to study the flotation of chalcopyrite. Weber and Paddock collision model (E_C-W&P) was taken for evaluation of the effect of bubble surface mobility on E_C. It was found that when the bubble diameter is 0.12?cm, reducing bubble velocity from 30 to 20?cm/s, the inertia force can be ignored for wider range of particle size. Corresponding particle size in cross-sectional point between GSE and Schulze collision models was introduced for better evaluation of the positive and negative particle inertial effects. The best agreement between them was taken for bubble diameter of 0.12?cm and velocity of 20?cm/s. It was concluded that the influence of bubble velocity is more effective than bubble diameter regarding its role on particle inertial forces in particle–bubble interaction.     

Particle-bubble collision models--a review

A critical review of the various models existing in the literature for the calculation of the collision efficiency between particles and single, rising gas bubbles is presented. Although all of these collision models predict that the collision efficiency increases with particle size, their dependence on the latter is different because of the various assumptions and hydrodynamic conditions used in each model. Collision efficiencies of quartz particles with single bubbles have been obtained from experimental flotation experiments under conditions where the attachment and stability efficiencies were at, or near, unity. These collision efficiencies were then used to test various collision models. Good agreement between the experimental and calculated collision efficiencies was only obtained with the Generalised Sutherland Equation. The differences in collision efficiencies obtained between the various models were mainly explained in terms of, firstly, the degree of mobility of the bubble surface and, secondly, a consideration of the inertial forces acting on the particles.     

A review of the role of wetting and spreading phenomena on the flotation practice

Wetting and spreading phenomena are the most important parameters for understanding of froth flotation practice. The wetting and spreading of fluids on the solid surface should be considered in the high efficiency flotation process. These phenomena involve surface tension forces, contact line dynamics, surface roughness and heterogeneity, contact angles, bubble–particle interactions and other factors. This review highlights the various concepts of contact angles and well-known equations in this respect and compares these equations. Based on this review, flotation selectivity and efficiency are highly dependent on solid–liquid contact angles and collision, collection, attachment, and stability efficiency could be predicted by wetting and spreading roles. In order to control flotation performance, efforts should be made to determine wetting characteristic of the flotation process. It is imperative that an improved understanding of wetting and spreading phenomena in the phase's interfaces will provide an improved and efficient flotation practice. It is proposed that future research should focus on the scientific and engineering aspect of wetting and spreading phenomena on flotation and on the development of a method to enhance flotation performance by controlling these phenomena.     

Surface and capillary forces encountered by zinc sulfide microspheres in aqueous electrolyte

The colloid probe technique was used to investigate the interactions between individual zinc sulfide (ZnS) microspheres and an air bubble in electrolyte solution. Incorporation of zinc ions into the electrolyte solution overcomes the disproportionate zinc ion dissolution and mimics high-volume-fraction conditions common in flotation. Determined interaction forces revealed a distinct lack of long-ranged hydrophobic forces, indicated by the presence of a DLVO repulsion prior to particle engulfment. Single microsphere contact angles were determined from particle-bubble interactions. Contact angles increased with decreasing radii and with surface oxidation. Surface modification by the absorption of copper and subsequently potassium O-ethyldithiocarbonate (KED) reduced repulsive forces and strongly increased contact angles.     

Modeling local flotation frequency in a turbulent flow field

Despite the significance of turbulent fluid motion for enhancing the flotation rate in several industrial processes, there is no unified approach to the modeling of the flotation rate in a turbulent flow field. Appropriate modeling of the local flotation (bubble-particle attachment) rate is the basic constituent for global modeling and prediction of flotation equipment efficiency. Existing approaches for the local flotation rate are limited to specific set of conditions like high or low turbulence. In addition, the combined effects of buoyant bubble rise and/or particle gravity settling are usually ignored. The situation is even vaguer for the computation of collision and attachment efficiencies which are usually computed using the gravity induced velocities although the dominant mode of flotation is the turbulent one. The scope of this work is clear: the development of a general expression for the flotation rate in a turbulent flow field which will cover in a unified and consistent way all possible sets of the problem parameters. This is achieved by using concepts from statistical approach to homogeneous turbulence and gas kinetic theory.     

Nanoparticle flotation collectors: mechanisms behind a new technology

This is the first report describing a new technology where hydrophobic nanoparticles adsorb onto much larger, hydrophilic mineral particle surfaces to facilitate attachment to air bubbles in flotation. The adsorption of 46 nm cationic polystyrene nanoparticles onto 43 μm diameter glass beads, a mineral model, facilitates virtually complete removal of the beads by flotation. As little as 5% coverage of the bead surfaces with nanoparticles promotes high flotation efficiencies. The maximum force required to pull a glass bead from an air bubble interface into the aqueous phase was measured by micromechanics. The pull-off force was 1.9 μN for glass beads coated with nanoparticles, compared to 0.0086 μN for clean beads. The pull-off forces were modeled using Scheludko's classical expression. We propose that the bubble/bead contact area may not be dry (completely dewetted). Instead, for hydrophobic nanoparticles sitting on a hydrophilic surface, it is possible that only the nanoparticles penetrate the air/water interface to form a three-phase contact line. We present a new model for pull-off forces for such a wet contact patch between the bead and the air bubble. Contact angle measurements of both nanoparticle coated glass and smooth films from dissolved nanoparticles were performed to support the modeling.     

Trajectory Analysis and Collision Efficiency during Microbubble Flotation

The hydrodynamic interaction between a rising bubble and a sedimenting particle during microbubble flotation is considered. The effects of attractive van der Waals forces and attractive or repulsive electrostatic forces are included. A mathematical model is presented which is used to perform a trajectory analysis and to calculate collision efficiencies between the bubble and particle. It is shown that collision efficiencies and the nature of the bubble-particle interactions are strongly dependent on the relative strengths of the van der Waals and electrostatic forces and on the lengthscales over which these forces act. It is demonstrated that optimal operating conditions can be suggested to achieve efficient microbubble flotation by correctly accounting for the interaction of van der Waals, electrostatic, and hydrodynamic forces. Copyright 1999 Academic Press.     

Exact and Approximate Expressions for Bubble-Particle Collision

The flotation microprocess of collision is investigated and an exact expression for the probability of collision (Pc) is developed based on the intermediate flow of Yoon and Luttrell (1). This expression for Pc only assumes that the bubble and particle are spherical and that the particle radius is less than the bubble radius (i.e., Rp < RB). In addition to removing the requirement that Rp < RB, the influence of a particle settling velocity is also included in the model development. The expression for Pc is shown to be a function of three dimensionless groups: (i) the magnitude of the dimensionless particle settling velocity, ||G ||; (ii) the bubble Reynolds number, ReB; and (iii) the ratio of particle to bubble radius, Rp/RB. The probability of collision model is compared to available experimental data and good agreement is shown. A parametric study is also completed for 0 1. Copyright 1999 Academic Press.     

The liquid flow force on a particle in the bubble-particle interaction in flotation

In this paper the problem of calculating the liquid flow force on a particle in interaction with an air bubble with a mobile surface in flotation as a function of the separation distance was solved. The force equation was obtained by first deriving the disturbed flow confined between the surfaces. The model for the force includes the separation distance between the bubble and the particle, the particle size, the bubble's Reynolds number, the bubble rise velocity, and the polar position of the particle on the bubble surface. The proposed equations provide an exact solution to the situation where the particle and the bubble are very close together. The attractive flow force and the surface forces are of similar orders of magnitude. Consequently, the models presented in this paper should provide a better estimate for calculating the forces on particles interacting with air bubbles in mineral flotation and other separation operations involving colloidal interactions.     

Microflotation Suppression and Enhancement Caused by Particle/Bubble Electrostatic Interaction

The processes of attachment and detachment of small or medium-sized particles to relatively large bubbles during microflotation are considered in terms of the heterocoagulation theory. Calculations are made for the conditions that the surface potentials are of similar sign and constant, that one of the surface potentials is small, that hydrophobic attraction is absent, and that there are no surface deformations. Under these conditions bubble-particle aggregates may form as a result of an electrostatic attraction which exceeds the repulsive van der Waals force at intermediate distances. Next to electrostatic and van der Waals forces, hydrodynamic and gravitational forces are considered. These forces may overcome the electrostatic repulsion at large distances and promote particle bubble attachment. Strong electrostatic attraction at small distances, arising at a large difference of the surface potentials of the bubble and the particle and of low electrolyte concentrations, can prevent subsequent detachment by hydrodynamic and gravitational forces. With increasing electrolyte concentration the electrostatic barrier increases and the attractive electrostatic force diminishes. As a result, a critical electrolyte concentration for microflotation exists. Above this concentration attachment may still occur but it is followed by detachment. At lower electrolyte concentrations the electrostatic attractive force prevents the detachment. The dependence of the critical electrolyte concentration on the values of the bubble and particle potentials and the Hamaker constant is calculated. The critical concentration does not depend on particle or bubble size if the absolute values of the total detachment force and the total pressing force coincide, which is the case for Stokes and potential flow. For every electrolyte concentration lower than the critical value there are two critical particle sizes that limit the flotation possibility. For small particle sizes attachment is impossible because the pressing force is smaller than the electrostatic barrier. For large particle sizes detachment cannot be prevented because the detachment force exceeds the maximum electrostatic attraction. A microflotation domain of intermediate particle sizes exists in which irreversible heterocoagulation occurs. Copyright 2001 Academic Press.     

Quantification of particle-bubble interactions using atomic force microscopy: A review

The attachment of particles to bubbles in solution is of fundamental importance to several industrial processes, most notably in the process of froth flotation. During this process hydrophobic particles attach to air bubbles in solution, which allows them to be separated as froth at the surface. The addition of chemicals can help to modulate these interactions to increase the yield of the minerals of interest. Over the past decade the atomic force microscope (AFM) has been adapted for use in studying the forces involved in the attachment of single particles to bubbles in the laboratory. This allows the measurement of actual DLVO (Derjaguin, Landau, Vervey and Overbeek) forces and adhesive contacts to be measured under different conditions. In addition contact angles may be calculated from features of force versus distance curves. It is the purpose of this article to illustrate how the colloid probe technique can be used to make single particle-bubble interactions and to summarise the current literature describing such experiments.     

Adsorption of modified dextrins on molybdenite: AFM imaging, contact angle, and flotation studies

The adsorption of three dextrins (a regular wheat dextrin, Dextrin TY, carboxymethyl (CM) Dextrin, and hydroxypropyl (HP) Dextrin) on molybdenite has been investigated using adsorption isotherms, tapping mode atomic force microscopy (TMAFM), contact angle measurements, and dynamic bubble-surface collisions. In addition, the effect of the polymers on the flotation recovery of molybdenite has been determined. The isotherms revealed the importance of molecular weight in determining the adsorbed amounts of the polymers on molybdenite at plateau coverage. TMAFM revealed the morphology of the three polymers, which consisted of randomly dispersed domains with a higher area fraction of surface coverage for the substituted dextrins. The contact angle of polymer-treated molybdenite indicated that polymer layer coverage and hydration influenced the mineral surface hydrophobicity. Bubble-surface collisions indicated that the polymers affected thin film rupture and dewetting rate differently, correlating with differences in the adsorbed layer morphology. Direct correlations were found between the surface coverage of the adsorbed layers, their impact on thin film rupture time, and their impact on flotation recovery, highlighting the paramount role of the polymer morphology in the bubble/particle attachment process and subsequent flotation.     

Influence of contact electrification on the collision of elastic particles with a rigid surface

The influence of the contact formation of an electrical double layer (EDL) on the collision of uncharged, perfectly elastic particles with a dry rigid surface is theoretically investigated. The kinetics of the formation of an EDL in the elastic collision of a particle, the work of the nonequilibrium separation of the plates of the EDL when it rebounds, and the magnitude of a charge gained by the particle on its collision are calculated.

It is shown that the nonequilibrium forces associated with the EDL can considerably reduce the rebound velocity of particles, in the case of their elastic collision, and even cause their sticking to the surface, when impinging against it at a velocity lower than the critical one.

The dependence of the critical collision velocity on the geometrical, mechanical, and electrosurface parameters of particles and the substrate is established.

Some known experimental data are well described by the expression for the rebound impingement velocity ratio, obtained from consideration of the energy balance.     

Solid particle in the boundary layer of a rising bubble

The hydrodynamic interaction of a solid particle and the boundary layer around a rising bubble is analyzed in the before-contact state (BCS) of a flotation act. The lagging of the particle behind the basic outer flow is accounted for. The forces acting on the particle are qualitatively examined. A new term is introduced in the force balance — the migration force. An expression for the collision efficiency is proposed that concerns a particle already entrained in the bubbles boundary layer.     

The role of surface forces in mineral flotation

Flotation is an interfacial separation technique, which plays a major role in mineral processing industry. It separates particles according to their wetting properties. In flotation pulp, particles and bubbles are highly dispersed in aqueous medium and in the presence of various flotation reagents. Almost all interfacial interactions including inter-particle, inter-bubble, and bubble-particle interactions in the complex pulp medium are driven by surface forces. Therefore, a fundamental understanding of the role of surface forces in flotation is a prerequisite to enhance practical flotation performance and adapt it for treatment of complex and refractory ores. In this paper, recent advances in the field of surface forces encountered in mineral flotation are reviewed. In particular, we highlight the latest progress in the attachment mechanism between bubble and particle with the aid of atomic force microscope and interference microscope. The current knowledge gap and future directions are also discussed.     

Dynamic aspects of small bubble and hydrophilic solid encounters

The capture of solid particles suspended in aqueous solution by rising gas bubbles involves hydrodynamic and physicochemical processes that are central to colloid science. Of the collision, attachment and aggregate stability aspects to the bubble-particle interaction, the crucial attachment process is least understood. This is especially true of hydrophilic solids. We review the current literature regarding each component of the bubble-particle attachment process, from the free-rise of a small, clean single bubble, to the collision, film drainage and interactions which dominate the attachment rate. There is a particular focus on recent studies which employ single, very small bubbles as analysis probes, enabling the dynamic bubble-hydrophilic particle interaction to be investigated, avoiding complications which arise from fluid inertia, deformation of the liquid-vapour interface and the possibility of surfactant contamination.     

A review of induction and attachment times of wetting thin films between air bubbles and particles and its relevance in the separation of particles by flotation

Bubble-particle attachment in water is critical to the separation of particles by flotation which is widely used in the recovery of valuable minerals, the deinking of wastepaper, the water treatment and the oil recovery from tar sands. It involves the thinning and rupture of wetting thin films, and the expansion and relaxation of the gas-liquid-solid contact lines. The time scale of the first two processes is referred to as the induction time, whereas the time scale of the attachment involving all the processes is called the attachment time. This paper reviews the experimental studies into the induction and attachment times between minerals and air bubbles, and between oil droplets and air bubbles. It also focuses on the experimental investigations and mathematical modelling of elementary processes of the wetting film thinning and rupture, and the three-phase contact line expansion relevant to flotation. It was confirmed that the time parameters, obtained by various authors, are sensitive enough to show changes in both flotation surface chemistry and physical properties of solid surfaces of pure minerals. These findings should be extended to other systems. It is proposed that measurements of the bubble-particle attachment can be used to interpret changes in flotation behaviour or, in conjunction with other factors, such as particle size and gas dispersion, to predict flotation performance.     

Flotation de-inking studies using model hydrophobic particles and non-ionic dispersants

A series of non-ionic alcohol ethoxylated surfactants (with HLB within the range of 11.1–12.5) were used as dispersants during flotation of mondisperse hydrophobised silica particles (representing ink particles) in de-inking formulations. Laboratory scale flotation experiments, contact angle, dynamic surface tension and thin film drainage experiments were carried out. The reduction in dynamic surface tension at the air/solution interface (which is dependent on the adsorption kinetics) followed the order C₁₀E₆>C₁₂E₈≈C₁₂E₆>C₁₄E₆ and these values were lower than sodium oleate, which is commonly used in de-inking systems. In addition the non-ionics adsorbed on the hydrophobised silica particles reducing the contact angle. These results indicated that the non-ionic surfactant with the highest CMC (C₁₀E₆) gave (a) the highest rate of adsorption at the air/solution interface (b) the froth with the greatest water content and higher froth volume (c) the lowest reduction in contact angle and (d) the highest flotation efficiency at concentrations above the CMC. It was also observed that flotation occurred, in spite of the fact that thin-film measurements indicated that the adsorption of non-ionic at the air/solution and silica/solution interfaces reduced the hydrophobicity of the particles, as indicated by an increase in stability of the aqueous thin film between the particle and air-bubble. This result suggests that the bubble-ink particle captures mechanism (occurring through rupture of the thin aqueous film separating the interfaces) is not the only mechanism controlling the flotation efficiency and that other parameters (such as the kinetics of surfactant adsorption, foaming characteristics, and bubble size) need to be taken into account. The kinetics is important with respect to the rate of adsorption of surfactant to both interfaces. Under equilibrium conditions, this may give rise to repulsive steric forces between the air-bubble and the particles (stable aqueous thin-films). However, a lower amount of surfactant adsorbed at a freshly formed air bubble or inkparticle (caused by slow adsorption rates) will produce a lower steric repulsive force allowing effective collection of particles by the bubble. Also, it was suggested that the influence of alcohol ethoxylates on bubble-size could effect the particle capture rate and mechanical entrainment of particles in an excessively buoyant froth, which will also play an important role in the flotation recovery.