Crossover Equation Of State Research Articles

Comprehensive simulation of heavy-ion collisions at nonzero baryon chemical potential

We present results of hydrodynamic modelling of Au-Au collisions from $\sqrt{s_{NN}}$ = 7.7 to 200 GeV. Our simulations have three novel components. Firstly, we use a Linear EXtrapolation of Ultrarelativistic nucleon-nucleon Scattering to nucleus-nucleus collisions (LEXUS) inspired Monte-Carlo initial state model. Secondly, we use a crossover equation of state at finite baryon densities without a critical point. Finally, we use departure functions derived from the quasiparticle theory of transport coefficients for hadronic matter at non-zero baryon densities.

Hybrid stars and the QCD phase transition with an NJL-type model

In this paper, we introduce a self-consistent mean field approximation to study the QCD phase transition and the structure of hybrid stars within the framework of NJL model. In our practice, a phenomenological parameter $\alpha$ is introduced, which reflects the weights of "direct" channel and "exchange" channel under a finite chemical potential. The mass-radius relation is obtained by solving the Tolman-Oppenheimer-Volkoff equation using a crossover equation of state (EOS). We calculate the density distribution in a two solar-mass hybrid star to show the effects of different parameters. We also calculate the tidal Love number $k_2$ and the deformability $(\Lambda)$. It is found that the stiffness of the EOS increases with $\alpha $, which allows us to obtain a hybrid star with a maximum mass of 2.40 solar-mass through our model. The observation of over 2.06 solar-mass neutron stars may indicates that the chiral transition may be a crossover on the whole $T-\mu$ plane.

Multiplicity scaling of light nuclei production in relativistic heavy-ion collisions

Using the nucleon coalescence model based on kinetic freeze-out nucleons from the 3D MUSIC+UrQMD and the 2D VISHNU hybrid model with a crossover equation of state, we study the multiplicity dependence of deuteron (d) and triton (t) production from central to peripheral Au+Au collisions at sNN= 7.7, 14.5, 19.6, 27, 39, 62.4 and 200 GeV and Pb+Pb at sNN=2.76 TeV, respectively. It is found that the ratio NtNp/Nd2 of the proton yield Np, deuteron yield Nd and triton yield Nt exhibits a scaling behavior in its multiplicity dependence, i.e., decreasing monotonically with increasing charged-particle multiplicity. A similar multiplicity scaling of this ratio is also found in the nucleon coalescence calculation based on kinetic freeze-out nucleons from a multiphase transport (AMPT) model. The scaling behavior of NtNp/Nd2 can be naturally explained by the interplay between the sizes of light nuclei and the nucleon emission source. We further argue that the multiplicity scaling of NtNp/Nd2 can be used to validate the production mechanism of light nuclei, and the collision energy dependence of this yield ratio can further serve as a baseline in the search for the QCD critical point in relativistic heavy-ion collisions.

Neutron stars with a crossover equation of state

The question of whether quark matter exists in neutron stars is a long standing one. Generally one finds that a first order phase transition from baryons to quarks softens the equation of state so much that the star would collapse into a black hole. We consider a crossover equation of state, similar to the crossover that is found in lattice QCD studies at finite temperature and zero or small baryon chemical potentials. We find that with reasonable parameters it may be possible to support neutron stars up to about 2.2 solar masses. In that case 1 to 10% of the pressure would be contributed by quark matter in the central core of the highest mass stars.

Application of a Crossover Equation of State to Describe Phase Equilibrium and Critical Properties of Propane

An equation of state that predicts the thermodynamic behavior of propane is formulated. This equation takes into account the global behavior that includes the singular thermodynamic behavior asymptotically close to the critical point and the crossover to the regular thermodynamic behavior far away from the critical point. The formulated equation based on the transformation of a truncated classical Landau expansion. This equation of state (EOS) can represent the thermodynamic properties of propane in a wide range of temperatures and densities around the critical point. Comparisons of the pressure P–ρ–T data measured by Mark Mclinden of NIST group calculated with crossover EOS and those computed by the EOS of Eric Lemmon and selected results of other experimentalists are presented, as well as the isochoric-specific heat data measured by Abdulagatov et al. of the Russian groups are presented. We also give the comparison with a set of isobaric-specific heat data of Yesavage et al. The description of the rectilinear diameter singularity near the critical point is also discussed.

Phase envelope calculations of synthetic gas systems with a crossover equation of state

We describe, in this work, a procedure for the calculation of the phase envelope of multi-component systems using a crossover Equation of State (EoS) based on the renormalization group theory and two different algorithms. The first algorithm utilizes pressure and temperature as natural variables, while the second uses volume and temperature. Our comparison shows that the second method is more suitable to a crossover EoS, as it avoids solving for the volume roots of the EoS, which is computationally intensive and potentially hampers the widespread use of such models in engineering applications. Moreover, we compare the simulated phase envelopes with the experimental data of 30 synthetic natural gas mixtures. The results indicate that the crossover SRK EoS has a similar performance to the classical model. Although larger deviations are observed for the representation of the bubble and dew-point curves, the crossover EoS yields a superior description of the critical points.

Application of a Crossover Equation of State to Describe Phase Equilibrium and Critical Properties of n-Alkanes and Methane/n-Alkane Mixtures

Crossover equations of state (EOSs) are models that incorporate density fluctuations into mean-field thermodynamic models, changing their behavior close to the critical point. In this way, they are capable of describing the analytical behavior of fluids far from the critical region and the asymptotic one near the critical point. Although several crossover EOSs have been developed in the last decades their use in modeling industrial processes is rather limited. In this work, we use the crossover Soave–Redlich–Kwong (CSRK) to describe phase equilibrium and critical properties of pure n-alkanes and methane/n-alkane binary mixtures and compare the results to two other modeling approaches of the SRK EOS. In the case of the pure fluids, CSRK gives an accurate overall description of the phase equilibrium and critical properties; nevertheless, a minor increase in the deviation of the saturation pressure and other properties is observed when compared to that of the mean-field model. For the binary mixtures, an imp...

Directed Flow in Heavy-Ion Collisions and Its Implications for Astrophysics

Analysis of directed flow ( v 1 ) of protons, antiprotons and pions in heavy-ion collisions is performed in the range of collision energies s N N = 2.7–39 GeV. Simulations have been done within a three-fluid model employing a purely hadronic equation of state (EoS) and two versions of the EoS with deconfinement transitions: a first-order phase transition and a smooth crossover transition. The crossover EoS is unambiguously preferable for the description of experimental data at lower collision energies s N N ≲ 20 Gev. However, at higher collision energies s N N ≳ 20 Gev. the purely hadronic EoS again becomes advantageous. This indicates that the deconfinement EoS in the quark-gluon sector should be stiffer at high baryon densities than those used in the calculation. The latter finding is in agreement with that discussed in astrophysics in connection with existence of hybrid stars with masses up to about two solar masses.

Prediction of thermodynamic behavior of binary mixtures by applying the crossover approach to Soave–Redlich–Kwong equation of state

Thermodynamic analysis of binary mixtures near the critical region is essential for many chemical process designs. In this research, based on isomorphism principle and incorporating general crossover approach the original Soave–Redlich–Kwong (SRK) equation of state (EOS) was developed for the binary mixtures. We have introduced an additional term in the crossover function in order to take into account the difference between the classical critical parameters and the real critical parameters. The applicability of this crossover EOS was verified against methane–ethane mixture to describe their thermodynamic properties over a wide range of thermodynamic states, because of their wide applications. It is shown that based on this approach we can received too much more accuracy for predicting thermodynamic properties in comparison with classical form of SRK EOS.

Net baryon fluctuations from a crossover equation of state

We have constructed an equation of state which smoothly interpolates between an excluded volume hadron resonance gas at low energy density to a plasma of quarks and gluons at high energy density. This crossover equation of state agrees very well with lattice calculations at both zero and nonzero baryon chemical potential. We use it to compute the variance, skewness, and kurtosis of fluctuations of baryon number, and compare to measurements of proton number fluctuations in central Au-Au collisions as measured by the STAR collaboration in a beam energy scan at the Relativistic Heavy Ion Collider. The crossover equation of state can reproduce the data if the fluctuations are frozen out at temperatures well below than the average chemical freeze-out.

Directed flow is a sensitive probe of deconfinement transition

Analysis of available data on directed flow (\(v_{1}\)) of protons, antiprotons and pions in heavy-ion collisions is performed in the range of incident energies relevant to the Nuclotron-based Ion Collider Facility (NICA). Simulations have been done within a three-fluid model employing a purely hadronic equation of state (EoS) and two versions of the EoS involving deconfinement transitions: a first-order phase transition and a smooth crossover transition. High sensitivity of the directed flow, especially the proton one, to onset of the deconfinement transition is found. The crossover EoS is favored by the majority of the considered experimental data. Future data from NICA could clarify certain inconsistency of data at \( E_{lab} = 2-8\)A·GeV.

Internal pressure of liquids from the calorimetric measurements near the critical point

A new relation between the internal pressure and isochoric heat capacity jump of liquids along the coexistence curve near the critical point was found. Our previously reported one- and two-phase isochoric heat capacities and specific volumes at saturation were used to calculate internal pressure of molecular liquids (water, carbon dioxide, alcohols, n-alkanes, DEE, etc.).The internal pressure derived from the calorimetric measurements was compared with the values calculated from the reference (NIST, REFPROP) and crossover equations of state. Locus of the isothermal and isochoric internal pressure maxima and minima was studied using calorimetric data and the reference and crossover equations of state near the critical point. The maximum of the internal pressure of light and heavy water around the temperature of 460K along the liquid saturation curve was found. We also found very simple relation between the internal pressure, ΔPintsat, and isochoric heat capacity, ΔCV, jumps near the critical point.

What can we learn from the directed flow in heavy-ion collisions at BES RHIC energies?

Analysis of directed flow ($v_1$) of protons, antiprotons and pions in heavy-ion collisions is performed in the range of collision energies $\sqrt{s_{NN}}$ = 2.7--39 GeV. Simulations have been done within a three-fluid model employing a purely hadronic equation of state (EoS) and two versions of the EoS with deconfinement transitions: a first-order phase transition and a smooth crossover transition. The crossover EoS is unambiguously preferable for the description of the most part of experimental data in this energy range. The directed flow indicates that the crossover deconfinement transition takes place in semicentral Au+Au collisions in a wide range of collision energies 4 \lsim\sqrt{s_{NN}}\lsim$ 30 GeV. The obtained results suggest that the deconfinement EoS's in the quark-gluon sector should be stiffer at high baryon densities than those used in the calculation. The latter finding is in agreement with that discussed in astrophysics.

Consistency of Vapor Pressure Equations at the Critical Point

In this work, it is shown that the most common approximations for the vapor-pressure equation of a fluid yield an inappropriate behavior for the second temperature derivative of the saturation pressure in the vicinity of the critical point. This fact gives rise to an unphysical divergent behavior for the change of the specific heat at vaporization (Δvcv) near the critical point. An expression for the vapor-pressure equation with the appropriate critical behavior is proposed in terms of a truncated Renormalization Group (RG) expansion. As an example, it is shown that the well-known Wagner and Pruss vapor-pressure equation and the IAPWS-95 result for water yield an incorrect critical behavior for Δvcv whereas the RG equation, in agreement with the results of a crossover equation of state, provides the appropriate critical behavior. An application to the Ambrose-Walton vapor pressure equation is also presented.

Reply to “Comments on ‘Experimental Measurement of Vapor Pressures and Densities at Saturation of Pure Hexafluoropropylene Oxide: Modeling Using a Crossover Equation of State’”

ADVERTISEMENT RETURN TO ISSUEPREVCorrespondenceNEXTReply to “Comments on ‘Experimental Measurement of Vapor Pressures and Densities at Saturation of Pure Hexafluoropropylene Oxide: Modeling Using a Crossover Equation of State’”Moussa Dicko, Alain Valtz, and Christophe Coquelet*View Author Information Mines Paristech, CEP/TEP Centre Energétique et Procédés, 35, rue Saint Honoré, 77305 Fontainebleau, FrancePhone: +33 1 64694962. Fax: + 33 1 64694968. E-mail: [email protected]Cite this: Ind. Eng. Chem. Res. 2011, 50, 15, 9476–9477Publication Date (Web):July 5, 2011Publication History Published online5 July 2011Published inissue 3 August 2011https://doi.org/10.1021/ie201274yCopyright © 2011 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views243Altmetric-Citations-LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (741 KB) Get e-AlertsSUBJECTS:Compressibility,Vapor pressure Get e-Alerts

Comments on “Experimental Measurement of Vapor Pressures and Densities at Saturation of Pure Hexafluoropropylene Oxide: Modeling Using a Crossover Equation of State”

ADVERTISEMENT RETURN TO ISSUEPREVCorrespondenceNEXTComments on “Experimental Measurement of Vapor Pressures and Densities at Saturation of Pure Hexafluoropropylene Oxide: Modeling Using a Crossover Equation of State”Serge Laugier*† and Dominique Richon‡View Author Information† I2M, UMR CNRS 5295 ENSCBP, 16 Avenue Pey Berland, 33607 Pessac, France‡ MINES ParisTech, CEP/TEP—Centre Énergétique et Procédés, 35 Rue Saint Honoré, 77305 Fontainebleau, France Phone: +33-5-40 00 66 64. Fax: + 33-5-40 00 27 31. E-mail: [email protected]Cite this: Ind. Eng. Chem. Res. 2011, 50, 15, 9473–9475Publication Date (Web):July 5, 2011Publication History Published online5 July 2011Published inissue 3 August 2011https://doi.org/10.1021/ie2011559Copyright © 2011 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views221Altmetric-Citations1LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (1 MB) Get e-AlertsSUBJECTS:Compressibility,Equation of state,Saturation,Theoretical and computational chemistry Get e-Alerts

Experimental Measurement of Vapor Pressures and Densities at Saturation of Pure Hexafluoropropylene Oxide: Modeling Using a Crossover Equation of State

Hydrofluoroalkenes, like hexafluoropropylene, can be considered as new working fluids for refrigeration systems and consequently volumetric and critical property data are required. In this study, a vibrating tube densitometer technique was used to determine densities at nine different temperatures between (263 and 358) K, and pressures between (0.04 and 15) MPa. The experimental uncertainties are ±0.0003 and ±0.0006 MPa for pressure, ± 0.02 K for temperature, ± 0.5% (relative) for vapor densities, and ±0.05% for liquid densities. A different equipment based on static method is used for the determination of pure component vapor pressures for temperatures between (231 and 359) K. The experimental uncertainties are ±0.0005 MPa for pressure and ±0.02 K for the temperature. Critical properties have been determined by direct measurement and also from utilization of experimental densities considering the asymptotic scaling law behavior. The Patel−Teja and crossover Patel−Teja equations of state are used to corre...

PVT measurements for pure methanol in the near-critical and supercritical regions

PVT properties of pure methanol were measured in the near-critical and supercritical regions. Measurements were made with a constant-volume piezometer immersed in a precision air thermostat. The maximum uncertainty of the density measurements was estimated to be 0.15%. The uncertainties of the temperature and pressure measurements were, respectively, 15 mK and 0.05%. Measurements were performed at seven near-critical isochores between 113 and 370 kg m −3 and at pressures from 1.4 to 40 MPa. The range of temperature was 423–653 K. Using the two-phase PVT data, the values of vapor–pressure and saturated liquid and vapor density were determined by means the analytical extrapolating technique in the temperature range from 423 to 512.7 K. The measured one-phase PVT data and saturated property data ( T S , P S , ρ ′ S , ρ ″ S ) for pure methanol were compared with the values calculated from fundamental IUPAC and crossover equations of state and with precise experimental PVT data reported by other authors. From the saturated liquid and vapor density and vapor–pressure data in the critical region the values of the critical parameters ( T C = 512.75 ± 0.1 K, P C = 8.120 ± 0.02 MPa, and ρ C = 271.6 ± 3 kg m −3) were extracted. For three isochores (113.5, 252.4, and 368.2 kg m −3) the measurements were performed in both cooling and heating regimes to estimate the effect of thermal decomposition (chemical reaction) on the PVT properties of methanol.

Universal Crossover Approach to Equation of State for Fluids

It is well known that any classical equation of state fails to describe the properties of fluids in the critical region, where the behavior of fluids is strongly affected by density fluctuations. In the present work, a universal approach to incorporate the effects of density fluctuations in the global behavior of one-component fluids is proposed. As an illustration of our general approach, a crossover generalization of a four-parametric cubic equation of state, which can be useful for engineering applications, is demonstrated. The obtained crossover equation reproduces Ising-like singular scaling behavior in the critical region and reduces to the original cubic equation of state far away from the critical point. In addition, the crossover equation of state is applied to describe thermodynamic properties of methane, ethane, carbon dioxide, and water. It is shown that incorporation of critical fluctuations leads to a significant improvement in the ability of the cubic equation to represent thermodynamic properties and liquid–vapor equilibrium of one-component fluids.

Molecular dynamic simulations and global equation of state of square-well fluids with the well-widths from λ = 1.1 to 2.1

We present the results of extensive new molecular dynamic (MD) simulations in the one-phase region for square well fluids with well widths λ = 1.10, 1.15, 1.20, 1.25, 1.375, 1.50, 1.75, 1.90, 2.0, and 2.10. These data have been used in developing a crossover equation of state (CR EOS) for square-well fluids with well widths 1.1 ≤ λ ≤ 2.1. The CR EOS incorporates non-analytic scaling laws in the critical region, and in the limit of low densities yields the exact second and third virial coefficients. Also in the high-temperature region, it reproduces first-order perturbation theory results. The CR EOS was tested against our new MD simulations, and earlier MD and Monte-Carlo (MC) simulations reported by other authors as well. Excellent agreement between calculated values and simulation data for all SW fluids is observed. In combination with the density-functional theory, the CR EOS is also capable of reproducing surface tension simulations with high accuracy. Application of the CR EOS for solid–liquid equilibrium calculations in combination with the Lennard–Jones and Devonshire cell model for the solid phase, is also discussed.