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Bubble attachment to hydrophobic solid surfaces is influenced by the liquid film instability. Inclusion of transiently formed holes within the film rather than the so-called hydrophobic force in the theory is expected to better describe and explain film rupture and triple contact line formation in the bubble–surface attachment process. The significance of surface hydrophobicity and hole formation renders the stochastic nature of the induction time of attachment. A combination of high-speed video microscopy and theoretical analysis was applied to investigate the induction time of attachment and critical film thickness of air bubbles rising freely perpendicularly to silica surfaces of different hydrophobicities. Film rupture occurred statistically for shorter induction times and thicker films on the more hydrophobic surface, rejecting the conjecture of hydrophobic force. Computed results of the critical base radius of the transient holes causing film rupture were merged together nicely, independently of surface hydrophobicity. The paper sheds light on the significance of hydrophobicity on the attachment process by means of a novel and easily implemented methodology, without relying on the debatable hydrophobic force. [ABSTRACT FROM AUTHOR]

Highlights • Bubble-particle detachment in isotropic turbulence is investigated. • The machine acceleration is analysed and quantified. • Confirmed acceleration as the first approximation for the inertial subrange. • Importance of transverse component of turbulence acceleration. • Components of turbulence acceleration should be used to predict detachment. Abstract The bubble-particle (BP) detachment is a significant factor in controlling the recovery of coarse particles in mechanical flotation cells. It has been quantified by balancing the restoring force of surface tension and the centrifugal force exerted on the particle-bubble aggregate by the turbulent flow field using a "machine acceleration". The concept of machine acceleration is useful because it links the mean energy dissipation rate of turbulence with the condition of the BP detachment. Here we further examine the concept of machine acceleration by applying the theory of isotropic turbulence. We confirm the known results of the first approximation for the inertial subrange. We also show that the turbulence acceleration has two principal components, i.e., the longitudinal and transverse components measured relatively to the BP centre-line. Significantly, the longitudinal component corresponds to the centrifugal force of turbulence against the restoring force of surface tension. The transverse component can be significant to quantifying the BP detachment if the turbulence shear is strong. We also extend the theory to cover the full range of isotropic turbulence, from the viscous to inertial subranges. Our estimation of the transition from the viscous to inertial subrange shows that the viscous effect can critically affect the BP detachment. Finally, our assessment of the contributions of the longitudinal and transverse components to the machine acceleration reveals the importance of the transverse component which can lead to a rather poor approximation for the machine acceleration as currently used. This paper shows that the effect of turbulence on the BP detachment should be better quantified using both the longitudinal and transverse components of turbulence acceleration rather than their modulus as the first approximation being termed the machine acceleration. [ABSTRACT FROM AUTHOR]

• Developed a CFD model to describe bubble-assisted copper matte transportation in slag. • No entrained matte for the lower bubble Re and Eo. • Matte contribution within slag depends on the higher Re and Eo. • Increasing Eo led to increasing film height and decreased film rupture time. Copper loss into the slag phase during the smelting process can be minimized by controlling gas bubble size and hydrodynamics. Here, bubble rising characteristics from copper matte to slag phase were investigated using the volume-of-fluid modelling approach, in which the continuous surface force model was adopted to define the surface tension parameters. The simulated results for bubble terminal velocities in bulk water and the literature data showed relative errors up to 4.51 %. The obtained qualitative and quantitative data from simulation at the liquid–liquid interface agreed well with the literature experimental results. The simulation setup was applied to investigate three different sizes of bubble rising dynamics from matte to slag phase with the bubble Reynolds number (Re) up to 1734 and the Eotvos number (Eo) up to 3.2. For low Re and Eo , the bubble rising velocity decreased before the matte film rupture and the bubble required a long time to complete that film drainage due to the balance of interfacial tension force and bubble buoyancy. No matte residue associated with the bubble rise in the slag phase was obtained because of restoring initial, non-deformed shape of bubbles. For the higher Re and Eo , quicker matte film drainage was obtained around the upper bubble surface while the entrained matte contribution to the slag phase was strongly dependent on the bubble-shape deformation, which was discussed with the well-known Grace diagram. The decreasing viscosity and increasing surface tension of the slag phase significantly affected the matte film height more than the film rupture time. The film height and rupture time increased and decreased with increasing Eo , respectively. The outcomes of our studies are useful for the design and operation of smetling furnaces in pyrometallurgical purification of metal concentrates. [ABSTRACT FROM AUTHOR]

Pyrite is a gangue mineral in the flotation of sphalerite activated by copper sulphate (CS). In this study, the attachment of air bubbles onto sphalerite and pyrite surfaces activated by CS was comparatively studied using a novel approach with High-Speed Video Microscopy (HSVM) and X-ray photoelectron spectroscopic (XPS). HSVM allowed for the in-situ determination of the liquid film Drainage Rate (DR) and Contact Angle (CA) of the bubble attachment. The results showed that after the activation sphalerite became hydrophobic by the formation of polysulphide as confirmed by XPS while pyrite remained hydrophilic. With increasing activation time and CS concentration, both DR and CA on the sphalerite surface rapidly increased at the beginning and reached constant values, while those on pyrite remained unchanged. The changes in the CA values of the sphalerite was successfully modelled by considering a second-order rate process for the CS activation which was proportional to initial copper concentration and available Zn active sites on the sphalerite surface. If both sphalerite and pyrite were simultaneously exposed to CS solutions (but not in the physical contact), the rate of CS activation of sphalerite remained unchanged when the ratio of sphalerite to pyrite surface areas exposed to CS solutions was equal to 1:1. However, the activation rate of sphalerite significantly dropped with increasing the sphalerite:pyrite surface area ratio from 1:3 to 1:6. The effect of the surface area ratio on the CS activation rate was prominent at activation times higher than 3 min. The XPS results for the mixed minerals showed the reduction in sphalerite Cu/Zn exchange and polysulphide/Cu ratios with increasing available pyrite surface area in CS solutions, indicating the significant drop in the CS activation of sphalerite in the presence of pyrite. The outcomes of this study provided further insights into the selective flotation of sphalerite from pyrite. [ABSTRACT FROM AUTHOR]

Only when the process of particle detachment is well understood and modelled can minerals recovery using the flotation process be modulated to achieve a high efficiency by suitably changing the operating parameters. This is vitally necessary for the recovery of coarse particles in an energy efficient way, as detachment is the key limiting factor in the successful recovery of large particles. However, until the detachment mechanism is more fully understood, an upper limit on the floatable particle diameter still remains unidentified. To assess the current state of knowledge available in this area, a comprehensive literature review on the mechanisms and models of the bubble-particle detachment process in froth flotation is presented. In general, the detachment process is considered to be a stochastic process, and is usually attributed to the dynamic interactions with the turbulent flow structures (eddies) in the flotation environment which cause particles to detach because of dissipating energy. In this paper, previous studies on bubble-particle detachment have been critically analyzed with respect to the formulation of the models in predicting the detachment probability of particles. The models are classified into three different categories: force balance analysis; energy balance analysis and empirical analysis of particle size compared to maximum floatable particle size. Attention is also paid to an understanding of the mechanisms of bubble-particle detachment in quiescent and turbulent liquid flow fields. The predictions of all these models have been compared with the published experimental data and it was found that models which take an accurate consideration of the influence of eddies on a particle’s detachment give the closest predictions. The generally held concept of bubble-particle detachment inside an eddy was experimentally validated, where a particle was observed to rotate on the surface of a bubble, resulting in a centrifugal acceleration 20 times that of gravitational acceleration. The aim of this paper is to review the developments and limitations of the existing models. The experimental work is reviewed so as to reveal the mechanisms of bubble-particle detachment. Therefore, the future development of models is identified in order to successfully predict particle detachment. [ABSTRACT FROM AUTHOR]

Highlights: [•] Some salts inhibit bubble coalescence beyond a critical concentration, . [•] has been modelled as a function of Hamaker constants of van der Waals attraction. [•] We show that the available models for under-predict the experimental data. [•] The van der Waals attractions do not govern the bubble coalescence in saline water. [Copyright &y& Elsevier]

Abstract: Flotation researchers have long hypothesised that particles have inherently different flotation rates under the same operating conditions because they have different induction times in the flotation cell. The relationship between flotation rate constant and induction time, however, has yet to be explored. Here we analysed the relationship between micro-flotation rate and back-calculated induction time for galena and sphalerite particles. The floatability of the particles was controlled by depression with potassium chromate (galena) and activation with copper sulphate (sphalerite). The bubble rise velocity vs. size in the micro-flotation experiments was determined by high speed video microscopy and followed the prediction for bubbles with the fully mobile air–water interface. Therefore, the theoretical analysis of the micro-flotation results was carried out, based on the potential flow model for water flow around a mobile bubble surface. The relationship between micro-flotation rate constant and back-calculated induction time was found to rapidly decay exponentially. In this model, flotation rate constant is highly sensitive to induction time. For example, a doubling or tripling of induction time results in an order-of-magnitude decrease in flotation rate constant. [Copyright &y& Elsevier]

Abstract: Atomic force microscopy (AFM) was used to examine how ethanol/water concentration affects the nanobubble bridging capillary force between a hydrophobic silica colloidal probe and a hydrophobic silica wafer. Nanobubbles were produced on the solid surfaces by a previously utilised method which uses solvent-exchange and surface scanning. In pure water a strong, long range attractive force (≈230 nm) with a single jump in step was measured, typical of an interaction between two nanobubbles attached to the hydrophobic surfaces. An increase in the ethanol concentration had little effect on the range of the force but dramatically reduced its magnitude. At an ethanol concentration of 40% by mass, the force became repulsive after the initial attractive jump in. Above an ethanol concentration of 40% by mass, the capillary force disappeared. The change in the force with ethanol concentration was explained using a capillary force model with constant volume and contact angle. The bridge geometry, contact angle, volume and rupture distance were determined for different ethanol concentrations. [Copyright &y& Elsevier]

• Measurement of bubble-galena attachment time using a developed apparatus. • Attachment time is greatly affected by xanthate chain length and bubble size. • Attachment time was modeled by the film drainage with multilayer dispersion forces. • This study sheds light on the principle for the bubble-surface attachment in flotation. Although available flotation experiments show that sulphide flotation recovery increases with increasing xanthate chain length, quantitative analysis to reveal the underlying mechanisms is missing. Herein, we investigate the chain length effect by using a recently developed attachment apparatus and an advanced theory to determine and validate the attachment time of air bubbles to galena surfaces in solutions of ethyl, propyl, butyl and amyl xanthate collectors. Specifically, the attachment time was accurately determined from either transient force curves or transient film thickness of the bubble-surface attachment. The theory was based on the film drainage theory and colloidal forces, which include the advanced multilayer dispersion (van der Waals) interactions and the electrical double-layer interaction. The multilayer dispersion theory has allowed us to describe the effect of galena hydrophobicity induced by the xanthate chain length in terms of interfacial gas enrichment (IGE) on the bubble-surface attachment. The experimental results show that the attachment time is greatly affected by both the hydrophobicity and the bubble size, and agree with the theoretical results. Critically, it was possible to accurately quantify the attachment time of the hydrophobised galena surfaces to bubbles using the measured transient force curves and the advanced multilayer dispersion theory incorporating the IGE layer. Finally, this study made it possible to explain the effect of the hydrophobicity and bubble size on attachment time and provides the principle for the attachment mechanism of hydrophobic minerals to air bubbles. [ABSTRACT FROM AUTHOR]

Asymmetry increases with Re , I and particle density. • Microturbulence effect on bubble-particle collision during bubble rise is investigated. • Asymmetry of water flow depends on turbulence intensity and bubble surface mobility. • Negative effects of the turbulence on collision interaction are unexpected but justified. Holistically, air bubbles in flotation must rise to the top surface while free solid particles must settle to the cell bottom. Inside the stator-rotor space of the mechanical flotation cells, the turbulence of mixing can surpass the gravity-driven motion of the bubble-particle suspension. Outside the space, the bubbles rise to the surface, but it is not known how the turbulence affects the bubble-particle interaction during the bubble rise. Here we numerically investigate the effect of microturbulence on the bubble-particle collision during the bubble rise. The focus is on the interaction asymmetry caused by the inertial forces and bubbles with fully mobile (MBS) or immobile (IMBS) surfaces at intermediate bubble Reynolds number (Re). The Reynolds-Averaged Navier-Stokes equations with the RNG k-ɛ turbulence model are solved for the mean water flow. Its fluctuating components are predicted using the stochastic formulation that is adopted with the discrete phase formulation for determining the particle grazing trajectories. The results show microturbulence influences the bubble-particle collision interaction. The asymmetry of the collision interaction is also affected by the microturbulence intensity. Its negative effects are found for the CCA (the critical collision angle, which also affects the bubble-particle attachment) and the overall collision efficiency. These negative effects are unexpected because turbulence has been postulated to enhance the collision interaction. Numerical results agree with the MBS model for overall collision efficiency and show some significant deviations for the IMBS model. This paper provides a potential technique to examine the microturbulence effect on attachment efficiency via the CCA. [ABSTRACT FROM AUTHOR]

Hydrodynamic behavior of fine particles and bubbles and their influences on the particle–bubble collision efficiency (Ec) in an electro‐flotation system were analyzed in this study. The influence of sodium oleate on the agglomeration of cassiterite particles and the effect of electrolyte (Na2SO4) concentration on the zeta potential of cassiterite were investigated in detail, respectively. Bubble trajectory was recorded by using a high‐speed camera to investigate the dynamic process in terms of bubble velocity. Moreover, bubble size was taken into account in the determination of the relationship between bubble velocity and Ec. The Reynolds number (Reb) was calculated to be 4.77 for hydrogen (H2) bubbles with a mean diameter of 52 μm. The highest recovery of cassiterite particles (<10 μm) was obtained by using 20 μm bubbles during flotation. The results indicate that the Yoon–Luttrell intermediate fluid (between the Stokes and potential flows) condition is applicable for the cassiterite electro‐flotation system, and Ec is improved by controlling the size and velocity of the hydrogen bubble, and the agglomeration of fine cassiterite particles in electro‐flotation. Additionally, it was greatly inspired to explore bubble–particle attachment in dissolved air flotation from these results. [ABSTRACT FROM AUTHOR]

Some salts have been proven to inhibit bubble coalescence above a certain concentration called the transition concentration. The transition concentration of salts has been investigated and determined by using different techniques. Different mechanisms have also been proposed to explain the stabilizing effect of salts on bubble coalescence. However, as yet there is no consensus on a mechanism which can explain the stabilizing effect of all inhibiting salts. This paper critically reviews the experimental techniques and mechanisms for the coalescence of bubbles in saline solutions. The transition concentrations of NaCl, as the most popularly used salt, determined by using different techniques such as bubble swarm, bubble pairs, and thin liquid film micro-interferometry were analyzed and compared. For a consistent comparison, the concept of TC95 was defined as a salt concentration at which the “percentage coalescence” of bubbles reduces by 95% relative to the highest (100% in pure water) and lowest (in high-salt concentration) levels. The results show a linear relationship between the TC95 of NaCl and the reciprocal of the square root of the bubble radius. This relationship holds despite different experimental techniques, salt purities and bubble approach speeds, and highlights the importance of the bubble size in bubble coalescence. The available theoretical models for inhibiting effect of salts have also been reviewed. The failure of these models in predicting the salt transition concentration commands further theoretical development for a better understanding of bubble coalescence in salt solutions. [ABSTRACT FROM AUTHOR]

Abstract: Recent research progress in hard rock mineral flotation shows that froth stability can be represented by air recovery, which is defined as the fraction of air entering a flotation cell that overflows the weir in unburst bubbles, and that air recovery has strong correlation with the separation performance of mineral flotation. Yet no experimental work on air recovery has been devoted to coal flotation. This paper studies air recovery in coal flotation and examines the links between air recovery, froth stability and coal flotation performance. A series of experiments were conducted using a laboratory-scale mechanical flotation cell at various methyl isobutyl carbinol (MIBC) concentrations and aeration rates. It was found that air recovery has a strong correlation with dynamic froth stability determined by measuring the maximum froth height in a non-overflowing froth column. At a fixed aeration rate (hydrodynamic condition) and various MIBC concentrations, a strong correlation between air recovery and coal flotation performance was also observed. [Copyright &y& Elsevier]

Abstract: Flotation occurs as a result of bubble–particle attachment. This is controlled by the particle surface properties which are created by surface liberation of valuable minerals and collector adsorption within the chemical environment. This paper examines the contribution of both collector dosage and liberation of valuable minerals to bubble–particle attachment time measurements. In order to evaluate particles of different liberation, the bubble–particle attachment time measurements were conducted with a sized fraction of concentrates and tails obtained by flotation of a copper sulfide ore (Northparkes Mine, Australia) in a mechanically agitated batch flotation cell. Quantitative mineral liberation analysis was performed to analyze all concentrates and tails. The results indicated that for particles with high Cu grade, a small increase of collector dosage resulted in a dramatic reduction of attachment time with no further increase on subsequent addition of collector. However, for particles with moderate Cu grade, the effect of collector addition on attachment time was reduced much less because valuable minerals were mainly moderately and poorly liberated. For particles with low Cu grade, collector addition made no difference. All these results confirmed that there is a highly non-linear correlation between mineral liberation, Cu grade, collector dosage and attachment time. [Copyright &y& Elsevier]

The influence of gas velocity (3.5,10, and 18mm/s), salt type (NaCl, NaF, NaBr, Nal and CsCl) and salt concentration (0.001-3 M) on bubble coalescence in a small bubble column were studied. The bubble coalescence was determined by the relative change in the measured light intensities passing through the salt solutions and clean deionised water. It was shown that the transition salt concentration for bubble coalescence inhibition (determined at 50% of bubble coalescence) of all investigated salts decreases with increasing superficial gas velocity. The difference in the transition concentration between NaCl, NaF, NaBr and CsCl does not significantly change with the gas velocity. However that difference between Nal and the other salts significantly decreases with increasing the gas velocity. The gas holdup significantly increases with NaCl, NaF, NaBr and CsCl concentrations but does not significantly change with Nal concentration. These new results imply that the transition salt concentration for bubble coalescence and gas holdup depend not only on the salt properties (i.e. the ion type and their combination) as previously reported, but also on the hydrodynamic conditions. [ABSTRACT FROM AUTHOR]

Abstract: Flotation is an important unit operation in the minerals industry, among others. Current state-of-the-art flotation modelling combines computational fluid dynamics (CFD) with user-defined algorithms based on the “induction time” concept to describe selective bubble–particle attachment and separation of hydrophobic and hydrophilic particles. We have undertaken experimental studies permitting direct observation of particle–bubble interaction and attachment at the microscale to provide empirical data for comparison with new theoretical predictions. Observations were made on a model system in which 150μm glass particles were dropped onto a captive 1.3mm air bubble formed in water within a glass cell. The interactions were recorded on high-speed digital video, permitting direct estimation of relevant parameters such as the approach velocity, and the duration of particle sliding over the bubble surface. A new experimental configuration has allowed the particle path toward, around, and away from the bubble to be totally unimpeded. Particle trajectories show a significant deviation at separations much larger than their own diameter; such deviations are due to the hydrodynamics. Comparisons with theoretical predictions indicate that the bubble surface exhibited mobility intermediate between “full slip” and “no slip”. Theoretical predictions for an immobile bubble surface were practically symmetrical about the bubble''s equator, while asymmetry was apparent in the theoretical predictions for a mobile bubble surface. However, the strongest asymmetries were seen in the observed particle trajectories and speeds. Particles dropping more centrally were seen to slide over the surface of the bubble. In several cases the sliding particle ‘jumped in’ toward the bubble, which is interpreted as the precise moment of attachment. This provides for a direct estimate of the threshold duration to achieve attachment, i.e. “induction time”. Among the events observed were rotation of the particle upon jumping in, and particle jump-in below the bubble''s equator. Explanations are proposed in terms of particle properties and flow phenomena. [Copyright &y& Elsevier]

Abstract: Flotation performance depends on bubble–particle attachment which is controlled by the particle surface properties which include the particle composition and the surface liberation of valuable minerals. This paper discusses the contribution of liberation of valuable minerals to bubble–particle attachment time measurements, under constant chemical conditions. The bubble–particle attachment time measurements were performed using a sized fraction from concentrates obtained at different times and tails by flotation of a copper–gold sulphide ore (Northparkes Mine, Australia) in a mechanically agitated batch flotation cell. All products and tails were analyzed using quantitative mineral liberation analysis. The results showed that there was a relationship between the time of the concentrate collected, the Cu grade of the sample and the bubble–particle attachment time, and that the measurements were most sensitive to the amount of unliberated material. The fast floating material was higher grade, with a lower attachment time indicating that the measured bubble–particle attachment time could be used to characterize flotation performance of an ore. [Copyright &y& Elsevier]

• A new paradigm of the bubble-particle detachment is discovered. • Bubble and particle do not detach at their triple contact line. • Detachment occurs at capillary neck of air-water interface near solid surface. • Detachment always leaves tiny residual volume of air on solid surface. • It contradicts traditional theories, urging further investigations. The flotation of coarse in particular partially liberated particles has attracted both industry and research interests in recent years as it can bring several benefits to existing operations, including the decrease in grinding energy and media consumption, the increase in plant throughput, and environmental benefits. The bubble-particle detachment is critical to this flotation process. Here, we have investigated the physics underlying the bubble-particle detachment and discovered a new paradigm, i.e., the bubble and particle do not detach at the three-phase gas-liquid-solid contact (TPC) line between the bubble and the particle, which contradicts the conventional consideration in the available theories. Our high-speed video movies show that the bubble-particle detachment does take place at a capillary neck of the air-water interface near the solid surface. The detachment always leaves a tiny residual volume of gas on the solid surface. Our experiments also show that the detachment interaction does not simply follow the slip mode of the TPC motion but rather a combined slip-stick mode of the TPC line relaxation. We rationalize our observations by considering the contact angle hysteresis, which always exists on the real particle surfaces having morphological roughness and chemical heterogeneity. The new evidence challenges the existing theories about the bubble-particle detachment interaction in flotation and urges further investigations to overcome the inconsistent predictions. [ABSTRACT FROM AUTHOR]