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.

Simulation of Gas Oil Hydrotreater Heat Exchange Tube and Crystallization Prediction of NH_(4)Cl by Thermodynamic Equilibrium

The hydrotreater system heat exchanger is one of the main pieces of heat exchange equipment in petrochemical enterprises.In recent years,oil resources have shown a deterioration trend of high sulfur and high acid content,with corrosion risk being prominent in oil processing.Taking the multi-medium flow corrosion risk of the hydrotreater heat exchanger pipeline in a petrochemical enterprise as the research object,based on the parameter characteristics of corrosive NH_(3) and HCl media under a high-temperature and high-pressure environment,the ammonium salt crystallization and deposition mechanism under multi-phase flow is revealed.The thermodynamic equilibrium curve is modified based on the thermodynamic principle and fugacity coefficient variation,and the prediction model of ammonium chloride crystallization in hydrotreater heat exchanger under high temperature and high pressure is constructed according to the modification.This study uses the mixture model,the flow-thermal coupling method,and the discrete phase model method to carry out the numerical simulation of multiphase flow and the numerical prediction of particle distribution characteristics in the heat exchanger pipeline of the hydrotreater heat exchange equipment,so as to realize the quantitative prediction of the particle crystallization deposition distribution in the pipeline.The results show that with the decrease of temperature,the crystallization occurs first on both sides of the center of the tube bundle,and more crystallization occurs in the lower half of the U-shaped tube,which may seriously lead to problems such as pipe blockage and under-deposit corrosion.

Solubility measurement,correlation and thermodynamic properties of 2,3,4-trichloro-1,5-dinitrobenzene in fifteen mono-solvents at temperatures from 278.15 to 323.15 K

The solubility of 2,3,4-trichloro-1,5-dinitrobenzene(TCDNB) was measured by a laser dynamic method over the temperature range from 278.15 K to 323.15 K under 0.1 MPa in fifteen mono-solvents(methanol,ethanol,isopropanol,n-butanol,toluene,dichloromethane,chloroform,tetrachloromethane,1,2-dichloroethane,acetone,ethyl acetate,acetonitrile,N-methylpyrrolidone(NMP),N,Ndimethylformamide dimethyl sulfoxide(DMF),dimethyl sulfoxide(DMSO).The solubility of TCDNB could be increased with increasing temperature in fifteen mono-solvents.TCDNB solubility is in the following order at 298.15 K:NMP>DMF>DMSO>toluene>acetone>ethyl acetate>dichloromethane>1,2-dich loroethane>chloroform>acetonitrile>tetrachloromethane>methanol>ethanol>n-butanol>isopropanol.The KAT-LSER model was used to investigate the solvent effect,which revealed that the hydrogen bond acidity of solvents has a greater effect on TCDNB solubility.The van't Hoff model,the modified Apelblat model,theλh model,and the non-random two liquid(NRTL)model were used to correlate the solubility of TCDNB.The calculated solubility data agreed well with the experimental data,and the modified Apelblat model fit best.Furthermore,the van't Hoff and Gibbs equations were also used to calculate the dissolution thermodynamic properties of TCDNB in various solvents.TCDNB dissolution could be an enthalpy-driven,non-spontaneous,and endothermic process in fifteen mono-solvents.The determination and fitting solubility of TCDNB,as well as the calculation of its thermodynamic properties,would be critical in the purification and crystallization of its preparation process research.

Crystallization thermodynamics of 2,4(5)-dinitroimidazole in binary solvents

2,4(5)-Dinitroimidazole(2,4(5)-DNI)is an important organic intermediate,and itself can also be used for energetic material.In this work,the solubility of 2,4(5)-DNI in(methanol+water,acetonitrile+water,acetone+water)binary solvents were measured by using a dynamic test method from 278.15 K to 323.15 K under 101.1 k Pa.The Jouyban–Acree model,van't Hoff–Jouyban–Acree model,Apelblat–Jouyb an–Acree model,Ma model,and Sun model were used to correlate the experimental data.The values of relative average deviation(RAD)and root-mean-square deviation(RMSD)were very small,indicating that the error between the experimental value and the correlated value was very small.The thermodynamic parameters such as dissolution enthalpy,dissolution entropy and Gibbs energy were calculated based on solubility data.High-purity of 2,4(5)-DNI was efficiently obtained by using cooling and dilution crystallization method.

Thermodynamic and Equilibrium Composition Analysis of Using Iron Oxide as an Oxygen Carrier in Nonflame Combustion Technology

Nonflame combustion technology （NFCT） is a harmonious energy utilization technology. There are not environmental-unfriendly gases such as NOx, CO2 discharged in the whole combustion process. Combustion processes realizes zero emission through this technology. Fe2O3 is involved as oxygen carrier, is examined thermodynamically, and the thermodynamic data of the redox reactions are calculated. Using the criteria of minimizing the Gibbs free energy, the equilibrium composition was investigated. The equilibrium analysis shows that producing complete oxidized resultants must have high molar ratio of Fe2O3/CH4. If quantity of Fe2O3 is not sufficient, more partial oxidized products such as CO, H2, even C will be produced.

GURTIN-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF A NON-LOCAL THERMAL EQUILIBRIUM SATURATED POROUS MEDIUM

Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fuid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de- formation of the solid phase, small velocity of the fuid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fuid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dy- namic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fuid-saturated elastic porous media, which have been discussed previously.

Analysis of equilibrium, kinetic, and thermodynamic parameters for biosorption of fluoride from water onto coconut(Cocos nucifera Linn.)root developed adsorbent

Drinking water with higher fluoride levels results in serious irremediable health problems that have attained a startle all over the world.Researches focused towards deflouridation through the application of biosorbents prepared from various plants are finding greater scope and significance.Present research is done on Cocos nucifera Linn.(coconut tree) one of the very commonly available plants throughout Kerala and around the globe.An adsorbent developed from the root portion of C.nucifera Linn.is used in the present study.Equilibrium study revealed that the fluoride uptake capacity is quite significant and linearly increases with initial adsorbate concentration.The adsorption data is analyzed for Langmuir, Freundlich, Temkin, and Dubinin–Radushkevich isotherm models at varying initial adsorbate concentrations(2–25 mg·L^(-1)).It is found that the adsorption of fluoride onto C.nucifera Linn.root adsorbent follows Langmuir isotherm.Langmuir isotherm constants "a" and "b" obtained are 2.037 mg·g^(-1) and 0.823 L·mg^(-1) at an adsorbent dose of 8 g·L^(-1) and temperature(26 ± 1) ℃.The mean free sorption energy, E obtained, is 9.13 kJ ·mol^(-1) which points out that the adsorption of fluoride onto C.nucifera Linn.root adsorbent is by chemisorption mechanism.The kinetic study also supports chemisorption with adsorption data fitting well with a pseudo-second-order kinetic model with an estimated rate constant K_2 of 0.2935 g·mg^(-1) min at an equilibrium contact time of 90 min.The thermodynamic study indicated the spontaneous and endothermic nature(ΔH =12.728 kJ·mol^(-1)) of fluoride adsorption onto the C.nucifera Linn.root adsorbent.Scanning Electron Microscopy(SEM), BET, FTIR, and EDX methods were used to analyze the surface morphology of adsorbent before and after fluoride adsorption process.Experiments on deflouridation using C.nucifera Linn.root adsorbent application on fluoride contaminated ground water samples from fields showed encouraging results.

THERMODYNAMIC EQUILIBRIUM OF Sb-Cl-H_2O SYSTEM

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Experimental thermodynamic research on equilibrium between silicon alloy and SiO_2-CaO-Al_2O_3 melt

The equilibria of Al and Ca between silicon alloy and the SiO 2 Al 2O 3 CaO ternary slags were investigated using graphite crucible at 1?550?℃. With increasing Al 2O 3 and CaO content in the slags, the Al and Ca content increase respectively. The variation of the impurities are also affected by the silica content in slag which provides the oxidant during the oxidation refining process. The distributions of the impurities Al and Ca in silicon were given in terms of isoconcentration curves for Al and Ca in the ternary slags of SiO 2 Al 2O 3 CaO. The present experimental work provided available data to analyze the action of Al and Ca during oxidation refining process for silicon alloy.

Thermodynamic Equilibrium Diagrams of Sulphur-Chromium System

The chemical and electrochemical equilibria in the presence of gaseous phase were investigated. Many substances, which consisted of sulphur and chromium, were considered. Various thermodynamic equilibria were calculated in different pressures. Calculation results were shown as log p-1/T and E-T diagrams. These diagrams may be used to study the corrosion of chromium in sulphur-containing circumstances. The diagrams are also used to thermodynamically determine the existence area of various substances and so on.

Thermodynamic equilibrium calculation on preparation of copper oxalate precursor powder

According to the principles of simultaneous equilibrium and mass balance,a series of thermodynamic equilibrium equations of Cu2+-C2O42--NH3-NH4+-H2O system at ambient temperature were deduced theoretically and the logarithm concentration versus pH value(lg[Cu 2+ ]T—pH)diagrams at different solution compositions were drawn.The results show that when pH is below 5.0,copper ion reacts with C2O42-directly and the morphology of copper precursor powder is of pie-shape;when pH is above 5.0,copper ion coordinates with ammonia,and the precipitation proceeds slowly accompanying with the release of copper ions from the multi-coordinated2+ 3Cu(NH) n (n=1,2,···,5)and the morphologies of copper precursor powder are respectively of rod aggregation shape(when 5.0<pH<8.0)and of rod-shape(when pH>8.0).Some experiments were performed to confirm the relation between the total concentration of copper ion and pH value.It is shown that the thermodynamic mathematical model is correct and the calculated values are basically accurate.

Thermodynamic geometry of the RN-Ad S black hole and non-local observables

This paper studies the thermodynamic geometry of the Reissner–Nordstr?m-anti-de Sitter(RN-AdS)black hole via detection of the non-local observables in the dual field theory,including the entanglement entropy and equal-time two-point correlation function.With the dimensional analysis,we construct the principle of corresponding states of black hole thermodynamics.As a result,our findings can be applied to black holes with different Ad S backgrounds.In this sense,the probe of the thermodynamic geometry of the RN-Ad S black hole though the non-local observables in dual field theory has been confirmed numerically.

Experimental measurement and thermodynamic modeling of binary and ternary solid–liquid phase equilibrium for the systems formed by L-arabinose,D-xylose and water

Solid–liquid phase equilibrium data for binary(L-arabinose–water) and(D-xylose–water) systems at temperatures from(269.85–298.05) K and ternary(L-arabinose–D-xylose–water) system at temperatures of 273.85 K,278.85 K and 284.45 K were measured at atmospheric pressure.The ternary phase diagrams of the systems were constructed on the base of the measured solubility.Two pure solid phases were formed at given temperatures,including pure L-arabinose and pure D-xylose,which were con firmed and determined by the method of Schreinemakers' wet residue.At the same temperature,the crystallization region of L-arabinose was larger than D-xylose's.The acquired solubility data were then correlated using the NRTL model,Wilson model and Xu model.The calculated solubility with the three models agreed well with the experimental values.

The Non—local Thermodynamical Equilibrium Effects on Opacity

Based on the detailed configuration accounting (DCA) model, a method is developed to include the resonant photoionization and the excitation-autoionization in the non-local thermodynamical equilibrium (NLTE) average atom(AA) model. Using this new model, the mean charge states and the opacity are calculated for NLTE high-Z plasmas and compared with other results. The agreement w ith AA model is poor at low electron density. The present results agree well with those of DCA model within 10%. The calculations show that the NLTE effects on opacity are strong.

Thermodynamic equilibrium of bismuth hydrometallurgyin chloride and nitrate solutions

Simultaneous equilibrium was applied to the thermodynamic analysis and calculation of Bi（Ⅲ）-X（Cl-, NO-3）-H2O systems, based on which the diagrams of the logarithm of equilibrium concentration of Bi（Ⅲ） of series precipitation vs pH value of these two systems at 25 ℃ were obtained, and the pH ranges of the stable zones of various precipitations were analyzed and determined. In Bi（Ⅲ）-Cl--H2O system, the variations of c0(Bi3+) and （c0（Cl-）） have little effect on the equilibria of Bi（OH）3-solution and BiOOH-solution, but has great influence on the （equilibrium） of BiOCl-solution. However, in Bi（Ⅲ）-NO-3-H2O system, the variations of c0(Bi3+) and c0（NO-3） have little effect on equilibria of Bi（OH）3-solution, BiOOH-solution and Bi2O3-solution. When pH value is high, Bi2O3 is the thermodynamic stable phase, its stable zone is the widest, almost including the stable zones of BiOCl or （BiONO3,） （Bi（OH）3） and BiOOH. Bi（OH）3 cannot be obtained from Bi（Ⅲ）-Cl--H2O system, even strong alkaline media. Bi2O3 can be obtained from the solution directly, and highly pure BiOCl or BiONO3 can also be obtained through strictly controlling pH value.

Contribution of biodiversity to ecosystem functioning:a non-equilibrium thermodynamic perspective

Ecosystem stays far from thermodynamic equilibrium. Through the interactions among biotic and abiotic components, and encompassing physical environments, ecosystem forms a dissipative struc- ture that allows it to dissipate energy continuously and thereby remains functional over time. Biotic regulation of energy and material fluxes in and out of the ecosystem allows it to maintain a homeostatic state which corresponds to a self-organized state emerged in a non-equilibrium thermodynamic system. While the associated self-organizational processes approach to homeostatic state, entropy （a measure of irre- versibility） degrades and dissipation of energy increases. We propose here that at a homeostatic state of ecosystem, biodiversity which includes both phenotypic and functional diversity, attains optimal values. As long as biodiversity remains within its optimal range, the corresponding homeostatic state is maintained. However, while embedded environmental conditions fluctuate along the gradient of accelerating changes, phenotypic diversity and functional diversity contribute inversely to the associated self-organizing proc- esses. Furthermore, an increase or decrease in biodiversity outside of its optimal range makes the eco- system vulnerable to transition into a different state.

Thermodynamic equilibrium diagram of the chlorine-titanium system

The chemical and electrochemical equilibria of the chlorine-titanium system in the presence of gaseous phase were investigated. Many species, which consisted of chlorine and titanium, were considered. Various thermodynamic equilibria were calculated in the different pressures at different temperatures. The calculated results were shown as log p-1/Tand E-T diagrams. These diagrams may be used as important tools for corrosion study and titanium production. The diagrams are also used to thermodynamically determine the existence areas of various species and so on.

Adsorption of Fe^(3+) Ions from Aqueous Solution by Natural and Synthetic Apatites: Kinetic, Equilibrium and Thermodynamic Study

In this study, the adsorption kinetics, equilibrium and thermodynamics of Fe3+ ions on natural (NAP) and synthetic (HAP) apaties were examined. The adsorption efficiency of Fe3+ onto the NAP and HAP was increased with increasing temperature. The kinetics of adsorption of Fe3+ ions was discussed using three kinetic models, the pseudo-first-order, the pseudo-second-order and the intra-particle diffusion model. The experimental data fitted very well the pseudo-second-order kinetic model. The initial sorption rate and the activation energy were also calculated. The activation energy of the sorption was calculated as 37.15 and 49.84 kJ·mol 1 for NAP and HAP, respectively. Experimental results were also analysed by the Langmuir, Freundlich and Dubinin–Redushkevich (D–R) isotherm equations at different temperatures. RL separation factor for Langmuir and the n value for Freundlich isotherm show that Fe3+ ions are favorably adsorbed by NAP and HAP. Various thermodynamic parameters such as enthalpy (ΔH), Gibbs free energy (ΔG) and entropy (ΔS) changes were computed and the results showed that the adsorption of Fe3+ ions onto NAP and HAP were spontaneous and endothermic in nature.

Coherent Application of a Contact Structure to Formulate Classical Non-Equilibrium Thermodynamics

This contribution presents an outline of a new mathematical formulation for Classical Non-Equilibrium Thermodynamics (CNET) based on a contact structure in differential geometry. First a non-equilibrium state space is introduced as the third key element besides the first and second law of thermodynamics. This state space provides the mathematical structure to generalize the Gibbs fundamental relation to non-equilibrium thermodynamics. A unique formulation for the second law of thermodynamics is postulated and it showed how the complying concept for non-equilibrium entropy is retrieved. The foundation of this formulation is a physical quantity, which is in non-equilibrium thermodynamics nowhere equal to zero. This is another perspective compared to the inequality, which is used in most other formulations in the literature. Based on this mathematical framework, it is proven that the thermodynamic potential is defined by the Gibbs free energy. The set of conjugated coordinates in the mathematical structure for the Gibbs fundamental relation will be identified for single component, closed systems. Only in the final section of this contribution will the equilibrium constraint be introduced and applied to obtain some familiar formulations for classical (equilibrium) thermodynamics.

Thermophysical properties of pure gases and mixtures at temperatures of 300-30000K and atmospheric pressure:thermodynamic properties and solution of equilibrium compositions

The equilibrium compositions and thermodynamic properties(density,enthalpy,etc at constant pressure)of plasma of pure gases and mixtures under local thermodynamic nonequilibrium have been calculated in this paper.The homotopy Levenberg-Marquardt algorithm was proposed to accurately solve nonlinear equations with singular Jacobian matrices,and is constructed by the Saha equation and Guldberg-Waage equation combined with mass conservation,the electric neutrality principle and Dalton’s partial pressure law,to solve the problem of dependence on the initial value in the process of iteration calculation.In this research,the equations at a higher temperature were solved and used as the auxiliary equations,and the homotopy control parameters’sequence of the homotopy equations was selected by equal ratios.For auxiliary equations,the iterative initial value was obtained by assuming that there were only the highestvalence atomic cations and electrons at this temperature,and the plasma equilibrium composition distribution with the required accuracy was ultimately solved under the current conditions employing the Levenberg-Marquardt algorithm.The control parameter sequence was arranged according to the geometric sequence and the homotopy step was gradually shortened to ensure continuity of the homotopy process.Finally,the equilibrium composition and thermodynamic properties of pure N_(2),Mg(30%)-CO_(2)(70%)and Mg(40%)-CO(50%)-N_(2)(10%)mixture plasma at atmospheric pressure were calculated and the calculation process of some specified temperatures was shown and analyzed.The calculation accuracy of equilibrium composition is higher than other findings in the literature.The results for the thermodynamic properties are in good agreement with data reported by the literature.