Type Equation Of State Research Articles

Trans-Cinnamic Acid Solubility Enhancement in the Presence of Ethanol As a Supercritical CO2 Cosolvent

Trans-3-phenyl-2-propenoic acid (cinnamic acid; trans-cinnamic acid) is widely used in food, cosmetics, and pharmaceuticals because of its reported antimicrobial, antifungal, and antioxidant properties. This paper is devoted to the experimental measurement of the solubility of solid trans-cinnamic acid in pure supercritical CO2 and in supercritical CO2 with ethanol as a cosolvent. Measurements were carried out at T = (313.15 to 343.15) K and at p = (10 to 40) MPa. Two different thermodynamic models were applied to represent the solubility data obtained: a cubic type equation of state, the Soave−Redlich−Kwong (SRK-EoS) was employed to correlate the solubility data and the group contribution associating EoS (GCA-EoS) was also applied but in a completely predictive manner. In addition, values for the thermophysical properties of trans-cinnamic acid are also advocated.

An Eulerian particle level set method for compressible deforming solids with arbitrary EOS

AbstractIn this study, an Eulerian, finite‐volume method is developed for the numerical simulation of elastic–plastic response of compressible solid materials with arbitrary equation of state (EOS) under impact loading. The governing equations of mass, momentum, and energy along with evolution equations for deviatoric stresses are solved in Eulerian conservation law form. Since the position of material boundaries is determined implicitly by Eulerian schemes, the solution procedure is split into two separate subproblems, which are solved sequentially at each time step. First, the conserved variables are evolved in time with appropriate boundary conditions at the material interfaces. In the present work a fourth‐order central weighted essentially non‐oscillatory shock‐capturing method that was developed for gas dynamics has been extended to high strain rate solids problems. In this method fluxes are determined on a staggered grid at places where solution is smooth. As a result, the method does not rely on the solution of Riemann problems but enjoys the flexibility of using any type of EOS. Boundary conditions at material interfaces are also treated by a special ghost cell approach. Then in the second subproblem, the position of material interfaces is advanced to the new time using a particle level set method. A fifth‐order Godunov‐type central scheme is used to solve the Hamilton–Jacobi equation of level sets in two space dimensions. The capabilities of the proposed method are evaluated at the end by comparing numerical results with the experimental results and the reported benchmark solutions for the Taylor rod impact, spherical groove jetting, and void collapse problems. Copyright © 2009 John Wiley & Sons, Ltd.

Experimental Determination of Shock Hugoniot for Water, Castor Oil, and Aqueous Solutions of Sodium Chloride, Sucrose and Gelatin

Shock waves are indispensable tools for medical applications, and hence their interactions with human tissue become one of the most important basic research topics. In this paper, the determination of shock Hugoniot curves for liquids that can model human tissue, namely water, castor oil, and aqueous solutions of sodium chloride, sucrose and gelatin, at 10 and 20 weight percent are presented. Underwater shock waves were generated by ignition of 10 mg silver azide pellets and time variations of over-pressures were measured and simultaneously the shock speed was measured by the time of flight technique. Then shock Hugoniot curves were obtained, by assuming the Tait type equation of state, to relate the estimated density and measured pressure values. Results show in the cases of aqueous solutions that increasing amount of additives into water causes only a very minute decrease in the compressibility of the solution. This difference was more pronounced in the case of sodium chloride, less for gelatin, and almost none for sucrose aqueous solution.

Infinite pressure behaviour of certain inverted type equations of state for solids

Abstract It is shown that a generalized version of inverted type equation of state (EOS) yields the recently proposed Saxena EOS [J. Phys. Chem. Solids 65 (2004) 1561] for a particular value of the parameter related to K ∞ ′ , the pressure derivative of bulk modulus at extreme compression. It is found that some other inverted type EOS due to earlier workers can also be derived from a generalized version. A common feature of the inverted equations considered in the present paper is that they yield negative values for K ∞ ′ . This is in strong contradiction and violation of the theory of infinite pressure extrapolation due to Stacey.

Coexistence properties of the Redlich–Kwong model for a fluid

It is shown in this paper that for pure substances obeying the van der Waals (VdW) equation of state (EOS) or Redlich–Kwong (RK) type equations of state below the critical temperature, it is possible to obtain with the help of the Maxwell equal areas rule the vapour pressure curve, the difference between the molar volume of the vapour and of the liquid, and the difference between the molar entropies of vapour and liquid; each property is obtained in the first step as a dimensionless expression, function of a dimensionless temperature. Any particular property of a particular fluid obeying VdW EOS or one type of RK EOS can be obtained from the corresponding dimensionless expression by multiplying it with a dimension unit which is a function of the particular temperature-dependent parameter a(T) of the EOS considered for the fluid. In the cases of VdW and the original RK (EOS), the dimensionless functions are unique for all the pure fluids that obey the EOS under consideration. A comparison of VdW, RK and RK–Soave (SRK) predictions with experimental vapour pressure data is exemplified for carbon dioxide.

Parameters for the attractive coefficient of the patel-teja-valderrama equation of state

A three-parameter form of the temperature dependence of the attractive term in cubic van der Waals type equations of state (AS; Almeida et al., 1991; Aznar and Silva-Telles, 1992) has been applied to a generalized equation of state known as the Patel-Teja-Valderrama equation (PTV; Valderrama, 1990). The parameters of the AS model in the PTV equation of state were calculated for 457 substances of different polarity, molecular size, and chemical nature. The parameters were calculated using vapor pressure data determined through accurate equations available in the literature (Wagner 1973, Antoine 1888, Frost and Kalkwarf, 1953). The deviations between the equation of state calculations and vapor pressure information are lower than 0.5% for most fluids. The study shows that both the generalized PTV cubic equation and the AS represent good tools for pressure-temperature calculations in engineering applications.

A simplified CEOS/ AE mixing rule and its applications for vapor–liquid and liquid–liquid equilibrium predictions

The new CEOS/ A E mixing rule recently developed by Twu et al. [Fluid Phase Equilib. 158–160 (1999) 271] is simplified and tested for high-pressure vapor–liquid equilibrium (VLE) and liquid–liquid equilibrium (LLE) predictions. This mixing rule has some significant features such as: (1) it is density dependent, (2) it is based on no reference-pressure, and (3) it automatically reduces to van der Waals mixing rule for normal mixtures. The mixing rule is used with any G E activity coefficient model such as NRTL, UNIQUAC, and UNIFAC. This approach can employ the available binary interaction parameters from those activity coefficient models without requiring any additional parameters or causing any thermodynamic inconsistency. It extends the predictive capability of the cubic type equation of state (CEOS) to highly nonideal mixtures, which have traditionally been handled using an activity coefficient approach. This work has tested various binary VLE/LLE systems including nonpolar, polar, and associating compounds. Overall, the accuracy of the mixing rule with a CEOS (with a modified alpha-function for each component) is comparable with that of the activity coefficient approach. For LLE, the mixing rule can predict the three different types of phase diagrams (with UCST, LCST, or both). This work also shows that the CEOS/ A E mixing rule can be applied to high-pressure systems for which the activity coefficient models have limited success.

Equation of state analog correlations for the viscosity and thermal conductivity of hydrocarbons and reservoir fluids

Based on the geometric similarity of P– V– T, T– μ– P and T– λ– P diagrams, viscosity ( μ) and thermal conductivity ( λ) data of hydrocarbons and their mixtures have been successfully correlated using a cubic equation of state (EOS) type equation. The advantages of using EOS-analog expressions are simple in form, applicable to both gas/liquid, high-pressure/low-pressure, and smooth phase transition of μ and λ in the near-critical region could be achieved. First, a modified viscosity correlation based on PR (Peng–Robinson) EOS type expression is presented, which improves the prediction of the viscosity of reservoir fluids (including CO 2-injected enhanced oil recovery systems). Then, the development of EOS type expression for fluid thermal conductivity is described. The results of extensive tests with data indicate the superiority of the proposed EOS-analog viscosity and thermal conductivity correlations over typical empirical and semi-empirical correlations used in the petroleum industry.

Prediction of the critical locus in binary mixtures using equation of state: II. Investigation of van der Waals-type and Carnahan–Starling-type equations of state

The ability to predict critical lines of members of the methane–, perfluoromethane– and water–alkanes homologous series is compared for van der Waals (vdW)-type and Carnahan–Starling (CS)-type equations of state. A temperature dependent combining rule for the binary attraction parameter is discussed and employed. It is found that the appropriate choice of the adjustable parameters yields quite accurate results for both equations. A new application of global phase diagrams is proposed for the quantitative description of real mixtures. In this diagram, the boundaries of the different types of phase behavior are presented in the k 12– l 12 plane. Analysis of this diagram has allowed us to reach conclusions that cannot be obtained by a simple fit of data points. In particular, it is demonstrated that the global phase diagram's shape defines the correlative ability of the equations. It is found that CS-type equations tend to predict a larger region of liquid–liquid immiscibility, the accuracy of the result depends on the particular experimental system. Changes in the density dependence of the attraction term of the two-parameter equations influence mostly the predicted critical volumes and not their qualitative performance. In addition, the development of a CS-type equation suitable for engineering calculations is discussed.

Single crystal X-ray diffraction studies of Na2MnF5 at high hydrostatic pressures

Abstract The crystal structure of Na2MnF5 has been investigated by high pressure single crystal and powder X-ray diffraction techniques. The unit cell parameters have been determined in the pressure range from ambient conditions to 2.93 GPa. The P21/c space group symmetry is retained in this pressure range. Above 3 GPa the single crystals collapse and a polycrystalline specimen is formed. Preliminary high pressure powder diffraction studies show that the transformation occurs in the range 3–4 GPa. The transition is reversed when the pressure is lowered. The structure of Na2MnF5 consists of parallel infinite chains of corner connected MnF6 octahedra that extend along [100]. The chains are held together via bonds to surrounding Na ions. A structure determination based on data collected at 2.34 GPa has been performed. With 199 observed independent reflection intensities, a simple structural model described by 31 parameters was refined to wR = 0.078 (R = 0.084). Major changes observed are decreased inter-chain distances, also reflected in significantly shortened Na–F distances for one of the Na atoms. The compressibility is smallest along the chain direction [100]. The isotropic bulk modulus B 0 obtained by fitting the relative volume changes to a Birch type equation of state is 48(4) GPa.

Modeling General Relativistic Perfect Fluids in Field-Theoretic Language

Skew-symmetric massless fields, their potentialsbeing r-forms, are close analogues of Maxwell's field(though the nonlinear cases also should be considered).We observe that only two of them (r = 2 and 3) automatically yield stress-energy tensorscharacteristic of normal perfect fluids. It is shownthat they naturally describe both nonrotating (r = 2)and rotating general relativistic perfect fluids (then a combination of r = 2 and r = 3 fields isindispensable) and possess every type of equation ofstate. Meanwhile, a free r = 3 field is completelyequivalent to the appearance of the cosmological term inEinstein's equations. Sound waves represent perturbationspropagating on the background of the r = 2 field. Someexotic properties of these two fields areoutlined.

Real gas effects on the prediction of ram accelerator performance

The analysis of ram accelerator performance is based on one-dimensional modelling of the flow process that propels the projectile. The conservation equations are applied to a control volume travelling with the projectile, and quasi-steady flow is assumed. To date the solution obtained, namely the generalized thrust equation, has been based on the ideal gas assumption. At the high level of pressure that is encountered during the ram accelerator process, this assumption cannot be regarded as adequate. Thus, a more appropriate equation of state (EOS) should be used instead. Depending upon the level of pressure, several equations of state are available for dense gaseous energetic materials. The virial type of EOS can be more or less sophisticated, depending upon the extent of complexity of the intermolecular modelling, and turns out to be totally appropriate for most gaseous explosive mixtures that have been investigated at moderate initial pressures, i.e., less than 10MPa. In the present case the Boltzmann EOS was applied. It is based on very simplified molecular interactions, which makes it relatively easy to use in calculations. Moreover, the energetic EOS needs to be taken into account. This concerns all the calorimetric coefficients, as well as the thermodynamic parameters, which can no longer be expressed as only a function of temperature. The higher the pressure level, the more sophisticated these corrections become, but the main relationships that account for real gas effects are basically the same. These include the use of a general form of analytical operators applied to correct the thermodynamic functions and coefficients. The equations governing the one-dimensional model were taken as a basis for the real gas corrections and were solved analytically. The parameters which play the most crucial roles in this correction can thus be highlighted. A complete set of equations involving the real gas effects are presented in this paper. The QUARTET code was used in this investigation, especially for determining chemical equilibrium compositions. This more accurate model can better predict the projectile acceleration of the thermally choked propulsive mode. Although the present analysis is applied to the fuel-rich methane-oxygen-nitrogen mixture currently used in the ram accelerator experiments, its general formulation makes it readily applicable to any other mixture. The projectile velocity and acceleration histories determined by the Hugoniot analysis for the thermally choked ram accelerator mode, assuming the Boltzmann EOS, turn out to be in much better agreement with experimental observations up to the CJ detonation velocity than that when based on the ideal gas assumption.

Extension of EOS non‐iterative methods to density calculations: Correlation of saturated molar volumes and heats of vaporization

AbstractSoave's direct calculation procedures for the vapor pressure of pure compounds with cubic equations of state (EOSs), have been extended to the calculation of phase densities at saturation for Peng‐Robinson (PR) type EOSs. These universal relations have been used to propose EOS‐based correlation methods for the pure compound saturated liquid and vapor molar volumes, at temperatures higher than the normal boiling point. The methods yield satisfactory results independently of the molecular nature of the chemical under consideration. The results for phase densities are used to correct the heats of vaporization predicted by the ZVPR‐EOS. Complete relative error information is provided for calculated heats of vaporization and correlated vapor and liquid phase molar volumes for more than one hundred compounds of industrial interest.

Description of accelerator and cosmic ray data in terms of relativistic hadron thermodynamics

Evidences for thermodynamical description of relativistic hadrons are presented. Relativistic hadron distribution does not obey any known statistics, though a prevailing term leads to Stephan — Boltzmann type equation of state. A common hadron state asymptotic regime is compatible with S-matrix models describing the low energy accelerator data with Pomeron exchange phenomenology. The gross features of giant showers can be explained in the frame of relativistic hadron thermodynamics. It cannot be achieved by S-matrix models with additional production of mini-jets.

The isochoric-, isobaric- and saturation-heat capacities of the Lennard-Jones fluid from equations of state and Monte Carlo simulations

Isochoric-, isobaric- and saturation-heat capacities are calculated from the modified Benedict-Webb-Rubin type equation of state (EOS) of Johnson et al. (1993) and from the van der Waals theory based EOS given by Mecke et al. (1995) for the Lennard-Jones fluid. The isochoric- and isobaric-heat capacities are also determined from NVT and NpT ensemble Monte Carlo simulations. A method is proposed for the determination of the saturation heat capacity using the appropriate fluctuation formulae in both ensembles. The EOS-based theoretical results show reasonable agreement with the simulation data. Comparing with real liquids the theoretical heat capacities based on EOSs, calculated along the vapour-liquid saturation curve, agree well with experimental data for argon and methane.

Effect of EOS on Break-Up of Shoemaker-Levy 9 Entering Jovian Atmosphere.

Break-up of Comet Shoemaker-Levy 9 entering Jovian atmosphere was studied with highly accurate hydrocode ExCIPHER by changing the equation of state (EOS) of the comet. The comet of radius 1.5 km was completely destroyed around the atmospheric pressure of 10 bar which is shallower than the result by Mac Low and Zahnle. Furthermore, the behavior of break-up is quite different from them. This behavior depends on the type of EOS. For hard material like water and ice, the impact of Jovian atmosphere caused incompressible surface wave propagating along the comet surface thus enhancing ablation loss in low pressure atmosphere. For ideal EOS, however, the surface wave did not appear since the comet was compressed upon impact and hence the ablation loss around 5 bar was quite low. Although the comet was broken into moderate pieces at 10 bar, most of the energy had already been lost well before the break-up. Surprisingly, however, the final disintegration occurred around 10 bar for tested EOS and even for planar geometry.

Solution of the High-Pressure Riemann problem for Solids Including Rigidity Effects

An analytical solution of the high-pressure Riemann problem for solids which satisfy the Grüneisen type equation of state has been obtained. Square of acoustic impedance along an isentrope passing through any thermodynamic states is written as a polynomial of the homogeneous solution, X of the differential equation for the isentropic pressure change. The form of equation of state, p ( v , ε ) were calculated based on this assumption. Furthermore, elastic effects are included into the equation of state, and the von Mises yielding condition is assumed to be valid up to very high pressures. As a typical example, the elastic-plastic Riemann problem for the case of aluminum are solved after rather simple calculation.

Leung-Griffiths model for the thermodynamic properties of mixtures of CO2 and C2H6 near the gas-liquid critical line

Leung and Griffiths have proposed a fundamental thermodynamic equation for a binary mixture near the critical line and have successfully applied it to the mixture of He3 and He4 in which the critical line is a nearly linear function of composition. We have used a Leung-Griffiths type equation of state to describe the thermodynamic properties of the mixture of carbon dioxide and ethane. The critical line of this mixture is, unlike that of He3 and He4, a nonlinear function of composition, and the azeotropic line extends to the critical line. Comparison of the predictions of the equation to experimental data shows a good agreement for the mixture of CO2 and C2H6.

Soft nonspherical repulsions and properties of non-polar liquids

In the present paper we have tried to appreciate the significance of repulsive forces in non-polar liquids and their responsibility for observed regularities. The model of soft convex bodies has been introduced for the description of nonspherical repulsions while the attractive forces have been treated by means of the mean field approximation. Using the perturbation expansion a van der Waals type equation of state has been derived; the thermodynamic functions depend, besides the dependence on the temperature and on the density, on two acentric factors. It has been found that the explicit inclusion of nonspherical repulsions gives rise to monotonic trends that are experimentally observed in the homologous series: the decrease of the critical compressibility factor and of the ratio TB/TC with increasing deviation of molecules from the spherical shape. The softness of repulsions then has enabled us to appreciate the temperature dependence of the second virial coefficient.

An equation of state for dense nitrogen

An empirical equation of state for nitrogen at high pressure and density is considered. It is shown that for nitrogen at densities greater than 0.6 g/cm3, by using available data [1–3] on static compression of gaseous nitrogen and shock compression of liquid nitrogen, it is possible to construct a Mie-Gruneisen type equation of state which gives a pressuredensity relationship close to experiment along the shock adiabat of liquid nitrogen and agrees with the calculations of other authors for temperature values beyond the shock-wave front [2–3]. Heat capacity, entropy, and Gruneisen coefficient values beyond the shock-wave front in liquid nitrogen are calculated.