Mixing rules in cubic equations of state applied to refrigerant mixtures

Two equations of state and four mixing rules are applied to the calculation of the bubble point pressure of several refrigerant mixtures. An equation of state proposed by one of the authors, known as the PTV equation, and a modified Soave-Redlich-Kwong equation of state, known as Predictive Soave-Redlich-Kwong (PSRK), have been used. The mixing rules considered in the study include the classic van der Waals mixing rule with one and with two parameters for the PTV equation, and a model that includes the excess Gibbs free energy for the PSRK equation. Eighteen data sets from the literature for five binary refrigerant mixtures containing R134A (CH₂FCF₃) were considered for analysis. A special program was implemented for these calculations in which the fundamental equation for phase equilibria, the equality of fugacity of each component in all phases, was applied. Correlations for the interaction parameters as functions of the acentric factor are proposed. We present conclusions about usefulness of the different models and a recommendation for the best equation of state + mixing rule combination for correlating vapor-liquid equilibrium in the refrigerant mixtures studied.     

Correlation and prediction of interface tension for fluid mixtures: An approach based on cubic equations of state with the wong-sandler mixing rule

Concentration profiles, interface thickness, and interface tensions have been calculated for mixtures applying the gradient theory to the Peng-Robinson equation of state. The approach is based on an accurate local fit of vapor-liquid equilibrium (VLE) data, and, for this purpose, the flexibility of the original Wong-Sandler mixing rule has been taken into account. Correlation and prediction capabilities of experimental interfacial tension data are analyzed for the quadratic mixing rule and the present approach. The method, which is discussed in detail in this work, provides an improved scheme for calculating interfacial properties, both for polar and nonpolar mixtures. According to results, a better correlation and prediction of the interfacial tensions can be obtained from an adequate interpolation of the VLE, using simple cubic equations of state. Examples are presented for binary and ternary mixtures.     

Phase equilibrium in binary aqueous mixtures of interest in alcoholic distillation using a modified PSRK equation of state

Phase equilibrium in binary mixtures that are found in wine and must distillation processes have been modeled using the predictive Soave-Redlich-Kwong equation, with original and modified molecular parameters. In wine and must distillation, the presence of polar substances found in the mixture to be distilled and the many components (i.e., those different from ethanol and water), called congeners, makes it difficult to model these mixtures. Thus, the prediction and correlation of the concentration of the distilled product, which is the most interesting variable, become very complex, and some experimental data are needed. The cases studied considered nine binary water + congener mixtures. The congeners considered are acetic acid, acetaldehyde, ethyl acetate, furfural, methanol, 3-methylbutanol, 2-methyl-1-propanol, 1-pentanol, and 1-propanol. These are the substances that are considered to be legal compounds by the Chilean legislation governing the production of a spirit called Pisco. The work allows evaluation of the advantages, disadvantages, and expected accuracy of this model. Comparison with available literature data is done.     

Simulation and Estimation of Vapor-Liquid Equilibrium for Asymmetric Binary Systems (CO2-Alcohols) Using Artificial Neural Network

Since it is not always possible to carry out experiments at all desired temperatures and pressures, generally thermodynamic models based on equations of state are used for estimation of vapor-liquid equilibrium. In this work, a method using artificial neural network (ANN) was designed and applied to simulate and estimate the VLE for the binary asymmetric systems containing CO₂ and Alcohols. The vapor-liquid equilibrium data of six systems include (CO₂-methanol), (CO₂-ethanol), (CO₂-1-butanol), (CO₂-2-butanol), (CO₂-1-pentanol) and (CO₂-2-pentanol) were used to developed the ANN for simulation of VLE. The results when using a developed ANN model or other methods such as SRK equations of state with LCVM, PSRK, WS, were compared with experimental data at various temperatures and pressures. Finally, it was observed that there is more qualitative and quantitative conformity between ANN model results and experimental data. Furthermore, the developed ANN model showed more accurate estimation over wide range of experimental conditions.     

Molecular models for the vapor-liquid equilibrium of simple binary mixtures

Simple analytical expressions are proposed for the calculation of the equilibrium pressure, as well as (for a given temperature and pressure) the mole fractions of both liquid and vapor phases at the vapor-liquid equilibrium of binary mixtures. They are based on a recently proposed molecular model for the vapor pressure of pure nonpolar fluids, which, for a given temperature, only requires as input the values of the two Lennard-Jones (LJ) molecular parameters and the acentric factor, which are parameters related to the molecular shape of each substance and whose values are readily available. The model for the equilibrium pressure of a binary mixture (which also permits one to obtain the liquid phase mole fraction) is similar to that derived from Raoult’s law, where a properly modified Lorentz-Berthelot mixing rule is used, the interaction parameters being given as simple functions of the temperature and composition with eight appropriate constants for each binary mixture. A different model is needed to calculate the vapor mole fraction in which five appropriate constants are needed for each mixture. Here, we show how the models reproduce accurately and straightforwardly the vapor liquid equilibrium properties (pressure, liquid mole fraction, and vapor mole fraction) of eight binary systems over a broad temperature range, including some data at or near the critical locus.     

Molecular models for the vapor-liquid equilibrium of simple binary mixtures

Simple analytical expressions are proposed for the calculation of the equilibrium pressure, as well as (for a given temperature and pressure) the mole fractions of both liquid and vapor phases at the vapor-liquid equilibrium of binary mixtures. They are based on a recently proposed molecular model for the vapor pressure of pure nonpolar fluids, which, for a given temperature, only requires as input the values of the two Lennard-Jones (LJ) molecular parameters and the acentric factor, which are parameters related to the molecular shape of each substance and whose values are readily available. The model for the equilibrium pressure of a binary mixture (which also permits one to obtain the liquid phase mole fraction) is similar to that derived from Raoult’s law, where a properly modified Lorentz-Berthelot mixing rule is used, the interaction parameters being given as simple functions of the temperature and composition with eight appropriate constants for each binary mixture. A different model is needed to calculate the vapor mole fraction in which five appropriate constants are needed for each mixture. Here, we show how the models reproduce accurately and straightforwardly the vapor liquid equilibrium properties (pressure, liquid mole fraction, and vapor mole fraction) of eight binary systems over a broad temperature range, including some data at or near the critical locus.     

Equation for the density of particle-reinforced metal matrix composites: A new approach

This paper presents a novel equation for the density of ceramic particle reinforced metal matrix composites. An overall density change occurs in composites due to the thermal mismatch between the metal matrix and the reinforcement. The thermal mismatch occurs because the coefficient of thermal expansion and the elastic properties are different for the matrix and the reinforcement. The values obtained using the proposed equation for density were compared with both the rule of mixtures for density and the experimental values obtained for aluminium and zinc alloy composites. The composite specimens were fabricated using compocasting technique (one of the types of liquid metallurgy route). The proposed mathematical model is found have better agreement with the experimental results at lower volume fractions of the reinforcement; however, some deviations were observed at higher volume fractions of the reinforcement. The proposed equation yields agreeable results for aluminium composites and fairly agreeable results for zinc alloy composites.     

Multiscale finite element analysis of bulk nano-particle fabrication by a mechanical method

A heterogeneous multiscale finite element approach is used to study the bulk mechanical alloying (BMA) process for nano-particles. Mechanical characteristics such as the load versus displacement relations and the heterogeneous distribution of maximum principle stress are calculated from the global analysis to support the subsequent local, small-scale, analysis. A simple local quasi-microscopic analysis of a six-ball contacting problem is conducted to determine the stress distribution in a particular particle. The Griffith fracture criterion is adopted to determine whether a particle will be forced to break into smaller fragments. To simulate the mixing process in the extruding stroke, particles in each element are randomly redistributed according to the uniform random distribution rule. The volume shrinkage effect is also considered. The relationships between the particle size, the fracture stress, and the applied stress in BMA are thus established. The goal of this paper is to explore fundamental mechanism for the nano-particle formation in BMA of brittle materials such as NaCl and Li₂NH.     

Local electric field investigation of Si2N2O and its electronic structure, elastic and optical properties

This paper demonstrates that the Clausius-Mosotti equation cannot be used for Si₂N₂O since the Lorenz approximation is invalid therein. Therefore a modified definition for the Lorenz electric field is suggested which can be derived from the optical dielectric constant calculated using the plane-wave pseudopotential method. In addition, other parameters of Si₂N₂O such as the energy band gap, density of states, elastic and optical properties are also given in this paper. Based on the new expression for local electric field, the modified Clausius-Mosotti equation is suggested, and then the dielectric constant of Si₂N₂O is discussed by using the additivity rule. It is found that the result of the phenomenological analysis of the dielectric constant is basically consistent with the experimental data and the first principles results, which explain the experimental observation that the dielectric constant of Si₂N₂O is enhanced with the increase of Li content. Also, the modified Clausius-Mosotti equation and the additivity rule are suggested to be used in predicting the dielectric behaviors of the new and complex compounds.     

Simplified prediction model for elastic modulus of particulate reinforced metal matrix composites

Some structural parameters of the metal matrix composite, including particulate shape and distribution do not influence the elastic modulus. A prediction model for the elastic modulus of particulate reinforced metal matrix Al composite was developed and improved. Expressions of rigidity and flexibility of the rule of mixing were proposed. A five-zone model for elasticity performance calculation of the composite was proposed. The five-zone model is thought to be able to reflect the effects of the MMC interface on elastic modulus of the composite. The model overcomes limitations of the currently-understood rigidity and flexibility of the rule of mixing. The original idea of a five-zone model is to propose particulate/interface interactive zone and matrix/interface interactive zone. By integrating organically with the law of mixing, the new model is found to be capable of predicting the engineering elastic constants of the MMC composite.     

Formation of Random Solid Solution in Multicomponent Alloys: from Hume-Rothery Rules to Entropic Stabilization

As proposed in the 1920s, the empirical Hume-Rothery rules have been guiding the alloy design for random solid solutions. In contrast, the recent proposal by Yeh et al. (Adv Eng Mater 6(5):299–303, 2004) suggested that formation of random solid solution could be attributed to the maximized configurational entropy of mixing of multicomponent alloys, also known as high entropy alloys. By taking into account the non-ideal mixing of atoms with inter-atomic correlations (correlated mixing), here we suggest that the idea of entropic stabilization could be theoretically connected with the Hume-Rothery rules. The non-ideal formulation of the configurational entropy of mixing of a multicomponent alloy rationalizes the recent data obtained from experiments and simulations, which show the temperature dependence of the configurational entropy of mixing, the metastability of random solid solution observed at a low temperature, and the coupled effect of atomic size and chemical bond misfit on the stability of random solid solution. Finally, we discuss the measures that one can take to maximize the configurational entropy of a multicomponent alloy by considering the possible correlations among their constituent elements.     

连铸中间罐内钢水的混合状态

通过连铸过程中钢液过渡状态成分的数学公式,分析了钢液成分变化的规律,同时计算出某台铸机钢液混合参数.分析了连铸中间罐试样的代表性和准确性,提出控制质量稳定性的建议.     

TIG brazing technology for zinc-coated sheet steel for bodywork

We propose a method for the assessment of the state of welded joints in terms of arc voltage signals and feed rate appraisal. The signals were recorded during laboratory tests. For the appraisal of the signals, we applied numerical parameters such as, for instance, kurtosis. On the basis of analysis results, we developed diagnostic rules which were written in the binary diagnostic matrix. The proposed method has been implemented in the form of software, the correctness of which has been verified on experimental data.     

Condensation of a gas-vapor mixture under the conditions of a corona discharge

The experimental data on the condensation of vapor from a gas-vapor mixture in the presence of an electric field are discussed. It is assumed that a corona discharge or, to be more accurate, its accompanying phenomena such as the unipolar charging of the medium and the electric wind, which produces intense mixing both of the medium and the condensate film, is the main factor influencing the intensification of the condensation in an electric field. The criteria of the similarity of the process, among which the main attention is drawn to the “electric” Reynolds number, which characterizes the interaction of the electric field with the medium, are considered. We also discuss the parameters of vapor-air mixtures, such as their density, viscosity, and ion mobility. A simplified method of the generalization of the experimental data on condensation in the presence of an electric field based on the concepts of a corona discharge is proposed.     

Analysis of Hidden Representations by Greedy Clustering

The hidden layer of backpropagation neural networks (NNs) holds the key to the networks' success in solving pattern classification problems. The units in the hidden layer encapsulate the network's internal representations of the outside world described by the input data. this paper, the hidden representations of trained networks are investigated by means simple greedy clustering algorithm. This clustering algorithm is applied to networks have been trained to solve well-known problems: the monks problems, the 5-bit problem and the contiguity problem. The results from applying the algorithm to problems with known concepts provide us with a better understanding of NN learning. These also explain why NNs achieve higher predictive accuracy than that of decision-tree methods. The results of this study can be readily applied to rule extraction from Production rules are extracted for the parity and the monks problems, as well as benchmark data set: Pima Indian diabetes diagnosis. The extracted rules from the Indian diabetes data set compare favorably with rules extracted from ARTMAP NNs terms of predictive accuracy and simplicity.     

Phase Equilibria in the System FeO-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript>-SiO<Subscript>2</Subscript>

Liquidus data are presented for mixtures in the ternary system FeO-Fe₂O₃-SiO₂ in equilibrium with a gas phase with O₂ pressures ranging from 10^?10.9 to 1 atm. Data obtained are combined with previously published data to construct lines of equal O₂ pressures and lines of equal CO₂/H₂ mixing ratios along the liquidus surface. Courses of crystallization of selected mixtures under conditions of constant total composition, constant O₂ pressures, and constant CO₂/H₂ mixing ratios are discussed.     

Thermodynamically Improbable Phase Diagrams

Phase diagrams showing very unlikely boundaries, while not explicitly violating thermodynamic principles or phase rules, are discussed. Phase rule violations in proposed phase diagrams often become apparent when phase boundaries are extrapolated into metastable regions. In addition to phase rule violations, this article considers difficulties regarding an abrupt change of slope of a phase boundary, asymmetric or unusually pointed liquidus boundaries, location of miscibility gaps, and gas/liquid equilibria. Another frequent source of phase diagram errors concerns the initial slopes of liquidus and solidus boundaries in the very dilute regions near the pure elements. Useful and consistent prediction can be made from the application of the van’t Hoff equation for the dilute regions.     

Thermochemical investigation of binary liquid mixtures in glass-forming oxide systems

Methods and equipment successfully employed in high- temperature calorimetry to measure partial and integral enthalpies of mixing in liquid oxide systems are reviewed with special attention given to the drop-mixing method. This technique has been used to measure enthalpies of mixing in binary liq-uid mixtures composed of network forming oxides (e.g. SiO₂) and network modifying oxides (e.g. Na₂O). Results for the systems Na₂O-SiO₂ and Na₂O- B₂O₃ are presented graphically. Entropies of mixing were estimated by combining enthalpies with available data on Gibbs energies of mixing. Prominent thermochemical features of glass-forming oxide melts are pointed out. The observed thermodynamic behavior is discussed in relation to its structural basis.     

Thermochemical investigation of binary liquid mixtures in glass-forming oxide systems

Methods and equipment successfully employed in high- temperature calorimetry to measure partial and integral enthalpies of mixing in liquid oxide systems are reviewed with special attention given to the drop-mixing method. This technique has been used to measure enthalpies of mixing in binary liq-uid mixtures composed of network forming oxides (e.g. SiO₂) and network modifying oxides (e.g. Na₂O). Results for the systems Na₂O-SiO₂ and Na₂O- B₂O₃ are presented graphically. Entropies of mixing were estimated by combining enthalpies with available data on Gibbs energies of mixing. Prominent thermochemical features of glass-forming oxide melts are pointed out. The observed thermodynamic behavior is discussed in relation to its structural basis.     

Form factor of the electron density of an anion specifically adsorbed on metal surface in an electrolyte

The character of distribution of electron density over the proximity of a halide anion specifically adsorbed at the s,p-metal-electrolyte solution interface boundary was considered. An assumption was made that the physical nature of the specific bonding of the anion is caused by mixing of electron waves of free electrons in the metal and the valent state of the anion as the electrons resonantly overcome the potential barrier between the anion and the metal. The physical (dissipative quantum) mechanism of microscopic processes is described using the Anderson impurity model, the Friedel sum rule, and the Parr conception of equalization of electronegativity values that determine the partial transfer of electron charge from the anion to the metal and the emergence of localized dipole at the interphase boundary. The equations renormalizing the microscopic parameters of the adsorption event to macroscopic state functions of the adsorption phase on an electrode were obtained. The chemical potential of the halide anion specifically adsorbed from electrolyte solution on an uncharged electrode is estimated. The mechanism under consideration explains the details of the dependences of polarization parameters of the electrode on anion and metal nature.