The determination of bubble size distribution is a prerequisite for the study of gas-liquid two-phase flow characteristics in electrolytic cells.Here the departure diameter of hydrogen bubbles and oxygen bubbles and t...The determination of bubble size distribution is a prerequisite for the study of gas-liquid two-phase flow characteristics in electrolytic cells.Here the departure diameter of hydrogen bubbles and oxygen bubbles and their detachment process from a nickel wire electrode during water electrolysis are studied using high-speed photography.The results show that in industrial alkaline environment,the departure diameters of most hydrogen bubbles and oxygen bubbles are generally smaller than 60μm and 250μm with the current density ranges from 0.15 to 0.35A/cm^(2).The adhesion force of hydrogen bubbles on a nickel wire is found to be so weak that they can separate with a tiny size.The diameters of oxygen bubbles conform to normal distribution,and its distribution range widens with the increase of current density.The theoretical analysis show that the comprehensive conversion rate of current-to-bubble is unexpectedly low especially at low current densities,which may be attributed to the loss of gas components caused by bubble detachment mode.The majority of oxygen bubbles detach by a sudden bounce after coalescence,which may bring strong disturbance to the concentration boundary layer.This also indicates the coalescence-induced bubble departure mode may occupy a dominant position in the electrolyzers.展开更多
In operating flotation plants, the viscosity of the pulp can vary significantly. Consequently, the resulting impact on bubble size is of interest as many plants experience seasonal changes in water temperature, or par...In operating flotation plants, the viscosity of the pulp can vary significantly. Consequently, the resulting impact on bubble size is of interest as many plants experience seasonal changes in water temperature, or particle size changes as ore hardness, mineralogy and throughput fluctuate. However, given its importance in flotation, there existed no mathematical relationship linking bubble size created in flotation machines to the key process variable of fluid viscosity. In this study, a program of investigation to develop such a model was utilizing a pilot-scale mechanical flotation machine, to investigate the effect of water viscosity due to temperature on bubble size distribution. The bubble sizes were determined using a specific bubble viewer and imaging technology. The temperature itself was varied as a method for introducing significant viscosity change. The viscosity-temperature effect introduced a correspondingly significant change in the water viscosity（1619 to 641 μPa·s）. It is suggested that a considerably stronger relationship may exist, yielding D32 versus（μ/μ20）0.776, and hence viscosity becomes an important design consideration for plants operating where pulp temperature fluctuations, very small particles or high solid fractions are present.展开更多
Effect of frothers in preventing bubble coalescence during flotation of minerals has long been investigated.To evaluate the performance of a frother,an apparatus to measure the bubble size is a basic necessity.McGill ...Effect of frothers in preventing bubble coalescence during flotation of minerals has long been investigated.To evaluate the performance of a frother,an apparatus to measure the bubble size is a basic necessity.McGill Bubble Size Analyzer(MBSA) or bubble viewer that has been developed and completed by McGill University's Mineral Processing Group during the last decade is a unique instrument to serve this purpose.Two parameters which are thought to influence the bubble size measurements by McGill bubble viewer include water quality and frother concentration in the chamber.Results show that there is no difference in Sauter mean(D32) when tap or de-ionized water was used instead of process water.However,the frother concentration,in this research DowFroth 250(DF250),inside the chamber exhibited a pronounced effect on bubble size.Frother concentration below a certain point can not prevent coalescence inside the chamber and therefore caution must be taken in plant applications.It was also noted that the frother concentration which has been so far practiced in plant measurements(CCC75-CCC95) is high enough to prevent coalescence with the bubble viewer.展开更多
The size of bubbles created in the flotation process is of great importance to the efficiency of the mineral separation achieved.Meanwhile,it is believed that frother transport between phases is perhaps the most impor...The size of bubbles created in the flotation process is of great importance to the efficiency of the mineral separation achieved.Meanwhile,it is believed that frother transport between phases is perhaps the most important reason for the interactive nature of the phenomena occurring in the bulk and froth phases in flotation,as frother adsorbed in the surface of rising bubbles is removed from the bulk phase and then released into the froth as a fraction of the bubbles burst.This causes the increased concentration in the froth compared to the bulk concentration,named as frother partitioning.Partitioning reflects the adsorption of frother on bubbles and how to influence bubble size is not known.There currently exists no such a topic aiming to link these two key parameters.To fill this vacancy,the correspondence between bubble size and frother partitioning was examined.Bubble size was measured by sampling-for-imaging(SFI)technique.Using total organic carbon(TOC)analysis to measure the frother partitioning between froth and bulk phases was determined.Measurements have shown,with no exceptions including four different frothers,higher frother concentration is in the bulk than in the froth.The results also show strong partitioning giving an increase in bubble size which implies there is a compelling relationship between these two,represented by CFroth/CBulk and D32.The CFroth/CBulkand D32 curves show similar exponential decay relationships as a function of added frother in the system,strongly suggesting that the frother concentration gradient between the bulk solution and the bubble interface is the driving force contributing to bubble size reduction.展开更多
This work aims to provide a relationship of how the key operational variables of frother type and impeller speed affect the size of bubble （D32）. The study was performed using pilot-scale equipment （0.8 m^3） that ...This work aims to provide a relationship of how the key operational variables of frother type and impeller speed affect the size of bubble （D32）. The study was performed using pilot-scale equipment （0.8 m^3） that is up to two orders of magnitude larger than equipment used for studies performed to date by others, and incorporated the key process variables of frother type and impeller speed. The results show that each frother family exhibits a unique CCC95-HLB relationship dependent on n （number of C-atoms in alkyl group） and m （number of propylene oxide group）. Empirical models were developed to predict CCC95 from HLB associated with other two parameters a and ft. The impeller speed-bubble size tests show that D32 is unaffected by increased impeller tip speed across the range of 4.6 to 9.2 m/s （representing the industrial operating range）, although D32 starts to increase below 4.6 m/s. The finding is valid for both coalescing and non-coalescing conditions. The results suggest that the bubble size and bubble size distribution （BSD） being created do not change with increasing impeller speed in the quiescent zone of the flotation.展开更多
To seek and describe the influence of bubble size on geometric and motion characteristics of the bubble,six nozzles with different outlet diameters were selected to inject air into water and to produce different bubbl...To seek and describe the influence of bubble size on geometric and motion characteristics of the bubble,six nozzles with different outlet diameters were selected to inject air into water and to produce different bubble sizes.High-speed photography in conjunction with an in-house bubble image processing code was used.During the evolution of the bubble,bubble shape,traveling trajectory and the variation of bubble velocity were obtained.Bubble sizes acquired varied from0.25to8.69mm.The results show that after the bubble is separated from the nozzle,bubble shape sequentially experiences ellipsoidal shape,hat shape,mushroom shape and eventually the stable ellipsoidal shape.As the bubble size increases,the oscillation of the bubble surface is intensified.At the stabilization stage of bubble motion,bubble trajectories conform approximately to the sinusoidal function.Meanwhile,with the increase in bubble size,the bubble trajectory tends to be straightened and the influence of the horizontal bubble velocity component on the bubble trajectory attenuates.The present results explain the phenomena related to relatively large bubble size,which extends the existing relationship between the bubble terminal velocity and the equivalent bubble diameter.展开更多
The specific results of the work investigating the effect of gas density and water temperature on bubble size were present.These were surrogate variables designed to investigate the effect of viscosity(varying water t...The specific results of the work investigating the effect of gas density and water temperature on bubble size were present.These were surrogate variables designed to investigate the effect of viscosity(varying water temperature) and altitude(varying gas density).The results show that there is a measurable but relatively small effect of gas density on bubble size.The D32 is revealed to increase proportionally as(ρ0/ρg)0.132.The projected impact on flotation kinetics at 4500 m versus sea level is small,of the order of 0.5% recovery loss for a bank of eight flotation cells.The effect of water temperature(4-40 °C) on bubble size is more significant than gas density.The relationship correlates with water viscosity values quite closely.A finding that D32 increases proportionally as(μ/μ20)0.776 highlights the importance of accounting for viscosity effects if,for example,large process temperature fluctuations or deviation from design/test conditions are expected.展开更多
The constant bubble size modeling approach(CBSM)and variable bubble size modeling approach(VBSM)are frequently employed in Eulerian–Eulerian simulation of bubble columns.However,the accuracy of CBSM is limited while ...The constant bubble size modeling approach(CBSM)and variable bubble size modeling approach(VBSM)are frequently employed in Eulerian–Eulerian simulation of bubble columns.However,the accuracy of CBSM is limited while the computational efficiency of VBSM needs to be improved.This work aims to develop method for bubble size modeling which has high computational efficiency and accuracy in the simulation of bubble columns.The distribution of bubble sizes is represented by a series of discrete points,and the percentage of bubbles with various sizes at gas inlet is determined by the results of computational fluid dynamics(CFD)–population balance model(PBM)simulations,whereas the influence of bubble coalescence and breakup is neglected.The simulated results of a 0.15 m diameter bubble column suggest that the developed method has high computational speed and can achieve similar accuracy as CFD–PBM modeling.Furthermore,the convergence issues caused by solving population balance equations are addressed.展开更多
A special experiment setup was designed to observe the interaction between bubbles and particle in flotation cell and to analyze the bubble characteristics such as bubble size, distribution and bubble-loading efficien...A special experiment setup was designed to observe the interaction between bubbles and particle in flotation cell and to analyze the bubble characteristics such as bubble size, distribution and bubble-loading efficiency. Bubbles in water-gas system and three-phase system were measured. The results indicate that with the current setup the bubbles as small as 10 μm can be easily distinguished. The average size of the bubbles generated under the given conditions in two-phase system is 410 μm at frother concentration of 0.004%, which is in good correspondence with the results of other works. The effect of frother on bubble size was probed. Increasing frother concentration from 0 to 0.004% causes a reduction of bubble size from 700 to 400 μm. The bubble loading efficiency was reported. The result indicates that the fine particle is more easily entrapped than the coarse particle. Some factors, which have effect on measurement accuracy were discussed. The aeration speed has a significant effect on the accuracy of results, if it surpasses 30 mL/s, and the image becomes unclear due to the entrapment of fine particle. Another factor, which can affect observing results, is the sampling position. At a wrong sampling position, the images become unclear.展开更多
Experiments were conducted to obtain the values of the Sauter bubble size, enrichment and recovery of bovine serum albumin （BSA） in a semi-batch col- umn fitted with a stainless steel sparger at elevated pressure. T...Experiments were conducted to obtain the values of the Sauter bubble size, enrichment and recovery of bovine serum albumin （BSA） in a semi-batch col- umn fitted with a stainless steel sparger at elevated pressure. The effects of Sur- face tension, surfactant concentration, foam/solution height ratio and air flow rate on the separation performance were investigated, and the results showed that good en- richments and recoveries can be achieved for bovine serum albumin operated at el- evated pressures. Especially the size of bubbles generated by the stainless steel sparger was smaller at higher pressures which is favorable to the foam separation process. Furthermore, the separation mechanism of bovine serum albumin operated at elevated pressure was also discussed.展开更多
A computational study was carried out on bubble dynamic behaviors and bubble size distributions in a pressurized lab-scale gas-solid fluidized bed of Geldart A particles.High-resolution 3-D numerical simulations were ...A computational study was carried out on bubble dynamic behaviors and bubble size distributions in a pressurized lab-scale gas-solid fluidized bed of Geldart A particles.High-resolution 3-D numerical simulations were performed using the two-fluid model based on the kinetic theory of granular flow.A finegrid,which is in the range of 3–4 particle diameters,was utilized in order to capture bubble structures explicitly without breaking down the continuum assumption for the solid phase.A novel bubble tracking scheme was developed in combination with a 3-D detection and tracking algorithm(MS3 DATA)and applied to detect the bubble statistics,such as bubble size,location in each time frame and relative position between two adjacent time frames,from numerical simulations.The spatial coordinates and corresponding void fraction data were sampled at 100 Hz for data analyzing.The bubble coalescence/break-up frequencies and the daughter bubble size distribution were evaluated by using the new bubble tracking algorithm.The results showed that the bubble size distributed non-uniformly over cross-sections in the bed.The equilibrium bubble diameter due to bubble break-up and coalescence dynamics can be obtained,and the bubble rise velocity follows Davidson’s correlation closely.Good agreements were obtained between the computed results and that predicted by using the bubble break-up model proposed in our previous work.The computational bubble tracking method showed the potential of analyzing bubble motions and the coalescence and break-up characteristics based on time series data sets of void fraction maps obtained numerically and experimentally.展开更多
Measurements of bubble size distribution require the understanding of the acoustic characteristics of the medium.The bubbles show highly nonlinear properties under finite amplitude acoustic excitation,so the acoustic ...Measurements of bubble size distribution require the understanding of the acoustic characteristics of the medium.The bubbles show highly nonlinear properties under finite amplitude acoustic excitation,so the acoustic fields from bubble population are easily observed at the second harmonics as well as at the fundamental frequency,which shows that the nonlinear coefficient increases obviously.The inversion method of bubble size distribution based on nonlinear acoustic effects can peel off the influence of complex environment and obtain the size distribution coefficient information of bubbles more accurately.The previous nonlinear inversion methods of bubble size distribution are mostly based on the nonlinear scattering cross-section characteristics of bubbles.However,the stability of inversion is not high enough.In this paper,we introduce a new acoustic inversion method for bubble size distribution,which is based on the nonlinear coefficients of bubble medium.Compared with other inversion methods based on linear or nonlinear scattering cross section,the inversion method based on nonlinear coefficients of bubble medium proposed in this paper shows good robustness in both simulation and experiment.展开更多
Two-phase flow with complex phase interfaces is commonly observed in both nature and industrial processes.The bubble size distribution(BSD) is a crucial parameter in gas-liquid two-phase flow,impacting various flow ch...Two-phase flow with complex phase interfaces is commonly observed in both nature and industrial processes.The bubble size distribution(BSD) is a crucial parameter in gas-liquid two-phase flow,impacting various flow characteristics including interfacial forces,void fraction distribution,and interfacial area transport.Throughout the flow progression,the BSD changes along the channel due to variations in pressure and interactions among bubbles.Accurately predicting the evolution of BSD can enhance the modeling of two-phase flow.This study presents a novel BSD evolution(BSDE) model,where the governing equation for the probability density function is formulated by considering the conservation of bubbles within a onedimensional control volume in the channel.The downstream BSD is predicted based on the upstream BSD and the effects of pressure variations and bubble interactions along the channel.To account for the multiscale nature of the two-phase flow,the bubbles are categorized into small groups(G_(1)) and large groups(G_(2)).Six distinct source term distributions for intra/inter bubble interactions have been developed.Each source term accounts for the distributions of consumed and generated bubbles,ensuring the conservation of bubble volume through constraints on model coefficients.The model has been tested on a tight-lattice rod bundle using experimental data,with deviations of less than 5% and 15% for G_(1)and G_(2) flow,respectively.Since the model development is independent of specific geometry,the framework of the BSDE model can also be effectively applied to channels of varying shapes.展开更多
The size and distribution patterns of bubbles within a laboratory-scale coarse-particle flotation column were examined using a high-speed camera-based dynamic measurement system.The effects of operational parameters s...The size and distribution patterns of bubbles within a laboratory-scale coarse-particle flotation column were examined using a high-speed camera-based dynamic measurement system.The effects of operational parameters such as superficial water velocity,air-flow rate,and frother dosage on bubble-size and distribution characteristics were investigated.This study aims to provide theoretical support for enabling fluidized-bed flotation within coarse-particle flotation columns.The results show that negative pressure for air inspiratory and bubble formation is generated by passing a high-speed jet through a throat,and the greatest number of bubbles are observed under natural inspiratory state at an air-liquid ratio of 1:3-1:2.5.Increasing the air-flow rate transforms the bubble diameter distribution from a peaked distribution to a more uniform distribution.Furthermore,the frother narrows the range of bubble-size distribution.A positive correlation exists between the bubble Sauter diameter and air-flow rate,with the bubble Sauter diameter bearing a negative correlation with the superficial water velocity and frother concentration.展开更多
Frothers facilitate the reduction of bubbles size by preventing bubbles coalescence and produce more stable froths.The collision probability of the bubbles and particles substantially increases by decreasing bubble si...Frothers facilitate the reduction of bubbles size by preventing bubbles coalescence and produce more stable froths.The collision probability of the bubbles and particles substantially increases by decreasing bubble size.For the same volume system,fewer bubbles result from a distribution of large-sized bubbles,and more bubbles result from a distribution of small-sized bubbles.In this research,fundamental two-phase frother characterization parameters were aimed to link with three-phase coal and talc flotation behavior.For this purpose,the effect of single and dual frother systems on inhibiting bubble coalescence was investigated with methyl isobutyl carbinol(MIBC),isooctanol(2 ethyl hexanol),pine oil,and Dowfroth 250.Based on the results of single frothers,isooctanol at the lowest critical coalescence concentration(CCC)value of 6×10^(−6) achieved the smallest bubbles with Sauter mean diameter of 0.80 mm.By blending Dowfroth 250 and pine oil,the bubbles size decreased significantly,reaching 0.45 mm.While the highest recoveries in coal flotation were obtained in single and frother blends where the bubbles size was measured as the smallest in two-phase system,and such a relationship was not found for talc flotation.展开更多
Over the past 60 years, the air concentration in water has been considered as a control index of cavitation erosion reduction and widely used in the designs of hydraulic structures. However, the mechanism of air entra...Over the past 60 years, the air concentration in water has been considered as a control index of cavitation erosion reduction and widely used in the designs of hydraulic structures. However, the mechanism of air entrainment against cavitation erosion has been paid good attention to. In the present work, the effect of air bubble size on cavitation erosion reduction was experimentally investigated. A device with micron-scale orifice diameters(10, 20 and 50 μm in size) was specially designed to introduce air bubbles into water. The experiments about the effect of air bubble size were conducted by means of a vibratory apparatus, including the behavior of formation and movement for single air bubble, the characteristics of cavitation erosion reduction at different air entrainment conditions. The findings demonstrate that high air concentration has significant effects on cavitation erosion reduction.But, a notable problem was that the size of air bubbles is of outstanding effect on cavitation erosion reduction. Small air bubbles support to alleviate cavitation erosion, even at same air concentration.展开更多
A new cavitating model by using bubble size distribution based on mass of bubbles is proposed. Liquid phase is treated with Eulerian framework as a mixture containing minute cavitating bubbles. Vapor phase consists of...A new cavitating model by using bubble size distribution based on mass of bubbles is proposed. Liquid phase is treated with Eulerian framework as a mixture containing minute cavitating bubbles. Vapor phase consists of various sizes of minute vapor bubbles, which is distributed to classes based on their mass. The change of bubble number density for each class was solved by considering the change of bubble mass due to phase change as well as generation of new bubbles due to heterogeneous nucleation. In this method the mass of bubbles is treated as an independent variable, in other word, a new coordinate, and dependant variables are solved in Eulerian framework for spatial coordinates and bubble-mass coordinate. The present method is applied to a cavitating flow in a convergent-divergent nozzle, and the two-phase flow with bubble size distribution and phase change was successfully predicted.展开更多
Due to a prolonged operation time and low mass transfer efficiency, the primary challenge in the aeration process of non-Newtonian fluids is the high energy consumption, which is closely related to the form and rate o...Due to a prolonged operation time and low mass transfer efficiency, the primary challenge in the aeration process of non-Newtonian fluids is the high energy consumption, which is closely related to the form and rate of impeller, ventilation, rheological properties and bubble morphology in the reactor. In this perspective, through optimal computational fluid dynamics models and experiments, the relationship between power consumption, volumetric mass transfer rate(kLa) and initial bubble size(d0) was constructed to establish an efficient operation mode for the aeration process of non-Newtonian fluids. It was found that reducing the d0could significantly increase the oxygen mass transfer rate, resulting in an obvious decrease in the ventilation volume and impeller speed. When d0was regulated within 2-5 mm,an optimal kLa could be achieved, and 21% of power consumption could be saved, compared to the case of bubbles with a diameter of 10 mm.展开更多
As is well known to mineral processing scientists and engineers, fine and ultrafine particles are difficult to float mainly due to the low bubble-particle collision efficiencies. Though many efforts have been made to ...As is well known to mineral processing scientists and engineers, fine and ultrafine particles are difficult to float mainly due to the low bubble-particle collision efficiencies. Though many efforts have been made to improve flotation performance of fine and ultrafine particles, there is still much more to be done. In this paper, the effects of nano-microbubbles （nanobuhbles and microbubbles） on the flotation of fine （-38 ＋ 14.36 μm） and ultrafine （-14.36 ＋ 5μm） chalcopyrite particles were investigated in a laboratory scale Denver flotation cell. Nano-microbubbles were generated using a specially-designed nano- microbubble generator based on the cavitation phenomenon in Venturi tubes. In order to better under- stand the mechanisms of nano-microbubble enhanced froth flotation of fine and ultrafine chalcopyrite particles, the nano-microbubble size distribution, stability and the effect of frother concentration on nano- bubble size were also studied by a laser diffraction method. Comparative flotation tests were performed in the presence and absence of nano-microbubbles to evaluate their impact on the fine and ultrafine chalcopyrite particle flotation recovery. According to the results, the mean size of nano-microbubbles increased over time, and decreased with increase of frother concentration. The laboratory-scale flotation test results indicated that flotation recovery of chalcopyrite fine and ultrafine particles increased by approximately 16-21% in the presence of nano-microbubbles, depending on operating conditions of the process. The presence of nano-microbubbles increased the recovery of ultrafine particles （-14.36 ＋ 5 μm） more than that of fine particles （-38 ＋ 14.36 μm）. Another major advantage is that the use of nano-microbubbles reduced the collector and frother consumptions by up to 75% and 50%, respectively.展开更多
The Eulerian–Lagrangian simulation of bubbly flow has the advantage of tracking the motion of bubbles in continuous fluid, and hence the position and velocity of each bubble could be accurately acquired. Previous sim...The Eulerian–Lagrangian simulation of bubbly flow has the advantage of tracking the motion of bubbles in continuous fluid, and hence the position and velocity of each bubble could be accurately acquired. Previous simulation usually used the hard-sphere model for bubble–bubble interactions, assuming that bubbles are rigid spheres and the collisions between bubbles are instantaneous. The bubble contact time during collision processes is not directly taken into account in the collision model. However, the contact time is physically a prerequisite for bubbles to coalesce, and should be long enough for liquid film drainage. In this work we applied the spring-dashpot model to model the bubble collisions and the bubble contact time, and then integrated the spring-dashpot model with the film drainage model for coalescence and a bubble breakage model. The bubble contact time is therefore accurately recorded during the collisions. We investigated the performance of the spring-dashpot model and the effect of the normal stiffness coefficient on bubble coalescence in the simulation.The results indicate that the spring-dashpot model together with the bubble coalescence and breakage model could reasonably reproduce the two-phase flow field, bubble coalescence and bubble size distribution. The influence of normal stiffness coefficient on simulation is also discussed.展开更多
基金support by the National Key R&D Program of China(2022YFB4202201)Ordos-Tsinghua Innovative&Collaborative Research Program in Carbon Neutrality,Science and Technology Department of Jiangsu Province under Grand BE2022040Support Plan for Young Excellent Talents of the Department of Energy and Power Engineering,Tsinghua University.
文摘The determination of bubble size distribution is a prerequisite for the study of gas-liquid two-phase flow characteristics in electrolytic cells.Here the departure diameter of hydrogen bubbles and oxygen bubbles and their detachment process from a nickel wire electrode during water electrolysis are studied using high-speed photography.The results show that in industrial alkaline environment,the departure diameters of most hydrogen bubbles and oxygen bubbles are generally smaller than 60μm and 250μm with the current density ranges from 0.15 to 0.35A/cm^(2).The adhesion force of hydrogen bubbles on a nickel wire is found to be so weak that they can separate with a tiny size.The diameters of oxygen bubbles conform to normal distribution,and its distribution range widens with the increase of current density.The theoretical analysis show that the comprehensive conversion rate of current-to-bubble is unexpectedly low especially at low current densities,which may be attributed to the loss of gas components caused by bubble detachment mode.The majority of oxygen bubbles detach by a sudden bounce after coalescence,which may bring strong disturbance to the concentration boundary layer.This also indicates the coalescence-induced bubble departure mode may occupy a dominant position in the electrolyzers.
基金the Chair in Mineral Processing at McGill University, under the Collaborative Research and Development Program of NSERC (Natural Sciences and Engineering Research Council of Canada) with industrial sponsorship from Vale, Teck Cominco, Xstrata Process Support, Agnico-Eagle, Shell Canada, Barrick Gold, COREM, SGS Lakefield Research and Flottec
文摘In operating flotation plants, the viscosity of the pulp can vary significantly. Consequently, the resulting impact on bubble size is of interest as many plants experience seasonal changes in water temperature, or particle size changes as ore hardness, mineralogy and throughput fluctuate. However, given its importance in flotation, there existed no mathematical relationship linking bubble size created in flotation machines to the key process variable of fluid viscosity. In this study, a program of investigation to develop such a model was utilizing a pilot-scale mechanical flotation machine, to investigate the effect of water viscosity due to temperature on bubble size distribution. The bubble sizes were determined using a specific bubble viewer and imaging technology. The temperature itself was varied as a method for introducing significant viscosity change. The viscosity-temperature effect introduced a correspondingly significant change in the water viscosity（1619 to 641 μPa·s）. It is suggested that a considerably stronger relationship may exist, yielding D32 versus（μ/μ20）0.776, and hence viscosity becomes an important design consideration for plants operating where pulp temperature fluctuations, very small particles or high solid fractions are present.
基金Project supported by the Chair in Mineral Processing at McGill University,under the Collaborative Research and Development Program of NSERC(Natural Sciences and Engineering Research Council of Canada)with industrial sponsorship from Vale,Teck Cominco,Xstrata Process Support,Agnico-Eagle,Shell Canada,Barrick Gold,COREM,SGS Lakefield Research and Flottec
文摘Effect of frothers in preventing bubble coalescence during flotation of minerals has long been investigated.To evaluate the performance of a frother,an apparatus to measure the bubble size is a basic necessity.McGill Bubble Size Analyzer(MBSA) or bubble viewer that has been developed and completed by McGill University's Mineral Processing Group during the last decade is a unique instrument to serve this purpose.Two parameters which are thought to influence the bubble size measurements by McGill bubble viewer include water quality and frother concentration in the chamber.Results show that there is no difference in Sauter mean(D32) when tap or de-ionized water was used instead of process water.However,the frother concentration,in this research DowFroth 250(DF250),inside the chamber exhibited a pronounced effect on bubble size.Frother concentration below a certain point can not prevent coalescence inside the chamber and therefore caution must be taken in plant applications.It was also noted that the frother concentration which has been so far practiced in plant measurements(CCC75-CCC95) is high enough to prevent coalescence with the bubble viewer.
基金Project supported by the Collaborative Research and Development Program of Natural Sciences and Engineering Research Council of Canada
文摘The size of bubbles created in the flotation process is of great importance to the efficiency of the mineral separation achieved.Meanwhile,it is believed that frother transport between phases is perhaps the most important reason for the interactive nature of the phenomena occurring in the bulk and froth phases in flotation,as frother adsorbed in the surface of rising bubbles is removed from the bulk phase and then released into the froth as a fraction of the bubbles burst.This causes the increased concentration in the froth compared to the bulk concentration,named as frother partitioning.Partitioning reflects the adsorption of frother on bubbles and how to influence bubble size is not known.There currently exists no such a topic aiming to link these two key parameters.To fill this vacancy,the correspondence between bubble size and frother partitioning was examined.Bubble size was measured by sampling-for-imaging(SFI)technique.Using total organic carbon(TOC)analysis to measure the frother partitioning between froth and bulk phases was determined.Measurements have shown,with no exceptions including four different frothers,higher frother concentration is in the bulk than in the froth.The results also show strong partitioning giving an increase in bubble size which implies there is a compelling relationship between these two,represented by CFroth/CBulk and D32.The CFroth/CBulkand D32 curves show similar exponential decay relationships as a function of added frother in the system,strongly suggesting that the frother concentration gradient between the bulk solution and the bubble interface is the driving force contributing to bubble size reduction.
基金Project supported by the Collaborative Research and Development Program of NSERC(Natural Sciences and Engineering Research Council of Canada) with Industrial Sponsorship from Vale,Teck Cominco,Xstrata Process Support,Agnico-Eagle,Shell Canada,Barrick Gold,COREM,SGS Lakefield Research and Flottec
文摘This work aims to provide a relationship of how the key operational variables of frother type and impeller speed affect the size of bubble （D32）. The study was performed using pilot-scale equipment （0.8 m^3） that is up to two orders of magnitude larger than equipment used for studies performed to date by others, and incorporated the key process variables of frother type and impeller speed. The results show that each frother family exhibits a unique CCC95-HLB relationship dependent on n （number of C-atoms in alkyl group） and m （number of propylene oxide group）. Empirical models were developed to predict CCC95 from HLB associated with other two parameters a and ft. The impeller speed-bubble size tests show that D32 is unaffected by increased impeller tip speed across the range of 4.6 to 9.2 m/s （representing the industrial operating range）, although D32 starts to increase below 4.6 m/s. The finding is valid for both coalescing and non-coalescing conditions. The results suggest that the bubble size and bubble size distribution （BSD） being created do not change with increasing impeller speed in the quiescent zone of the flotation.
基金Project(51676087)supported by the National Natural Science Foundation of China
文摘To seek and describe the influence of bubble size on geometric and motion characteristics of the bubble,six nozzles with different outlet diameters were selected to inject air into water and to produce different bubble sizes.High-speed photography in conjunction with an in-house bubble image processing code was used.During the evolution of the bubble,bubble shape,traveling trajectory and the variation of bubble velocity were obtained.Bubble sizes acquired varied from0.25to8.69mm.The results show that after the bubble is separated from the nozzle,bubble shape sequentially experiences ellipsoidal shape,hat shape,mushroom shape and eventually the stable ellipsoidal shape.As the bubble size increases,the oscillation of the bubble surface is intensified.At the stabilization stage of bubble motion,bubble trajectories conform approximately to the sinusoidal function.Meanwhile,with the increase in bubble size,the bubble trajectory tends to be straightened and the influence of the horizontal bubble velocity component on the bubble trajectory attenuates.The present results explain the phenomena related to relatively large bubble size,which extends the existing relationship between the bubble terminal velocity and the equivalent bubble diameter.
基金Project supported by the Collaborative Research and Development Program of NSERC(Natural Sciences and Engineering Research Council of Canada)with Industrial Sponsorship from Vale,Teck Cominco,Xstrata Process Support,Agnico-Eagle,Shell Canada,Barrick Gold,COREM,SGS Lakefield Research and Flottec
文摘The specific results of the work investigating the effect of gas density and water temperature on bubble size were present.These were surrogate variables designed to investigate the effect of viscosity(varying water temperature) and altitude(varying gas density).The results show that there is a measurable but relatively small effect of gas density on bubble size.The D32 is revealed to increase proportionally as(ρ0/ρg)0.132.The projected impact on flotation kinetics at 4500 m versus sea level is small,of the order of 0.5% recovery loss for a bank of eight flotation cells.The effect of water temperature(4-40 °C) on bubble size is more significant than gas density.The relationship correlates with water viscosity values quite closely.A finding that D32 increases proportionally as(μ/μ20)0.776 highlights the importance of accounting for viscosity effects if,for example,large process temperature fluctuations or deviation from design/test conditions are expected.
基金the National Natural Science Foundation of China(21625603)for supporting this work。
文摘The constant bubble size modeling approach(CBSM)and variable bubble size modeling approach(VBSM)are frequently employed in Eulerian–Eulerian simulation of bubble columns.However,the accuracy of CBSM is limited while the computational efficiency of VBSM needs to be improved.This work aims to develop method for bubble size modeling which has high computational efficiency and accuracy in the simulation of bubble columns.The distribution of bubble sizes is represented by a series of discrete points,and the percentage of bubbles with various sizes at gas inlet is determined by the results of computational fluid dynamics(CFD)–population balance model(PBM)simulations,whereas the influence of bubble coalescence and breakup is neglected.The simulated results of a 0.15 m diameter bubble column suggest that the developed method has high computational speed and can achieve similar accuracy as CFD–PBM modeling.Furthermore,the convergence issues caused by solving population balance equations are addressed.
文摘A special experiment setup was designed to observe the interaction between bubbles and particle in flotation cell and to analyze the bubble characteristics such as bubble size, distribution and bubble-loading efficiency. Bubbles in water-gas system and three-phase system were measured. The results indicate that with the current setup the bubbles as small as 10 μm can be easily distinguished. The average size of the bubbles generated under the given conditions in two-phase system is 410 μm at frother concentration of 0.004%, which is in good correspondence with the results of other works. The effect of frother on bubble size was probed. Increasing frother concentration from 0 to 0.004% causes a reduction of bubble size from 700 to 400 μm. The bubble loading efficiency was reported. The result indicates that the fine particle is more easily entrapped than the coarse particle. Some factors, which have effect on measurement accuracy were discussed. The aeration speed has a significant effect on the accuracy of results, if it surpasses 30 mL/s, and the image becomes unclear due to the entrapment of fine particle. Another factor, which can affect observing results, is the sampling position. At a wrong sampling position, the images become unclear.
文摘Experiments were conducted to obtain the values of the Sauter bubble size, enrichment and recovery of bovine serum albumin （BSA） in a semi-batch col- umn fitted with a stainless steel sparger at elevated pressure. The effects of Sur- face tension, surfactant concentration, foam/solution height ratio and air flow rate on the separation performance were investigated, and the results showed that good en- richments and recoveries can be achieved for bovine serum albumin operated at el- evated pressures. Especially the size of bubbles generated by the stainless steel sparger was smaller at higher pressures which is favorable to the foam separation process. Furthermore, the separation mechanism of bovine serum albumin operated at elevated pressure was also discussed.
基金supported by the National Natural Science Foundation of China(21908062)。
文摘A computational study was carried out on bubble dynamic behaviors and bubble size distributions in a pressurized lab-scale gas-solid fluidized bed of Geldart A particles.High-resolution 3-D numerical simulations were performed using the two-fluid model based on the kinetic theory of granular flow.A finegrid,which is in the range of 3–4 particle diameters,was utilized in order to capture bubble structures explicitly without breaking down the continuum assumption for the solid phase.A novel bubble tracking scheme was developed in combination with a 3-D detection and tracking algorithm(MS3 DATA)and applied to detect the bubble statistics,such as bubble size,location in each time frame and relative position between two adjacent time frames,from numerical simulations.The spatial coordinates and corresponding void fraction data were sampled at 100 Hz for data analyzing.The bubble coalescence/break-up frequencies and the daughter bubble size distribution were evaluated by using the new bubble tracking algorithm.The results showed that the bubble size distributed non-uniformly over cross-sections in the bed.The equilibrium bubble diameter due to bubble break-up and coalescence dynamics can be obtained,and the bubble rise velocity follows Davidson’s correlation closely.Good agreements were obtained between the computed results and that predicted by using the bubble break-up model proposed in our previous work.The computational bubble tracking method showed the potential of analyzing bubble motions and the coalescence and break-up characteristics based on time series data sets of void fraction maps obtained numerically and experimentally.
基金the National Natural Science Foundation of China(Grant Nos.11674074 and 61701133).
文摘Measurements of bubble size distribution require the understanding of the acoustic characteristics of the medium.The bubbles show highly nonlinear properties under finite amplitude acoustic excitation,so the acoustic fields from bubble population are easily observed at the second harmonics as well as at the fundamental frequency,which shows that the nonlinear coefficient increases obviously.The inversion method of bubble size distribution based on nonlinear acoustic effects can peel off the influence of complex environment and obtain the size distribution coefficient information of bubbles more accurately.The previous nonlinear inversion methods of bubble size distribution are mostly based on the nonlinear scattering cross-section characteristics of bubbles.However,the stability of inversion is not high enough.In this paper,we introduce a new acoustic inversion method for bubble size distribution,which is based on the nonlinear coefficients of bubble medium.Compared with other inversion methods based on linear or nonlinear scattering cross section,the inversion method based on nonlinear coefficients of bubble medium proposed in this paper shows good robustness in both simulation and experiment.
基金supported by the National Natural Science Foundation of China (12322510 and 12275174)the Shanghai Rising-Star Program (22QA1404500)+1 种基金the Science and Technology Commission of Shanghai Municipality (24DZ3100300)the Lingchuang Project of China National Nuclear Corporation
文摘Two-phase flow with complex phase interfaces is commonly observed in both nature and industrial processes.The bubble size distribution(BSD) is a crucial parameter in gas-liquid two-phase flow,impacting various flow characteristics including interfacial forces,void fraction distribution,and interfacial area transport.Throughout the flow progression,the BSD changes along the channel due to variations in pressure and interactions among bubbles.Accurately predicting the evolution of BSD can enhance the modeling of two-phase flow.This study presents a novel BSD evolution(BSDE) model,where the governing equation for the probability density function is formulated by considering the conservation of bubbles within a onedimensional control volume in the channel.The downstream BSD is predicted based on the upstream BSD and the effects of pressure variations and bubble interactions along the channel.To account for the multiscale nature of the two-phase flow,the bubbles are categorized into small groups(G_(1)) and large groups(G_(2)).Six distinct source term distributions for intra/inter bubble interactions have been developed.Each source term accounts for the distributions of consumed and generated bubbles,ensuring the conservation of bubble volume through constraints on model coefficients.The model has been tested on a tight-lattice rod bundle using experimental data,with deviations of less than 5% and 15% for G_(1)and G_(2) flow,respectively.Since the model development is independent of specific geometry,the framework of the BSDE model can also be effectively applied to channels of varying shapes.
基金supported by the National Key R&D Program of China(Nos.2023YFC3904202,2022YFC2904500)Major Science and Technology Program of Yunnan Province,China(No.202202AB080012).
文摘The size and distribution patterns of bubbles within a laboratory-scale coarse-particle flotation column were examined using a high-speed camera-based dynamic measurement system.The effects of operational parameters such as superficial water velocity,air-flow rate,and frother dosage on bubble-size and distribution characteristics were investigated.This study aims to provide theoretical support for enabling fluidized-bed flotation within coarse-particle flotation columns.The results show that negative pressure for air inspiratory and bubble formation is generated by passing a high-speed jet through a throat,and the greatest number of bubbles are observed under natural inspiratory state at an air-liquid ratio of 1:3-1:2.5.Increasing the air-flow rate transforms the bubble diameter distribution from a peaked distribution to a more uniform distribution.Furthermore,the frother narrows the range of bubble-size distribution.A positive correlation exists between the bubble Sauter diameter and air-flow rate,with the bubble Sauter diameter bearing a negative correlation with the superficial water velocity and frother concentration.
基金Project(ID42787)supported by the Istanbul Technical University,BAP(Scientific Research Project)Department,Turkey。
文摘Frothers facilitate the reduction of bubbles size by preventing bubbles coalescence and produce more stable froths.The collision probability of the bubbles and particles substantially increases by decreasing bubble size.For the same volume system,fewer bubbles result from a distribution of large-sized bubbles,and more bubbles result from a distribution of small-sized bubbles.In this research,fundamental two-phase frother characterization parameters were aimed to link with three-phase coal and talc flotation behavior.For this purpose,the effect of single and dual frother systems on inhibiting bubble coalescence was investigated with methyl isobutyl carbinol(MIBC),isooctanol(2 ethyl hexanol),pine oil,and Dowfroth 250.Based on the results of single frothers,isooctanol at the lowest critical coalescence concentration(CCC)value of 6×10^(−6) achieved the smallest bubbles with Sauter mean diameter of 0.80 mm.By blending Dowfroth 250 and pine oil,the bubbles size decreased significantly,reaching 0.45 mm.While the highest recoveries in coal flotation were obtained in single and frother blends where the bubbles size was measured as the smallest in two-phase system,and such a relationship was not found for talc flotation.
基金supported by the National Natural Science Foundation of China(Grant No.51409187)the Fundamental Research Funds for the Central Universities(Grant No.2016B09914)
文摘Over the past 60 years, the air concentration in water has been considered as a control index of cavitation erosion reduction and widely used in the designs of hydraulic structures. However, the mechanism of air entrainment against cavitation erosion has been paid good attention to. In the present work, the effect of air bubble size on cavitation erosion reduction was experimentally investigated. A device with micron-scale orifice diameters(10, 20 and 50 μm in size) was specially designed to introduce air bubbles into water. The experiments about the effect of air bubble size were conducted by means of a vibratory apparatus, including the behavior of formation and movement for single air bubble, the characteristics of cavitation erosion reduction at different air entrainment conditions. The findings demonstrate that high air concentration has significant effects on cavitation erosion reduction.But, a notable problem was that the size of air bubbles is of outstanding effect on cavitation erosion reduction. Small air bubbles support to alleviate cavitation erosion, even at same air concentration.
文摘A new cavitating model by using bubble size distribution based on mass of bubbles is proposed. Liquid phase is treated with Eulerian framework as a mixture containing minute cavitating bubbles. Vapor phase consists of various sizes of minute vapor bubbles, which is distributed to classes based on their mass. The change of bubble number density for each class was solved by considering the change of bubble mass due to phase change as well as generation of new bubbles due to heterogeneous nucleation. In this method the mass of bubbles is treated as an independent variable, in other word, a new coordinate, and dependant variables are solved in Eulerian framework for spatial coordinates and bubble-mass coordinate. The present method is applied to a cavitating flow in a convergent-divergent nozzle, and the two-phase flow with bubble size distribution and phase change was successfully predicted.
基金financial support of the National Natural Science Foundation of China(21776122).
文摘Due to a prolonged operation time and low mass transfer efficiency, the primary challenge in the aeration process of non-Newtonian fluids is the high energy consumption, which is closely related to the form and rate of impeller, ventilation, rheological properties and bubble morphology in the reactor. In this perspective, through optimal computational fluid dynamics models and experiments, the relationship between power consumption, volumetric mass transfer rate(kLa) and initial bubble size(d0) was constructed to establish an efficient operation mode for the aeration process of non-Newtonian fluids. It was found that reducing the d0could significantly increase the oxygen mass transfer rate, resulting in an obvious decrease in the ventilation volume and impeller speed. When d0was regulated within 2-5 mm,an optimal kLa could be achieved, and 21% of power consumption could be saved, compared to the case of bubbles with a diameter of 10 mm.
基金the Tarbiat Modares University (TMU), the Iran Mineral Processing Research Center (IMPRC) and the IMIDRO for the technical assistance and financial support
文摘As is well known to mineral processing scientists and engineers, fine and ultrafine particles are difficult to float mainly due to the low bubble-particle collision efficiencies. Though many efforts have been made to improve flotation performance of fine and ultrafine particles, there is still much more to be done. In this paper, the effects of nano-microbubbles （nanobuhbles and microbubbles） on the flotation of fine （-38 ＋ 14.36 μm） and ultrafine （-14.36 ＋ 5μm） chalcopyrite particles were investigated in a laboratory scale Denver flotation cell. Nano-microbubbles were generated using a specially-designed nano- microbubble generator based on the cavitation phenomenon in Venturi tubes. In order to better under- stand the mechanisms of nano-microbubble enhanced froth flotation of fine and ultrafine chalcopyrite particles, the nano-microbubble size distribution, stability and the effect of frother concentration on nano- bubble size were also studied by a laser diffraction method. Comparative flotation tests were performed in the presence and absence of nano-microbubbles to evaluate their impact on the fine and ultrafine chalcopyrite particle flotation recovery. According to the results, the mean size of nano-microbubbles increased over time, and decreased with increase of frother concentration. The laboratory-scale flotation test results indicated that flotation recovery of chalcopyrite fine and ultrafine particles increased by approximately 16-21% in the presence of nano-microbubbles, depending on operating conditions of the process. The presence of nano-microbubbles increased the recovery of ultrafine particles （-14.36 ＋ 5 μm） more than that of fine particles （-38 ＋ 14.36 μm）. Another major advantage is that the use of nano-microbubbles reduced the collector and frother consumptions by up to 75% and 50%, respectively.
基金the National Natural Science Foundation of China(Grant No.91434121)Ministry of Science and Technology of China(Grant No.2013BAC12B01)+1 种基金State Key Laboratory of Multiphase complex systems(Grant No.MPCS-2015-A-03)Chinese Academy of Sciences(Grant No.XDA07080301)
文摘The Eulerian–Lagrangian simulation of bubbly flow has the advantage of tracking the motion of bubbles in continuous fluid, and hence the position and velocity of each bubble could be accurately acquired. Previous simulation usually used the hard-sphere model for bubble–bubble interactions, assuming that bubbles are rigid spheres and the collisions between bubbles are instantaneous. The bubble contact time during collision processes is not directly taken into account in the collision model. However, the contact time is physically a prerequisite for bubbles to coalesce, and should be long enough for liquid film drainage. In this work we applied the spring-dashpot model to model the bubble collisions and the bubble contact time, and then integrated the spring-dashpot model with the film drainage model for coalescence and a bubble breakage model. The bubble contact time is therefore accurately recorded during the collisions. We investigated the performance of the spring-dashpot model and the effect of the normal stiffness coefficient on bubble coalescence in the simulation.The results indicate that the spring-dashpot model together with the bubble coalescence and breakage model could reasonably reproduce the two-phase flow field, bubble coalescence and bubble size distribution. The influence of normal stiffness coefficient on simulation is also discussed.
