Effects of frothers on bubbles size and flotation performance of hydrophobic minerals

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.

Effect of grain size on gas bubble evolution in nuclear fuel:Phase-field investigations

Numerous irradiation-induced gas bubbles are created in the nuclear fuel during irradiation, leading to the change of microstructure and the degradation of mechanical and thermal properties. The grain size of fuel is one of the important factors affecting bubble evolution. In current study, we first predict the thermodynamic behaviors of point defects as well as the interplay between vacancy and gas atom in both UO_(2) and U_(3)Si_(2) according to ab initio approach. Then, we establish the irradiation-induced bubble phase-field model to investigate the formation and evolution of intra-and inter-granular gas bubbles. The effects of fission rate and temperature on the evolutions of bubble morphologies in UO_(2) and U_(3)Si_(2) have been revealed. Especially, a comparison of porosities under different grain sizes is examined and analyzed. To understand the thermal conductivity as functions of grain size and porosity, the heat transfer capability of U_(3)Si_(2) is evaluated.

Influence of bubble diameter and solids concentration on bubble stability: Development of a novel analytical approach

The properties and thickness of the bubbles in the froth control the flotation process. There is no work showing how to measure bubble film composition and thickness by a straightforward manner. In this work, a novel approach, a custom-designed bubble cell associated with layer interferometry(in the UV-vis region) and FT-IR spectroscopy was used to investigate the effect of solid particle type(hydrophilic vs hydrophobic), concentration and bubble diameter on stability of a bubble blown in air. Stability was quantified by measuring bubble lifetime and hydrated film thickness. Kerosene with silicone oil as a foaming agent was used to evaluate the impact of bubble diameter(test series I). Frother solutions(MIBC, Dowfroth 250, Hexanol and F-150) were used for the solid type concentration experiments(test series II). In the first series of experiments, it was determined that as the diameter of a bubble increased from 10 to 25 mm, so did the hydrated film thickness from 350 to 1000 nm. In the second series, as the silica concentration increased(0 to 10%), an increase in bubble lifetime and hydrated film thickness was resulted(130%-250%). An impact of solid hydrophobicity was found but to a lesser degree than expected. It is possible that the small particle size(<0.1 m) of silica was responsible for this behavior. The findings are used to interpret the effect of solids in flotation froth.

THEORETICAL AND EXPERIMENTAL STUDIES ON BUBBLE DIAMETER AND GAS HOLDUP IN AERATED STIRRED TANKS

Experiments were carried out in geometrically similar vessels with diameters of 0.287, 0.495 and 1.1m respectively. Bubble diameter distribution was measured with a dual electric conductivity probe placed in the tanks. Gas holdup was measured by spillover method. Considering the coalescence of bubbles in the upper circulation region of the aeration stirred tank, introducing the concepts of turbulence decay and effective viscosity of gas-liquid system into this work, and taking into account the equilibrium between the surface energy of the bubbles and the energy supplied by agitation, mathematical models for bubble diameter and mean gas holdup were derived. The mathematical models were confirmed by experimental data.

Estimation of diameter and surface area flux of bubbles based on operational gas dispersion parameters by using regression and ANFIS

Adaptive neuro fuzzy inference system (ANFIS) procedure and regression methods were used to predict the Sauter mean bubble (bubble diameter) and surface area flux of the bubble in a flotation process. The operational conditions of flotation, impeller peripheral speed, superficial gas velocity, and weight percent solids were used as inputs of methods. By using the mentioned operational conditions, the non linear regression results showed that Sauter mean, and surface area flux of the bubble are predictable variables, where the coefficients of determination (R 2 ) are 0.57 and 0.74, respectively. To increase the accuracy of prediction an ANFIS model with cluster radius of 0.4 was applied. ANFIS model was capable of estimating both Sauter mean, and surface area flux of the bubble, where in a testing stage, satisfactory correlations, R 2 = 0.78, and 0.86, were achieved for Sauter mean, and surface area flux of bubble, respectively. Results show that the proposed ANFIS model can accurately estimate outputs and be used in order to predict the parameters without having to conduct the new experiments in a laboratory.

Evaluation of effect of viscosity changes on bubble size in a mechanical flotation cell

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.

Effect of bubble morphology and behavior on power consumption in non-Newtonian fluids’aeration process

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.

A novel approach to prevent bubble coalescence during measurement of bubble size in flotation

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.

Effects of initial bubble size on geometric and motion characteristics of bubble released in water

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.

Effect of some operational variables on bubble size in a pilot-scale mechanical flotation machine

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.

Correspondence of bubble size and frother partitioning in flotation

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.

Experimental Determination and Modeling of Bubble Size Distributions in Bubble Columns

Using a five point conductivity technique local values of bubble size,bubble velocity and gas fractionhave been experimentally determined in a 288 mmID and 4.3 m high bubble column as a function of axial andradial position for the air/water and CO2/N2/aqueous MDEA systems.The experimental results are comparedwith predictions from a fundamental two-fluid model.The implementation of a non-steady lateral drag term inthe two-fluid model has been shown.In addition to improving the physical realism of the model,it is found togive slight improvements in the predictions of the distributions of local bubble size.Predictions of bubble size arefound in reasonable agreement with experimental values in the heterogeous flow regime,whereas they are stil1found to be unreliable at low gas velocities.Local void predictions are found in reasonable agreement with experi-mental values,but deviations occur in the homogeneous flow regime towards the wall.This is attributed to defi-ciencies in the simplified bubble size

BUBBLE SIZES AND HOLDUP STRUCTURE IN BUBBLE COLUMNS DETERMINED BY DYNAMIC GAS DISENGAGEMENT

A new model for determining bubble size distributions in bubble columns by the dynamic gasdisengagement(DGD)technique is developed.It is based on an idea of non-uniform steady statedirstribution of bubble dispersion.Interpreting the axial non-uniformity,this model gives axial gasholdup distributions.If assuming an axially homogeneous dispersion,a radial gas holdup distributioncan be obtained.The Sauter mean diameters or specific interfacial areas for several systems areestimated by the technique.The results for an air-water system agree with those measured by afive-point conductivity probe technique.The obtained axial gas holdup distributions agree well withreported measurements and the radial gas holdup distributions are also reasonable.

Bubble size as a function of some situational variables in mechanical flotation machines

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.

Bubble size modeling approach for the simulation of bubble columns

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.

Bubble size estimation using interfacial morphological information for mineral flotation process monitoring

To relate froth structural information with mineral flotation performance, segmentation analysis was performed on froth images characterized by fully occupied convex bubbles with white spots effect. An improved valley edge detection method was proposed to extract structural features and overcome fake white spot edges seriously affecting the segmentation performance. After preprocessing, detection template was designed based on the local minimal intensity, and a binary image containing segmented boundaries was obtained by applying logical rules, thinning and filtering. Statistical features such as bubble size were estimated for control purpose. Experimental results demonstrate that the proposed method avoids over-segmentation or ill-segmentation caused by uneven illumination, and the industrial application reveals the reliability of bubble size estimation.

Bubble size measurement in three-phase system using photograph technology

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.

Effects of Pressure on Bubble Size and Separation of BSA by a Semi-batch Foaming Process

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.

Bubble Size Distribution for Waves Propagating over A Submerged Breakwater

Experiments are carried out to study the characteristics of active bubbles entrained by breaking waves as these propagate over an abruptly topographical change or a submerged breakwater. Underwater sounds generated by the entrained air bubbles are detected by a hydrophone connected to a charge amplifier and a data acquisition system. The size distribution of the bubbles is then determined inversely from the received sound frequencies. The sound signals are converted from time domain to time-frequency domain by applying Gabor transform. The number of bubbles with different sizes are counted from the signal peaks in the time-frequency domain. The characteristics of the bubbles are in terms of bubble size spectra, which account for the variation in bubble probability density related to the bubble radius r. The experimental data demonstrate that the bubble probability density function shows a - 2.39 power-law sealing with radius for r 〉 0. 8 mm, and a- 1.11 power law for r 〈0.8 mm.

Computational study of bubble coalescence/break-up behaviors and bubble size distribution in a 3-D pressurized bubbling gas-solid fluidized bed of Geldart A particles

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.