New Equation Of State Research Articles

Protoneutron star cooling with a new equation of state

Using a new numerical EOS (equation of state) table calculated by Shen et al., we performed numerical simulations of protoneutron star cooling. The EOS is based on the relativistic mean field theory, and the parameters in its Lagrangian have been chosen to reproduce the experimental properties of both stable and unstable nuclei. Furthermore, the numerical table covers such a wide range of thermodynamical quantities (temperature, 0 ∼ 100 MeV; electron fraction, 0 ∼ 0.56; density, 10 5.1 ∼ 10 15.4 g/cc) that cooling simulations even for 50 seconds could be done without troubles. The quasistatic evolution of protoneutron stars was investigated in detail with a numerical code including neutrino transfer (MGFLD scheme). Dependencies both on EOS and on initial models and implications to the SN1987A constraint on neutrino oscillation models are discussed.

Equation of state for square-well fluids: development of a coordination number model

A new expression for the coordination number of square-well fluids is developed. This expression meets the low density and close-packed density boundary conditions. On the basis of this model, a new equation of state (EOS) is introduced. This EOS needs the square-well potential function parameters—that is, R, σ, and ε/ k—as input parameters. When these parameters are used as adjustable parameters, the EOS accurately describes the thermodynamic properties of normal fluids. The average absolute error for calculating the saturated vapor pressure, liquid density, vapor volume and enthalpy of vaporization of pure fluids was found to be 6.85, 3.95, 8.68, and 4.75%, respectively. Also, for a wide range of temperature and pressure, the compressed liquid density of methane and 1,1-difluoroethane were predicted accurately. The average absolute error was found to be 4.13 and 1.43% for methane and 1,1-difuoroethane, respectively.

Equations of State for Technical Applications. II. Results for Nonpolar Fluids

New functional forms have been developed for multiparameter equations of state for non- and weakly polar fluids and for polar fluids. The resulting functional forms, which were established with an optimization algorithm which considers data sets for different fluids simultaneously, are suitable as a basis for equations of state for a broad variety of fluids. The functional forms were designed to fulfill typical demands of advanced technical applications with regard to the achieved accuracy. They are numerically very stable and their substance-specific coefficients can easily be fitted to restricted data sets. In this way, a fast extension of the group of fluids for which accurate empirical equations of state are available becomes possible. This article deals with the results found for the non- and weakly polar fluids methane, ethane, propane, isobutane, n-butane, n-pentane, n-hexane, n-heptane, n-octane, argon, oxygen, nitrogen, ethylene, cyclohexane, and sulfur hexafluoride. The substance-specific parameters of the new equations of state are given as well as statistical and graphical comparisons with experimental data. General features of the new class of equations of state such as their extrapolation behavior and their numerical stability have been discussed in a preceding article. Results for typical polar fluids will be discussed in a subsequent article.

A cubic hard-core equation of state

In this work, a new method to determine a suitable repulsive term for cubic equations of state is introduced. Based on this method and by using a simplified molecular theory of hard-core fluids, a new two constant parameter cubic equation of state is presented. The proposed equation of state is applied for PVT and VLE calculations of different pure fluids and fluid mixtures. The results are compared with those obtained by two commonly used cubic equations of state. The comparisons indicate that the new equation of state yields better results.

A new equation of state for porous materials with ultra-low densities

A thermodynamic equation of state is derived which is appropriate forinvestigating the thermodynamic variations along isobaric paths to predictcompression behaviours of porous materials. This equation-of-state model istested on porous iron, copper, lead and tungsten with different initial densities.The calculated Hugoniots are in good agreement with the correspondingexperimental data published previously. This shows that this model cansatisfactorily predict the Hugoniots of porous materials with wide porosity andpressure ranges.

Some recent advances of shock wave physics research at the Laboratory for ShockWave and Detonation Physics Research

Progress made in recent years on three topics that have been investigated at theLaboratory for Shock Wave and Detonation Physics Research are presented in thisreport. (1) A new equation of state (EOS) has been derived which canbe used from a standard state to predict state variable change along anisobaric path. Good agreements between calculations for some representativemetals using this new EOS and experiments have been found, covering awide range from hundreds of MPa to hundreds of GPa and from ambienttemperature to tens of thousands of GPa. (2) An empirical relation of Y/G = constant(Y is yieldstrength, Gis shear modulus) at HT–HP has been reinvestigated and confirmed by shockwave experiment. 93W alloy was chosen as a model material. The advantage ofthis relation is that it is beneficial to formulate a kind of simplified constitutiveequation for metallic solids under shock loading, and thus to faithfully describethe behaviours of shocked solids through hydrodynamic simulations. (3) Anattempt at microstructure characterization for a failure wave in shocked glass hasbeen carried out for the first time. Analyses on both the fractal dimension of thecracks’ propagating path and the degree of damage in the failed regionqualitatively revealed that ZF1 glass has a much less damaged structure thanK9glass at nearly the same loading stress. Based on the aboveanalysis, we conjecture inhomogeneous immiscible phases, more inK9than in ZF1, distributed in the glass body of the intrinsic factor, exhibitingas numerous locally strained spots due to the shock induced differentcompressibilities between the matrix and the immiscible phases. When the surfacecracks, activated by the shearing action of one-dimensional strain loading,propagate and arrive at the strained spot boundaries, new cracks would begenerated, accompanied by crack turning and branching, and thus cause glassbody fracturing and fragmenting. In other words, the more numerous the strainedspots are, the more severely damaged the structure of the shocked glass.

A new equation of state (hsft) based on fractal theory

This paper describes the molecular distribution of fluids by some fractal characteristics based on the current understandings of microstructures in fluids. The coordination relation was derived according to this fractal model, and the molecular mean potential function for simple square-well fluids was proposed. By applying this new mean potential function, a new equation of state (EOS) named HSFT was derived from statistical mechanics. Vapor pressures and saturated liquid densities of about 200 pure substances were correlated by the proposed model. Resulting equation parameters were further generalized by acentric factor ω and critical compressibility factor Zc. Saturated properties for 180 substances and enthalpies of vaporization for 115 substances, including compounds with strong polarity, were calculated by the generalized HSFT equation. Compared with several other equations of state, satisfactory results computed by HSFT equation imply that the generalized HSFT equation possesses better adaptability and reliability.

NON-MINIMAL COUPLING, VARIABLE SPEED OF LIGHT AND COSMOLOGY

Presently, there exists some renewed interest in time varying speed of light theories as possible solutions of the major cosmological problems1. It is often believed that the local Lorentzian invariance is broken if the speed of light in a vacuum is not a constant. We point out that this belief is not necessarily founded and that a variable speed of light is perfectly consistent with general relativity under the assumption of non-minimal coupling between electromagnetism and curvature. Two kinds of arguments may be invoked in favour of such an assumption. First, a theorem due to Horndeski2shows that in a four-dimensional space-time the Einstein-Maxwell field equations are not the only second-order vector potential field equations which stem from a Lagrangian scalar density, are consistent with the charge conservation and reduce to Maxwell's equations in a flat space-time (see also3). Second, according to QED4,5, vacuum polarization induces tidal gravitational effects which imply that photons propagating in a curved space-time have velocities exceeding the value of the "Lorentzian structural constant" c. The modified electromagnetic field equations given by Horndeski2are studied here in the geometrical optics limit. Considering the case of Friedmann-Robertson-Walker cosmological models, we find the value of the speed of light as a function of the energetic content of the universe. We deduce from this result a new equation of state for a photon gas and we discuss the consequences of this equation on the evolution of the scale factor during the radiation-dominated era.

An Equation of State for Electrolyte Solutions Covering Wide Ranges of Temperature, Pressure, and Composition

An equation of state has been developed for electrolyte solutions over wide ranges of temperature, pressure, and composition. The equation is in terms of the Helmholtz free energy and contains three terms accounting for the various interactions in solution: a Peng−Robinson term for the interactions between uncharged species, a Born term for the charging free energy of ions, and a mean spherical approximation term for the electrostatic interactions between ions. The equation of state was fitted to experimental data for 138 aqueous electrolyte solutions at 25 °C and 1 bar and to data for aqueous NaCl, NaBr, CaCl2, Li2SO4, Na2SO4, K2SO4, and Cs2SO4 solutions from 0 to 300 °C and from 1 to 120 bar. The equation does well in correlating activity coefficients, osmotic coefficients, densities, and free energies of hydration over the entire range of conditions. The simplicity and wide range of applicability of the new equation of state make it particularly well suited for use in engineering applications.

New equation of state for transport properties: calculation for the thermal conductivity and the viscosity of halogenated hydrocarbon refrigerants

A new transport equation of state to estimate the thermal conductivity and the viscosity of the dense fluid for halogenated hydrocarbon refrigerants is presented and the relationships between the reduced residual transport properties and the reduced density were determined. This approach originated from the phenomenological similarity between the reduced residual transport properties and the reduced density in terms of pressure and temperature over the entire thermodynamic surface. The new equation can be used to calculate the thermal conductivity and the viscosity of the dense fluid including the vapor and liquid region with high accuracy, based on the calculation on the transport properties of gases at low pressure. The only input data needed are the critical parameters, molecular weight and acentric factor. The method is based on the concept of the transport equation of state describing the transport properties in terms of pressure and temperature by pressure explicit equations similar to a thermal equation of state. Coherence between the transport properties and equilibrium properties over the entire fluid range was reflected. The absolute average deviation of the thermal conductivity of halogenated hydrocarbon refrigerants is 4.8% with a maximum deviation of 18.0%, and the absolute average deviation of the viscosity of halogenated hydrocarbon refrigerants is 4.4% with a maximum deviation of 15.6%, using the new equation. A new generalized correlation to estimate the thermal conductivity of halogenated hydrocarbon refrigerants at low pressure is also proposed. The range of application of this new formula is for reduced temperatures between 0.6 and 1.2 and for values of the critical compressibility factor between 0.225 and 0.283. The calculation deviation is within ±7%, and the total absolute average deviation is 2.7% compared with the experimental data.

P–ρ–T and Ps–ρs–Ts properties of methanol + water and n-propanol + water solutions in wide range of state parametersElectronic supplementary information (ESI) available: Tables of values of the coefficients in eqn. (1), eqn. (7), eqn. (8) and eqn. (9). See http://www.rsc.org/suppdata/cp/b1/b109077c/

The P–ρ–T and Ps–ρs–Ts properties of methanol + water and n-propanol + water solutions in a wide range of state parameters have been investigated in a constant volume piezometer installation. The experiments were carried out for the methanol + water solutions in the temperature range 298.15 to 523.15 K, at mole fractions of methanol of x = 0.25, x = 0.50, x = 0.75, from the bubble point pressure up to 60 MPa and also for n-propanol + water solutions in the temperature range 373.15 to 573.15 K, at the x = 0.25, x = 0.50, x = 0.75 mole fractions of n-propanol, in the pressures range 0.1 to 5.25 MPa, in the 0.6628–118.6103 kg m−3 density interval. The experimental uncertainties are ΔT = ± 3 mK for temperature, ΔP = ± 5×10−2×P for pressure, Δρ = ± 3×10−2×ρ for density in liquid phases, and Δρ = ± 9×10−2×ρ in the vapor phase. A new equation of state was derived for correlation of the experimental data of methanol + water solutions. The experiments could be reproduced with deviations not exceeding experimental uncertainty. The data obtained for the n-propanol + water solution allowed us to establish the equation of state in virial form and thus the second and the third virial coefficients are calculated. The virial coefficients were obtained by two independent methods, namely, graphical and analytical. The temperature and mole fraction dependence of the coefficients of the equations of state are described.

Correlation of the solubility of low-volatile organic compounds in near- and supercritical fluids. Part I: applications to adamantane and β-carotene

A new simplified form of an equation of state suitable for the correlation of pVT-data is presented. The new equation of state is capable to model pVT-data in the low- and high-pressure regions as well as in the critical region. Taking a fugacity approach as a basis, we have calculated the solubility of several low-volatile solid organic compounds, in particular of the globular molecule adamantane in CO 2 and the natural dyestuff β-carotene in three compressed gases, i.e. CO 2, CClF 3, and N 2O. For all systems except β-carotene+N 2O solubility data measured up to 100 MPa and more (180 MPa for β-carotene+CO 2 and+CClF 3) are available. Experimental results for the systems β-carotene+CO 2 and+CClF 3 are also reported. Here, adamantane serves as an example for a relatively high-soluble substance, while β-carotene represents low-soluble solutes. Solubility maxima, which have been found experimentally as a function of pressure or density at constant temperature, are considered in the correlations.

An equation of state for the hard-sphere chain fluid based on the thermodynamic perturbation theory of sequential polymerization

New equations of state for freely jointed hard-sphere chain fluids are developed. The equations of state are based on the thermodynamic perturbation theory. The new equations of state use the contact values of the radial distribution function (RDF) for monomer–dimer mixtures, which is derived from the multidensity Ornstein–Zernike theory. These RDFs are composed of a monomer reference term, the Carnahan–Starling or the Percus–Yevick expression, and an additional bond contribution. These equations of state are then extended to real fluids. To calculate the phase equilibrium properties of nonassociating chain fluids, a dispersion contribution is added to the repulsive hard-chain reference term. With the new equations of state of chain fluids supplemented with the dispersion term, the vapor pressures and the coexisting densities of several real fluids are calculated.

Effects of a New Equation of State on Cepheid Pulsation Models

AbstractWe present the results of several numerical experiments aimed at testing the dependence of theoretical observables predicted by Cepheid hydrodynamical models on the equation of state (EOS). We focus our attention on nonlinear and time-dependent Cepheid convective models at solar chemical composition. We find that current predictions for both the blue and red edge of the instability strip present a mild dependence on the EOS. The same outcome applies to the morphology of the lightcurves.

Crossover behavior of linear and star polymers in good solvents

Monte Carlo simulation calculations for the mean-square end-to-end distance and second virial coefficient for model linear and star polymers composed of hard spheres with square-well attractions are presented. For these polymers, two types of crossover behavior are observed: (i) crossover from the Gaussian chain to the Kuhnian chain limits and (ii) crossover from the semiflexible chain to the Kuhnian chain limits. A crossover theory for the properties of dilute linear and star polymers under good solvent conditions is presented. This model directly relates the properties of the monomer–monomer interaction to the renormalized parameters of the theory. The predictions of the crossover theory are in good agreement with simulation data. A new equation of state for linear and star polymers in good solvents is presented. The equation of state captures the scaling behavior of polymer solutions in the dilute/semidilute regimes and also performs well in the concentrated regimes, where the details of the monomer–monomer interactions become important. This theory is compared to Monte Carlo simulation data for the volumetric behavior of tangent hard-sphere polymers.

Equation of state based on the thermodynamic perturbation theory of sequential polymerization for associating molecules and polymers

Recently, we developed new equations of state for the freely jointed hard sphere chain fluids, which are based on the thermodynamic perturbation theory (TPT) of sequential polymerization. The equations of state use the contact values of the radial distribution function (RDF) for monomer–dimer mixtures, which is derived from the multidensity Ornstein–Zernike (MOZ) theory. In this work, we extend one of these equations of state to real fluids such as hydrocarbons, alkanols and polymers. In order to calculate the phase equilibrium properties of real fluids, a dispersion contribution is added to the repulsive hard chain reference term. We also use the dispersion term that is a power series initially fitted by Alder et al. for square-well fluid. The universal constants that are included in the dispersion term are revised to accurate PVT for ethane. The vapor pressures and the coexisting densities of several real fluids are calculated with the new equation. We find a good agreement between the predictions of the model and experimental data.

Fermionic massive modes along cosmic strings

The influence on cosmic string dynamics of fermionic massive bound states propagating in the vortex, and getting their mass only from coupling to the string forming Higgs field, is studied. Such massive fermionic currents are numerically found to exist for a wide range of model parameters and seen to modify drastically the usual string dynamics coming from the zero mode currents alone. In particular, by means of a quantization procedure, a new equation of state describing cosmic strings with any kind of fermionic current, massive or massless, is derived and found to involve, at least, one state parameter per trapped fermion species. This equation of state exhibits transitions from subsonic to supersonic regimes while the massive modes are filled.

A new cubic equation of state for simple fluids: pure and mixture

A two-parameter cubic equation of state is developed. Both parameters are taken temperature dependent. Methods are also suggested to calculate the attraction parameter and the co-volume parameter of this new equation of state. For calculating the thermodynamic properties of a pure compound, this equation of state requires the critical temperature, the critical pressure and the Pitzer’s acentric factor of the component. Using this equation of state, the vapor pressure of pure compounds, especially near the critical point, and the bubble point pressure of binary mixtures are calculated accurately. The saturated liquid density of pure compounds and binary mixtures are also calculated quite accurately. The average of absolute deviations of the predicted vapor pressure, vapor volume and saturated liquid density of pure compounds are 1.18, 1.77 and 2.42%, respectively. Comparisons with other cubic equations of state for predicting some thermodynamic properties including second virial coefficients and thermal properties are given. Moreover, the capability of this equation of state for predicting the molar heat capacity of gases at constant pressure and the sound velocity in gases are also illustrated.

An equation of state for hydrogen fluoride

Using a similar approach as Lencka and Anderko [AIChE J. 39 (1993) 533], we developed an equation of state for hydrogen fluoride (HF), which can correlate the vapor pressure, the saturated liquid and vapor densities of it from the triple point to critical point with good accuracy. We used an equilibrium model to account for hydrogen bonding that assumes the formation of dimer, hexamer, and octamer species as suggested by Schotte [Ind. Eng. Chem. Process Des. Dev. 19 (1980) 432]. The physical and chemical parameters are obtained directly from the regression of pure component properties by applying the critical constraints to the equation of state for hydrogen fluoride. This equation of state together with the Wong–Sandler mixing rule as well as the van der Waals one-fluid mixing rule are used to correlate the phase equilibria of binary hydrogen fluoride mixtures with HCl, HCFC-124, HFC-134a, HFC-152a, HCFC-22, and HFC-32. For these systems, new equation of state with the Wong–Sandler mixing rule gives good results.

The Euler Equations for Multiphase Compressible Flow in Conservation Form: Simulation of Shock–Bubble Interactions

The Euler equations, together with an equation of state, govern the motion of an inviscid compressible fluid. Here, a new equation of state for volumes containing both gas and liquid is derived; this allows the Euler equations for two substances, here air and water, to be expressed in pure conservation form. This in turn allows simulation of shocks in water interacting with small bubbles of air as the meniscus no longer needs to be tracked explicitly. Extension to three space dimensions is shown to be straightforward.A test case showing how a shock wave in water interacts with a small (two-dimensional) air bubble is presented. Simulations of a shock wave interacting with two air bubbles, and a small multiphase region (comprising 50% water and 50% air by volume) are then given.