Classical First-order Model Research Articles

Amorphous silica effects on copper flotation: A kinetic and selectivity investigation

Amorphous silica has been recently recognized for its adverse effects on copper flotation, but its impact remains poorly understood. This study investigates the effects of varying amorphous silica content on the kinetics and selectivity of copper flotation. Results show a significant reduction in chalcopyrite from approximately 99 % to 86 % with increasing amorphous silica content, attributed to increased pulp viscosity and slowed flotation kinetics. The classical first-order kinetic model provided the best fit for the flotation kinetics data, revealing that higher amorphous silica content prolongs the time required to achieve ultimate recovery. Results also show that amorphous silica deteriorated flotation selectivity and increased gangue recovery via entrainment, with complex variations depending on amorphous silica content. A small amount of amorphous silica was identified to significantly impair flotation kinetics and selectivity, leading to a deterioration in overall flotation performance.

Inactivation of Byssochlamys fulva during ohmic heating of tomato juice.

Ohmic heating is an emerging direct thermal technology, which uses electricity to heat food products volumetrically. Ohmic heating provides thermal and non-thermal effects like electropermeabilization to inactivate microorganisms. In this study, ohmic heating was used to inactivate Byssochlamys fulva in tomato juice. The main and interaction effects of initial pH (3.5 and 4.5) and voltage gradient (15 and 20 V/cm) were investigated on mold inactivation during ohmic heating at 88, 93, and 98 °C for 20, 10 and 5 min, respectively. The pH, acidity, total soluble solids, and Dvalue were compared. The results showed that pH and voltage gradient had significant effects on Dvalue and Zvalue (p < 0.05). In order to model the survival behavior of Byssochlamys fulva, due to the nonlinearity of the curves, Weibull model gave more accurate estimation compared to classical first-order model.

Influence of particle size on the separation performance and flotation kinetics of foundry dust

The high-efficiency separation of foundry dust (FD) is imperative for its resource utilization, which contributes to promoting cleaner production and environmental protection in the foundry industry. In order to strengthen the flotation performance of high-quality coal dust in the FD, a systematized investigation was carried out to explore the influence of particle size on the contact angle, separation performance, and flotation kinetics of the FD. The results indicate that the pretreatment process increases the contact angle of the FD, and the liberation degree of coal dust decreases with the decrease of particle size. The fine particles of −53 µm can reduce the separation performance, resulting in a lower coal dust recovery of 60.79%. The coarse particles of −212 + 75 µm and intermediate particles of 75–53 µm possess better flotation results compared to the unclassified FD. The coal dust recovery in the coarse particles can reach up to 84.68%, and the obtained coal dust exhibits a pristine surface and splendid purity. The results of flotation kinetics analysis found that classical first-order model is suitable for characterizing flotation process of the FD with different particle sizes. The flotation rate constant drops as particle size reduces, revealing that the floatability of FD can be significantly improved via a classification method. This may provide a valuable method and scientific guidance for efficient separation and resource utilization of the FD.

Investigation into the influence of droplet size on the stability of diesel emulsions based on multiple light scattering

Diesel oil emulsification is a common method to enhance the coal slime flotation, but difficult to apply industrially due to its unstable characteristics. In this paper, based on the multiple light scattering technique and the statistical Box-Behnken design (BBD) tests, the effect of the process parameters such as shear speed (A), shear time (B), and the mass ratio of SDBS to Span80 (C) on turbiscan stability index (TSI) value was systematically studied, and the relationship between emulsion stability and emulsion droplet size was also explored. The results showed that the destabilization of emulsified diesel (ED) was related to gravity migration and an increase in droplet size and was well fitted by the classical first-order kinetic model with R2 > 0.99. The significant order in which the three factors negatively affect the TSI value is, shear speed (A) > the mass ratio of SDBS to Span80 (C) > shear time (B), with shear speed ranging from 1000 to 16000 rpm, with shear time from 10 to 15 min, and with ratio of Span 80/SDBS from 0.45 to 1.48, respectively. Analysis of variance (ANOVA) revealed a high R2 value of the regression model equation (R2 = 0.9857) and fitted to a second-order polynomial equation using multiple regression analysis. The representative particle size (D50) has a positive linear correlation with the TSI value, indicating the smaller the particle size, the more stable the ED. The theoretical analysis using the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory and Stokes-Richardson-Zaki model demonstrated that the smaller ED droplets have the greater energy barrier to overcome before coalescing and lower rising velocity to move to the upper oil phase, and hence better stability.

Flotation separation of coal dust from foundry dust enhanced by pre-soaking assisted mechanical stirring

Foundry dust is the main refractory solid waste in the foundry industry, and its resource utilization is a top priority for realizing green and cleaner production. The massive amount of coal dust in foundry dust is a potential impediment to the recycling of foundry dust, and the efficient separation of coal dust is crucial to solving the above problems. In this paper, the flotation separation of coal dust from foundry dust enhanced by pre-soaking assisted mechanical stirring was reported. The influence of pre-soaking, stirring speed, and stirring time on the flotation results of foundry dust was systematically studied, and the enhancement mechanism was analyzed based on the microstructure and hydrophobicity of foundry dust. Flotation kinetics experiments with different stirring time were conducted to clarify the flotation process of foundry dust. The results indicate that the pre-soaking of foundry dust is beneficial for the water-absorbing swelling of clay minerals coated on the surface of coal dust, and the subsequent mechanical stirring pretreatment promotes the monomer dissociation of foundry dust, which increases the contact angle of foundry dust and considerably improves the flotation results. The optimal stirring speed and stirring time were 2400 rpm and 30 min, respectively. The classical first-order model presented the highest degree of fitting with the flotation data among the five flotation kinetics models. Therefore, the pre-soaking assisted mechanical stirring is a promising method for promoting flotation separation and the complete recycling of foundry dust.

Effects of Flotation Reagents on Flotation Kinetics of Aphanitic (Microcrystalline) Graphite

The flotation method is widely used for the preliminary beneficiation of aphanitic (microcrystalline) graphite. However, there is limited literature regarding the effects of flotation reagents on the flotation kinetics of aphanitic graphite. In this study, six commonly used flotation kinetic models were used to fit the flotation experimental data of aphanitic graphite. The classical first-order model was found to be most suitable for describing flotation kinetics of aphanitic graphite. The modified flotation rate constant (Km) was then applied to evaluate the effects of collector, frother, and inhibitor on aphanitic graphite flotation kinetics. Compared to diesel oil and terpineol oil, kerosene and 2-octanol produced a greater Km. The highest Km was obtained at an inhibitor dosage of 15 mg/L.

Insight into the effects of grinding media on the flotation kinetics of chalcopyrite

The grinding medium has a significant effect on the flotation performance of chalcopyrite. Flotation kinetics is considered an excellent tool for evaluating flotation performance. In this study, the effects of two grinding media, cast iron balls (CIB) and ceramic balls (CB), on the flotation kinetics of chalcopyrite were investigated. The chalcopyrite particles produced by grinding with CB medium exhibited higher performance in terms of both experimental recovery and cumulative ultimate recovery (ɛ∞) than those with CIB medium because of the formation of fewer FeOOH on the chalcopyrite surfaces. The classical first-order model (ε=ε∞1-e-kt) showed the best agreement with the experimental recovery data in the case of grinding with the CB medium, whereas either the second-order model with a rectangular distribution of floatabilities (ε=ε∞1-1ktln1+kt) or the classical first-order model (ε=ε∞1-e-kt) was considered the optimum model in the case of the CIB grinding medium depending on the experimental conditions.

Environmentally-friendly emulsion-like collector prepared from waste oil: Application in floatation recovery of unburned carbon in coal fly ash

The decarbonization of waste coal fly ash (CFA) and the reuse of waste oil are concerned in this study. The waste oil in kitchen waste was purified and emulsified into emulsion-like collector to reduce the dependence of CFA flotation on non-renewable collector. The feasibility of preparing microemulsion from waste oil by using OP-10 as surfactant, n-pentanol or n-hexanol as co-surfactants was studied. The pseudo ternary phase diagram was used to analyze the emulsification performance. Emulsification results show that waste oil can be prepared into microemulsion under harsh conditions. The concept of an emulsion-like, which does not require water, was proposed because the flotation process was carried out in an aqueous environment. Three emulsion-like (M waste oil:SAR = M2:8, M5:5, M8:2) were used to verify the effect of the ratio of surfactant on the decarburization efficiency. The flotation results show that the carbon removal rate can reach 94.64% under the conditions of appropriate reagent ratio and dosage. In addition, the flotation kinetic analysis was verified, nonlinear fitting results show that the classical first-order model can more accurately explain the flotation kinetic characteristics of CFA flotation by emulsion-like collector. XPS analysis results show that the content of carbon-based hydrophobic groups in CFA is only 59.9%, which indicates that the assistance of collector is necessary to improve the flotation efficiency. The present study realizes the goal of “treating waste with waste” and provides an innovative idea to realize the reuse of CFA and waste oil.

Modeling the Inactivation of &amp;lt;i&amp;gt;Byssochlamys fulva&amp;lt;/i&amp;gt; During Ohmic Heating of Lime Juice

This study was carried out to reduce <i>Byssochlamys fulva</i> PTCC 5062 in lime juice. The main and interaction effects of pH (3.5 and 4.5) and voltage gradient (15 and 20 V/cm) were investigated on mold inactivation during ohmic heating at 88, 93, and 98°C. The results showed that pH and voltage gradient had significant effects on D_value and Z_value (p<0.01). In order to model the survival behavior of <i>Byssochlamys fulva PTCC 5062</i>, due to the nonlinearity of the curves, Weibull model was found to give more accurate estimation compared to classical first-order model. The results of D_value showed that like conventional method, the temperature is the most influential factor affecting the reduction of this heat-resistant mold. It has also been demonstrated that at lower pH and higher voltage gradient, <i>Byssochlamys fulva</i> PTCC 5062 is more sensitive to temperature. This study showed that the highest inactivation rate of this mold was achieved at 98°C, 20 V/cm and pH=3.5.

Effect of particle size on magnesite flotation based on kinetic studies and machine learning simulation

This research focused on the effect of particle size and flotation time on magnesite flotation, and the flotation performance of various size fractions were predicted by a machine learning (ML) method. Four kinetic models were used to fit the recovery of MgO and SiO2 in various size fractions of magnesite flotation. The results demonstrated that the flotation of magnesite exhibits good agreement with the classical first-order kinetic model. Besides, the effect of various particle sizes on MgO recovery and selectivity index was predicted by ML method. It was shown that the proposed ML model could accurately reproduce the effects of particle size and flotation time on magnesite flotation performance. Furthermore, the developed model revealed that the optimal mean size range for magnesite flotation is 30 to 48 μm. Therefore, this paper is of great significance to the application of ML methods in the prediction of various magnesite size flotation performance.

Relationship model between pore wetting and floatability of active carbon: Potential guidance on porous mineral flotation

The water-filled pores have an observable influence on the flotation of porous minerals such as low-rank coal, zeolite, sepiolite, etc. This paper was to perform the fundamental study of pores wetting of the porous minerals using different hydrophobic active carbons as the samples combined with 1H low-field nuclear magnetic resonance (1H LF-NMR) and micro flotation tests. The relationship between wetting percentage measured by the 1H LF-NMR (WPL) and weighting (WPW) for hydrophilic and hydrophobic samples at different wetting times fitted the first-order linear curve, indicating that the 1H LF-NMR characterizing the pore wetting was feasible. The pores of hydrophilic and hydrophobic samples were quickly wetted during 0–10 min wetting, after that their wetting rates were significantly decreased. The micropores and transition pores in the samples of different hydrophobic were mainly wetted. Interestingly, models of total wetting percentages of different hydrophobic samples fitting to wetting times were both the classical first-order model of flotation kinetics. The flotation recoveries of hydrophilic and hydrophobic powder active carbons were gradually decreased at wetting time of 0–10 min, then those stay almost constant, which reflected the effects of pore wetting on the floatability of samples. This paper provides some potential guidance for porous mineral flotation.

The potential of acoustic sound to improve flotation kinetics

Improving the kinetics of flotation with a given feed often involves adding more reagents or changing the reagent scheme. However, this approach could greatly increase operational cost and cause downstream problems. The present work demonstrates a novel approach to improving the flotation kinetics by applying acoustic sound on flotation. Quartz particles were used as model particles and the flotation tests were carried out in batch mode. The experimental variables were focused on sound frequency (250–500 Hz) and amplitude (90–125 dB). The flotation recovery-versus-time data were fitted to the classical first-order kinetic model and two other kinetics models considering the distribution of rate constants. It was found that use of acoustic sound at 350 Hz and above 110 dB and at 400 Hz and 125 dB could increase the apparent flotation rate constant, suggesting that acoustic sound when applied at proper conditions can improve the flotation kinetics.

Heterocoagulation between coal and quartz particles studied by the mineral heterocoagulation quantifying system

Heterocoagulation between mineral particles, which is also called slime coating, is an intractable problem that deteriorates the separation efficiency in mineral flotation. To date, although diverse methods of characterizing mineral heterocoagulation are available, there is short of quantitative characterization. In the present work, a novel method named Mineral Heterocoagulation Quantifying System was developed to quantitatively characterize heterocoagulation. The heterocoagulation between coal and quartz particles was measured at different pH values and sodium hexametaphosphate (SHMP) concentrations. With the heterocoagulation degree given by the Mineral Heterocoagulation Quantifying System at different time, the heterocoagulation kinetics was analyzed for the first time. It was found that the heterocoagulation rate in the present work can be fitted to a classical first-order model. The zeta potential distribution measurements were also conducted to characterize heterocoagulation and the results were consistent with that given by the Mineral Heterocoagulation Quantifying System. The inter-particle force calculation based on the Deyaguin-Landau-Verwey-Overbeek (DLVO) theory was conducted to validate the heterocoagulation results.

Effects of particle size on the flotation behavior of coal fly ash

The effect of particle size on the flotation behavior of coal fly ash was investigated in this study. Three narrow particle size fractions, −125 + 74 μm, −74 + 45 μm, and −45 μm, and the unclassified particle size fraction of −500 μm of coal fly ash were chosen to study the basic properties by the measurement of induction time, contact angle, and wetting heat. Furthermore, flotation kinetic tests of coal fly ash with different particle size fractions were conducted. The results show that particle size significantly affects the flotation kinetics of coal fly ash, and the intermediate particle size fractions of −125 + 74 μm and −74 + 45 μm had better flotation performance and higher flotation rate than the fine particle size of −45 μm. Six flotation kinetic models were used to fit the test data of the cumulative unburned carbon recovery in the coal fly ash flotation. The parameters of flotation rate (k), maximum unburned carbon recovery (ε∞), and correlation coefficient (R2) were analyzed in detail. The fitted results from the data showed that, for each size fraction, the froth flotation of coal fly ash can be best described by the classical first-order model.

Flotation behavior of pyrite in sub-bituminous and meta-bituminous coals with starch depressant in a microflotation cell

Removal of pyrite from coals is very important to reduce the emission of SO2 during coal combustion. The selective flotation of pyrite from coal is challenging due to the hydrophobic nature of both coal and pyrite particles. The surface properties of coal vary significantly with the degree of coalification. The present paper investigates the flotation behavior of pyrite from sub-bituminous and meta-bituminous coal which has different ranks and surface properties. XRD, XPS, contact angle, UV–visible spectroscopy, SEM and zeta potential measurements were used to characterize their differences in mineralogy and surface chemistry. The classical first-order model and the potential flow model were used for flotation kinetic studies and to back-calculate the induction times, respectively. Efficient selective flotation of pyrite from the sub-bituminous and meta-bituminous coal was observed in the presence of potassium amyl xanthate collector and starch depressant. The flotation recoveries of pyrite from the sub-bituminous coal and the meta-bituminous coal were over 95%, with pyrite grade of over 95% in the concentrates.

Effects of particle size on flotation performance in the separation of copper, gold and lead

In order to investigate the effect of particle size on the flotation performance in the separation of copper-gold-lead, froth products of various size fractions were collected as a function of flotation time. The optimum dosage of potassium dichromate (K2Cr2O7) and sodium diethyldithiocarbamate (DDTC) were determined by flotation conditional tests. Six flotation kinetic models were used for fitting the experimental data of copper, gold and lead cumulative recovery using 1stOpt and Origin software. Flotation rate constant (k), the maximum recoveries values (R∞), and the multitude correlation coefficient (R2) of each model, as well as the separation efficiency (SE) and the distribution index (D.I.) were calculated to study the changing trend of flotation parameters for various size fractions. The results demonstrated that the favorable size fraction for the copper-gold-lead separation flotation was −74 + 20 μm. The classical first-order model was considered as the optimum model to adapt to the coppergold-lead separation flotation process in this investigation. The flotation rates of the coarser size fractions were greater than those with relatively finer size fractions, while longer flotation time may contribute to improving the recovery of the fine size fraction, and had little impact on the recovery of coarse-grained. The separation efficiency with respect to intermediate size fractions was greater than both the coarse and ultra-fine size fractions whether it is for copper-lead separation flotation or for gold-lead separation flotation. The most reasonable size fraction for gold enriched in the copper concentrate was −58 + 20 μm, while the coarse size fraction of −100 + 74 μm was found to be against to the selective enrichment of gold.

A comparative study of two-stage flotation of Zn and Pb oxide minerals using anionic, cationic, and mixed (cationic/anionic) collectors

A lead-zinc carbonate ore sample containing 2.5% Pb and 9.39% Zn was used in this research work. The sample was prepared from the Darreh-Zanjir mine located in the Yazd province (Iran). Influences of the influential factors on flotation of smithsonite and cerussite were investigated. Among the different parameters involved, dosages of the dispersant, depressants, sulfidizing agent, and collectors de-sliming prior to lead or zinc flotation were essential for the effective recovery and grade of the Zn and Pb flotation concentrates. In addition, the anionic, cationic, and mixed (cationic/anionic) collectors were employed for flotation of smithsonite. The results of reverse and cumulative flotation of both Zn and Pb were relatively low in comparison with the direct process without depressant. Flotation of smithsonite using mixed collectors (Armac C+KAX) showed promising results. Also dosages of chemicals in the cleaning stage for the Zn and Pb concentrates were optimized, and finally, after the cleaner stage for both lead and zinc, a cerussite concentrate with Pb grade and recovery of 49.82% and 60.06%, respectively, and smithsonite concentrate with Zn grade and recovery of 35.47% and 68.56%, respectively, were obtained under the optimal conditions. Furthermore, kinetics of Zn and Pb oxide mineral flotations in the rougher and cleaner stages were studied, which showed that some kinetics models, especially the classical first-order model, could predict the flotation behaviour of the Zn and Pb oxide minerals.

Comparison of air and oily bubbles flotation kinetics of long-flame coal

This paper focuses on the difference in kinetics of air and oily bubbles flotation of long-flame coal. Six flotation kinetic models were taken to fit the air and oily bubbles flotation results by the software MATrix LABoratory. The findings indicated that the conventional flotation was greater than the oily-bubble flotation in flotation rate in the early stage, and these two flotation processes exhibited different variation laws in cumulative concentrate yield with flotation time. Additionally, it was found that the classical first-order model could provide an excellent fit to the experimental data for the conventional flotation, yet all the studied kinetic models showed a great deviation in fitting to oily-bubble flotation data. Consequently, an improvement for flotation kinetic models was conducted by subtracting the delay constant in the oily-bubble flotation to attain an excellent fitting. Finally, the delay constant for the oily-bubble flotation was determined to be about 0.7500 min, while the improved classical first-order model was found to give the best fit to the oily-bubble flotation data. This study may contribute to a better understanding of the oily-bubble flotation characteristics.

Effects of Xanthate on Flotation Kinetics of Chalcopyrite and Talc

This paper investigated the effects of using or not using potassium butyl xanthate (PBX) as a collector on the flotation kinetics of talc and chalcopyrite. By means of atomic force microscopy (AFM), Fourier-transform infrared spectroscopy (FTIR), a contact angle measuring instrument and particle size analyzer, the underlying causes behind the flotation rate changes of talc and chalcopyrite are analyzed. Experimental results showed that in collectorless flotation, the law of change in the flotation rate constant (k) of the two minerals over time is independent of pH, and k values of chalcopyrite are much smaller than those of talc. In the presence of PBX, the flotation speed of chalcopyrite greatly increases, and the k values of chalcopyrite are far larger than those of talc. This is mainly because the amount of xanthate adsorbed on the surface of chalcopyrite is large and the adsorption is in the form of chemisorption, while the adsorption of xanthate on the talcum surface is in very small amounts and in the form of physical adsorption. Simulation results indicated that the collectorless flotation of chalcopyrite conform to the classical first-order kinetics model and the Kelsall model, whereas that of talc only conform to the latter, which is due to the layered structure of talc. In the presence of the collector, talc flotation conforms to the two model, because talc has a higher floatability and particle morphology has less influence on the flotation rate.

Flotation kinetics of the removal of unburned carbon from coal fly ash

ABSTRACTUnburned carbon (UC) in coal fly ash indicates the waste of energy source and is an obstacle to the utilization of coal fly ash. The purpose of this study was to investigate the flotation kinetics of the removal of UC from coal fly ash. The collector and frother dosage are key factors for coal fly ash flotation. Six flotation kinetic models were applied to fit the flotation kinetic tests data. The fitted results showed that the classical first-order model had better consistency with the experimental data. The contact angle of flotation concentrates decreased as the flotation time was extended which revealed the decrease of flotation rate.