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.     

Direct measurement of hydrophobic particle–bubble interactions in aqueous solutions by atomic force microscopy: Effect of particle hydrophobicity

Direct measurements of the interaction forces between a spherical silica particle and a small air bubble have been conducted in aqueous electrolyte solutions by using an atomic force microscope (AFM). The silica particle was hydrophobized with a silanating reagent, and the interaction forces were measured by using several particles with different surface hydrophobicities. In the measured force curves, a repulsive force was observed at large separation distances as the particle moved towards the bubble. The origin of the repulsive force was attributed to an electrostatic double-layer force because both the particle and bubble were negatively charged. After the repulsive force, an extremely long-range attractive force acted between the surfaces. These results indicate that the intervening thin water film between the particle and bubble rapidly collapsed, resulting in the particle penetrating the bubble.

The instability of the thin water film between the surfaces suggests the existence of an additional attractive force. By comparing the repulsive forces of the obtained force curves with the DLVO theory, the rupture thickness was estimated. The hydrophobicity of the particle did not significantly change the rupture thickness, whereas the pH of the solution is considered to be a critical factor.     

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.     

Exact and global rational approximate expressions for resistance coefficients for a colloidal solid sphere moving in a quiescent liquid parallel to a slip gas-liquid interface

In this paper mathematical expressions have been developed to describe the hydrodynamic resistance force on a colloidal particle as it slides along a slip surface of a gas bubble held stationary in a quiescent liquid. The particle size was considered to be sufficiently small relative to the bubble size so that the bubble surface could be locally approximated to a planar interface. The modeling incorporated a bispherical coordinate transformation to solve the equations governing the liquid creeping flow disturbed by the particle. Exact numerical solutions for the resistance coefficients of the particle-shearing motion parallel to the slip bubble surface were obtained as a function of the separation distance from the bubble surface. Finally, simplified analytical rational approximations for the whole range of the separation distance were presented, which were in good agreement with the exact numerical result. Importantly, the approximations for the modeling and simulation of the bubble-particle interactions are mathematically tractable.     

Influence of very small bubbles on particle/bubble heterocoagulation

Very small bubbles which partially coat the surface of particles influence whether or not heterocoagulation between a particle and a bubble occurs. The electrostatic and van der Waals forces of interaction between particles and bubbles were calculated as a function of electrolyte concentration, particle size, and the size and distributions of these very small bubbles present on the particle surface. The height of the surface force barrier was compared with the hydrodynamic pressing force under conditions of flotation. The presence of these very small bubbles has a profound effect on the interaction between particles and bubbles and, in particular, strongly decreases the critical particle radius for heterocoagulation.     

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.     

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.     

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.     

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.     

Molecular Dynamics Simulation: Influence of External Electric Field on Bubble Interface in Air Flotation Process

Molecular dynamics(MD) simulation was performed to investigate the influence of external electric field on the vapour-liquid interface of the bubble during the process of toluene separation by air flotation. The physicochemical properties of vapour-liquid interface, surface tension, probability of a hydrogen bonding near the vapour-liquid interface and the viscosity of liquid phase caused by external electric field were analyzed. The results show that the angle between the water molecule dipole moment and the normal z axis in the vapour phase changes smaller when the external electric field is applied. The surface tension and the probability of hydrogen bonding near the vapour-liquid interface increase with the increase of electric field strength. And the viscosity also increases under an external electric field. The results confirm that the external electric field has a positive effect on the performance of bubbles in air flotation, which may provide useful guidance for the combination of electric field and air flotation technology.     

Surface chemicals concepts of flotation de-inking

This review outlines the important parameters, which influence the flotation de-inking and discusses the surface chemical aspects of the process. Although, it has been established increasing temperature and pH facilitate the release of ink particles from the fibre during pulping (prior to flotation), it has not yet been completely established to what extent these parameters increase or decrease the efficiency of the primary flotation step. In fact, increasing temperature appears to decrease the flotation rate and also an increase in pH can retard the flotation due to a reduction in capture efficiency between the air bubbles and the ink particles decreasing the flotation in the cell. In addition, the size, shape and roughness of the ink particles influence this bubble/particle capture mechanism. Bubble frequency and bubble size is influenced by surface tension (type and concentration of frother) but X-ray studies also indicate that the fibre consistency can influence the bubble shape and flow patterns causing channelling and re-circulation of bubble flow in the cell. Tests with different gases (oxygen and nitrogen instead of air) show no significant gains in optical and mechanical properties of the fibre. Fatty acids with higher chain length and lower degree of saturation are less soluble and ensure lower carry-over but less foaming and also less fibre recovery. The primary mechanisms of fatty acid flotation involves precipitation of calcium soap, followed by micro-encapsulation of ink through a hetero-coagulation mechanism, followed by the bubble/ink particle capture step. In the use of nonionic surfactant, cloud point and HLB are important parameters, which influence brightness, washing and flotation efficiency. Optimum flotation occurs with slight excess of fatty acid to reduce surface tension and optimum calcium levels ensuring that most of the calcium is removed in the process. A lower calcium level gives lower stock loss but a high calcium has a detrimental effect, causing scaling and deposition. A critical nonionic/fatty acid balance is needed to minimize stock loss during the flotation. New chemicals need to be developed to increase selectivity, reduce entrainment and increase the process efficiency. Also, the underlying knowledge linking structural/function relationship for de-inking chemicals in relationship to the heterogenity at the pulps needs to be established. Further progress could help in the treatment of higher fibre content pulps, reducing water and chemical consumption and reducing redeposition of the ink on the fibre.     

Influence of surface topography on the interactions between nanostructured hydrophobic surfaces

Nanostructured particle coated surfaces, with hydrophobized particles arranged in close to hexagonal order and of specific diameters ranging from 30 nm up to 800 nm, were prepared by Langmuir-Blodgett deposition followed by silanization. These surfaces have been used to study interactions between hydrophobic surfaces and a hydrophobic probe using the AFM colloidal probe technique. The different particle coated surfaces exhibit similar water contact angles, independent of particle size, which facilitates studies of how the roughness length scale affects capillary forces (previously often referred to as "hydrophobic interactions") in aqueous solutions. For surfaces with smaller particles (diameter < 200 nm), an increase in roughness length scale is accompanied by a decrease in adhesion force and bubble rupture distance. It is suggested that this is caused by energy barriers that prevent the motion of the three-phase (vapor/liquid/solid) line over the surface features, which counteracts capillary growth. Some of the measured force curves display extremely long-range interaction behavior with rupture distances of several micrometers and capillary growth with an increase in volume during retraction. This is thought to be a consequence of nanobubbles resting on top of the surface features and an influx of air from the crevices between the particles on the surface.     

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.     

Forces between a hard surface and an air–aqueous interface with and without films

The adsorption of particles to air–aqueous interfaces is vital in many applications, such as mineral flotation and the stabilization of food foams. The forces in the system determine whether a particle will attach to an air–aqueous interface. The forces between a particle and an air–aqueous interface are influenced by Derjaguin–Landau–Verwey–Overbeek forces (i.e. van der Waals and electrostatic forces), non–Derjaguin–Landau–Verwey–Overbeek forces (e.g. hydrophobic, hydrodynamic, structural, and capillary forces), liquid drainage, and liquid flow. As an air–aqueous interface can be deformed by a particle, the forces measured between an air–aqueous interface and a particle can differ from those measured between two hard surfaces separated by liquid. The presence of a film at an air–aqueous interface can also change the forces.     

Bubble-solid interactions in water and electrolyte solutions

Surface forces between an air bubble and a flat mica surface immersed in aqueous electrolyte solutions have been investigated using a modified surface force apparatus. An analysis of the deformation of the air bubble with respect to the mutual position of the bubble and the mica surface, the capillary pressure, and the disjoining pressure allows the air-liquid surface electrical potential to be determined. The experiments show that a long-range, double-layer repulsion acts between the mica (which is negatively charged) and an air bubble in water and in various electrolyte solutions at low concentration, thereby indicating that the air bubble surface is negatively charged. However, there is clear evidence that charge regulation occurs at the air-water interface to maintain a constant surface potential, and as a result of this, the charge at this interface changes from negative to positive as the bubble approaches the mica surface. Because of the attraction that arises as a result of the charge reversal, a finite force is required to separate the bubble from the mica, though the mica remains wetted by the aqueous phase. At the low concentrations investigated, the potential on the gas-liquid interface is independent of the electrolyte type within experimental uncertainty.     

Simultaneous measurement of structural and hydrodynamic forces between colloidal surfaces in complex fluids

An AFM study was performed to measure the effect of approach/retraction speed on the interaction force between a colloidal particle and a flat substrate in aqueous solutions containing silica nanospheres at concentrations of 4.5 and 6.5 vol.%. The total force consisted of contributions of electrostatic, depletion, structural and hydrodynamic forces. The hydrodynamic component of the force could be isolated by comparing the force profiles measured upon approach and retraction. It was found that when the hydrodynamic component was subtracted from the total force, the resulting force profiles measured at scan speeds of 80, 800, 2400, 4800 and 11,200 nm/s all overlaid, indicating that the surface forces (electrostatic, depletion and structural) were not affected by the scan speed. This result was further supported by an approximation of the rates of viscous and diffusive motion in the gap region. In addition, the variation of the hydrodynamic force with particle/plate separation distance agreed relatively well with a prediction made using the mobility correction factor developed for simple fluids, suggesting that the nanoparaticles do not alter the flow in the lubrication layer at these concentrations.     

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.     

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.     

Selective recovery of micrometer particles from mixtures using a combination of selective aggregation and dissolved-air flotation

Particle–particle separation in biotechnology has gained interest over the years due to the large number of processes that yield particle mixtures. Direct isolation of the product-containing particles is a logical and efficient downstream processing route in these processes. Dissolved-air flotation is applicable for these separations when the particles that require separation have different interactions with the air bubbles and/or differ in aggregation behaviour.

In this work, model particles consisting of micrometer-sized protein-coated polystyrene particles were used to investigate the requirements for the application of dissolved-air flotation for particle–particle separation in biotechnology. These model particles have heterogeneous surfaces with surface groups (brushes) that extend out into the solution. Therefore, steric (or brush) repulsion and so-called hydrophobic interactions between the particles need to be taken into account. The flotation behaviour of the protein-coated particles was related to the size of the aggregates and the foaming behaviour of the proteins. Prediction of their aggregation behaviour was performed on the basis of calculations of the Van der Waals, electrostatic, hydrophobic and brush interactions. The brush interaction force proves to be essential for the prediction of the aggregation behaviour of the particles.