Van Der Waals One-fluid Approximation Research Articles

Thermal conductivity of the Lennard-Jones fluid: An empirical correlation

In this work, is presented an empirical correlation on the thermal conductivity of the Lennard-Jones fluid based on extensive non-equilibrium molecular dynamics simulations results (103 points). Finite size and cutoff radius effects are investigated and taken into account to develop the correlation. This last, composed of low-density, residual and critical enhancement contributions, is built for a wide range of thermodynamics states, even at the vicinity of the critical point, and yields an average absolute deviation of 1.29% compared to our simulations. In addition, a careful analysis of the different contributions to the microscopic flux is carried out which sheds light on the underlying mechanism of the results. Finally, are discussed the limitations of the proposed model when applied to real simple fluids and mixtures using a standard corresponding states scheme and the van der Waals one-fluid approximation.

Electric field dependence of phase equilibria of binary Stockmayer fluid mixtures

A perturbation theory based study of the effect of an external electric field on the phase equilibrium properties of binary Stockmayer fluids is presented. The dipole–dipole interaction and the applied field are treated as independent perturbations to a Lennard–Jones mixture, and the reference fluid is treated by the van der Waals one-fluid approximation. A third-order free energy expression in the electric field strength is established, and the dielectric constant is calculated for a needle-shaped sample parallel to the field direction. We present and discuss vapour–liquid and liquid–liquid equilibrium curves at a given temperature for some dipolar mixtures exposed to an electric field, including chlorodifluoromethane + difluoromethane and acetonitrile + methanol. A sufficiently high electric field may result in massive shifts of vapour pressures and critical or azeotropic points, and can considerably alter the properties of coexisting phases. The vapour pressure decreases with increasing field strength.

Evaluation of mixing and combining rules for asymmetric Lennard–Jones chain mixtures: Effect of segment diameter, energy interaction, and chain length

Equations of state (EOS) capable of accurately representing the thermodynamic properties of chain molecules are of academic and industrial interest. In many cases, the systems of interest are composed by highly asymmetrical molecules, i.e., of different chain length, segment diameter, and segment interaction energy. The aim of this work is to evaluate mixing and combining rules (M&CR) for a SAFT-type equation of state. In the first part of this work, M&CR from literature are used together with the Wertheim Thermodynamic Polymerization Theory, in its dimer version, to calculate thermodynamic properties and then compare to those from molecular simulations. A data bank of compressibility factor and residual internal energy of Lennard–Jones chain asymmetrical mixtures was prepared for this purpose. In order to perform a systematic evaluation of M&CR, the one-fluid mixing rule (1FMR) and van der Waals one-fluid approximation (vdW1F) were coupled with the Berthelot combining rule (CR) and different CR for segment diameter, including Lorentz, Chen et al. [J. Chen, J. Lu, Y. Li, Fluid Phase Equilib. 140 (1997) 37], and a CR with one adjustable parameter. Results from comparisons with simulated data show that the 1FMR along with the Lorentz–Berthelot CR fails to represent thermodynamic properties of binary mixtures with simultaneous asymmetry in chain length and segment diameter. On the other hand, the density-dependent Chen et al. CR and vdW1F, only tested for Lennard–Jones sphere and hard-sphere chain asymmetrical mixtures, shows good performance in calculating compressibility factor and residual internal energy of asymmetrical mixtures of Lennard–Jones chains. The CR proposed in this work, with one optimized parameter, presented even better results than the Chen et al. CR, allowing a better description of simulated data employing a simpler rule.

Molecular Dynamics Study of the Lennard−Jones Fluid Viscosity: Application to Real Fluids

A predictive scheme of viscosity for pure fluids and mixtures of simple molecules is presented. First, using molecular dynamics data from the literature and also from our own study, a representative correlation of the viscosity of a Lennard-Jones fluid is developed for a wide range of thermodynamic states. Second, a corresponding states scheme is proposed which allows the transposition of the previous results to real fluids. For some simple molecules, this scheme induces deviations lower than 5% in conditions covering gas, liquid, and supercritical states. For larger molecules, the results are poorer but can be strongly improved by fitting the atomic diameter. Then, it is shown for simple binary and multicomponent mixtures that, by using merely a van der Waals one-fluid approximation and the Lorentz-Berthelot rules, results are as good as for pure fluids. Finally, the limitations of such a scheme are shown when applied on the methane + toluene asymmetric mixture.

Excess molar enthalpies of (ethane + ethene), (ethane + chloromethane), (propane + chloromethane), and (butane + chloromethane) calculated from cubic equations of state and the principle of corresponding states—a comparison with experimental results

Excess molar enthalpies H m E are calculated using equations of state and the principle of corresponding states for four binary mixtures: (ethane + ethene), (ethane + chloromethane), (propane + chloromethane), and (butane + chloromethane), at temperatures from 298.15 to 363.15 K and pressures from 5 to 15 MPa, so that a comparison can be made with recently obtained experimental calorimetric results. Four cubic equations of state (van der Waals, Redlich-Kwong, Soave, and Peng-Robinson) and the principle of corresponding states, used together with the van der Waals one-fluid approximation (vdW1), are examined. The only adjustable parameter was the binary interaction parameter k 12 in Berthelot's combining rule. It was adjusted for each type of mixture and set at different values for the equation of state calculations or the principle of corresponding states prediction, but set independent of temperature, pressure, and a particular equation of state. Usually, reasonably good comparisons are obtained between the experimental results and the H m E( p, T) surface calculated from the equations of state and from the principle of corresponding states. (Vapor + liquid) equilibria for (ethane + chloromethane) at p = 5 MPa were also calculated using the k 12 determined from the H m E results, and compared with experimental results. The agreement is best for the Soave and the Peng-Robinson equations, with the other equations and the principle of corresponding states predicting equilibrium mole fractions that are low.

Application of generalized van der Waals theory and approximations of radial distribution functions to the development of mixing rules

Li, M.-H. and Huang, F.-N., 1994. Application of generalized van der Waals theory and approximations of radial distribution functions to the development of mixing rules. Fluid Phase Equilibria, 96: 155-172. Based on generalized van der Waals partition function theory and approximations of radial distribution functions, mixing rules for the attractive part of an equation of state have been presented for extension of an augmented hard-core equation of state to mixtures. Two approximations, the van der Waals one-fluid approximation and the mean density approximation, are applied in this study. Within the framework of the conformal solution theory, the properties of a hypothetical fluid were calculated from the attractive part of an augmented hard-core equation of state. As a preliminary test of the method, an augmented hard-sphere equation of state has been applied. For polar systems in which components do not differ appreciably in size, both the MDA and the VDW models yield satisfactory results for the vapor-liquid equilibrium calculations. However, for strongly non-ideal fluid systems, the MDA is superior to the VDW. Adopting the mixing rules for the repulsive hard-core mixtures to describe structure effects, the proposed method can, in principle, be used to extend any accurate augmented hard-core equation of state to mixtures.

Application of approximations to mixture radial distribution functions to the development of mixing rules

Abstract Li M.-H. and Wang Y.-L., 1992. Application of approximations to mixture radial distribution functions to the development of mixing rules. Fluid Phase Equilibria, 72: 89-110. The mixing rules utilizing the approximations for mixture radial distribution functions have been presented for extension of an equation of state of polar fluids to mixtures. The van der Waals one-fluid approximation and the mean density approximation (MDA) for radial distribution functions in a mixture have been applied to derive mixing rule models. To investigate further the composition dependence of the MDA, the composition-dependent cross-interaction energy parameter is also introduced; the resulting model is referred to as the modified mean density approximation (MMDA). In calculations of the vapor-liquid equilibria for non-ideal fluid mixtures, satisfactory results were obtained by the MMDA. When performing the vapor-liquid equilibrium calculations for systems with data over a wide range of temperatures, the MMDA also yielded reasonable results. Furthermore, the proposed method can be used to extend any existing accurate corresponding-states-type pure-fluid equation of state to mixtures.

How good is conformal solutions theory for phase equilibrium predictions?: Gibbs ensemble simulations of binary Lennard-Jones mixtures

It is generally believed that conformal solutions theory is valid only for mixtures with components having small differences in energy and size intermolecular potential parameters. To test this assumption, we have used the Gibbs ensemble Monte Carlo simulation technique to calculate phase diagrams of binary Lennard-Jones mixtures obeying the Lorentz—Berthelot combining rules for size parameter ratios equal to 0.5, 1.0 and 1.5 and for energy parameter ratios equal to 0.50, 0.66, 0.75 and 1.00. We generally find good agreement between simulation and theoretical predictions based on an equation of state for the pure Lennard-Jones fluid and the van der Waals one-fluid approximation. Our results establish the validity of conformal solutions theory for simple mixtures of much greater degree of asymmetry than previous investigations.

A modified van der Waals one-fluid approximation based on a simple perturbed hard-sphere equation of state

A modification of van der Waals one-fluid approximation is proposed. This is based on a simple perturbed equation of state which consists of the van der Waals type attractive term and the Carnahan-Starling (for pure fluids) type or the Mansoori-Carnahan-Starling-Leland (for mixtures) type repulsive term. The new mixing rules have been tested with computer simulation results for Lennard-Jones fluids. The results, especially in highly dense regions, are satisfactory.

Generalized equation of state for Lennard-Jones fluids—I. Pure fluids and simple mixtures

An extensive computer simulation (molecular dynamics) has been done for the calculation of PVT data of Lennard-Jones fluids and their binary equimolar mixture in a wide range of pressures and temperatures. The two pure fluids used form a somewhat artificial model which has either a weaker or stronger attractive interaction compared with argon, but is the same size as argon. Their Lorentz-Berthelot mixture is the now well-used LB-2-1 model. The obtained PVT data, together with existing data for argon, are used to establish optimized coefficients in a modified BWR-type equation of state used by Nicolas et al. This new generalized equation has been proved to reproduce PVT relations of both model and real fluids if optimized potential parameters are used for the latter. A preliminary account is given for the validity of van der Waals one-fluid approximation in the description of rather simple model mixtures such as LB-2-1.

Excess volumes and excess enthalpies of the mixtures tetrachloromethane + cycloalkane and trichloromethane + cycloalkane: Calculation in terms of equations of state of the van der Waals type

The excess volumes and excess enthalpies for equimolar compositions and a temperature of 298.15 K for the binary liquid mixture of tetrachloromethane and trichloromethane with cyclopentane, cyclohexane and cyclooctane were calculated in terms of equations of state of the van der Waals type, the Redlich-Kwong equation of state and an equation following from the Flory theory. The pure-component parameters were evaluated in three different ways. The equations of state with pure-component parameters determined from gas-liquid critical constants yielded poor agreement with experiment. The best agreement with experiment was yielded by the Snider-Herrington equation with the pure-component parameters evaluated from molar volumes and thermal pressure coefficients and by the Flory equation. The Frisch equation extended to mixtures by using the van der Waals one-fluid approximation gave a good agreement with experiment in case of mixtures of molecules of approximately the same size. The excess entropies and the values of temperature derivatives of excess functions were as well calculated and compared with available experimental data.

Equations of state of polydisperse hard-disc and hard-sphere systems

The influence of a “continuous” distribution of particle sizes on the equation of state of dispersion of hard-discs and hard-spheres is discussed. The van der Waals one-fluid approximation gives simple expressions for the change in pressure with degree of polydispersity. For hard-spheres at low volume fraction, good agreement is obtained with the exact Percus—Yevick result.

Thermodynamics of n-alkane + dimethylsiloxane mixtures. Part 1.—Gas–liquid critical temperatures and pressures

Gas–liquid critical temperatures Tcm have been determined for four mixtures: (i) n-hexane + hexamethyldisiloxane, (ii) n-octane + hexamethyldisiloxane, (iii) n-octane + octamethyltrisiloxane, and (iv) n-octane + 2,2,4,4-tetramethylpentane. Using a statistical model based upon the van der Waals one-fluid approximation, values of Tcm for each mixture are related to a parameter ζ which is proportional to the energy of interaction between the unlike molecular species. Gas–liquid critical pressures pcm are reported for mixtures (i), (ii) and (iii), and the results are discussed in terms of possible deviations from the Lorentz combining rule of collision diameters.