A Nonclassical Model of a Type 2 Mixture with Vapor–Liquid, Liquid–Liquid, and Three-Phase Equilibria

A model with nonclassical exponents is developed for phase equilibria of a Type 2 mixture with vapor–liquid equilibrium (VLE) and liquid–liquid equilibrium (LLE). Starting with a Leung–Griffiths model for a Type 1 mixture with only VLE, the model adds a Schofield parametric construction to describe LLE and a three-phase locus. Care is taken to suppress a spurious and artificial phase boundary. The model is applied to VLE data of carbon dioxide+methane. It is conjectured that this mixture upon cooling would undergo liquid–liquid separation, but it freezes before such virtual LLE can be observed. Experimental bubble curves and the LLE structure from a classical equation of state are accurately modeled.     

Vapor–Liquid Equilibria of Silicon by the Gibbs Ensemble Simulation

Vapor–liquid equilibrium simulations of silicon were performed using the Stillinger–Weber potential with the Gibbs ensemble Monte Carlo method (GEMC). In the low temperature region, from about 3000 to 3500 K, our calculations show the stability of phases and good agreement with several experimental results. On the whole, there is little dependence on the size of the system except near the estimated critical point of silicon: T _c = 7500 ± 500 K and _c = 750 ± 100 kg · m^–3 as determined by the law of rectilinear diameter. Above 3500 K, vapor–liquid coexistence properties which have not been obtained by experiment are derived.     

Vapor–Liquid Equilibria of Alternative Refrigerants by Molecular Dynamics Simulations

Alternative refrigerants HFC-152a (CHF₂CH₃), HFC-143a (CF₃CH₃), HFC-134a (CF₃CH₂F), and HCFC-142b (CF₂ClCH₃) are modeled as a dipolar two-center Lennard–Jones fluid. Potential parameters of the model are fitted to the critical temperature and vapor–liquid equilibrium data. The required vapor–liquid equilibrium data of the model fluid are computed by the Gibbs–Duhem integration for molecular elongations L=0.505 and 0.67, and dipole moments *²=0, 2, 4, 5, 6, 7, and 8. Critical properties of the model fluid are estimated from the law of rectilinear diameter and critical scaling relation. The vapor–liquid equilibrium data are represented by Wagner equations. Comparison of the vapor–liquid equilibrium data based on the dipolar two-center Lennard–Jones fluid with data from the REFPROP database shows good-to-excellent agreement for coexisting densities and vapor pressure.     

Joule–Thomson Inversion in Vapor–Liquid–Solid Solution Systems

Solid phase precipitation can greatly affect thermal effects in isenthalpic expansions; wax precipitation may occur in natural hydrocarbon systems in the range of operating conditions, the wax appearance temperature being significantly higher (as high as 350 K) for hyperbaric fluids. Recently, methods for calculating the Joule–Thomson inversion curve (JTIC) for two-phase mixtures, and for three-phase vapor–liquid–multisolid systems have been proposed. In this study, an approach for calculating the JTIC for the vapor–liquid–solid solution systems is presented. The JTIC is located by tracking extrema and angular points of enthalpy departure variations versus pressure at isothermal conditions. The proposed method is applied to several complex synthetic and naturally occurring hydrocarbon systems. The JTIC can exhibit several distinct branches (which may lie within two- or three-phase regions or follow phase boundaries), multiple inversion temperatures at fixed pressure, as well as multiple inversion pressures at given temperature.     

Deterministic Model of Homophase and Heterophase Fluctuations in a Liquid–Vapor System

Within the framework of the assembly-type catastrophe model, a nonlinear dynamic equation (DE) homogeneous in the parameter t with an aftereffect is constructed, in which t characterizes the deviation of the reduced density of a thin surface layer on the liquid-vapor interface from the mean density of the vapor-liquid system. This equation is used to treat a second-order nonlinear DE with a variable damping coefficient for a vapor-liquid system excited by periodic impacts (acts of evaporation and condensation of molecules). This DE is integrated over a finite time interval to find a two-dimensional mapping whose numerical solution describes the chaotic dynamics of the density in time, including homophase and heterophase fluctuations. For this system, the bifurcation diagrams are constructed and the Lyapunov exponents are found.     

Experimental Determination of Densities and Isobaric Vapor–Liquid Equilibria of Methyl Acetate and Ethyl Acetate with Alcohols (C3 and C4) at 0.3 MPa

The densities and excess volumes were determined at 298.15 K for the methyl acetate + 1-propanol, methyl acetate + 1-butanol, and ethyl acetate + 1-butanol mixtures. The vapor–liquid equilibria data at 0.3 MPa for these binary systems were obtained using a stainless steel equilibrium still. The activity coefficients were obtained from the experimental data using the Hayden and O’Connell method and the Yen and Woods equation. The binary systems in this study showed positive deviations from ideality. The experimental VLE data were verified with the point-to-point test of van Ness using the Barker routine and the Fredenslund criterion. The different versions of the UNIFAC and the ASOG group contribution models were applied.     

Vapor–Liquid Equilibria for the 1,1,1-Trifluoroethane (HFC-143a)+1,1,1,2-Tetrafluoroethane (HFC-134a) System

A vapor–liquid equilibrium apparatus has been developed and used to obtain data for the binary HFC-143a+HFC-134a system. Fifty-four equilibrium data are obtained for the HFC-143a+HFC-134a system over the temperature range from 263.15 to 313.15 K at 10 K intervals. The experimental data were correlated with the Carnahan–Starling–De Santis (CSD) and Peng–Robinson (PR) equations of state. Based upon the present data, the binary interaction parameters for the CSD and PR equations of state were calculated for six isotherms for the HFC-143a+HFC-134a system. The binary interaction parameters for both equations of state were fitted by a linear equation as a function of temperature. The present data were in good agreement with the calculated results from the CSD equation of state, and the deviations were less than 1.0% with the exception of two points.     

Measurements of Vapor–Liquid Equilibria in the Systems NH3–H2O–NaOH and NH3–H2O–KOH at Temperatures of 303 and 318 K and Pressures 0.1 MPa<p<1.3 MPa

A static method has been used to obtain vapor–liquid equilibrium data for the systems ammonia (NH₃)–water (H₂O)–potassium hydroxide (KOH) and ammonia–water–sodium hydroxide (NaOH) at temperatures of 303 and 318 K and pressures from 0.1 to 1.3 MPa. The salt concentration in the liquid phase was chosen in the range from 2 to 60 mass% salt in water. In both systems NH₃–H₂O–NaOH and NH₃–H₂O–KOH, solid–liquid–vapor equilibria were observed. In the NH₃–H₂O–KOH system, liquid–liquid–vapor equilibrium was observed at 318 K and 1.1 MPa but at yet unknown concentrations of the liquid phases.     

Methane Gas Hydrates Viewed through Unified Solid–Liquid–Vapor Equations of State

The phase behavior of methane gas hydrates (clathrates) has been investigated with unified equations of state for solid–liquid–vapor phases. This is a new way to look at the clathrate-containing system, being radically different from the traditional statistical thermodynamic model for clathrates. The present paper includes modifications and refinements of the previously published method with the unified equations of state. The univariant three-phase equilibrium lines containing clathrates have been successfully predicted with the present equation-of-state model for a wide temperature and pressure range. Particularly, the phase behavior in very high-pressure regions has been modeled for the first time by the present work. Although the present results at high pressures are still tentative, they will shed some light on the unsettled problem of high pressure phases as reported in the literature.     

Critical Outflow of a Vapor–Liquid Flow through a Grain Layer

High Temperature - Based on previous experimental studies, we carried out a numerical simulation of the process of the critical outflow of a vapor–liquid flow in cylindrical channels filled...     

Vapor–Liquid Critical Surface of Ternary Difluoromethane+Pentafluoroethane+1,1,1,2-Tetrafluoroethane (R-32/125/134a) Mixtures

The plane of vapor–liquid criticality for ternary refrigerant mixtures of difluoromethane (R-32)+pentafluoroethane (R-125)+1,1,1,2-tetrafluoroethane (R-134a) was determined from data on the vapor–liquid coexistence curve near the mixture critical points. The compositions (mass percentage) of the mixtures studied were 23% R-32+25% R-125+52% R-134a (R-407C), 25% R-32+15% R-125+60% R-134a (R-407E), and 20% R-32+40% R-125+40% R-134a (R-407A). The critical temperature of each mixture was determined by observation of the disappearance of the meniscus. The critical density of each mixture was determined on the basis of meniscus disappearance level and the intensity of the critical opalescence. The uncertainties of the temperature, density, and composition measurements are estimated as ±10 mK, ±5 kg·m^–3, and ±0.05%, respectively. In addition, predictive methods for the critical parameters of R-32/125/134a mixtures are discussed.     

The Convective Instabilities in a Liquid–Vapor System with a Non-equilibrium Evaporation Interface

Rayleigh–Marangoni–Bénard instability in a system consisting of a horizontal liquid layer and its own vapor has been investigated. The two layers are separated by a deformable evaporation interface. A linear stability analysis is carried out to study the convective instability during evaporation. In previous works, the interface is assumed to be under equilibrium state. In contrast with previous works, we give up the equilibrium assumption and use Hertz–Knudsen’s relation to describe the phase change under non-equilibrium state. The influence of Marangoni effect, gravitational effect, degree of non-equilibrium and the dynamics of the vapor on the instability are discussed.     

An Improved Computational Method for the Calculation of Mixture Liquid–Vapor Critical Points

Knowledge of critical points is important to determine the phase behavior of a mixture. This work proposes a reliable and accurate method in order to locate the liquid–vapor critical point of a given mixture. The theoretical model is developed from the rigorous definition of critical points, based on the SRK equation of state (SRK EoS) or alternatively, on the PR EoS. In order to solve the resulting system of \(C+2\) nonlinear equations, an improved method is introduced into an existing Newton–Raphson algorithm, which can calculate all the variables simultaneously in each iteration step. The improvements mainly focus on the derivatives of the Jacobian matrix, on the convergence criteria, and on the damping coefficient. As a result, all equations and related conditions required for the computation of the scheme are illustrated in this paper. Finally, experimental data for the critical points of 44 mixtures are adopted in order to validate the method. For the SRK EoS, average absolute errors of the predicted critical-pressure and critical-temperature values are 123.82 kPa and 3.11 K, respectively, whereas the commercial software package Calsep PVTSIM’s prediction errors are 131.02 kPa and 3.24 K. For the PR EoS, the two above mentioned average absolute errors are 129.32 kPa and 2.45 K, while the PVTSIM’s errors are 137.24 kPa and 2.55 K, respectively.     

Analytical Representation of the Curves of Liquid–Vapor Phase Equilibrium for Saturated Hydrocarbons

A unified two-parameter approximation formula is used to derive analytical dependences for P(T) curves of liquid–vapor phase equilibrium of saturated hydrocarbons C _n H_{2n + 2} (alkanes) with numbers 1 n 20 from methane (n = 1) to eicosane (n = 20). Two approximation options are given, namely, that involving the use of individual values of parameters for each alkane, and that in the form of a unified formula in which the only parameter characterizing an individual component is the number n.     

Liquid–Liquid Interfacial Tension in Ternary Monotectic Alloys Al–Bi–Cu and Al–Bi–Si

The liquid–liquid interfacial tension in the ternary monotectic alloys Al_34.5-x Bi_65.5Cu _x and (Al_0.345Bi_0.655)_100-x Si _x (mass%) has been determined as a function of its Cu (Si) content by a tensiometric technique. It is established that the interfacial tension gradually increases when either Cu or Si is added to Al–Bi alloys. The increase of can be related to the increase of the miscibility gap (both width and height) when Cu (Si) is added to the Al–Bi binary. The temperature dependences of the interfacial tension in binary Al_34.5Bi_65.5 and ternary Al_23.25Bi_65.5Cu_11.25 and (Al_0.345Bi_0.655)₉₅Si₅ monotectic alloys are well described by the power function with the critical-point exponent .     

A Novel Fullerene Hydroxamic Acid for the Liquid–Liquid Extraction,Separation, Preconcentration,and Spectrophotometric and ICP‐AES Determination of Vanadium

Abstract

A new reagent N‐phenyl‐(1,2 methanofullerene C₆₀)61‐formohydroxamic acid (PMFFA) is reported for extraction and trace determination of vanadium(V) in nutritional and biological substrates. The extraction mechanism of vanadium from 6 M HCl media is investigated. The influence of PMFFA, diverse ions, and temperature on the distribution constant of vanadium examined. The over all stability constant (log β₂ K _e ) and extraction constant (K _ex) are 20.89 ± 0.02 and 8.0 ± 0.02 × 10^?15, respectively in chloroform. The thermodynamics parameters are calculated and kinetics of vanadium transport is discussed. The system obeys Beer's law in the range of 3.2–64.0 ng mL^?1 of vanadium(V). The molar absorptivity is 7.96 × 10⁵ L mol^?1 cm^?1, at 510 nm. The PMFFA–vanadium(V) complex chloroform extract in chloroform was directly inserted into plasma for ICP‐AES measurement, which increases the sensitivity by 50 folds and obey Beer's law in the range of 50–1200 pg mL^?1 of vanadium(V). The method is applied for determination vanadium in real standard samples, sea water, and environmental samples.     

Study of (Solid–Liquid) Phase Equilibria for Mixtures of Energetic Material Stabilizers and Prediction for Their Subsequent Performance

Solid-liquid equilibria for three binary mixtures of 2-nitrodiphenylamine (1) + diphenylamine (2), ethyl centralite (1) + N-ethyl-4-nitro-N-nitrosoaniline (2), and 2,2 $^{\prime }$ -dinitrodiphenylamine (1) + N-ethyl-4-nitro-N-nitrosoaniline (2) were measured using a differential scanning calorimeter. Simple eutectic behaviors for these systems were observed. The experimental results were correlated by means of original and modified NRTL, Wilson, and UNIQUAC equations. The root–mean–square deviations of the solubility temperatures for all measured data vary from 0.63 K to 3.73 K and depend on the particular model used. The best solubility correlation was obtained with the UNIQUAC model.     

Simulating Retention in Gas–Liquid Chromatography: Benzene, Toluene, and Xylene Solutes

Accurate predictions of retention times, retention indices, and partition constants are a long sought-after goal for theoretical studies in chromatography. Although advances in computational chemistry have improved our understanding of molecular interactions, little attention has been focused on chromatography, let alone calculations of retention properties. Configurational-bias Monte Carlo simulations in the isobaric–isothermal Gibbs ensemble were used to investigate the partitioning of benzene, toluene, and the three xylene isomers between a squalane liquid phase and a helium vapor phase. The united-atom representation of the TraPPE (transferable potentials for phase equilibria) force field was used for all solutes and squalane. The Gibbs free energies of transfer and Kovats retention indices of the solutes were calculated directly from the partition constants (which were averaged over several independent simulations). While the calculated Kovats indices of benzene and toluene at T=403 K are significantly higher than their experimental counterparts, much better agreement is found for the xylene isomers at T=365 K.     

Liquid–liquid phase equilibria,density difference,and interfacial tension in the Al–Bi–Si monotectic system

We have performed thermodynamic calculation of the phase equilibria in the ternary monotectic system Al–Bi–Si. The liquid–liquid miscibility gap in the Al–Bi–Si system extends over almost the entire concentration triangle. The thermal analysis data for (Al_0.345Bi_0.655)_100−x Si _x alloys (x = 2.5, 5, 7.5, and 10 wt%) excellently agree with the calculated phase diagram. The experimental density difference of the coexisting liquid phases shows a good agreement with the density difference calculated in the approximation of ideal solution using the densities of pure elements and the compositions of L′ and L′′ from the thermodynamic calculation. The liquid–liquid interfacial tension in the (Al_0.345Bi_0.655)_100−x Si _x liquid alloys increases with Si content. The experimental temperature dependence of the interfacial tension is well described by the power low in reduced temperature (T _C–T) at approach of the critical temperature with the exponent μ = 1.3, which is close to the value predicted by the renormalization group theory of critical behavior.