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The Effect of Bubble Size on Fine Particle Flotation
Abstract
Expressions for the probability of collision (Pc) and adhesion (Pa) have been derived for fine particle flotation by calculating the trajectory of particles as they flow past a bubble in streamline How. Three different flow regimes have been considered in the present work, i.e., Stokes, potential and intermediate. For the intermediate flow conditions in which most flotation operations are carried out, the particle trajectories have been determined using an empirical stream function derived in the present work. For the case of a very hydrophobic coal sample, the values of the probability of collection (P) determined experimentally have been found to be in close agreement with the theoretically predicted Pc values over a range of bubble and particle sizesThe expression for Pa has been derived by determining the time it takes for a particle to slide along the surface of a bubble after collision. It has been assumed that the bubble-particte adhesion occurs when the sliding time is equal to or exceeds the induction time, which varies with the particle hydrophobicity. Pa is shown to be a function of particle size, bubble size and induction time. The values of Pa predicted in the present work are in good agreement with the results of microflotation tests conducted on a coal sample.
... where Ec is the collision efficiency, Ea is the attachment efficiency, and Es is the stability efficiency of a bubble-microalgae aggregate. These efficiencies can be affected by both bubble size and microalgae size [100]. The collision efficiency (Ec) between bubbles and microalgae increases with decreasing bubble size [100]. ...
... These efficiencies can be affected by both bubble size and microalgae size [100]. The collision efficiency (Ec) between bubbles and microalgae increases with decreasing bubble size [100]. An increase in the number of bubbles also increases the collision efficiency between bubbles and microalgae [27]. ...
... Hassanzadeh et al. [101] selected bubbles of different sizes (0.08, 0.12, and 0.15 cm) and experimentally confirmed that small bubbles have higher collision efficiency than large bubbles. Yoon and Luttrell [100] found that the Ea tended to increase with the bubble size increase when the bubble size was <350 μm, and the bubble size continued to increase resulting in a decrease in the Ea when the bubble size was larger than 350 μm. Coward et al. [102] further compared the effects of bubble size and rise velocity on microalgae flotation efficiency. ...
... The drop density is 1000 kg/m 3 , the background density is 500 kg/m 3 , the surface tension is 0.02361 N/m, the drop diameter is 4 cm, the domain diameter is 6 cm squared, and computa- Grace et al. (1976). For reference the rise velocity of a 1 mm air bubble in water for a pure and contaminated system are also drawn, after Clift et al. (1978, Fig. 7 Yoon and Luttrell (1989) and Reay and Ratcliff (1975) Fielden et al. (1996) and Englert et al. (2009) ...
... This process of "first encounter" was a widely debated subject (Pyke, 2004) and it was not until cinematographic evidence of Bogdanov and Filanovski (1940) and the seminal paper of Sutherland (1948), that the "encounter" theory of Gaudin (1932) became widely accepted. Schuhmann (1942) was probably the first to consider bubble-particle collision efficiency as a fundamental parameter in the calculation of the flotation rate constant (Yoon and Luttrell, 1989). Gaudin (1932, p. 88-92) made a geometric analysis of the probability of 29 Figure 2.2. ...
... Even though the applicability of Eq.(2.29) to real systems is very restricted, this geometric collision kernel forms the basis for most flotation models. Yoon and Luttrell (1989) recognised that the key to an accurate geometric collision model is the derivation of the appropriate stream function. The correct stream function produces the correct critical stream tube radius r c , as schematically depicted in Fig. 2.3. ...
Bubble-particle interaction is a key phenomenon in many industrial applications, for example in mineral froth flotation. Flotation systems are typically characterised by high void fraction of dispersed phases and often multiple surface active compounds are present. The complexity of bubble-particle interaction has lead researchers to develop simplified models for dilute systems and typically physical and physico-chemical aspects are left out.
This work discusses a modelling framework for analysis of bubble-particle interaction in the presence of soluble surfactants. The model includes full momentum coupling between gas, liquid, and solid phases using a coupling between Computational Fluid Dynamics (CFD) and the Discrete Element Method (DEM) named CFDEM. CFDEM is an open source modelling framework where the CFD code OpenFOAM and the DEM code LIGGGHTS interact.
To accommodate topological changes of the bubble surface during break-up and coallescence the Volume Of Fluid (VOF) method was used. Solid particles are tracked in a Lagrangian frame of reference and experience forces due to collisions and the presence of the gas-liquid interface. A comprehensive model has been developed where particle-interface forces are modelled as a hyperbolic function of the gradient of the phase fraction. Particles can be captured within the interfacial region and can detach from the bubble when the balance of forces so dictates. DLVO and non-DLVO forces, as well as inertial forces, form part the total stress balance and contribute to the momentum equation of all phases. Variable interfacial tension is taken into account by implementation of a volumetric transport equation for soluble surfactant in the bulk fluid and within the interfacial gas-liquid region. The method is fully mass conservative and combines higher order physical momentum coupling with physico-chemical momentum. The sub-models used need further study, but to the authors knowledge the model presented is the first to couple all momenta in a comprehensive modelling framework for bubble-particle interaction.
The main value of this work is that the computational framework is modular and easily extensible to include more accurate sub-models. The Lagrangian particles are in fact dynamic lists that can be populated by the properties appropriate to the system. These properties accommodate further development and help to identify future research needs in the field of flotation modelling.
... Te energy that the turbulence contributes leads to the unwanted dissociation of the mineral particle from the bubble. Negative bias is used to keep the fow of tailings lower than the feed fow to recover more faky graphite [44,47,48]. Te bubbles in column fotation have a large lower limit in terms of diameter. ...
... Te water's streamlines allow the fne particles to move. Te foat recovery is decreased in this way, but only for fne and ultrafne particles [48,49]. ...
Due to its numerous and major industrial uses, graphite is one of the significant carbon allotropes. Refractories and batteries are only a couple of the many uses for graphite. A growing market wants high-purity graphite with big flakes. Since there are fewer naturally occurring high-grade graphite ores, low-grade ores must be processed to increase their value to meet the rising demand, which is predicted to increase by >700% by 2025 due to the adoption of electric vehicles. Since graphite is inherently hydrophobic, flotation is frequently used to beneficiate low-grade ores. The pretreatment process, both conventional and unconventional; liberation/grinding methods; flotation methods like mechanical froth flotation, column flotation, ultrasound-assisted flotation, and electroflotation; and more emphasis on various flotation reagents are all covered in this review of beneficiation techniques. This review also focuses on the different types of flotation reagents that are used to separate graphite, such as conventional reagents and possible nonconventional environmentally friendly reagents.
... The simplest way to calculate it is by accounting for the streamlines of the fluid carrying a particle in close proximity to a bubble (Von Smoluchowski 1917, Sutherland 1948. This approach has been studied in details (Michael andNorey 1969, Flint andHowarth 1971) and advanced for larger Stokes and Reynolds numbers Finch 1987, Yoon andLuttrell 1989), but up to a certain intermediate level (up to Re = 400) of turbulence, because the general assumption (flow around a bubble) is the same. There is turbulence in the flotation cells in reality. ...
... Evidently the collision rate should depend on the size of the bubbles, their concentration and the speed of the impeller. The scenario of collision between a bubble and a particle has been studied by number of authors (Sutherland 1948, Philippoff 1952, Dobby and Finch 1986, Yoon and Luttrell 1989, Dai, Fornasiero et al. 1999, thus introducing the contact time as the time of sliding of the particle on the bubble after which the particle retracts from the bubble. Another important parameter is the induction time (often called attachment time) defined as the time, that the bubble needs to capture the particle. ...
This work analyses the basic problems of the fine particles flotation and suggests new ways to overcome them. It is well accepted that the poor recovery of fine particles is due to the small collision rate between them and the bubbles due to the significant difference between their sizes. This common opinion is based on a theory, assuming in its first version a laminar regime, but later has been advanced to intermediate turbulence. It accepts that the particles are driven by the streamlines near the bubbles. In reality, the high turbulence in the flotation cells causes myriads of eddies with different sizes and speeds of the rotation driving both bubbles and particles. Yet, a theory accounting for high turbulence exists and states that the collision rate could be much higher. Therefore, we assumed that the problem consists of the low attachment efficiency of the fine particles. Basically, two problems could exist (i) to form a three-phase contact line (TPCL) the fine particle should achieve a certain minimal penetration into the bubble, requiring sufficient push force; (ii) a thin wetting film between the bubble and the particle forms, thus increasing the hydrodynamic resistance between them and making the induction time larger than the collision time. We assumed particles with contact angle θ = 80°, and established a lower size flotation limit of the particles depending mostly on the size of the bubbles, with which they collide. It spans in the range of Rp = 0.16 m to Rp = 0.40 m corresponding to bubbles size range of Rb = 50 m to Rb = 1000 m. Hence, thermodynamically the particle size fraction in the range of Rp = 0.2 m to Rp = 2 m are permitted to float but with small flotation rate due to the small difference between the total push force and maximal resistance force for formation of TPCL. The larger particles approach slowly the bubbles, thus exceeding the collision time. Therefore, most possibly the cavitation of the dissolved gas is the reason for their attachment to the bubbles. To help fine particles float better, the electrostatic attraction between bubbles and particles occurred and achieved about 92% recovery of fine silica particles for about 100 sec. The procedure increased moderately their hydrophobicity from θ ≈ 27.4° to θ ≈ 54.5°. Electrostatic attraction between bubbles and particles with practically no increase of the hydrophobicity of the silica particles ended in 47% recovery. All this is an indication of the high collision rate of the fine particles with the bubbles. Consequently, both, an increase in the hydrophobicity and the electrostatic attraction between particles and bubbles are key for good fine particle flotation. In addition, it was shown experimentally that the capillary pressure during collision affected significantly the attachment efficiency of the particles to the bubbles.
... The simplest way to calculate it is by accounting for the streamlines of the fluid carrying a particle in close proximity to a bubble (Von Smoluchowski 1917, Sutherland 1948. This approach has been studied in details (Michael andNorey 1969, Flint andHowarth 1971) and advanced for larger Stokes and Reynolds numbers Finch 1987, Yoon andLuttrell 1989), but up to a certain intermediate level (up to Re = 400) of turbulence, because the general assumption (flow around a bubble) is the same. There is turbulence in the flotation cells in reality. ...
... Evidently the collision rate should depend on the size of the bubbles, their concentration and the speed of the impeller. The scenario of collision between a bubble and a particle has been studied by number of authors (Sutherland 1948, Philippoff 1952, Dobby and Finch 1986, Yoon and Luttrell 1989, Dai, Fornasiero et al. 1999, thus introducing the contact time as the time of sliding of the particle on the bubble after which the particle retracts from the bubble. Another important parameter is the induction time (often called attachment time) defined as the time, that the bubble needs to capture the particle. ...
Abstract: This paper studies the effect of the type and concentration of selected frothers and collectors
mix system on the bubble sizes (Sauter mean diameter, SMD) of bubbling flow produced in a micro
flotation cell and the determination of bubble size distribution (BSD). The usage of dodecyl amine
hydrochloride (DAH) collector on the critical coalescence concentration of commercial frothers PPG200,
PPG400, and PPG600 was investigated in detail. The results of these studies showed that the usage of
DAH decreased the CCC of these frothers. Each frother + collector mixing system exhibited its unique
ability in preventing coalescence of the bubbles in the order of PPG200 < PPG400 < PPG600. The factorial
experiments established that the type of the frother, collector, and their concentration had a major effect
on the size of the bubbles. The BSD in the presence of PPG600 + DAH mix system resulted in a little bit
wider BSD which indicated the effect of frother type in mixed systems.
... Hence, reducing the intensity of cell agitation to a point sufficient for maintaining particles in suspension is the optimum condition for efficient recovery in the flotation of coarse particles [5,17,59,75]. These parameters generally result in an overall increase in the circuit's capacity for coarse and ultra-coarse flotation circuits, and faster response rates than CFCs [17,42,77]. ...
... Large volumes of finely split bubbles effectively float coarse particles since they quickly bind to hydrophobic sites on the particles, causing bubble-particle clusters to develop, increasing the drag force required to lift the particles [3]. In other words, smaller bubbles can enhance flotation kinetics by increasing the likelihood of particle-bubble collision and attachment [61,77]. In practice, maintaining a bubble interfacial flux far below the flooding threshold, generally around 60 /s, dictates the inter-relationship between bubble size and gas flux [73,76]. ...
Since comminution within mineral beneficiation plants is the most energy consumer unit, the effective separation of coarse particles has generated considerable interest in the ore processing industry. Due to the inherent challenges faced with floating coarse particles using conventional flotation cells (CFCs), a number of attempts were made to develop new technologies that could efficiently and cost-effectively treat them. Fluidized-bed flotation cells (FBFCs), as novel developments such attempts, have proven a higher potential than CFCs for processing coarse particles. HydroFloat, NovaCell, and Reflux Flotation Cell are three main developed FBFCs for processing coarse particles. The quiescent nature and other characteristics of FBFCs allow for longer retention time, reduced particle buoyancy constraints, a near absence of coarse particle detachment from the bubble, and increased bubble-liquid segregation capacity, which leads to an excellent coarse particle recovery. These properties assist FBFCs in processing coarse particles environmentally friendly.
... The combined application of small and conventional bubbles presented the potential to alleviate issues related to fine particle flotation and exploit the benefits of small bubbles as much as possible [7,9,[17][18][19][20]. ...
Nanobubble-containing water (NW) was applied to the flotation of lead and zinc minerals (D50=4 µm or D90=22 µm) to enhance the recovery of ultrafine valuable particles and prevent their loss to the tailings. Two separate bi-level factorial designs were implemented to optimize the NW portion (volume of necessary water for pulp preparation substituted with NW), potassium ethyl xanthate (PEX), potassium amyl xanthate (PAX), and frother dosage, to each discrete concentrate. Based on the statistical analysis results, frother dosage was the most influential parameter, where raising it from 25 to 50g/t increased the recovery of lead and zinc by 12.25 and 3.34%, respectively. The substitution of tap water (TW) with 100% NW improves lead and zinc recovery by 7.46% and 1.41%, respectively. Based on the approved response surfaces, PEX=160g/t, NW=100%, and frother=50g/t minimize lead loss to the tailings (76.29% recovery to concentrate), and PEX=80 g/t, PAX=39.75g/t, NW=79.82%, and frother=48.16g/t minimize zinc loss to the tailings (94.27% recovery to concentrate).
... Bubble-particle attachment occurs only when the induction time (time required for film rupture between bubble and particle) is shorter than the sliding time (time taken for a particle to slide over the bubble surface) [56]. The reduction in bubble size results in a decrease in the bubble rise velocity, thereby prolonging the sliding time and favoring bubble-particle attachment [18,57]. Secondly, NBs can attach to MPs through hydrophobic interactions, increasing the contact angle of particles and enhancing the probability of collision and flotation by larger-sized bubbles [58,59]. ...
... Flotation technologies have been employed to improve the flotation performance of fly ash. These methods involved increasing the hydrophobicity of fine carbon particles through collector addition and enhancing the probability of collision and attachment by decreasing bubble size and increasing the apparent particle size [23,24]. ...
... The enrichment of minerals with the flotation method depends on selectively making mineral surfaces hydrophobic by adjusting the pH of the medium and introducing the appropriate size of air bubbles [2][3][4][5]. If minerals do not possess surface properties akin to the attachment air bubbles, chemicals called collectors are added to make the mineral hydrophobic [6,7]. Additionally, the efficiency of flotation is strongly related to the collecting ability of air bubbles, and their behavior is generally controlled with the use of chemicals ...
Recent studies in the flotation of fine particles have necessitated new techniques and analyses for developing various strategies. Particularly, the improvements in flotation chemistry including the selection of the type of frother, collector, and other reagents have become very significant. In this study, the effect of different commercial polypropylene glycol frothers (PPG200, 400, and 600) in the presence of dodecylammonium hydrochloride (DAH) was investigated for their contribution to flotation recoveries and bubble–particle attachment time values of fine quartz minerals. Zeta potential measurements with DAH were also carried out as a function of pH and reagent concentration to justify the effect of collector usage alone on the charge of particles. A linear increase in flotation recoveries against collector concentration, e.g., 7.4% recovery at 1 × 10−5 mol/L DAH and 65.4% recovery at 1 × 10−3 mol/L DAH, was obtained. In this context, the contribution of frothers was particularly important in that a recovery of 15.91% in the absence of the frother and a modest increase to 19.70% was obtained upon the addition of PPG600 at its critical coalescence concentration (CCC) of 3 ppm. Finally, a strong correlation was found between the bubble–particle attachment time and flotation recovery as a function of collector concentration (lowest attachment time vs. highest flotation recovery). The latter correlation is very promising because bubble attachment time leads to various micro-mechanisms in flotation including bubble film thinning, bubble rupture, and induction time, and consequently, frother efficiency in the presence and absence of a collector. As a result, the experimental findings were gathered to achieve a consistent base for further fundamental studies on the application of the synergistic effect of frothers and collectors in the flotation of fine particles.
... These flotation processes are particularly interesting for the recovery of microparticles like microplastics or fine particles (Swart et al. 2022). However, one major limitation of this technique is the requirement for generating extremely small bubbles to capture the smallest particles, as emphasized by Yoon et Luttrell (1989). Dissolved gas flotation is one existing technology used to generate micron-sized bubbles. ...
Motivated by the dynamics of microbubbles in dissolved gas flotation processes, we consider theoretically the approach between two shear-free translating and growing bubbles. We make use of the lubrication assumption to obtain the thin film flow between the bubbles. We demonstrate that the lubrication force between the bubbles involves two distinct components: one viscous and one inertial. Both components exhibit weak singular behavior, scaling logarithmically with the ratio of bubble radius to film thickness. To assess the accuracy of our findings, we compare the obtained solution to results from Stokes flow and potential flow theory. The comparison demonstrates that our current results are reliable, provided that we combine the lubrication forces with a constant term that cannot be derived from the lubrication assumption alone. We illustrate the relevance of the solution to determine the drainage time of a small bubble rising to a free surface, and the drainage rate of expanding bubbles under force-free conditions. Remarkably, our findings exhibit good agreement with available experimental data.
... This physical picture, however, assumes a laminar flow at low Reynolds numbers. This approach has been advanced by Yoon and Luttrell [16] to Re = 400. The application of this approach to real flotation reactor predicted a low frequency of bubble-fine particles collisions, thus misleading the flotation 2 of 27 research community that this is the basic problem for the low recovery of the fine particles. ...
Abstract: This paper analyses the basic obstacles preventing the fine particles from floating and suggests solutions for the wetting zone between the bubble and the particle during their collision. It has been shown in our recent paper that the basic problem of fine particle flotation is not the low frequency of collisions with the bubbles, but it consists of the efficiency of these collisions. Moreover, there exists a thermodynamic lower size limit for flotation of fine hydrophobized particles in the sub-micron range, and it is weakly dependent on the size of the bubbles. It was shown that fast flotation with high recovery of fine particles can be achieved by means of: (i) electrostatic attraction between particles and bubbles; (ii) a significant increase in the level of their hydrophobicity; (iii) existence of fine bubbles in the flotation cell. It was shown as well that the drainage of the wetting film between bubbles and particles is unimportant, but the deformation of the bubble by the particle during their clash plays a major role in its rupturing. Electrostatic attraction between bubbles and fine silica particles was achieved with hexylamine. It causes a moderate increase of their hydrophobicity from contact angle = 39.5 • ± 2.5 • to contact angle = 51.7 • ± 7.5 • and gave almost 90% recovery within 2 min. Unfortunately, the selectivity of this collector is unsatisfactory if the fine silica particles are mixed with fine magnesite particles. It was shown that even being hydrophilic, the recovery of fine particles can jump to almost 50% if strong electrostatic attraction with the bubbles exists. It was demonstrated as well with the collector hexamethyldisilazane causes significant increase of the hydrophobicity of the fine silica particles (contact angle ≈ 90 •) results in skin flotation with 100% recovery when alone and 97% recovery when being mixed with fine magnesite particles (51/49). A new collector significantly increasing the hydrophobicity of magnesite fine particles was tested (disodium dodecyl phosphate) resulting in 89% recovery of fine magnesite particles alone and about 98% recovery in a mixture with fine silica particles.
... Two main approaches to overcome the detrimental effects of fine particles on flotation are reducing the size of bubbles (Basařová, Jan, and Mária 2019;Bournival, Ata, and Jameson 2017;Park, Chun, and Liguang 2022;Yoon and Luttrell 1989) and incrementing particle size (i.e. aggregation) (Atalay and Özbayoğlu 1992;Dhawan et al. 2015;McDonald and Kawatra 2017;Rulyov, Dontsova, and Ja Korolyov 2005). ...
Flotation process is the most common beneficiation method of almost all types of minerals. The desirable result of the process is dependent on various factors. One of the most effective parameters in this regard is the particle size. Generally, acceptable results can be obtained by adjusting particle size in an optimum and specific range, and flotation of coarser or finer than this range is always intricate and problematic. Specifically, in the case of fine and ultra-fine particles, this complexity becomes more aggravated most importantly because of the massive specific area and the reduction of particle-bubble collision and attachment probabilities. There is a vast amount of literature on fine particles flotation using micro- and nanobubbles, intensified flotation machines, and different chemical reagents, however, the most promising procedure in this regard can be considered as the increment of particle sizes via agglomeration and flocculation techniques combined with flotation. This technique provides great opportunities for recovering fine and ultra-fine particles economically and increment of sustainable processing. However, there are some gaps and obscure points such as the exact mechanism of bubble-floc adsorption, interaction between flocs and reagents, pulp properties variations due to flocculation, and its effects on flotation behavior. This paper categorizes and describes diverse aspects of this combined novel technique in detail and provides a comprehensive source for readers to have a deeper insight into this intricate process. First of all, the physicochemical characteristics of the process have been described thoroughly from perspectives including the type and structure of applied chemicals, influential parameters, and involved adsorption mechanisms. It is followed by a detailed interpretation of different floc-flotation techniques as well as their cons and pros, effective parameters, and possible improvement and optimization approaches. Further, some similar techniques such as oil agglomeration, hydrophobic-hydrophilic Separation, and carrier flotation were described and compared with present technique of floc-flotation. Technological aspects of the process as well as an industrial case study of this technique were other areas which have been investigated in this paper and finally, scientific and technical gaps in this branch of flotation technology were extracted to open-up new horizon ahead of researchers active and/or interested in this field.
... Fine particles show different behavior compared to coarser particles and their main characteristics are: (1) higher surface area per unit mass (higher collector consumption), (2) tendency to follow the fluid flow around a bubble more easily than a larger particle (greater entrainment tendency), (3) slower flotation rate and (4) more susceptible to the chemistry of the pulp and to the ions contained in this [5]. Recent advancements have been developed which aim to increase the bubble-particle collision efficiency, either by reducing the bubble size [11][12][13][14] or by increasing the apparent particle size [15,16]. However, both approaches are practically difficult to implement on an industrial scale. ...
The froth flotation technique can be considered one of the most efficient methods for the separation of minerals. Prior to utilizing any physicochemical separation method, the size of the mined ore must be decreased to facilitate the release of the valuable materials. This practice, along with the increased exploitation of ores that carry fine mineral particles caused the production of fine and ultrafine particles which are difficult to recover with classical enrichment methods, due to their different characteristics compared to coarser particles. It is established that fine and ultrafine particles are difficult to float, leading to losses of valuable minerals, mainly due to their low collision efficiency with bubbles. Moreover, fine particles require higher reagent consumption due to the fact that have a higher specific area, and finally, their flotation is limited by low kinetic energy. Flotation of fines can be enhanced by either decreasing bubble diameter or increasing their apparent size, or moreover, by enhancing the collector’s adsorption (their hydrophobic behavior) using alternative reagents (non-ionic co-collectors). In the present research, flotation experiments on a hybrid electrolytic flotation column that can produce microbubbles (−50 μm), were carried out for recovering fine magnesite (−25 μm) particles. In addition, the synergistic effect of anionic/non-ionic collectors were studied for the enhancement of fines recovery. Experimental flotation results so far designate the enhancement of fine magnesite particle recovery by approximately 8% with the addition of microbubbles. Finally, the synergistic effect of anionic/non-anionic collectors led to the improvement of flotation recovery by almost 12%.
... Compared to 2200 rpm, the bubble loading area growth rate decreased by 7.66 percentage points when the conditioning speed increased to 2500 rpm due to the fluid bypass and the effects of reagent desorption [7,16]. It is evident that an insufficient or excessive conditioning speed fails to improve the surface hydrophobicity of coal particles [30]. Therefore, there is an optimal conditioning speed for HIC. ...
The mechanism of high-intensity conditioning (HIC) has not been thoroughly revealed, and therefore this work investigates the effect of HIC on the surface hydrophobicity of coal with different particle sizes and the possible formation of particle–bubble clusters. The results show that different HIC conditions are required for coarse and fine particles. Coarse particles (+75 μm) require a higher turbulence intensity to increase collector dispersion, thereby increasing the adsorption of the collector. Fine particles (−75 μm) require a lower turbulence intensity to reduce the desorption of the collector. In this study, the optimum HIC conditions for coarse and fine particles are “2200 rpm + 1 min” and “1300 rpm + 1 min”, respectively. Interestingly, it seems that the adsorption capacity between fine particles and the collector is weaker than that for coarse particles. A non-enclosed HIC system produces up to 1.78 × 104/g bubbles in coarse particle–bubble clusters, and the mean bubble diameter is approximately 87 μm. The cluster achieves pre-mineralization and increases the apparent particle size, which is expected to improve flotation.
... The onset of the development of kinetic models is due to Sutherland [38]. Since then, several authors have contributed to understanding flotation kinetics through developing particle-bubble collision efficiency models [39][40][41]. Clift, Grace and Weber [42] and Schulze [43] contributed with hydrodynamic considerations of bubble motion. Bubble-rise velocity models were developed by Karamanev and Nikolov [44]. ...
Geometallurgical models are commonly built by combining explanatory variables to obtain the response that requires prediction. This study presented a phosphate plant with three concentration steps: magnetic separation, desliming and flotation, where the yields and recoveries corresponding to each process unit were predicted. These output variables depended on the ore composition and the collector concentration utilized. This paper proposed a solution based on feature engineering to select the best set of explanatory variables and a subset of them able to keep the model as simple as possible but with enough precision and accuracy. After choosing the input variables, two neural network models were developed to simultaneously forecast the seven geometallurgical variables under study: the first, using the best set of variables; and the second, using the reduced set of inputs. The forecasts obtained in both scenarios were compared, and the results showed that the mean squared error and the root mean squared error increase in all output variables evaluated in the test set was smaller than 2.6% when the reduced set was used. The trade-off between simplicity and the quality of the model needs to be addressed when choosing the final neural network to be used in a 3D-block model.
... 207,215 The EF decreases with the bubble radius for the collision efficiency decreases with the bubble size. 214,216,217 In addition, the relationship between the particle size and thickness of the cavity at the bottom of the bubble after the formation of the top jet droplet causes the EF of the top jet droplet to be divided into two regions. (1) 2r p > d, only a portion of the particles [d/(2r p )] stays in the bulk water, and the particle number in the top jet drop, 214 as shown in Fig. 23. ...
The phenomenon of a bubble bursting to generate droplets exists in industrial and environmental systems and has a subtle impact on our daily lives. A bubble generated by gas injection or heating rises to the free surface and undergoes floating, drainage, and eventually bursting processes to produce film and jet droplets. The interrelated processes make it difficult to understand the characteristics of a bubble burst. Thus, a summary of the individual stages of a single bubble from generation to burst is necessary. First, we describe the calculation method and simple expressions for the shape of a bubble floating on a free surface. Next, we discuss the bubble drainage model and its influencing factors as this directly determines the time evolution of the film thickness. As an essential factor that affects the film thickness, the bubble drainage time is defined as the bubble lifetime. We compare the bubble lifetime distributions in the published literature and explore the associated influencing factors. Then, we investigate the bubble bursting dynamics and focus on the bubble film opening process once a hole appears on its surface. As a legacy of bubble burst, we explore the production process, size, and number of film and jet droplets. Finally, we discuss the enrichment phenomenon and the enrichment factors of film and jet droplets when releasing particles entrained by droplets. This review considers a series of processes for bubble burst to generate droplets and concentrates on the mechanism and experimental correlations with a summary and future prospects.
... Farrokhpay et al. (2021), Dai et al. (2000) and De F. Gontijo et al. (2007) have reported that low collision and attachment efficiencies are key contributing factors to the poor recovery of fine particles via flotation method. Collision efficiency decreases with decreasing particle size due to their small inertia (Sutherland, 1948;Yoon and Luttrell, 1989). When fine particles shadow the aerodynamics around bubbles, they are unable to have any form of contact (collision) with the bubble to enable attachment which subsequently results in the loss of the mineral particles to tailings (Miettinen et al., 2010;Subrahmanyam and Forssberg, 1990). ...
The fall in the tail and trunk of the popular "elephant curve" relating ore/mineral particle size to recovery has been a case study for some decades. Research works done have shown that recovery is optimum at particle sizes ranging from 15 to 150 µm, evident in the recovery to particle size plots. The effect of particle size on flotation recovery is not facile for both coarse-and fine-grained ores. This can be attributed to the contrasting favourable conditions that exist for both fine and coarse particle sizes. Detachment as a result of strong turbulence in conventional flotation cells is attributed as the cause of low recovery in coarse particles flotation. However, strong turbulence is a requirement in fine particle flotation due to the high collision efficiency generated in turbulent environments. Conversely, low collision and attachment efficiency with the bubbles present significant challenges in the flotation of fine-grained valuable minerals. Over the years, significant research in froth flotation has been carried out to promote collision efficiency, bubble attachment and froth stability in fine particles flotation, special particle surface modifications and flotation cells have been identified. This paper reviews key challenges associated with the flotation of fine particles and ongoing efforts aimed at enhancing their recoveries.
... Ahmed & Jameson (1985) showed that the bubble size distribution in the flotation process has a significant effect on the mineral recovery rate. Yoon & Luttrell (1989) reported that by reducing the bubble size tenfold, the flotation rate increased almost a hundredfold. ...
The flotation process allows particles and oil to separate from wastewater with high efficiency. Therefore, it is widely used in engineering and is a multidisciplinary field of study. In this study, a new generation flotation method is developed as an alternative to conventional flotation methods. Some experiments are conducted to determine the performance of this new system. It is known that the air-demand rate in the flotation process directly improves flotation performance. For this purpose, maximum aeration efficiency and bubble properties in the flotation cell supported by the newly developed head gated conduit are examined. A pilot-scale flotation system is installed for the experimental study. With the help of high resolution and high-speed cameras, parameters such as air bubble density, air bubble size, dead zone volume and penetration depth are determined. In addition, the images recorded during the flotation process are examined with professional image processing techniques. Experimental results showed that the Froude number, jet plunge angle and cell water levels have a significant impact on air-demand in the new system.
HIGHLIGHTS
Bubble size, dead zones and penetration depth were obtained by image analysis at the flotation cell.;
The amount of bubbles was monitored during flotation different experiments.;
The size of the Froude number has a significant effect on the amount of air bubbles.;
Flotation system with a cell supported by conduit will be an alternative to the conventional flotation methods.;
... Bubble size reduction is often desirable in the flotation process as it can greatly improve bubble-particle collision probability and thus flotation kinetics (Ahmed and Jameson, 1985;Yoon, 2000;Yoon and Luttrell, 1989). Microbubbles can be simply produced by passing a gas stream through a micro-porous diffuser in water, but this method often has high energy and maintenance requirements. ...
The present paper describes gas dispersion in an air-sparged laboratory scale bubble column containing aqueous solutions of single electrolytes (NaCl, CaCl2, MgCl2, MgSO4, and AlCl3) and mixed electrolytes (NaCl-CaCl2 and NaCl-CaCl2-MgCl2-AlCl3) at different ionic strengths and air flow rates, with oscillatory air supply and conventional steady air supply, respectively. The gas dispersion was investigated by a light-scattering technique (turbidity measurement) and bubble size measurement. The oscillatory air supply was generated from steady air flow using a fast-switching solenoid valve and was characterized by measuring the pressure of the output air of the solenoid valve as a function of time. It was found that for each electrolyte solution tested, oscillatory air supply at a certain frequency and amplitude could give better gas dispersion than steady air supply, and the degree of improvement of gas dispersion varied with the electrolyte type and concentration and air flow rate. At each air supply mode tested, either the intensity of scattered light or the Sauter mean diameter of bubbles would scale with the ionic strength, following a decreasing trend. A cooperative effect of electrolyte addition and oscillatory air supply on gas dispersion was generally found. The combined effect of electrolyte addition and oscillatory air supply on bubble size was significant, being up to almost a 2/3 decrease in the Sauter mean diameter. The present work highlights the importance of flow condition for controlling bubble generation and coalescence in saline water and has significant implications for seawater flotation of minerals.
... Incorporating SAP can improve the frost resistance of concrete, so that the pore diameter and interval of concrete increase less after freeze-thaw. MNBW, as the mixing concrete water, has a certain synergistic effect with SAP to improve the frost resistance of concrete [28] . Figs. [13][14][15][16][17][18]. are the appearance of concrete at the age of 28 days and concrete after 200 freezethaw cycles. ...
Shotcrete was prepared by using micro-nano bubble water as mixing concrete water in cooperation with air-entraining agent (AOS-R) and superabsorbent polymer (SAP), and its frost resistance performance was experimentally studied. The results show that the incorporation of AOS-R and SAP will reduce the 28-day strength of concrete, but MNBW can compensate for the strength loss to a certain extent. The frost resistance of concrete mixed with alkali accelerators is inferior to that of concrete mixed with the alkali-free accelerator. The incorporation of AOS-R or SAP into shotcrete can improve its frost resistance to in some degree as well. Given the frost resistance of concrete mixed with SAP is not as effective as AOS-R, MNBW can play a synergistic effect to improve the frost resistance of concrete. The main reason why the AOS-R improves the frost resistance of concrete is that it generates a large number of small bubbles to isolate the water transmission channel which manage to relieve the crystallization pressure of water. MNBW improves the frost resistance of concrete, because it refines the pore structure and increases the density of concrete.
... In this case, a large total surface area of microbubbles is available for contact with bitumen. The collision probability between a single bubble and a bitumen droplet is determined as follows 56 = i k j j j j j y ...
... The poor flotation of fine particles is often due to the low bubble-particle collision efficiency, affected by the ratio of the particle to bubble diameter. Studies showed that decreasing bubble size can result in increasing the efficiency of fine particle flotation [7][8][9][10]. ...
Ultrafine bubbles were applied to the rougher flotation of the lead and zinc minerals, and the effects of the particle size (−38, −75, and − 106 μm) and collector concentration (potassium ethyl xanthate: 60, 80, 100, and potassium amyl xanthate: 10, 20, 30 g/t) were investigated on the lead and zinc recovery by implementing central composite and two-level full factorial designs, respectively. Considering the results, particle size was the most effective variable which substantially enhanced the lead recovery from 27.6 to 63.65%, and the zinc recovery from 59.92 to 84.88%. Also, the introduction of ultrafine bubbles improved the lead and zinc recoveries by about 7.41 and 1.22%, respectively. It could be concluded that the adsorbed ultrafine bubbles helped collectors in making the particle surface hydrophobic, and consequently reduced the reagent consumption. In conclusion, the application of ultrafine bubbles to the lead‑zinc flotation proved to be beneficial from the metal recovery aspect.
... Although the number of BNBs was much higher than that of BMBs, its effect on inducing particle aggregation was relatively weak. This is because, on the micro-scale, the probability of collision between particles and bubbles increases with a decrease in the bubble size [50]. BMBs can easily collide and adhere with quartz particles to form flocs. Additionally, the apparent size of flocs is much higher than that of quartz ore; it is easier to collide and adhere with conventional flotation bubbles [51]. ...
The present work investigates the synergetic effect of bulk micro and nano-bubbles (BMNBs) on the flotation performance of pure quartz particles. For this purpose, micro-and nano- bubble sizes in different proportions were generated through hydrodynamic cavitation. Aqueous dispersions with diverse properties were created by altering the preparation time (0, 1, 2, 3, 5 and 7 min), aeration rate (0, 0.5, 1, 1.5 and 2 L/min) and aging time (0, 0.5, 1, and >3 min). Micro- and nano-bubbles were characterized using focused beam reflection measurements (FBRM) and nanoparticle tracking analysis (NTA), respectively. Micro-flotation of quartz particles was performed using an XFG-cell in the presence and absence of BMNBs using Cetyltrimethylammonium bromide (CTAB) as a collector. Characterization of bubble sizes showed that the bulk micro-bubbles (BMBs) and bulk nanobubbles (BNBs) diameter ranged from 1-10 μm and 50-400 nm, respectively. It was disclosed that the preparation parameters and aging time of BMNB water considerably affected the number of generated bubbles. According to the results, the practical possibility of using BMBs and BNBs was based on the technical advantages, such as the higher recovery of quartz particles. When BNBs and BMBs coexist, the recovery of fine quartz particles was significantly improved, while in the presence of only BNBs the promotion of flotation recovery was not significant. That was mainly related to the aggregate via bridging, which was an advantage for quartz flotation. In comparison, no aggregates were detected when only nano-bubbles were present in the bulk solution.
Flotation is a physicochemical process that is used for the separation of hydrophobic particles from hydrophilic ones. This method is widely used in mineral processing for the selective separation of valuable minerals. It is also used in water treatment and recycling processes. In the flotation of minerals, hydrophobic particles form bubble-particle aggregates as a result of micro-events, namely collision, attachment, and detachment. The aggregates float to the top of the flotation cell as a concentrate, while the hydrophilic particles, which are not attached to bubbles, sink to the bottom of the cell and are taken out as tailings in direct flotation. The concentrate and tailing positions in the cell are reversed for reverse flotation applications. To achieve high flotation recoveries, particles shall securely attach to air bubbles and stay attached as they rise to the top of the cell inside the flotation cell. The most critical parameter affecting the stability of bubble-particle aggregates is the size of the particles. The optimum size range for traditional mechanical flotation cells is typically between 20 and 150 µm for metal sulfides. The flotation recovery decreases outside this range due to high turbulence within the cell for coarser particles and low bubble-particle collision probability for the finer end of the particle size spectrum. In recent years, however, many studies have become available that promise improvement in recovery for finer and coarser ends of the particle size spectrum. In this chapter, the development of new technologies to increase the efficiency of the flotation of fine and coarse particles is discussed. General flotation theory and parameters affecting the recovery of particles are explained in detail. Relatively new technologies such as the Jameson cell, Concorde cell, Hydrofloat, Jet Diffuser Flotation Column, NovaCell and Reflux flotation cell have significant potential for both fine and coarse particle sizes.
This review highlights the benefits and applications of coarse particle flotation, the challenges associated with coarse particles during the flotation process, and recent developments in improving coarse particle flotation. Recovering particles at a large size through flotation has numerous applications, including early gangue rejection , tail scavenging, and roughing tasks. It offers several benefits in terms of technical, economic, and sustainability aspects. However, it is not without its challenges. These challenges involve the detachment of particles due to turbulence, the transfer of coarse particles from the pulp phase to the froth phase, and the persistence of coarse particles in the froth phase. Recent technological advancements have shown promising results in efficiently recovering particles much larger than those traditionally targeted in the flotation process. Fluidized-bed flotation technology is particularly effective in achieving high coarse particle recovery. The development of processes aimed at enhancing bubble-particle attachment has also shown improvements in coarse particle recovery.
The bubble motion behavior and the inclusion removal during the argon injection processing through the down leg of an Ruhrstahl–Heraeus (RH) unit have been investigated using physical modelling, numerical simulating, and theoretical calculations. From the results obtained, it was found that the micro-bubbles generated by argon injection through the down leg can be sent to the ladle below by the downward liquid steel. Increasing the up-leg argon flow rate and decreasing the down-leg argon flow rate as well as the gas nozzle size are beneficial to produce small and dispersed bubbles. Increasing the down-leg argon flow rate would favor an increase of bubble number density. When the up-leg volume argon flow rate is 161 m3/h, the bubbles experience a longer exposure in the vertical direction: for the conditions of the argon nozzle diameter ranging from 0.2 to 0.8 mm and the down-leg argon flow rate from 120 to 1200 mL/min, the largest sinking depth of the bubbles can be controlled to surpass 2.44 m—that is, the lowermost bubbles are close to the bottom of the ladle. The largest spreading length of the bubbles in the horizontal direction is from 0.93 to 2.03 m under all the conditions, corresponding to 32 to 71 pct of the ladle diameter. The down-leg has a large space to set many argon nozzles. Increasing the total down-leg flow rate by the layout of adding the number of the argon nozzles can significantly improve the bubble dispersion and number density. Using the argon injection through down-leg technique can remove nearly all the 50 μm diameters inclusions. The removal efficiency of the inclusions with diameter of 20 μm reaches 55 pct. For the 10 μm diameters inclusions, the removal efficiency is over 10 pct.
The removal of inclusions in liquid steel has always been the focus of research, and the removal of inclusions is mainly through the process of the inclusion through the slag–steel interface. The inclusion removal process can be subdivided into inclusions in molten steel grew up rise, in steel–slag interface through separation, adsorb dissolved in molten slag 3 steps. Based on the microscopic process of three steps, this article summarizes and discusses the mathematical model, fluid mechanics model, and experimental verification method of inclusion removal process, analyzes limiting and influencing factors of inclusion removal process, and comprehensively describes the numerical simulation research progress of inclusion removal process. With the development of numerical simulation techniques and experimental equipment, some progress has been made in the study of interfacial removal of inclusions. The inclusion interface removal behavior can be analyzed semiquantitatively based on dynamic force model. The computational fluid dynamics model has advantages in studying the phenomena of the inclusion interface, and the phase‐field method is often used to simulate the removal process of the inclusion interface. The combination of water model and numerical simulation, high‐temperature laser confocal method, and other methods is of great help to explore the interface behavior of inclusions.
In this paper, the size-density distribution of coarse middling coking coal (CMCC) with different grinding fineness and flotation concentrates was investigated. Then, the flotation behaviors and liberation characteristics of different size-density fractions in ground CMCC were analyzed, and the different size-density fractions were divided into five categories: most-beneficial, secondary-beneficial, poorly liberated, insignificant-pollution, and serious-pollution. Based on the content of particles with different liberation characteristics, an evaluation index of the liberation characteristic of ground CMCC, namely, the liberation perfection index (LPI), was proposed. The results indicated that grinding changed the size-density composition of CMCC, which affected the flotation performance. Insufficient grinding and overgrinding were not beneficial to flotation. Insufficient grinding caused a higher content of poorly liberated particles and a lower content of most-beneficial particles. Overgrinding increased the content of serious-pollution particles and reduced the content of most-beneficial particles. The size order of the LPI values of different ground CMCC was consistent with the flotation efficiency, and the LPI values of the other two similar samples were overall positively correlated with their flotation performance, suggesting that the method is universal.
The main mechanism of flotation is bubble-particle interaction, which is strongly dependent on the particle size and the bubble size distribution (BSD). It is known that air bubbles are responsible for collecting and delivering hydrophobic particles from the pulp to the foam zone. Controlling the size and distribution of bubbles generated is essential to promote greater bubble-particle interaction. The aim of this study was to investigate the influence of bubble size on the flotation performance of apatite of a low-grade phosphate ore for different particle sizes: fine (d32 = 13.95 µm), intermediate (d32 = 50.86 µm), and coarse (d32 = 108.96 µm). Through the results, it was possible to identify the best bubble size range for each particle size studied. The fine particles showed a better flotation performance when medium-sized bubbles (800–1,000 µm) were used, while the coarse particles had an improved performance when large bubbles (d32 > 1,000 µm) were used. However, the best flotation result was obtained with intermediate particles, which accepted a large range of bubble size distribution under different operating conditions since the collision and attachment mechanisms are favored in this particle size range.
Bubble-particle collision efficiency in the existing flotation literature is determined in a single bubble-particle system assuming an ideal flow field in absence of any turbulence which does not fully represent reality of the actual flotation systems. To address this knowledge gap, in this study, we numerically computed collision efficiency in a multi-bubble-particle system (particle diameter dP = 30 µm, bubble diameter dB = 1 mm) using a two-way coupled Eulerian-Lagrangian 3D computational fluid dynamics model with different solids concentrations (0.385 %–3.080 %) at turbulence intensities (Ti = 0 %–20 %). Collision efficiency of multiple particles with a single central bubble was determined in presence of different configurations of neighbouring bubbles. Two simplified multi-bubble configurations – monolayer and multilayer comprising different number of bubbles/layer, were investigated. It was noted that side-by-side collisions in monolayer configuration did not occur because particles did not have sufficient time and kinetic energy to migrate to a surrounding bubble. On contrary, in multilayer configurations, particles traversing around a leading bubble had a chance to get entrained in the rear wake and collide with a trailing bubble which resulted in higher collision efficiency compared to monolayer configurations. Modelling showed that bulk energy dissipation rate increased with number of bubbles per layer, number of bubble layers, turbulence intensity and solids concentration. For the lowest and highest solids concentration, the optimal collision efficiency occurred at Ti = 20 %, while for the intermediate solid concentration, it occurred at Ti between 4 % and 11 %. In all cases, collision efficiency increased with the energy dissipation rate.
One of the main challenges facing the flotation of base metal oxide minerals is their fine sizes of particles as a result of fine grinding to achieve a desired degree of liberation for low-grade and finely disseminated complex ores. This study aims at studying hydrophobic aggregation and in situ gas nucleation of fine copper oxides with sodium dodecyl sulfate (SDS) as a selective collector to enhance CuO recovery. Experimental results by in situ and real time particle size measurement using focused beam reflectance measurement (FBRM) coupled with particle vision measurement (PVM) showed an enhanced aggregation of fine CuO by SDS adsorption. Particle aggregation assisted by gas nuclei which were generated in situ on CuO by high intensity agitation (HIA) was visualized by total internal reflection fluorescence microscopy (TIRFM). It is the enhanced aggregation with nanobubbles as bridges that improved its recovery from fine silica. Coupled with the calculation using the extended DLVO theory, contact angle and zeta potential of fine particles were measured to understand the critical role of hydrophobic forces in aggregation of fine CuO particles. The copper ions dissolved from the fine copper oxide were found to inadvertently activate fine silica flotation which could be effectively depressed by ethylene diamine tetraacetic acid (EDTA). A combination of SDS with EDTA was proposed and demonstrated to achieve selective recovery of fine copper oxide from fine silica gangue. The results from this study provide directions for enhancing copper recovery from low grade and finely disseminated copper oxidize ores, in particular from tenorite ores.
Fast agglomeration by emulsion binders to capture fine, hydrophobic particles has been developed in the past few years as an alternative to froth flotation by small air bubbles. This new method consists of mixing a particle suspension and saltwater-filled droplets covered with semi-permeable oil layers. These droplets expand due to an osmotic flux of water caused by the presence of salt inside the droplets. To better understand the physics underlying this novel particle capture method, we investigate binary interactions between droplets and particles. The current work examines the dynamics of a rigid spherical particle and a semi-permeable spherical drop that expands due to osmosis in an external, pure-extensional flow field. The droplet is governed by an expansion-diffusion problem, which is coupled to the set of dynamical equations governing the relative particle trajectory. By performing multiple trajectory simulations, we calculate transient collision efficiencies, which can be used to determine the collision kernel for population dynamics. We also use these simulations to better understand the evolution of the microstructure by determining the transient behaviour of the pair distribution function. Our results indicate that the presence of drop expansion increases the collision efficiency of the system, especially for very small particles, which are the most difficult to capture by froth flotation. Moreover, although the presence of slow salt diffusion inside the drops can mitigate this improvement, the contribution of expansion to the collision efficiency may still be considerable, even in the absence of hydrophobic or other attractive forces.
Fluorite (calcium fluoride—CaF2), also known as fluorspar, is an industrial mineral used in metallurgy, hydrofluoric acid production, and ceramics manufacturing. Based on the results from a previous study, a low-grade fluorspar by-product (20.0% CaF2) originating from the exploitation of a rare earth carbonatite deposit can be improved to 75.4% by combining magnetic separation and acid leaching. The present research aimed to develop and optimize a column flotation process to increase the purity of this fluorspar by-product by removing residual silicate minerals and meeting the requirements for ceramic manufacturing (> 85% CaF2). The optimal flotation conditions required for maximizing the recovery and improving the grade of a fluorspar by-product were identified using a conventional approach combined with a response surface methodology (Box-Behnken design). Optimal fluorspar flotation was achieved under the following conditions: 3.6 g/kg of sodium oleate as the collector, 2 g/kg of sodium silicate as the pH modifier and depressant, a conditioning time of 35 min, a flotation time of 7 min, and a solid-to-liquid ratio (S/L) of the pulp of 5%. Under these conditions, 86.8% fluorspar recovery was achieved, and the grade increased from 76.5% in the feed (metallurgical grade) to 88.6% (ceramic grade) in the final concentrate. The silicon content decreased from 5.66% in the feed to 1.12% in the fluorspar concentrate. Using magnetic separation before the flotation improves the final content of fluorspar in the concentrate with the final grade of 94.4%.
The collisional interaction process between bubbles and particles is considered to play an important role in flotation. This paper aims to investigate the effect of particle hydrophobicity on the bubble-particle collision and subsequent interaction process. Four types of bubble-particle interaction behaviors were observed, namely the non-collision, the collision but without attachment, the attachment with jump-in after collision, and the attachment without jump-in after collision. The ‘jump-in’ event was interpreted as the rupture of the water film, providing the formation and growth of a ‘three-phase contact line’ (TPCL). The mildly hydrophobic particle could attach to the bubble surface without the rupture of the water film, whereas the highly hydrophobic particle had the higher collision and attachment probability. The significant effect of particle hydrophobicity was found in the observed particle trajectories and velocities. The distance between the bubble and the particle of weakly hydrophobicity and mildly hydrophobicity remained almost constant in the particle sliding process on the bubble surface. However, the highly hydrophobic particle was observed to jump in instantaneously after a short interaction time. Influenced by hydrodynamic drag, the maximum sliding velocity of any particles near the bubble’s equatorial plane was higher than the particle terminal velocity, and highly hydrophobic particle had a higher difference. The analysis of the individual force components of particle provides valuable insights into the kinematic properties of particle as it slides. The hydrodynamic drag coefficient decreased with an increase in the particle contact angle, implying the highly hydrophobic particle had a smaller hydrodynamic drag. Additionally, the reaction force was introduced for the first time to satisfy the radial force balance relationship, and explanations were proposed in terms of its source.
Experiments were carried out to determine the characteristics of bubbles originated in still tap water by a porous polyethylene pipe used as an air sparger.
Local bubble populations were sampled at various regions of the pipe cross-section and at various air flow-rates to assess the effects of the surface local orientation and flow conditions on bubble dimensions.
It was discovered that at the bottom of the pipe the size distribution of the bubbles is almost invariant with respect to air flow. On the contrary, at other locations bubble dimensions increased with the air flow-rate and the surface inclination.
Statistical analyses proved that the distributions of bubble diameters and their mean values are better modeled by the Gamma distribution than the Log-Normal distribution.
Local populations were merged to get the corresponding global populations. It was discovered that the bubbles from the upper half of the pipe cross-section have a higher weight in determining the properties of global populations.
Global bubble populations from the whole cross-section of the pipe were directly measured at low air flow-rates. Their mean diameters were used to validate the merging procedure.
Two Koide-like correlations were successfully implemented to model as a function of the Froude and Weber numbers the dimensionless mean diameter and the dimensionless Sauter mean diameter of the global bubble populations. The Froude and Weber numbers were computed based on the flow of air through the porous wall, which was successfully modeled with the Forchheimer equation for compressible fluids.
Wear reduces velocity and turbulence by reducing the volume of impeller blades; yet there is a lack of knowledge on flotation cells. Additionally, there is a lack of knowledge in the literature regarding the effect of blade wear on bubble–particle interactions. Hence, computational fluid dynamics simulations investigated artificial impeller blade wear of a laboratory–scale Denver cell. Simulations of chalcopyrite flotation showed that blade wear increased floatability of 10 μm particles by 1.4 %, but decreased that of 180 μm particles by 3.0 %. Accordingly, it is proposed that curved surfaces due to wear increased ε (volume–averaged ε [m²/s³]: no–wear 20.5 and wear 25.8), increasing collision of fine particles and detachment of coarser particles. These were supported by results from large eddy simulation and particle image velocimetry measurements using three–dimensional (3D) printed impellers. Finally, experimental results from flotation experiments using 3D printed impellers and 250–300 μm methylated quartz confirmed a floatability decrease (2.1 %–3.8 %) due to wear.
The native starches are the carbohydrate polymer consisting of glucose units, which can be used as an efficient depressant in hematite flotation. This study explores the effects of starch with various molecular structures on the hematite flotation via the particle-bubble interaction. Three starches (NS, WS and G50) with different amylose (AM) to amylopectin (AP) ratios were applied to investigate the collision and adhesion behaviors of hematite particles onto a bubble through a homemade observation setup. The results showed that the probability of collision and adhesion increased and decreased separately after adding starches. Contact angle measurement and particle size analysis indicated that starch with higher AP content was more likely to aggregate mineral particles to increase the collision probability, while it is easier to make the hematite surface hydrophilic to reduce the adhesion probability. Furthermore, based on the experimental results and previous theories, a modified Yoon-Luttrell model was proposed to explain the interaction between hematite particles and bubbles, and the role of starch molecular structure in this model was also discussed.
The development and production of oil and gas fields would eventually result in a considerable amount of oily generated water, posing serious risks to humans and the environment. Nowadays, the oil concentration in the drainage stream of the produced water is strictly regulated, and many countries have established strict emission standards. As an indispensable oily wastewater treatment technology, flotation technology has attracted much attention because of its maturity, economy, practicality, and relative efficiency. Firstly, this paper summarizes and compares flotation techniques, such as dissolved gas flotation, induced gas flotation, electroflotation, and compact flotation units widely used in produced water treatment offshore in recent years. Considering the complexity of the mechanism of oil removal by air flotation, the mechanism of the oil droplet-bubble interaction is further discussed. The effects of flocculant, PH, and salinity on the oil droplet-bubble interaction in the flotation process were summarized from the perspective of the microscopic colloidal interface, which has a specific guiding role in improving the oil removal efficiency in the gas flotation process. Finally, the research status of produced water treatment by air flotation is summarized, and the feasible research direction is put forward.
Alkali-free liquid accelerator additive has been widely used in shotcrete construction in recent years. However, due to their large dosage, high cost, poor adaptability, and insufficient early strength, there are certain difficulties in promotion and use. Because of its unique properties, micro-nano bubble (MNB) water can shorten the setting time of cement and increase the early strength of cement. Therefore, this study uses micro-nano bubble (MNB) water instead of ordinary water to be used in conjunction with an alkali-free liquid accelerator additive to improve the early strength. In this study, the addition of micro-nano bubble water can significantly shorten the initial and final setting time of cement paste, and the addition of micro-nano bubble water after cyclic shear for 8 min can increase the 1-day compressive strength of the cement mortar by 28.7% and the 7-day compressive strength by 22.7%. The late strength has no reduced phenomenon, and the flexural strength is also significantly improved, which effectively solves the problem of low early strength of the alkali-free liquid accelerator additive. It is analyzed and characterized by microscopic characterization methods such as SEM, XRD, hydration temperature test, the micro-nano bubble water used as mixing cement mortar water has a faster hydration process, better compactness, more uniform structure, faster consumption of C3S and C3A than ordinary water, and higher early hydration temperature peak.
The collision efficiencies of pairs of spheres at small Reynolds numbers (
Collision efficiencies are calculated for gravitation and interception of spherical particles on cylindrical and spherical collectors. Using numerical solutions to the complete Navier-Stokes equations available in the literature efficiencies are calculated up to collector Reynolds numbers of 100. Electrical and surface forces are neglected while the particles are assumed to be small relative to the collector and to follow Stokes' law. Equations are provided relating the interceptional collision efficiency to the collector Reynolds number and to the particle-to-collector radius ratio.
Numerical solutions of the transient uniform flow around a sphere are obtained. The transition takes place between an initial potential flow and a fully developed viscous field. The fluid is incompressible, homogeneous, and its flow is governed by the complete Navier-Stokes equations. The range of Reynolds number studied is Re = 1–1000 where a recirculatory wake appears and the nonlinear terms are essential, that is, they cannot be neglected or approximated. The flow is assumed to be axisymmetric throughout this range. A time-dependent stream function-vorticity formulation is adopted. The solution is obtained by constructing a finite difference approximation to the vorticity transport equation on an expanding spherical polar grid system. Central differencing of second-order accuracy both in time (Dufort-Frankel) and space is utilized. Experiments with numerical stability show an appreciable deviation from linearized stability analysis due to the large gradients of vorticity in the field. Quantitative physical results are obtained. The geometrical parameters characterizing the recirculatory wake compare favorably with those recorded in physical experiments. The detailed distribution of the vorticity on the sphere agrees with results obtained via the steady-state approach at Re = 10, 40, and 100. The computed drag coefficient CD agrees well with the standard drag curve over the range of Reynolds numbers investigated.
From the examination of data from detailed plant surveys and associated laboratory batch testing, the principal effects of particle size in flotation have been identified. The current state of knowledge concerning the role of this variable is discussed in terms of the evidence presented. It is concluded that the minimum degree of hydrophobicity necessary for the flotation of a particle depends upon its size and as a result, recovery-size curves are a valuable diagnostic aid to the assessment of flotation performance. Entrainment is shown to be an important contributory mechanism to the recovery of fine particles which, when coupled with a low rate of genuine flotation, can account for much of the observed behaviour of such fines. The significance of particle size and its consequences in flotation research, in plant operations and in control schemes has been under-rated. The separate conditioning or flotation or both of separate size fractions seems inevitable as ores become increasingly difficult to concentrate.
Trajectories are calculated for particles in the path of a spherical bubble rising in an infinite pool of liquid. From grazing trajectories, collision efficiences are calculated corresponding to values of a particle inertia parameter K down to 0·001 and a particle gravity parameter G up to 0·3 for both Stokes and potential flow fields around the bubble. Limiting values of collision efficiency corresponding to K → 0 are derived and are shown to be the same for both potential and Stokes solutions. The solutions of the equations of motion are verified experimentally and the existence of an optimum bubble size for recovering an ore particle by flotation is demonstrated. From a simplified description of a bubble assemblage, it is shown that the collision efficiency of particles with bubbles in a swarm can be several times as large as those calculated from a single sphere model even at large bubble separations.
Relaxation methods are outlined, and the present problem formulated in modified spherical polar co-ordinates. The results of calculations made for R = 5, 10, 20, 40 are presented in the form of stream function and vorticity distributions; and further results of pressure distributions, velocity distributions, and drag coefficients, calculated from them . These results are shown to compare favourably with experimental work, showing a steady trend from symmetrical Stokes’s flow, towards boundary layer flow. The phenomenon of separation of the forward flow and development of a circulating wake, is explained and illustrated, the first formation of a wake being a R = 17.
Zusammenfassung Damit eine Luftblase an einer Mineraloberflche haften soll, ist notwendig, da sie diese eine gewisse geringste Zeit, die
Induktionszeit, berhrt hat. Die Induktionszeiten sind in verschiedenen Fllen sehr verschieden. Es sind solche Zeiten krzer
als 0,1 sec und lnger als 1 Tag gemessen worden. Die Variationen beruhen teils auf der Gre der Luftblase, eine kleine Blase
gibt krzere Induktionszeit als eine groe, teils auf der Behandlung der Oberflche. Die bei der Flotation gebrauchten Sammler
verkrzen sie, drckende Reagenzien verlngern sie.
The results of a numerical evaluation of the Navier-Stokes equations of motion for the case of a viscous fluid streaming past a sphere are presented in terms of the length of the standing eddy behind the sphere and in terms of the angle of flow separation at the sphere. Emphasis was placed on calculating these quantities at Reynolds numbers between 20 and 40 where no reliable theoretical or experimental values are available. In support of these calculations, it is shown that the values for the drag on a sphere previously calculated by us from the Navier-Stokes equations of motion by the same numerical technique as that used for calculating the eddy length and angle of flow separation agree well with our recent, extensive drag measurements for a wide Reynolds number interval. Our results are used to make a comparison between drag and flow field as predicted by analytical solutions and numerical solutions to the Navier-Stokes equations of motion. Some limitations of the analytical solutions to predict correct values for the drag, and to describe the correct nature of the flow field, are pointed out. It is shown further that a plot of [(D/Ds) – 1] versus log NRe, where D is the actual drag on a sphere, Ds is the Stokes drag, and NRe is the Reynolds number, reveals that the variation of the drag on a sphere with Reynolds number follows well defined régimes, which correlate well with the régimes of the flow field around a sphere. A similar relationship between ‘drag-régime’ and flow field pattern is discussed for the case of viscous flow past a cylinder.
Trajectories are calculated for small particles introduced upstream into a fluid flowing past a fixed sphere. Unseparated potential flow is taken as the velocity profile for the fluid, and the effect of gravity is included in the formulation when it acts along the axis of symmetry. Using a numerical procedure, particle trajectories which graze the sphere, and the corresponding collision efficiencies, are calculated for values of the Stokes number σ. When gravity is neglected, an analytic solution is obtained for large values of σ which is in good agreement with the numerical results for σ as low as 5. These results are compared with those of Sell (1931) and Langmuir & Blodgett (1946). When gravity is included, a critical value of the Stokes number σc is calculated for which no collisions occur until σ > σc.
Normal and tangential velocities in the boundary layer and out into the free stream have been obtained using a non-disturbing flow visualization technique for uniform laminar flow around a sphere. The non-similar data are available in tables at 2.5° intervals from 20° from the front to about 15° past the separation point a t Reynolds numbers of 290, 750, 1300 and 3000. Stream functions calculated by LeClair using a numerical solution of the Navier-Stokes equation at Re 21 300 are not in good agreement with measured values from 30° to 60°, but are in much better agreement around the separation point. Too few grid points near the sphere where the tangential velocities rise to a maximum above free-stream values may account for the difference.
A theoretical treatment is presented which attempts to quantify the benefits obtained by using smaller bubbles or larger particles in dispersed air flotation. The limited experimental data obtained so far suggest that the theory is sound, particularly in its prediction of the effect of bubble size.On présente un traitement théorique par lequel on cherche à déterminer quantitativement les avantages qu'on obtient en employant des bulles plus petites ou des particules plus grosses flottant dispersees dans l'air. Les résultats maigres qu'on a obtenus expéiimentalement jusqu'ici tendent à indiquer que la théorie est bien fondée, surtout en ce qui a trait à sa prédiction de l'effet des dimensions des bulles.
This study was undertaken to ascertain the accuracy of finite-difference solutions for flow around spherical particles in the intermediate Reynolds number range. Comparison of the results with experimental data on drag coefficients, frontal stagnation pressure, and wake geometry indicated good agreement. The approximate solutions, in which the Galerkin method and asymptotic analytical predictions were utilized, were evaluated by using the finite-difference solutions as a standard. These methods were used to calculate the effect of uniform and nonuniform mass efflux on the drag and flow characteristics around a sphere. Theoretical solutions indicated that nonuniform mass efflux can significantly reduce the drag on a submerged object. Ranges of applicability of the approximate methods were established.
The effective collision cross-sections between pairs of small water droplets, falling freely through air under the influence of gravity, have been computed on the assumption of hydrodynamical effects alone being important. It has been assumed that each droplet tends to fall freely at its terminal velocity with respect to the surrounding medium, which also moves under the influence of the motion of a neighbouring droplet. By the use of previously computed fields of flow of a viscous medium around a uniformly translated sphere, the trajectories of motion of one droplet with respect to another were computed for a range of droplets having radii between 4 μ and 200 μ.
It is found that the collision cross-sections increase to values considerably greater than the corresponding geometrical cross-section as the droplets approach equality of size. As the difference in size increases, the collision cross-section decreases to values close to the geometrical cross-section, and finally decreases to zero. For any one particular size of the collecting droplet there is a minimum size of collected droplet below which no collection is possible. This size decreases with increasing size of the larger droplet greater than 10 μ in radius. For droplets smaller than 10 μ in radius, collision can occur only between droplets of nearly equal size. The results could account for coalescence becoming an important factor in the rapid formation of raindrops for droplets of radii greater than 10 μ.
A collection is presented of black-and-white photographs illustrating
the variety of fluid phenomena which can be studied by means of flow
visualization techniques. The order of presentation is in general from
low speeds to high: creeping and laminar flow; boundary layer
separation; vortices, instability and turbulence; free surface flow and
natural convection; subsonic flow, shock waves, and supersonic flow
(including the hypersonic regime). Reynolds numbers are based on
diameter unless otherwise specified. The flow visualization techniques
employed include smoke filaments in air, bubbles in fluids, metal
particles in oils, gases having different optical characteristics such
as CO2 in air, differently colored fluids, and light sheet illumination.
An Introduction to the Theory of Flotation
- V J Klassen
- V A Mokrousov