A. Mulero

Recommended Correlations for the Surface Tension of Common Fluids

Available values of the surface tension of 81 common fluids were fitted by using the same model presently used in the REFPROP program V9.0 by NIST. A set of data was built for every fluid by including mainly those values given in the DIPPR and DETHERM databases. For some fluids, other available sources of data were added in order to obtain adequate sets. For every fluid, we checked the accuracy of the REFPROP program and we made a new fit in order to improve the performance of the correlation. We found good general agreement between the REFPROP predictions and the data for 44 fluids, and therefore only very slight improvements are made for them. For the other 37 fluids, the REFPROP correlation can be more clearly improved. In particular, our new correlation is significantly more accurate for ammonia, deuterium, ethanol, and neon, because the version of REFPROP used gives values in clear disagreement with other data sources.

Equations of state for hard spheres. A review of accuracy and applications

Twenty two different analytical expressions for the compressibility factor of the hard sphere system have been collected and reviewed in order to perform two applications: Firstly, the accuracy of these expressions in reproducing six available computer simulation data sets for the hard sphere system, some of which are very recent, is tested. It is shown that there is not a direct relation between the simplicity or complexity of their analytical form and their accuracy. Secondly, the expressions, together with the Verlet–Weis formula for the temperature dependence of the molecular diameter, have been used to reproduce our molecular dynamics results for the pressure of the Lennard-Jones reference system proposed in the Weeks–Chandler–Andersen theory. We conclude that the approximation of using hard sphere equations of state together with the Verlet–Weis formula is very accurate at temperatures and densities near the Lennard-Jones critical point. At densities close to the triple point or to the liquid curve in the liquid–vapour equilibrium, the coincidence is adequate (deviations around 3%) only if the appropriate hard sphere equation of state is used.

On the universal behavior of some thermodynamic properties along the whole liquid-vapor coexistence curve

When thermodynamic properties of a pure substance are transformed to reduced form by using both critical- and triple-point values, the corresponding experimental data along the whole liquid-vapor coexistence curve can be correlated with a very simple analytical expression that interpolates between the behavior near the triple and the critical points. The leading terms of this expression contain only two parameters: the critical exponent and the slope at the triple point. For a given thermodynamic property, the critical exponent has a universal character but the slope at the triple point can vary significantly from one substance to another. However, for certain thermodynamic properties including the difference of coexisting densities, the enthalpy of vaporization, and the surface tension of the saturated liquid, one finds that the slope at the triple point also has a nearly universal value for a wide class of fluids. These thermodynamic properties thus show a corresponding apparently universal behavior along the whole coexistence curve.

Recommended Correlations for the Surface Tension of Several Fluids Included in the REFPROP Program

Accurate correlations are given for the temperature dependence of the surface tension of 37 fluids included in NISTs REFPROP program. The surface tension of these fluids was not included in the most recent version of this program, V9.12. A set of data was constructed for each of these fluids by including principally the values given in the DIPPR, DETHERM, and TDE databases and Wohlfarth and Wohlfarths book. For some fluids, other available sources of data were added in order to obtain adequate sets. The correlation expression used is the same as used for other fluids in REFPROP. For 31 fluids it was enough to use two adjustable coefficients, whereas four coefficients were needed for the other 6 fluids. For 19 fluids, the mean average percentage deviation was below 1%, and for another 16 it ranged from 1% to 2%.

Molecular thermodynamic models for the vapor-liquid equilibrium of nonpolar fluids

We propose simple expressions giving the main vapor-liquid properties for 42 nonpolar fluids. These expressions are molecular models based on a perturbative procedure, where the Lennard-Jones (LJ) system is taken as reference, the perturbed expressions being simple polynomial functions of the temperature for a given substance. The molecular parameters used, which are the only input needed in the molecular models, are the two LJ parameters, related to molecular size and the molecular interaction intensity, and the acentric factor, related to the molecular shape. The proposed molecular models are extrapolatable outside the temperature range used in the fit and seem to be easily applicable to other nonpolar fluids.

Simple modifications of the van der Waals and Dieterici equations of state: vapour–liquid equilibrium properties

Recent studies have considered simple (i.e., no adjustable parameters) modifications to the van der Waals and Dieterici equations of state. It is still unclear, however, at least for the calculation of vapour–liquid equilibrium properties, whether the appropriate repulsive term is that of the classical van der Waals equation or that given by the Carnahan–Starling equation for hard spheres. Moreover, the studies on the Carnahan–Starling–Dieterici equation of state have raised the interesting question of the comparison between the van der Waals (summed terms) and Dieterici (multiplied terms) approaches. We study here the suitability of six families of equations of state in obtaining the main vapour–liquid properties of simple fluids. These families include, together with the aforementioned equations, a variable exponent in the power-law temperature dependence. The main aims are to identify the best choice of a simple predictive equation of state, and to determine whether the Carnahan–Starling repulsive equation is a clearly acceptable alternative to the traditional van der Waals repulsive term, and whether the Dieterici-type equations can give better results than those based on the van der Waals equation.

Modification of the soave equation of state suggested by using computer simulation

Abstract A suitable function of the form f ( P , υ, T ) = 0, known as the equation of state, can be used to evaluate many important properties of pure substances and mixtures. At present, no single equation of state exists that is equally suitable for all the properties for any large range of substances. Even for substances with similar physicochemical properties, the equations of state are only valid in some particular range of temperatures and densities. Because the powerful technique of computer simulation yields results that can be considered as “exact” for a given model, such simulation data can be used for a comparison with the results of a determined equation of state. In this work, molecular dynamics simulation data for a Lennard—Jones system are compared with the predictions given by the empirical Soave equation of state. The results lead to the proposal of a modification of the Soave equation of state at high densities.

Chemical potential for simple fluids from equations of state

The chemical potential for both the hard-sphere and the Lennard-Jones systems is calculated from analytical equations of state proposed in the literature and results are compared with data obtained by different authors from computer simulations. Eighteen equations of state for hard spheres, some of them recently published, were considered, and for the Lennard-Jones system three semi-empirical equations and two semi-theoretical ones, one of the latter being proposed by us in a previous work. Good agreement, except for particular expressions and/or particular temperature or density ranges, is found for most cases and for both hard-sphere and Lennard-Jones fluids. Our results indicate that the use of expressions which are more complex than the Carnahan—Starling equation for hard spheres or than our proposal for Lennard-Jones fluids is not needed to obtain the chemical potential accurately.

On the linear dependence of the pressure and the thermodynamic properties on the perturbation parameter using the WCA theory

Abstract The linearity of the pressure, the potential energy, the internal energy, the Helmholtz free energy, and the entropy on the perturbation parameter λ in the Weeks-Chandler-Andersen (WCA) theory is discussed. Computer simulation results are used to evaluate the contributing integral terms for the pressure and several thermodynamic properties. The linear and non-linear behavior of these integral terms are analyzed. (Results show that the pressure, the potential energy, the internal energy, and the Helmholtz free energy, maintain their linear dependence with respect to the perturbation parameter λ. It is also found that attractive interactions are important in determining the entropy of the system. Also, the entropy shows a non-linear behavior with respect to λ.

Improving the prediction of liquid saturation densities from models based on the corresponding states principle

The liquid saturation density of pure fluids is commonly predicted using models based on the corresponding states principle. Nevertheless, it is well-known that these models are not always accurate near the triple point. In this work we use simple modifications of several of those models in order obtain good accuracy at any temperature. In particular, for each model we change a fixed coefficient to a variable coefficient, which permits the model to reproduce exactly the value of the density at the triple point. The accuracy of a model based on a scale-variable-reduced-coordinate framework, and of a new simple predictive model recently proposed by us is also checked. This latter model does not contain adjustable coefficients but only two variable coefficients that depend on the temperature and density at both the critical and the triple point. We find that a simple modification of the well-known and straightforward Rackett model gives excellent accuracy (mean average absolute deviation 0.9%) in the whole temperature range for 107 fluids of different kinds.