Degree Of Entrainment Research Articles

Study of the effect of airflow rate and agitation speed on entrainment of ash particles in bottom ash flotation

To enhance the recovery and grade of the final product, reducing the entrainment of the hydrophilic particles during flotation is critical. We conducted the improvement of entrainment to reduce the amount of ash in the concentrate with the purpose of recovering high-quality unburned carbon from the bottom ash and reusing it as fuel in power plant. In this study, we investigated the effects of airflow rate and agitation speed on the entrainment of hydrophilic particles. In the self-aerating flotation machine, it was difficult to independently control the agitation speed and airflow rate, resulting in the degree of entrainment of 0.74. By independently controlling the airflow in which hydrophobic particles can float under conditions of the degree of entrainment with 0.7 (low agitation speed: 900 rpm), the combustible recovery and unburned carbon content of concentrate were 93.71% and 93.60%, respectively. The degree of entrainment was found to be 0.57, and entrainment could be minimized through independent control of airflow rate and agitation speed. To minimize entrainment, it is effective to inject air that can suspend hydrophobic particles in a low agitation speed condition.

Effect of platy gangue minerals in sulfide flotation: Part I-transport rates

Observations from operating flotation plants suggest that the presence of the platy gangue mineral mica leads to significantly reduced concentrate grades. The combined effects of gangue particle shape (platy vs globular) and particle size on flotation has not been systematically investigated. Flotation tests were conducted on ground ore mixed with different amounts of sized mica (platy) or silica (globular) minerals. This essentially allowed us to alter the already present non-sulfide gangue (NSG) composition in a controlled manner and to investigate gangue size and shape effects on flotation recovery. The use of purposefully added mineral particles with narrow size distributions improved our ability to determine the different pathways by which hydrophilic particles of various sizes and shapes are transported through the froth. Cumulative mineral and water recovery data for each composition was used to calculate the degree of NSG entrainment for each ore plus adulterant (mica or silica). Analysis of the degree of entrainment vs adulterant particle size and shape showed that the addition of mica typically results in higher gangue recovery compared to when silica is added at comparable concentrations. The data for recovery when mica was added followed a trend associated with typical entrainment behavior, i.e., there was a decrease in the degree of entrainment with increasing mica particle size up to about 100μ. However, for greater mica size fractions, an increase in the degree of entrainment was observed. The reason for this behavior is discussed in the part II companion to this paper (Bhambhani, T., Farinato, R., Somasundaran, P., Nagaraj, D., 2022. Effect of play gangue minerals in sulfide flotation: Part 2: Mechanisms, Submitted to Minerals Engineering). The entrainment effects of mica were also evidenced to be concentration dependent. For coarser fractions of mica added to the ore pulp, where the degree of entrainment now increases with mica size, an increase in concentration of mica in that pulp resulted in a steeper increase in the degree of entrainment with mica particle size. This suggested second-order effects arising from particle-particle interactions. Similar results were seen with silica; however, deviations in the degree of entrainment vs particle size plots were less pronounced or required greater concentrations to be seen.

Energy flow and dissipation in heterogeneous ensembles of coupled phase oscillators

We present analytical expressions and numerical results for the rates of energy exchange between oscillators and with the environment in a heterogeneous ensemble of globally coupled mechanical phase oscillators. The system is in stationary motion under the combined action of an external harmonic excitation, coupling, and friction. Individual moments of inertia and friction coefficients are different between oscillators. Three dynamical regimes, with different degrees of entrainment with the external excitation, are characterized. In two of these regimes, the rates of energy exchange show nontrivial dependence on the moments of inertia and friction coefficients, suggesting that the transfer of power between different parts of the ensemble can be manipulated by a convenient choice of the individual parameters.

Effect of scrubbing medium’s particle size distribution and scrubbing time on scrubbing flotation performance and entrainment of microcrystalline graphite

ABSTRACT In this study, we investigated the effect of the scrubbing medium’s particle size distribution on the scrubbing flotation performance of microcrystalline graphite. A simplex lattice mixture design approach using Design-Expert software was employed for proportioning testing of the scrubbing media. Three different sizes of scrubbing medium (A: 1 mm, B: 2 mm, and C: 3 mm) were mixed to obtain different particle size distributions. The results showed that a linear mixture model was suitable for fitting this mixture design, and the particle size distribution of the scrubbing medium was 3 mm. Hence, we studied the effect of scrubbing time on the flotation performance of the scrubbing flotation process. The flotation results indicated that graphite quality was enhanced by increasing the scrubbing time, and the optimum scrubbing time for this graphite was 45 min when maximum enrichment efficiency was acquired. Also, we investigated the effect of the scrubbing medium’s particle size compositions on gangue entrainment in the scrubbing flotation process. It was concluded that the degree of entrainment under the composition of scrubbing size 1 mm (16.67%), 2 mm (16.67%), and 3 mm (66.66%) was reduced compared to the other two compositions (scrubbing size 2 mm (50%) and 3 mm (50%) as well as scrubbing size 3 mm (100%)). This conclusion was proved using analyses of froth bubble size and scanning electron microscopy and energy dispersive x-ray spectroscopy (SEM-EDS).

Study of dust collection effectiveness in cyclonic-vortex action apparatus

The object of research is the efficiency of dust collection of fine dust in an apparatus with an intense turbulent mode of phase interaction. One of the most problematic areas of the existing dust and gas cleaning equipment is the low efficiency of collecting fine dust. Effective cleaning of exhaust gases from dust involves the use of multi-stage cleaning systems, including wet and dry dust cleaning devices, which entails high capital and operating costs. These disadvantages are eliminated in the developed design of the cyclone-vortex dust collector with two contact zones. The device implements both dry and wet dust collection mechanisms, which allows for high efficiency of dust removal at high productivity. The conducted studies of the total and fractional efficiency of dust collection when changing the operating parameters of the developed device showed that the efficiency of collecting fine dust is 98–99 %. The increase in the efficiency of dust collection in the dry stage of the device is due to an increase in centrifugal force. In the wet stage of contact, the efficiency reaches its maximum values due to the vortex crushing of the liquid in the nozzle zone of the apparatus. Studies of the fractional efficiency of the apparatus show that with an increase in the diameter of the captured particles, the efficiency of the dust collection process for dry and wet stages, as well as the overall efficiency, increases. With an increase in the density of irrigation, the overall efficiency of dust collection in the apparatus increases. It has been established that an increase in the efficiency of capturing highly dispersed particles occurs due to turbulent diffusion, the value of which is determined by the frequency of turbulent pulsations and the degree of entrainment of particles during the pulsating motion of packed bodies. To describe the results obtained, a centrifugal-inertial model for a dry contact stage and a turbulent-diffusion model of solid particle deposition for a wet contact stage are proposed, which make it possible to calculate the dust collection efficiency of the contact stages, as well as the overall efficiency of the cyclone-vortex apparatus. The results obtained show the prospects of using devices of this design at heat power plants and other industries.

Energy exchange in globally coupled mechanical phase oscillators

We study the stationary dynamics of energy exchange in an ensemble of phase oscillators, coupled through a mean-field mechanical interaction and added with friction and an external periodic excitation. The degree of entrainment between different parts of the ensemble and the external forcing determines three dynamical regimes, each of them characterized by specific rates of energy exchange. Using suitable approximations, we are able to obtain analytical expressions for those rates, which are in satisfactory agreement with results from numerical integration of the equations of motion. In some of the dynamical regimes, the rates of energy exchange show nontrivial dependence on the friction coefficients-in particular, nonmonotonic behavior and sign switching. This suggests that, even in this kind of stylized model, power transfer between different parts of the ensemble and to the environment can be manipulated by a convenient choice of the individual oscillator parameters.

Froth properties and entrainment in lab-scale flotation: A case of carbonaceous sedimentary phosphate ore

In flotation, the froth characteristics strongly influence the separation process as they are linked to water recovery, bubble size, entrainment of gangue particles, flotation rate constants and finally grade and recovery. In the case of a high-grade apatite ore with a high mass pull in lab-scale flotation, significant changes in pulp and froth properties occur, such that the froth stability decreases with increasing flotation time. These changes can be related to different particle and reagent concentrations. We describe the change of entrainment in a rich apatite ore batch flotation with time more precisely by measuring froth properties using a Dynamic Froth Analyzer (DFA). It is concluded that the degree of entrainment is not only dependent on particle size but also the pulp density due to its effect on particle settling and also froth properties in varying resistance to drainage. Through a combination of time-resolved dynamic froth analysis and automated mineralogy, we identify the dynamic effects governing in the froth and compare the entrainment results with existing models. Furthermore, our analyses offer novel support for the extension of the common understanding of the entrainment phenomena.

Mitigating the negative effects of clay minerals on gold flotation by a lignosulfonate-based biopolymer

The objective of this study was to identify various mechanisms responsible for the poor flotation of a high-clay-content gold ore and then develop a remedial solution. Compared to the flotation of a clean gold ore with a low clay content, obtained from the same flotation plant, the flotation of the high-clay-content gold ore produced much lower gold grade and gold recovery. The degree of entrainment (ENT) was calculated and it was found that a high mechanical entrainment of gangue minerals occurred in the flotation of the high-clay-content gold ore, contributing to the low gold grade in flotation. Electrochemical impedance spectroscopic (EIS) measurements were conducted to detect a possible clay slime coating on gold surface during flotation. It was observed that a clay slime coating did not occur on gold surface in the flotation of the high-clay-content gold ore, and therefore slime coating was not the reason for the poor gold flotation performance. Rheological measurements show that the high-clay-content gold ore slurry exhibited a non-Newtonian behaviour with a high apparent viscosity, contributing to the low gold recovery in flotation. Based on the previous studies, a lignosulfonate-based biopolymer (DP-1777) was used to mitigate the negative effects of clay minerals in the flotation of the high-clay-content gold ore. It was found that DP-1777 improved both gold grade and gold recovery significantly through the reduction of mechanical entrainment and pulp viscosity, respectively.

Being Conscious of the Absent Stimuli: 2 - Entrained Computations

It was proposed that consciousness to result from quantum computations supported by nested well controlled oscillatory cortical activity, which may be disclosed by analysis of EEG activity. Oscillatory activity is easily entrained by external stimulation; e.g. periodic stimuli or well parsed verbal sound packs. These two concurrent cortical computations (e.g., click perception and language understanding) may share different degrees of entrainment, depending on stimulus properties and the nature of the task to be solved. This entrainment may promote interference between the concurrent conscious computations. The purpose of the present paper is to investigate this possible interference, by asking people to correlated click occurrence to the words being listened in order to force phase locking between cyclic cortical activity involved in click analysis and language decoding. EEG was recorded while volunteers solved the task. Results confirmed the computational cross taking errors because both text understanding impoverished and sensory perception errors increased as cortical activity entrainment enhanced. Event Related Analysis pointed to some EEG components that may be involved in the process.

The mechanism responsible for the effect of frothers on the degree of entrainment in laboratory batch flotation

The effect of frothers on the degree of entrainment is important for selective flotation, but the mechanism underpinning the effect is still poorly understood. In this study, gangue only batch flotation tests were performed using fully liberated quartz in a 3.5L conventional Agitair flotation cell, and the degree of entrainment was assessed at different frother concentrations using Dowfroth 250 and MIBC. Results show that the effect of frothers on the degree of entrainment was the consequence of changes in the upward liquid motion across the pulp/froth interface. The frothers changed the bubble size, resulting in a change in liquid content and liquid velocity at the interface. The change in interface liquid velocity then changed the drag force which determined the motion of a particle against the downward gravitational force on the particle due to its weight, resulting in a change in the amount of hydrophilic solid particles following the water phase and being recovered in the water phase, and hence the degree of entrainment. The results also suggest that the classification of hydrophilic solid particles occurred at the interface region.

Characteristics of the Nordic Seas overflows in a set of Norwegian Earth System Model experiments

Global ocean models with an isopycnic vertical coordinate are advantageous in representing overflows, as they do not suffer from topography-induced spurious numerical mixing commonly seen in geopotential coordinate models. In this paper, we present a quantitative diagnosis of the Nordic Seas overflows in four configurations of the Norwegian Earth System Model (NorESM) family that features an isopycnic ocean model. For intercomparison, two coupled ocean-sea ice and two fully coupled (atmosphere-land-ocean-sea ice) experiments are considered. Each pair consists of a (non-eddying) 1° and a (eddy-permitting) 1/4° horizontal resolution ocean model. In all experiments, overflow waters remain dense and descend to the deep basins, entraining ambient water en route. Results from the 1/4° pair show similar behavior in the overflows, whereas the 1° pair show distinct differences, including temperature/salinity properties, volume transport (Q), and large scale features such as the strength of the Atlantic Meridional Overturning Circulation (AMOC). The volume transport of the overflows and degree of entrainment are underestimated in the 1° experiments, whereas in the 1/4° experiments, there is a two-fold downstream increase in Q, which matches observations well. In contrast to the 1/4° experiments, the coarse 1° experiments do not capture the inclined isopycnals of the overflows or the western boundary current off the Flemish Cap. In all experiments, the pathway of the Iceland-Scotland Overflow Water is misrepresented: a major fraction of the overflow proceeds southward into the West European Basin, instead of turning westward into the Irminger Sea. This discrepancy is attributed to excessive production of Labrador Sea Water in the model. The mean state and variability of the Nordic Seas overflows have significant consequences on the response of the AMOC, hence their correct representations are of vital importance in global ocean and climate modelling.

On the Influence of Array Size and Jet Spacing on Jet Interactions and Confluence in Round Jet Arrays

This work uses computational models to study the effects of confluence and jet-to-jet interactions for inline matrices of confluent round jets. In total, 12 different confluent jet arrangements, having various jet array sizes and dimensionless jet spacing, S/d0, have been investigated. The array size varies from 6 × 6 to 10 × 10 jets, while S/d0 varies between 1.75≤S/d0≤4.0. The Reynolds number, based on the nozzle exit diameter, is between 2200 and 6600. The results show that both jet spacing and jet array size largely influence the jet-to-jet interactions and flow field development in confluent jet arrays. The jet interactions in the investigated setups result in regions of negative static pressure between jets, jet deformation, high spanwise velocity, and jet displacement. Generally, smaller jet spacing and larger array size result in stronger influence of jet interactions. After the jets have combined, the confluent jets form a zone with constant maximum streamwise velocity and decay of turbulence intensity, called a confluent core zone (CCZ). During the CCZ, the combined jet will have asymmetric spreading rates leading to axis-switching. The entrainment rate of the CCZ is constant, but the volumetric flow rate of the combined jet is substantially affected by the degree of entrainment before the jets have combined.

Entrainment in froth flotation: The degree of entrainment and its contributing factors

In froth flotation, the degree of entrainment affects the concentrate grade and it is often assumed to be only a function of particle size in models. Literature suggests that other variables might also have a significant impact on the degree of entrainment. In this study, a factorial batch flotation experiment using a mixture of liberated chalcopyrite and two liberated gangue minerals, quartz and hematite, was performed to investigate the effects of these other variables (including impeller speed, gas flow rate, froth height and the specific gravity of gangue mineral) on the degree of entrainment. Results show that the degree of entrainment varied significantly as the flotation test conditions changed. Particle density and the interaction between gas flow rate and froth height had a statistically significant effect on the average degree of entrainment measured for the entire test. The degree of entrainment also significantly changed with flotation time throughout each experiment. It is hypothesised that these effects are a consequence of the degree of entrainment being affected by the weight of particles (not just their size) because of its effect on particle settling as well as the froth structure which provides varying resistance to particle drainage. It is concluded that models for the degree of entrainment that incorporate only particle size are not sufficient to predict gangue recovery and concentrate grade in an industrial application.

EEG oscillations entrain their phase to high-level features of speech sound

Phase entrainment of neural oscillations, the brain's adjustment to rhythmic stimulation, is a central component in recent theories of speech comprehension: the alignment between brain oscillations and speech sound improves speech intelligibility. However, phase entrainment to everyday speech sound could also be explained by oscillations passively following the low-level periodicities (e.g., in sound amplitude and spectral content) of auditory stimulation—and not by an adjustment to the speech rhythm per se. Recently, using novel speech/noise mixture stimuli, we have shown that behavioral performance can entrain to speech sound even when high-level features (including phonetic information) are not accompanied by fluctuations in sound amplitude and spectral content. In the present study, we report that neural phase entrainment might underlie our behavioral findings. We observed phase-locking between electroencephalogram (EEG) and speech sound in response not only to original (unprocessed) speech but also to our constructed “high-level” speech/noise mixture stimuli. Phase entrainment to original speech and speech/noise sound did not differ in the degree of entrainment, but rather in the actual phase difference between EEG signal and sound. Phase entrainment was not abolished when speech/noise stimuli were presented in reverse (which disrupts semantic processing), indicating that acoustic (rather than linguistic) high-level features play a major role in the observed neural entrainment. Our results provide further evidence for phase entrainment as a potential mechanism underlying speech processing and segmentation, and for the involvement of high-level processes in the adjustment to the rhythm of speech.

True Flotation and Entrainment of Kaolinitic Ore in Batch Tests

A new method for true flotation and entrainment evaluation is proposed and compared with three renowned methods. Therefore, reverse froth flotation tests were conducted in a laboratory Denver cell with a kaolinitic ore. The evaluation of entrainment and true flotation was based on the recoveries of iron, titanium, and manganese oxides (FeO, TiO2, and MnO), and the contributions of each oxide on kaolin minerals determined by electronic microprobe. The effect of particle size in the flotation process was analyzed by particle size distributions of four fractions (<25 µm; +25–45 µm, +45–63 µm; and >63 µm). The contribution of entrainment is similar for the three oxides and the degree of entrainment decreases with increasing particle size; however, the recovery by true flotation is different because of its discriminatory effect on minerals. MnO has the greatest recovery, as a consequence of the major contribution of its hydrophobic minerals, while FeO has the lowest recovery values. The results of the proposed method, developed for fully liberated feeds, are coherent with those obtained by the other three methods, despite the slightly overestimated contribution of entrainment in the case of fraction greater than 63 µm.

An experimental study of the recovery of hydrophilic silica fines in column flotation

This paper presents results of tests performed to investigate the effect of gas rate (1.2–2.5 cm/s), hydrophilic fines content (5–20% w/w silica) and froth depth (10–30 cm) on fines recovery in a laboratory-scale flotation column operating without wash-water addition and absence of floatable particles. A model was developed based on the entrainment coefficients presented by [Trahar, W.J., 1981. A rational interpretation of the role of particle size in flotation. International Journal of Mineral Processing 8, 289–327], which describes the mass contribution of the different size classes to the solids recovered in the concentrate. The entrainment model of [Zheng, X., Johnson, N.W., Franzidis, J.P., 2006. Modelling of entrainment in industrial flotation cells: water recovery and degree of entrainment. Minerals Engineering 19, 1191–1203] was also tested. The results show both models described well the dependence of the mass flow rate of hydrophilic solids in the concentrate.

Water entrainment due to spillway surface jets

Strong flow entrainment has been observed downstream of spillways constructed with flow deflectors. This water entrainment has important environmental and ecological impacts because it improves the mixing of powerhouse and spillway flows, but may negatively impact fish migration or create adverse flow conditions. Most studies found in the literature attempt to explain this entrainment with turbulent mixing. Both reduced-scale hydraulic models and single-phase, isotropic RANS models grossly under-predict the degree of entrainment observed in prototypes. In this paper, an anisotropic model that accounts for the bubble volume fraction and attenuation of the normal velocity fluctuations at the free surface is presented. The model adequately predicts the main mechanisms causing water entrainment and compares well against experimental data for a round surface jet and for Brownlee Dam at model scale. It is shown that appropriate entrainment can only be captured if the turbulence anisotropy and the two-phase nature of the flow are modelled.

A compartment model for the mass transfer inside a conventional flotation cell

A model is developed by taking into account the simultaneous mechanisms of true flotation and entrainment in a conventional flotation cell. The total volume of the cell is divided into three compartments: pulp collection zone, pulp quiescent zone and froth region, with the mechanisms being modeled as occurring at the same time but originating at different places: true flotation from the collection zone and entrainment from the quiescent one. A particle is referred to as suspended in water or attached to an air bubble, depending upon its original state before crossing the pulp–froth interface (whether or not it remains in that state all the way to the concentrate launder). The model is obtained by solving a set of equations describing the mass conservation of solids and water between adjacent compartments. The principal mass transfer factors are identified as: the flotation rate constant, the mean residence time in the collection zone, the froth recovery of attached particles, the degree of entrainment through the froth and the water recovery from the feed to the concentrate. The development presented here allows the intricate nature of the mass transfer in a flotation cell to be reduced to one single equation, overcoming the need of numerical methods for simulation purposes. Moreover, it is shown that reliable prediction of grade and recovery can be obtained without detailed information on the pulp hydrodynamics or on any froth sub-process either than drainage, bubble bursting and bubble coalescence.

Dynamics of multiple swirling burner flows

Numerical predictions of four counter and co-rotating swirling flows issuing from small-scale low NOx burners have been performed and compared to laser Doppler anemometry (LDA) measurements. The results demonstrate that the near-burner features, such as the central reverse flow zones and the mixing of the burner jets, are resolved correctly by the computational model. Predicted tangential velocity components are in good agreement with the LDA measurements, and show the correct swirl velocity profiles and rate of decay. The anti-gearing phenomenon associated with the entrainment pattern of the counter and co-rotating burner arrays, where flow is entrained into the centre of the array against the direction of swirl, is captured by the LDA measurements and is predicted by the CFD model. Predicted rates of entrainment of surrounding air by the counter and co-rotating burners intimate that a counter-rotating burner array entrains at a greater rate than a single burner. A co-rotating system, however, entrains at a lower rate. The ability to control levels of entrainment may provide the means of further controlling air staging in real furnaces. The research demonstrates that multi-burner systems may be characterised in terms of the number of burners, their rotational direction, the burner pitch and the degree of entrainment.

Laboratory model studies of Mediterranean outflow adjustment in the Gulf of Cadiz

Results are presented from a series of laboratory modelling studies carried out as part of the international multidisciplinary project CANIGO. The focus of interest has been the phenomenon of flow adjustment within the Gulf of Cadiz of the Mediterranean outflow plume, modelled by a turbulent, negatively-buoyant jet discharging into a rotating stratified reservoir scaled to the idealised topography of the Gulf. The results show that the fully developed flow pattern that forms close to the entrance to the Gulf consists of a relatively intense jet that divides when it encounters the southern Iberian coastal boundary; part of the jet is deflected westwards to form a boundary current at intermediate depth along the coastline and part is deflected eastwards and back towards the Strait to form a closed weak circulation near the diverging right wall of the Gulf. Within this closed circulation (the typical horizontal dimensions of which scale with the source Froude number when normalised with the inertial radius), small-scale eddy features are embedded. The degree of entrainment into the descending turbulent jet is seen to be determined primarily by the receiving water Froude number (and is relatively insensitive to the Burger and Rossby numbers of the flow), resulting in the formation of a boundary current of intermediate density that follows the Iberian coastal boundary with a typical velocity determined primarily by the effective driving head at the source and weakly by the Burger number of the flow.