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.

Confirmation of the First Law of Thermodynamics in Theory and Extended Bernoulli Equation

The internal energy change of ideal gas does not depend on the volume and pressure. The internal energy change of real gas has not any relation with the volume and pressure, which had been proved. If the internal energy change had not any relation with the volume and pressure, we could confirm the first law of thermodynamics in theory. Simultaneously, the internal energy change is the state function that shall be able to be proved in theory. If the internal energy change depended on the volume and pressure, we could not prove that the internal energy change is the state function and the chemical thermodynamics theory is right. The extended or modified Bernoulli equation can be derived from the energy conservation law, and the internal energy change, heat, and friction are all considered in the derivation procedure. The extended Bernoulli equation could be applied to the flying aircraft and mechanical motion on the gravitational field, for instance, the rocket and airplane and so on. This paper also revises some wrong ideas, viewpoints, or concepts about the thermodynamics theory and Bernoulli equation.

Numerical computation algorithm of explosion equations and thermodynamics parameters of mine explosives

A new numerical algorithm is presented to simulate the explosion reaction process of mine explosives based on the equation of state, the equation of mass conservation and thermodynamics balance equation of explosion products. With the affection of reversible reaction of explosion products to explosion reaction equations and thermodynamics parameters considered, the computer program has been developed. The computation values show that computer simulation results are identical with the testing ones.

A thermodynamic Approach to Rate Equations in Continuum Physics

纸探讨率方程的明确的表达，经由客观时间衍生物，在连续统物理以内。客观性的概念被考察，区别与其意思相对 Galilee 的框架被限制为平衡方程的不变性的材料框架不在乎被做。客观时间衍生物被定义离开在欧几里德几何学的框架的集合以内不变的适当的地的张肌特性。率方程被要求包含客观时间衍生物并且与热力学的第二条法律一致。这里，客观时间衍生物的一般结构被建立，物理文学的已知的衍生物被显示是特别盒子。到改正想法，下次，一个率方程与高顺序的坡度经由 Maxwell-Cattaneo 方程的归纳为热传导的模型被考虑作为在 Guyer-Krumhansl 方程。热力学的限制被调查，热流动的选择衍生物，期望的效果在压力张肌上被导出。

PREDICTION ON THERMODYNAMIC PROPERTIES OF TERNARY LIQUID ALLOYS FROM WILSON EQUATION

An attempt was made on applying the Wilson equation to predict the thermodynamic proper- ties of ternary liquid alloys.The activity of each component in ternary liquid alloys was found to be conveniently calculated from the equation with the related binary bimolecular interaction parameters.The calculated values are in fair agreement with experimental data,and are veri- fied to be reliable by the criterion of classical thermodynamics.

PREDICTION OF THERMODYNAMIC PROPERTIES OFTHE FeO-CaO-SiO_2 MELTS FROM WILSON EQUATION

An attempt was made to use the Wilson equation to predict the thermodynamic properties of the FeO-CaO-SiO2 melts at 1673 and 1873K. The activities of component FeO in the ternary melts at a given temperature were found to be conveniently calculated from the equation only with related binary parameters at different temperatures.The predicted values are in agreement with the ternary experimental data.

Calculating detonation performance of explosives by VLWR thermodynamics code introduced with universal VINET equation of state

Thermodynamic calculation is the theoretical basis for the study of initiation and detonation,as well as the prerequisite for forecasting the detonation performance of unknown explosives.Based on the VLWR(Virial-Wu)thermodynamic code,this paper introduced the universal solid equation of state(EOS)VINET.In order to truly reflect the compressibility of nanocarbon under the extremely high-temperature and high-pressure environment in detonation,an SVM(support vector machine)was utilized to optimize the input parameters of carbon.The detonation performance of several explosives with different densities was calculated by the optimized universal EOS,and the results show that the thermodynamic code coupled with the universal solid EOS VINET can predict the detonation performance parameters of explosives well.To investigate the application of the thermodynamic code with the improved VINET EOS in the working capacity of explosives,the interrelationship between pressure P-particle velocity u and pressure P-volume V were computed for the detonation products of TNT and HMX-based PBX(HMX:binder:insensitive agent=95:4.3:0.7)in the CJ isentropic state.A universal curve proposed by Cooper was used to compared the computed isentropic state,where the ratio of pressure to CJ state were plotted against the ratio of velocity to CJ state.The parameters of the JWL(Jones-Wilkins-Lee)EOS for detonation products were obtained by fitting the P-V curve.The cylinder tests of TNT and HMX-based PBX were numerically simulated using the LS-DYNA,it is verified that,within a certain range,the improved algorithm has superiority in describing the working capacity of explosives.

MOLECULAR THERMODYNAMIC MODEL FOR FLUIDS CONTAINING ASSOCIATED MOLECULES

With the statistical mechanical theory for square-well-chain fluids as the basic princi-ples,a molecular thermodynamic model including expressions for the Helmholtz function and thecompressibility factor for associated square-well-chain fluids has been developed.Employment ofthe shield-sticky concept enables the corporation of association bonds between in the model.Good agreement with computer-simulation results for dimer-linear quadrimer systems is obtained.Satisfactory correlation for vapor pressures and saturated liquid volumes of pure substances con-taining associated molecules(such as carboxylic acids,alcohols,amines,water,etc.)with four mo-lecular parameters indicates the applicability of the model.

GENERAL EXPRESSIONS OF CONSTITUTIVE EQUATIONS FOR ISOTROPIC ELASTIC DAMAGED MATERIALS

The general expressions of constitutive equations for isotropic elastic damaged materials were derived directly from the basic law of irreversible thermodynamics. The limitations of the classical damage constitutive equation based on the well-known strain equivalence hypothesis were overcome. The relationships between the two elastic isotropic damage models (i.e. single and double scalar damage models) were revealed. When a single scalar damage variable defined according to the microscopic geometry of a damaged material is used to describle the isotropic damage state, the constitutive equations contain two 'damage effect functions', which describe the different influences of damage on the two independent elastic, constants. The classical damage constitutive equation based on the strain equivalence hypothesis is only the first-order approximation of the general expression. It may be unduly simplified and may fail to describe satisfactorily the damage phenomena of practical materials.

Quantum Physics Can Be Understood in Terms of Classical Thermodynamics

Quantum physics can be understood in terms of classical thermodynamics, which is already considered to be a complete field. However, inconsistencies in classical thermodynamics have been discovered in the area of solid-oxide fuel cells (SOFCs). The use of samarium-doped ceria (SDC) electrolytes in SOFCs lowers the open-circuit voltage (OCV) below the Nernst voltage (Vth). The low OCV is calculated with Wagner’s equation, included in the Nernst-Planck equation, which is based on the first and second thermodynamic laws. Experimental and theoretical limitations of Wagner’s equation have been discovered. Considering the separation of the Boltzmann distribution and Maxwell’s Demon, only carrier species having sufficient energy to overcome the activation energy can contribute to current conduction, as determined by incorporating different constants in the definitions of the chemical and electrical potentials. This means that an additional thermodynamic law is needed. Furthermore, quantum physics can be explained by the additional thermodynamic law.

Thermodynamic Consistency and Thermomechanical Dynamics (TMD) for Nonequilibrium Irreversible Mechanism of Heat Engines

The irreversible mechanism of heat engines is studied in terms of thermodynamic consistency and thermomechanical dynamics (TMD) which is proposed for a method to study nonequilibrium irreversible thermodynamic systems. As an example, a water drinking bird (DB) known as one of the heat engines is specifically examined. The DB system suffices a rigorous experimental device for the theory of nonequilibrium irreversible thermodynamics. The DB nonlinear equation of motion proves explicitly that nonlinear differential equations with time-dependent coefficients must be classified as independent equations different from those of constant coefficients. The solutions of nonlinear differential equations with time-dependent coefficients can express emergent phenomena: nonequilibrium irreversible states. The couplings among mechanics, thermodynamics and time-evolution to nonequilibrium irreversible state are defined when the internal energy, thermodynamic work, temperature and entropy are integrated as a spontaneous thermodynamic process in the DB system. The physical meanings of the time-dependent entropy, T(t)dS(t), , internal energy, dƐ(t), and thermodynamic work, dW(t), are defined by the progress of time-dependent Gibbs relation to thermodynamic equilibrium. The thermomechanical dynamics (TMD) approach constitutes a method for the nonequilibrium irreversible thermodynamics and transport processes.

Mathematical Model to Elaborate the Table of Thermodynamic Properties

Purpose: The aim of this scientific contribution is to show the potential that integral calculus has offered to the analysis of thermodynamic processes. Method: Application of Integral Calculus. In this context, the document covers the theoretical principles of integral calculus, such as Theoretical framework and background, Geometric interpretation of the primitive, Primitive existence theorem. Results: Integral calculus and generalized thermodynamic models, and their applications in various thermodynamic analysis contacts such as the Generalized Enthalpy Model, the Generalized Entropy Model, and the Generalized Model applied to gas mixtures and the General Model to elaborate the properties table. Conclusion: The mathematical analysis developed in this document is very useful in engineering and applied physics environments, a fact that supports its common pedagogical practice in university institutions.

Bell’s Non-Locality Theorem Can Be Understood in Terms of Classical Thermodynamics

Bell’s non-locality theorem can be understood in terms of classical thermodynamics, which is already considered to be a complete field. However, inconsistencies in classical thermodynamics have been discovered in the area of solid-oxide fuel cells (SOFCs). The use of samarium-doped ceria electrolytes in SOFCs lowers the open-circuit voltage (OCV) to less than the Nernst voltage. This low OCV has been explained by Wagner’s equation, which is based on chemical equilibrium theory. However, Wagner’s equation is insufficient to explain the low OCV, which should be explained by fluctuation and dissipation theorems. Considering the separation of the Boltzmann distribution and Maxwell’s demon, only carrier species with sufficient energy to overcome the activation energy can contribute to current conduction, as determined by incorporating different constants into the definitions of the chemical and electrical potentials. Then, an energy loss equal to the activation energy will occur because of the interactions between ions and electrons. This energy loss means that an additional thermodynamic law based on an advanced model of Maxwell’s demon is needed. In this report, the zero-point energy can be explained by this additional ther-modynamic law, as can Bell’s non-locality theorem.

Thermodynamic Fit Functions of the Two-Phase Fluid and Critical Exponents

Two-phase fluid properties such as entropy, internal energy, and heat capacity are given by thermodynamically defined fit functions. Each fit function is expressed as a temperature function in terms of a power series expansion about the critical point. The leading term with the critical exponent dominates the temperature variation between the critical and triple points. With β being introduced as the critical exponent for the difference between liquid and vapor densities, it is shown that the critical exponent of each fit function depends (if at all) on β. In particular, the critical exponent of the reciprocal heat capacity c﹣1 is α=1-2β and those of the entropy s and internal energy u are?2β, while that of the reciprocal isothermal compressibility?κ﹣1T is γ=1. It is thus found that in the case of the two-phase fluid the Rushbrooke equation conjectured α +?2β + γ=2 combines the scaling laws resulting from the two relations c=du/dT and?κT=dlnρ/dp. In the context with c, the second temperature derivatives of the chemical potential μ and vapor pressure p are investigated. As the critical point is approached, ﹣d2μ/dT2 diverges as c, while?d2p/dT2 converges to a finite limit. This is explicitly pointed out for the two-phase fluid, water (with β=0.3155). The positive and almost vanishing internal energy of the one-phase fluid at temperatures above and close to the critical point causes conditions for large long-wavelength density fluctuations, which are observed as critical opalescence. For negative values of the internal energy, i.e. the two-phase fluid below the critical point, there are only microscopic density fluctuations. Similar critical phenomena occur when cooling a dilute gas to its Bose-Einstein condensate.

Thermodynamic Performance Characteristics of a Brownian Microscopic Heat Engine Driven by Discrete and Periodic Temperature Field

A Brownian microscopic heat engine with a particle hopping on a one-dimensional lattice driven by adiscrete and periodic temperature field in a periodic sawtooth potential is investigated.In order to clarify the underlyingphysical pictures of the heat engine, the heat flow via the potential energy and the kinetic energy of the particles areconsidered simultaneously.Based on describing the jumps among the three states, the expressions of the efficiency andpower output of the heat engine are derived analytically.The general performance characteristic curves are plotted bynumerical calculation.It is found that the power output-efficiency curve is a loop-shaped one, which is similar to onefor a real irreversible heat engine.The influence of the ratio of the temperature of the hot and cold reservoirs and thesawtooth potential on the maximum efficiency and power output is analyzed for some given parameters.When the heatflows via the kinetic energy is neglected, the power output-efficiency curve is an open-shaped one, which is similar to onefor an endroeversible heat engine.

Statistical mechanics and artificial intelligence to model the thermodynamic properties of pure and mixture of ionic liquids

In this paper, the volumetric properties of pure and mixture of ionic liquids are predicted using the developed statistical mechanical equation of state in different temperatures, pressures and mole fractions. The temperature dependent parameters of the equation of state have been calculated using corresponding state correlation based on only the density at 298.15 K as scaling constants. The obtained mean of deviations of modified equation of state for density of all pure ionic liquids for 1662 data points was 0.25%. In addition, the performance of the artificial neural network(ANN) with principle component analysis(PCA) based on back propagation training with28 neurons in hidden layer for predicting of behavior of binary mixtures of ionic liquids was investigated. The AADs of a collection of 568 data points for all binary systems using the EOS and the ANN at various temperatures and mole fractions are 1.03% and 0.68%, respectively. Moreover, the excess molar volume of all binary mixtures is predicted using obtained densities of EOS and ANN, and the results show that these properties have good agreement with literature.

Enhancing asphaltene precipitation modeling by cubic-PR solid model using thermodynamic correlations and averaging techniques

Cubic equation-of-state solid models are one of the most widely used models to predict asphaltene precipitation behavior.Thermodynamic parameters are needed to model precipitation under different pressures and temperatures and are usually obtained through tuning with multi asphaltene onset experiments.For the purpose of enhancing the cubic Peng–Robinson solid model and reducing its dependency on asphaltene experiments,this paper tests the use of aromatics and waxes correlations to obtain these thermodynamic parameters.In addition,weighted averages between both correlations are introduced.The averaging is based on reported saturates,aromatics,resins,asphaltene(SARA)fractions,and wax content.All the methods are tested on four oil samples,with previously published data,covering precipitation and onset experiments.The proposed wax-asphaltene average showed the best match with experimental data,followed by a SARA-weighted average.This new addition enhances the model predictability and agrees with the general molecular structure of asphaltene molecules.

New insight into prediction of phase behavior of natural gas hydrate by different cubic equations of state coupled with various mixing rules

Progress in hydrate thermodynamic study necessitates robust and fast models to be incorporated in reservoir simulation softwares. However, numerous models presented in the literature makes selection of the best,proper predictive model a cumbersome task. It is of industrial interest to make use of cubic equations of state(EOS) for modeling hydrate equilibria. In this regard, this study focuses on evaluation of three common EOSs including Peng–Robinson, Soave–Redlich–Kwong and Valderrama–Patel–Teja coupled with van der Waals and Platteeuw theory to predict hydrate P–T equilibrium of a real natural gas sample. Each EOS was accompanied with three mixing rules, including van der Waals(vd W),Avlonitis non-density dependent(ANDD) and general nonquadratic(GNQ). The prediction of cubic EOSs was in sufficient agreement with experimental data and with overall AARD% of less than unity. In addition, PR plus ANDD proved to be the most accurate model in this study for prediction of hydrate equilibria with AARD% of 0.166.It was observed that the accuracy of cubic EOSs studied in this paper depends on mixing rule coupled with them,especially at high-pressure conditions. Lastly, the present study does not include any adjustable parameter to be correlated with hydrate phase equilibrium data.

Thermodynamical quantities around a RNAdS black hole

The entropy density, energy density, pressure and equation of state around the RNAdS black hole are calculated in the WKB approximation on the Teukolsky-type master equation. The appearance of spin-dependent terms is demonstrated. The existence of these terms shows that the black hole radiation is not exactly thermal radiation and the black hole entropy is not strictly proportional to the area of the event horizon.

A Phenomenological Gradient Approach to Generalized Constitutive Equations for Isotropic Fluids

An extension of the linear irreversible thermodynamics is proposed through the inclusion of the first gradients of velocity and of the classical local state parameters as additional independent variables in the fundamental energy state equation of a fluid system. We show that consistency of this hypothesis with the energy balance equation leads to generalized nonlinear constitutive equations, which we discuss in terms of an isotropic non-Newtonian viscous fluid.