The interaction between particles and bubbles

The Challenges and Prospects of Recovering Fine Copper Sulfides from Tailings Using Different Flotation Techniques: A Review

Flotation is a common mineral processing method used to upgrade copper sulfide ores; in this method, copper sulfide mineral particles are concentrated in froth, and associated gangue minerals are separated as tailings. However, a significant amount of copper is lost into tailings during the processing; therefore, tailings can be considered secondary resources or future deposits of copper. Particle–bubble collision efficiency and particle–bubble aggregate stability determines the recovery of target particles; this attachment efficiency plays a vital role in the selectivity process. The presence of fine particles in the flotation circuit is because of excessive grinding, which is to achieve a higher degree of liberation. Complex sulfide ores of markedly low grade further necessitate excessive grinding to achieve the maximum degree of liberation. In the flotation process, fine particles due to their small mass and momentum are unable to collide with rising bubbles, and their rate of flotation is very slow, further lowering the recovery of target minerals. This collision efficiency mainly depends on the particle–bubble size ratio and the concentration of particles present in the pulp. To overcome this problem and to maintain a favorable particle–bubble size ratio, different techniques have been employed by researchers to enhance particle–bubble collision efficiency either by increasing particle size or by decreasing bubble size. In this article, the mechanism of tailing loss is discussed in detail. In addition, flotation methods for fine particles recovery such as microbubble flotation, column flotation, nanobubble flotation, polymer flocculation, shear flocculation, oil agglomeration, and carrier flotation are reviewed, and their applications and limitations are discussed in detail.

The hydrophobic force for bubble–particle attachment in flotation – a brief review

Both exponential decay and power decay laws could be employed to quantitatively describe the hydrophobic force between bubble and particle.

Direct observation of pH-induced coalescence of latex-stabilized bubbles using high-speed video imaging

The coalescence of pairs of 2 mm air bubbles grown in a dilute electrolyte solution containing a lightly cross-linked 380 nm diameter PEGMA-stabilized poly(2-vinylpyridine) (P2VP) latex was monitored using a high-speed video camera. The air bubbles were highly stable at pH 10 when coated with this latex, although coalescence could be induced by increasing the bubble volume when in contact. Conversely, coalescence was rapid when the bubbles were equilibrated at pH 2, since the latex undergoes a latex-to-microgel transition and the swollen microgel particles are no longer adsorbed at the air-water interface. Rapid coalescence was also observed for latex-coated bubbles equilibrated at pH 10 and then abruptly adjusted to pH 2. Time-dependent postrupture oscillations in the projected surface area of coalescing P2VP-coated bubble pairs were studied using a high-speed video camera in order to reinvestigate the rapid acid-induced catastrophic foam collapse previously reported [Dupin, D.; et al. J. Mater. Chem. 2008, 18, 545]. At pH 10, the P2VP latex particles adsorbed at the surface of coalescing bubbles reduce the oscillation frequency significantly. This is attributed to a close-packed latex monolayer, which increases the bubble stiffness and hence restricts surface deformation. The swollen P2VP microgel particles that are formed in acid also affected the coalescence dynamics. It was concluded that there was a high concentration of swollen microgel at the air-water interface, which created a localized, viscous surface gel layer that inhibited at least the first period of the surface area oscillation. Close comparison between latex-coated bubbles at pH 10 and those coated with 66 microm spherical glass beads indicated that the former system exhibits more elastic behavior. This was attributed to the compressibility of the latex monolayer on the bubble surface during coalescence. A comparable elastic response was observed for similar sized titania particles, suggesting that particle size is a significant factor in defining the interfacial elasticity of particle-coated bubbles.

The detachment of particles from coalescing bubble pairs

This paper is concerned with the detachment of particles from coalescing bubble pairs. Two bubbles were generated at adjacent capillaries and coated with hydrophobic glass particles of mean diameter 66 microm. The bubbles were then positioned next to each other until the thin liquid film between them ruptured. The particles that dropped from the bubble surface during the coalescence process were collected and measured. The coalescence process was very vigorous and observations showed that particles detached from the bubble surfaces as a result of the oscillations caused by coalescence. The attached particles themselves and, to some extent the presence of the surfactant had a damping affect on the bubble oscillation, which played a decisive role on the particle detachment phenomena. The behaviour of particles on the surfaces of the bubbles during coalescence was described, and implications of results for the flotation process were discussed.

Influence of surface active substances on bubble motion and collision with various interfaces

Bubble motion as a function of distance from a point of its detachment and phenomena occurring during the bubble approach and collision with liquid/gas and liquid/solid interfaces in pure water and solutions of various surface active substances are described and discussed. It is showed that presence of surface active substance has a profound influence on values of the terminal velocity and profiles of the local velocity. At low solutions concentrations there are three distinct stages in the bubble motion: (i) a rapid acceleration, (ii) a maximum velocity value followed by its monotonic decrease, and (iii) attainment of the terminal velocity, while at high concentrations (and in pure water) there are only stages (i) and (iii). It is showed that the bubble terminal velocity decreases rapidly at low surfactant concentration, but there can be found some characteristic concentrations (adsorption coverage's) above which the velocity almost stopped to decrease. Immobilization of the bubble surface resulting from adsorption of the surface active substances (surface tension gradients inducement) causes over twofold lowering of the bubble velocity. Presence of the maximum on the local velocity profiles is an indication that a stationary non-uniform distribution of adsorption coverage (needed for immobilization the bubble interface) was not established there. When the rising bubble arrives at liquid/gas interface or liquid/solid interface there can be formed either foam or wetting film or three-phase contact (TPC). It is showed that prior to the foam and/or wetting film formation the bubble colliding with the interfaces can bounce backward and simultaneously its shape pulsates rapidly with a frequency over 1000 Hz. It is rather unexpected that even in the case of the free surface the bubble's shape and consequently its surface area can vary so rapidly. It shows straightforward that on such a rapidly distorted interface the adsorption coverage can be very different from that at equilibrium. This fact should be taken into account more appropriately in the discussion of the mechanism of formation and stabilization of various dispersed systems (e.g. foams, emulsions). Bubble collision with solids and formation of the three-phase contact is a necessary condition for flotation separation. It is rather common understanding that immediate attachment should occur in the case of hydrophobic surface, while there should be no attachment in the case of the hydrophilic ones. It is reported that even in the case of such hydrophobic solid surface as Teflon, the bubble attachment did not need to occur at first collision and in distilled water the bubble can bounce a few times without attachment. Presence of frother facilitates the bubble attachment to hydrophobic solid surface. Time scale of the TPC formation is very short, of an order of single ms. It was observed that presence of a micro-bubble at the solid surface facilitated drastically an attachment of the colliding bubble. Roughness of Teflon surface increases probability of the bubble attachment-most probably-as a result of higher probability of micro- and/or nano-bubbles presence at the solid surface.

Heterocoagulation of chalcopyrite and pyrite minerals in flotation separation

Heterocoagulation between various fine mineral particles contained within a mineral suspension with different structural and surface chemistry can interfere with the ability of the flotation processes to selectively separate the minerals involved. This paper examines the interactions between chalcopyrite (a copper mineral) and pyrite (an iron mineral often bearing gold) as they approach each other in suspensions with added chemicals, and relates the results to the experimental data for the flotation recovery and selectivity. The heterocoagulation was experimentally studied using the electrophoretic light scattering (ELS) technique and was modelled by incorporating colloidal forces, including the van der Waals, electrostatic double layer and hydrophobic forces. The ELS results indicated that pyrite has a positive zeta potential (zeta) up to its isoelectric point (IEP) at approximately pH 2.2, while chalcopyrite has a positive zeta up to its IEP at approximately pH 5.5. This produces heterocoagulation of chalcopyrite with pyrite between pH 2.2 and pH 5.5. The heterocoagulation was confirmed by the ELS spectra measured with a ZetaPlus instrument from Brookhaven and by small-scale flotation experiments.

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.

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.

The dynamic nature of contact angles as measured by atomic force microscopy

Atomic force microscopy appears to be a useful tool for determining the contact angle for small particles. It is shown in this paper that the contact angle of a spherical polyethylene particle changes with the speed of the AFM piezoelectric translator. Such dynamic behavior of the contact angle and other uncertainties such as the position of the three-phase contact on the particle surface during bubble-particle interaction make it difficult to decide whether or not the AFM single-particle contact angle can be used to describe the hydrophobic state of the particle surface.

Quasistatic detachment of a sphere from a liquid interface

In this paper the problem of removing a spherical particle initially attached to a liquid-gas interface is analytically treated. In particular, the Derjaguin equation for small radii is used to derive a closed-form approximate expression for the work of detachment of the sphere from the interface. Expressions corresponding to the prescribed displacement condition and the applied force condition, which seems to be the relevant condition for the flotation separation process, are presented. A special effort has been made to closely compare analytical results with data obtained through the exact numerical treatment of the detachment process. Results show that proposed expressions are sufficiently accurate to calculate the energy required to detach the sphere from the interface as soon as the sphere radius is small compared to the capillary length. Validity limits are specified.

Wetting film stability and flotation kinetics

Single bubble experiments performed with different size fractions of quartz particles and different, but known, contact angles revealed two modes of flotation dynamics in superclean water. (1.) A monotonic increase of collection efficiency Ecoll with increasing particle size was observed at high particle hydrophobicity and, correspondingly, a low wetting film stability (WFS). (2.) At low particle hydrophobicity and, correspondingly, high WFS, an extreme dependence of Ecoll on particle size was observed. The use of superclean water in our experiments prevented the retardation of bubble surface movement caused by surfactants or other impurities that is usual for other investigations and where particle-bubble inertial hydrodynamic interactions are suppressed. In the present study the free movement of the bubble surface enhances particle-bubble inertial interaction, creating conditions for different flotation modes, dependent on WFS. At the instant of inertial impact, a particle deforms the bubble surface, which may cause its rebound. Where the stability of the thin water film, formed between opposing surfaces of a bubble and a particle, is low, its rupture is accompanied with three phase contact line extension and contact angle formation before rebound. This prevents rebound, i.e. the first collision is accompanied by attachment. A high WFS prevents rupture during an impact. As a result, a contact angle does not arise and rebound is not prevented. However, rebound is accompanied by a second collision, the kinetic energy of which is smaller and can cause attachment at repetitive collision. These qualitative considerations are confirmed by the model quantification and comparison with measured Ecoll. For the first time the Sutherland equation (SE) for Ecoll is confirmed by experiment for smaller particle sizes and, correspondingly, very small Stokes numbers. The larger the particle size, the larger is the measured deviation from the SE. The SE is generalized, accounting for the centrifugal force, pressing hydrodynamic force and drainage in the low WFS case and, correspondingly, attachment occurs at first collision or during sliding. The derived generalized Sutherland equation (GSE) describes experimental data at low WFS. However, its application without account for possible rebound does not explain the measured extreme dependence in the case of high WFS. The theory for drainage during particle impact and the beginning of rebound enables conditions for either attachment or rebound in terms of the normal component of the impact velocity and the critical film thickness to be derived. Combining this condition with the GSE allowed the equation for Ecoll to be derived, accounting for attachment area shrinkage and attachment during a repetitive collision. This equation predicts the extreme dependence. Thus the WFS determines the modes of flotation dynamics and, in turn, probably affects the mechanisms, which control the flotation domain. At low WFS its upper boundary is controlled by the stability of the particle-bubble aggregate. At high WFS the upper boundary can be controlled by rebound because the latter reduces the attachment efficiency by a factor of 30 or more even with repetitive collision.