Thermodynamic theory of flotation for a complex multiphase solid -liquid system and high-entropy flotation

The flotation of complex solid–liquid multiphase systems involve interactions among multiple components,the core problem facing flotation theory.Meanwhile,the combined use of multicomponent flotation reagents to improve mineral flotation has become an important issue in studies on the efficient use of refractory mineral resources.However,studying the flotation of complex solid–liquid systems is extremely difficult,and no systematic theory has been developed to date.In addition,the physical mechanism associated with combining reagents to improve the flotation effect has not been unified,which limits the development of flotation theory and the progress of flotation technology.In this study,we applied theoretical thermodynamics to a solid–liquid flotation system and used changes in the entropy and Gibbs free energy of the reagents adsorbed on the mineral surface to establish thermodynamic equilibrium equations that de-scribe interactions among various material components while also introducing adsorption equilibrium constants for the flotation reagents adsorbed on the mineral surface.The homogenization effect on the mineral surface in pulp solution was determined using the chemical potentials of the material components of the various mineral surfaces required to maintain balance.The flotation effect can be improved through synergy among multicomponent flotation reagents;its physical essence is the thermodynamic law that as the number of compon-ents of flotation reagents on the mineral surface increases,the surface adsorption entropy change increases,and the Gibbs free energy change of adsorption decreases.According to the results obtained using flotation thermodynamics theory,we established high-entropy flotation theory and a technical method in which increasing the types of flotation reagents adsorbed on the mineral surface,increasing the adsorption entropy change of the flotation reagents,decreasing the Gibbs free energy change,and improving the adsorption efficiency and stability of the flotation reagents improves refractory mineral flotation.

Advances in depressants for flotation separation of Cu–Fe sulfide minerals at low alkalinity:A critical review

The flotation separation of Cu–Fe sulfide minerals at low alkalinity can be achieved using selective depressants.In the flotation system of Cu–Fe sulfide minerals,depressants usually preferentially interact with the pyrite surface to render the mineral surface hydrophilic and hinder the adsorption of the collector.This review summarizes the advances in depressants for the flotation separation of Cu–Fe sulfide minerals at low alkalinity.These advances include use of inorganic depressants (oxidants and sulfur–oxygen compounds),natural polysaccharides (starch,dextrin,konjac glucomannan,and galactomannan),modified polymers (carboxymethyl cellulose,polyacrylamide,lignosulfonate,and tricarboxylate sodium starch),organic acids (polyglutamic acid,sodium humate,tannic acid,pyrogallic acid,salicylic acid,and lactic acid),sodium dimethyl dithiocarbamate,and diethylenetriamine.The potential application of specific inorganic and organic depressants in the flotation separation of Cu–Fe sulfide minerals at low alkalinity is reviewed.The advances in the use of organic depressants with respect to the flotation separation of Cu–Fe sulfide minerals are comprehensively detailed.Additionally,the depression performances and mechanisms of different types of organic depressants on mineral surfaces are summarized.Finally,several perspectives on depressants vis-à-vis flotation separation of Cu–Fe sulfide minerals at low alkalinity are proposed.

Activation mechanism of ammonium oxalate with pyrite in the lime system and its response to flotation separation of pyrite from arsenopyrite

The activation properties of ammonium oxalate on the flotation of pyrite and arsenopyrite in the lime system were studied in this work.Single mineral flotation tests showed that the ammonium oxalate strongly activated pyrite in high alkalinity and high Ca^(2+)system,whereas arsenopyrite was almost unaffected.In mineral mixtures tests,the recovery difference between pyrite and arsenopyrite after adding ammonium oxalate is more than 85%.After ammonium oxalate and ethyl xanthate treatment,the hydrophobicity of pyrite increased significantly,and the contact angle increased from 66.62°to 75.15°and then to 81.21°.After ammonium oxalate treatment,the amount of ethyl xanthate adsorption on the pyrite surface significantly increased and was much greater than that on the arsenopyrite surface.Zeta potential measurements showed that after activation by ammonium oxalate,there was a shift in the zeta potential of pyrite to more negative values by adding xanthate.X-ray photoelectron spectroscopy test showed that after ammonium oxalate treatment,the O 1s content on the surface of pyrite decreased from 44.03%to 26.18%,and the S 2p content increased from 14.01%to 27.26%,which confirmed that the ammonium oxalatetreated pyrite surface was more hydrophobic than the untreated surface.Therefore,ammonium oxalate may be used as a selective activator of pyrite in the lime system,which achieves an efficient flotation separation of S-As sulfide ores under high alkalinity and high Ca2+concentration conditions.

Adsorption of sodium oleate at the microfine hematite/aqueous solution interface and its consequences for flotation

The adsorption of sodium oleate(NaOL)at the microfine hematite/aqueous solution interface was investigated in this paper.Experimental research indicated that negative effects stemmed from the dissolution of the microfine hematite(D50=19.21μm)could be effectively eliminated via the appropriate dosage of NaOL at alkali pH conditions.Solution chemistry calculation and adsorption test results indicated that RCOO
and(RCOO)_(2)^(2-) ions were responsible for microfine hematite flotation at pH 8.2.Zeta potential and FTIR measurements confirmed the co-adsorption of molecular and ionic oleate species occurred at pH 8.2.X-ray photoelectron spectroscopy(XPS)results further indicated that oleate species interacted with hematite surfaces mainly through chemisorption,giving rise to molecule/colloid formation of oleate and Fe―OL complex compound.Time-of-flight secondary ion mass spectrometry(ToF-SIMS)results demonstrated that oleate species adsorbed onto the hematite surfaces with a thickness of a few nanometers.Furthermore,the normalized peak intensity of C4H7+ions on the hematite sample at pH 8.2 increased remarkably comparing with corresponding result of hematite sample at pH 6.8.The new findings of the present study well revealed the dissolution of microfine hematite and the pH effects on the hematite flotation,as well as the adsorption characteristics of oleate species.

Effect of dissolved components of malachite and calcite on surface properties and flotation behavior

In general,malachite is recovered via sulfidization–xanthate flotation,although many unsatisfactory flotation indexes are frequently obtained as a result of the presence of associated calcite.This phenomenon occurs because the dissolved components of malachite and calcite affect the flotation behavior of both minerals.In this study,the effect of the dissolved components derived from malachite and calcite on the flotation behavior and surface characteristics of both minerals was investigated.Flotation tests indicated that malachite recovery decreased when the calcite supernatant was introduced,while the presence of the malachite supernatant increased the recovery of calcite.Dissolution and adsorption tests,along with zeta potential measurements,X-ray photoelectron spectroscopy,Fourier transform infrared spectrometry,and timeof-flight secondary ion mass spectrometry demonstrated that the Ca species in the calcite supernatant were adsorbed on the malachite surface,which hindered the interaction of Na2S with malachite,thereby resulting in the insufficient adsorption of sodium isoamyl xanthate(NaIX)on the surface of malachite.By contrast,the Cu species in the malachite supernatant were adsorbed on the calcite surface,and they provided active sites for the subsequent adsorption of Na_(2)S and NaIX.

Enhanced sulfidization of azurite surfaces by ammonium phosphate and its effect on flotation

Although azurite is one of the most important copper oxide minerals,the recovery of this mineral via sulfidization-xanthate flotation is typically unsatisfactory.The present work demonstrated the enhanced sulfidization of azurite surfaces using ammonia phosphate((NH_(4))_(3)PO_(4)) together with Na_(2)S,based on micro-flotation experiments,time-of-flight secondary ion mass spectrometry(ToF-SIMS),X-ray photoelectron spectroscopy(XPS),zeta-potential measurements,contact angle measurements,Fourier-transform infrared(FT-IR)spectroscopy,and ultraviolet-visible(UV-Vis)spectroscopy.Micro-flotation experiments showed that the floatability of azurite was increased following the simultaneous addition of(NH_(4))_(3)PO_(4)and Na_(2)S.ToF-SIMS and XPS analyses demonstrated the formation of a high content of S species on the azurite surface and an increase in the number of Cu(I)species after exposure to(NH_(4))_(3)PO_(4)and Na_(2)S,compared with the azurite-Na_(2)S system.The zeta potential of azurite particles was negatively shifted and the contact angle on the azurite surface was increased with the addition of(NH_(4))_(3)PO_(4)prior to Na_(2)S.These results indicate that treatment with(NH_(4))_(3)PO_(4) enhances the sulfidization of azurite surfaces,which in turn promotes xanthate attachment.FT-IR and UV-Vis analyses confirmed that the addition of(NH_(4))_(3)PO_(4) increased the adsorption of xanthate with reducing the consumption of xanthate during the azurite flotation process.Thus,(NH_(4))_(3)PO_(4) has a beneficial effect on the sulfidization flotation of azurite.

Sulfidization regulation of cuprite by pre-oxidation using sodium hypochlorite as an oxidant

The direct sulfidization of cuprite is inefficient because cuprite is a copper-oxide mineral with a strong surface hydrophilicity.In this study,oxidant was used to modify cuprite surfaces to regulate the sulfidization of cuprite.Microflotation tests showed that the flotation recovery of pre-oxidized cuprite was nearly25% higher than that of direct sulfidization flotation,which indicates that the cuprite surface activity was enhanced after pre-oxidation by Cu(Ⅰ) species(weak affinity with sulfur ions) transformation to Cu(Ⅱ)species(strong affinity with sulfur ions).Zeta potential,scanning electron microscopy-energy dispersive X-ray spectroscopy,X-ray photoelectron spectroscopy,and time-of-flight secondary ion mass spectrometry results showed that pre-oxidation improved cuprite sulfidization and promoted the formation of copper-sulfide species on the cuprite surfaces.The mineral surface stability and thus,xanthate species adsorption on the cuprite surfaces were improved.The surface-adsorption measurements and infrared spectroscopy showed that a large amount of xanthate species was adsorbed onto the sulfidized cuprite surfaces after pre-oxidation,which enhanced the cuprite hydrophobicity and improved the cuprite flotation.

Flotation of copper oxide minerals:A review

Copper oxide minerals are important copper resources,which include malachite,azurite,chrysocolla,cuprite,etc.Flotation is the most widely used method for the enrichment of copper oxide minerals in the mineral processing industry.In this paper,the surface properties of copper oxide minerals and their effects on the mineral flotation behavior are systematically summarized.The flotation methods of copper oxide minerals and the interaction mechanism with reagents are reviewed in detail.Flotation methods include direct flotation(using chelating reagents or a fatty acid as collector),sulfidization flotation(using xanthate as collector),and activation flotation(using chelating reagents,ammonium/amine salts,metal ions,and oxidant for activation).An effective way to realize efficient flotation of copper oxide minerals is to increase active sites on the surface of copper oxide minerals to enhance the interaction of collector with the mineral surface.Besides,various perspectives for further investigation on the efficient recovery of copper oxide minerals are proposed.

Adsorption behavior and mechanism of copper ions in the sulfidization flotation of malachite

Malachite is one of the main minerals used for the industrial enrichment and recovery of copper oxide resources, and copper ions are unavoidable metal ions in the flotation pulp. The microflotation, contact angle, and adsorption experiments indicated that pretreatment with an appropriate concentration of copper ions could improve the malachite recovery, and the addition of excess copper ions reduced the hydrophobicity of the malachite surface. The results of zeta potential tests indicated that sodium sulfide and butyl xanthate were also adsorbed on the surface of malachite pretreated with copper ions. X-ray photoelectron spectroscopy(XPS) results indicated that —Cu—O and —Cu—OH bonds were formed on the surface of the samples. After pretreatment with an appropriate concentration of copper ions, the number of —OH groups on the mineral surface decreased, whereas the number of Cu—S groups on the mineral surface increased, which was conducive to the sulfidization of malachite. After adding a high concentration of copper ions, the —OH groups on the mineral surface increased, whereas the number of Cu—S groups decreased, which had an adverse effect on the sulfidization flotation of malachite. Time-of-flight secondary ion mass spectrometry showed that pretreatment with copper ions resulted in a thicker sulfidization layer on the mineral surface.

Utilization of DTAB as a collector for the reverse flotation separation of quartz from fluorapatite

Reverse flotation desilication is an indispensable step for obtaining high-grade fluorapatite. In this work, dodecyltrimethylammoni- um bromide (DTAB) is recommended as an efficient collector for the reverse flotation separation of quartz from fluorapatite. Its collectivity for quartz and selectivity for fluorapatite were also compared with figures corresponding to the conventional collector dodecylamine hydrochlor- ide (DAC) via microflotation experiments. The adsorption behaviors of DTAB and DAC on minerals were systematically investigated with surface chemical analyses, such as contact angle determination, zeta potential detection, and adsorption density measurement. The results re- vealed that compared to DAC, DTAB displayed a similar and strong collectivity for quartz, and it showed a better selectivity (or worse col- lectivity) for fluorapatite, resulting in a high-efficiency separation of the two minerals. The surface chemical analysis results showed that the adsorption ability of DTAB on the quartz surface was as strong as that of DAC, whereas the adsorption amount of DTAB on the fluorapatite surface was much lower than that of DAC, which is associated with the flotation performance. During the floatation separation of the actual ore, 8wt% fluorapatite with a higher grade can be obtained using DTAB in contrast to DAC. Therefore, DTAB is a promising collector for the high-efficiency purification and sustainable utilization of valuable fluorapatite recourses.

Quantization of Action for Elementary Particles and the Principle of Least Action

The uncertainty principle is a fundamental principle of quantum mechanics, but its exact mathematical expression cannot obtain correct results when used to solve theoretical problems such as the energy levels of hydrogen atoms, one-dimensional deep potential wells, one-dimensional harmonic oscillators, and double-slit experiments. Even after approximate treatment, the results obtained are not completely consistent with those obtained by solving Schrödinger’s equation. This indicates that further research on the uncertainty principle is necessary. Therefore, using the de Broglie matter wave hypothesis, we quantize the action of an elementary particle in natural coordinates and obtain the quantization condition and a new deterministic relation. Using this quantization condition, we obtain the energy level formulas of an elementary particle in different conditions in a classical way that is completely consistent with the results obtained by solving Schrödinger’s equation. A new physical interpretation is given for the particle eigenfunction independence of probability for an elementary particle: an elementary particle is in a particle state at the space-time point where the action is quantized, and in a wave state in the rest of the space-time region. The space-time points of particle nature and the wave regions of particle motion constitute the continuous trajectory of particle motion. When an elementary particle is in a particle state, it is localized, whereas in the wave state region, it is nonlocalized.