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 impr...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 i展开更多
The particle-size distribution of adsorbents usually plays an important role on the adsorption performance. In this study, population balance equation(PBE) is utilized in the simulation of an adsorption process to mod...The particle-size distribution of adsorbents usually plays an important role on the adsorption performance. In this study, population balance equation(PBE) is utilized in the simulation of an adsorption process to model the time-dependent adsorption amount distribution on adsorbent particles of a certain size distribution. Different adsorption kinetics model can be used to build the adsorption rate function in PBE according to specific adsorption processes. Two adsorption processes, including formaldehyde on activated carbon and CO_(2)/N_(2)/CH_(4) mixture on 4A zeolite are simulated as case studies, and the effect of particle-size distribution of adsorbent is analyzed. The simulation results proved that the influence of particle-size distribution is significant. The proposed model can help consider the influence of particlesize distribution of adsorbents on adsorption processes to improve the prediction accuracy of the performance of adsorbents.展开更多
Different mathematical methods, including linearization, differential, integration and nonlinear least squares approximation (Newton-Marquardt method), were used to fit different kinetic equations, such as zero-order,...Different mathematical methods, including linearization, differential, integration and nonlinear least squares approximation (Newton-Marquardt method), were used to fit different kinetic equations, such as zero-order, first-order (i. e, membrane diffusion), second-order, parabolic-diffusion, Elovich, two-constant equations, to the experimental data of Pb2+ and Cu2+ adsorption on variable charge soils and kaolinite. Assuming each M2+ occupied two adsorption sites, two more equations, the so-called surface second-order equation and third-order equation were derived and compared with the above equations according to the fitting results, which showed that the second-order equation and surface second-order equation, being one equation in different expressions under some conditions, were better than the other equations in describing the Pb2+ and Cu2+ adsorption kinetics, and the latter was the best.展开更多
Inverse gas chromatography at infinite dilution is a powerful technique that can be advantageously used to characterize the surface physicochemical properties of solid substrates as oxides and polymers in both forms o...Inverse gas chromatography at infinite dilution is a powerful technique that can be advantageously used to characterize the surface physicochemical properties of solid substrates as oxides and polymers in both forms of powder or fibres. In the case of polymer, this technique can be used to determine the second order transition phenomena temperatures. This paper was devoted to the determination of the glass transition temperature of polylactide polymer. The dispersive component of the surface energy ?of polylactides was determined by inverse gas chromatography at infinite dilution. Various theoretical models were used to deduce the dispersive component of the surface energy of the solid substrates. These models are based on the calculation of the molecular areas of adsorbed molecules on the polymer surface: geometrical model, cylindrical molecular model, liquid density model, BET method, Kiselev results and the two-dimensional Van der Waals and Redlich-Kwong equations. The curves relative to the variation of as a function of the temperature showed a specific graph with a maximum value of ?at a certain particular temperature characteristic to the investigated polylactide polymer. In fact, the maxima of ?indicated the presence of glass transition temperature Tg of polylactide whatever the molecular model used. This study showed a glass transition temperature equal to 64°C confirming that obtained by other studies.展开更多
This study investigates the heat and mass transfer mechanism of a marine engifie exhaust-powered adsorption refrigerating system by using irreversible thermodynamics. The equations of entropy-production rate and the l...This study investigates the heat and mass transfer mechanism of a marine engifie exhaust-powered adsorption refrigerating system by using irreversible thermodynamics. The equations of entropy-production rate and the linear phenomenological equations of thermodynamic flux and force are established. The conventional experimental facilities of unit tube are developed and the phenomenological coefficients are obtained by fitting the experimental data. It is concluded that the thermodynamic process in the adsorbent bed is determined by the coupling effect of the heat and mass transfer; furthermore, the mass transfer is determined by the heat transfer. Taking some measures to increase heat transfer can improve the performance of the adsorption refrigerating system. The conclusions presented in this paper may be of value to the engineering applications of the system.展开更多
基金supported by the Yunnan Science and Technology Leading Talent Project(No.202305AB350005)National Science Foundation for Young Scientists of China(No.51404118).
文摘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 i
基金Financial support from the National Natural Science Foundation of China (21706075)。
文摘The particle-size distribution of adsorbents usually plays an important role on the adsorption performance. In this study, population balance equation(PBE) is utilized in the simulation of an adsorption process to model the time-dependent adsorption amount distribution on adsorbent particles of a certain size distribution. Different adsorption kinetics model can be used to build the adsorption rate function in PBE according to specific adsorption processes. Two adsorption processes, including formaldehyde on activated carbon and CO_(2)/N_(2)/CH_(4) mixture on 4A zeolite are simulated as case studies, and the effect of particle-size distribution of adsorbent is analyzed. The simulation results proved that the influence of particle-size distribution is significant. The proposed model can help consider the influence of particlesize distribution of adsorbents on adsorption processes to improve the prediction accuracy of the performance of adsorbents.
基金Project supported by the N ational Natural Science Foundation of China.
文摘Different mathematical methods, including linearization, differential, integration and nonlinear least squares approximation (Newton-Marquardt method), were used to fit different kinetic equations, such as zero-order, first-order (i. e, membrane diffusion), second-order, parabolic-diffusion, Elovich, two-constant equations, to the experimental data of Pb2+ and Cu2+ adsorption on variable charge soils and kaolinite. Assuming each M2+ occupied two adsorption sites, two more equations, the so-called surface second-order equation and third-order equation were derived and compared with the above equations according to the fitting results, which showed that the second-order equation and surface second-order equation, being one equation in different expressions under some conditions, were better than the other equations in describing the Pb2+ and Cu2+ adsorption kinetics, and the latter was the best.
文摘Inverse gas chromatography at infinite dilution is a powerful technique that can be advantageously used to characterize the surface physicochemical properties of solid substrates as oxides and polymers in both forms of powder or fibres. In the case of polymer, this technique can be used to determine the second order transition phenomena temperatures. This paper was devoted to the determination of the glass transition temperature of polylactide polymer. The dispersive component of the surface energy ?of polylactides was determined by inverse gas chromatography at infinite dilution. Various theoretical models were used to deduce the dispersive component of the surface energy of the solid substrates. These models are based on the calculation of the molecular areas of adsorbed molecules on the polymer surface: geometrical model, cylindrical molecular model, liquid density model, BET method, Kiselev results and the two-dimensional Van der Waals and Redlich-Kwong equations. The curves relative to the variation of as a function of the temperature showed a specific graph with a maximum value of ?at a certain particular temperature characteristic to the investigated polylactide polymer. In fact, the maxima of ?indicated the presence of glass transition temperature Tg of polylactide whatever the molecular model used. This study showed a glass transition temperature equal to 64°C confirming that obtained by other studies.
文摘This study investigates the heat and mass transfer mechanism of a marine engifie exhaust-powered adsorption refrigerating system by using irreversible thermodynamics. The equations of entropy-production rate and the linear phenomenological equations of thermodynamic flux and force are established. The conventional experimental facilities of unit tube are developed and the phenomenological coefficients are obtained by fitting the experimental data. It is concluded that the thermodynamic process in the adsorbent bed is determined by the coupling effect of the heat and mass transfer; furthermore, the mass transfer is determined by the heat transfer. Taking some measures to increase heat transfer can improve the performance of the adsorption refrigerating system. The conclusions presented in this paper may be of value to the engineering applications of the system.
