One-fluid Theory Research Articles

Excess enthalpies of { xN 2 + (1 − x)CO}(I) at 83.82 K: experiment and theory

The excess molar enthalpies H m E {xN 2 +(1−x)CO}(1) have been determined at 83.82 K using a low-temperature batch calorimeter. The value of H m E (x=0.5) at mixture saturation pressure is (41.2 ± 1.1) J·mol −1 . The results for H m E are in good agreement with the values derived from published phase equilibria. The ability of two theoretical methods to predict the excess enthalpy was tested. The simple van der Waals one-fluid theory gives good results; however. a spherical reference-based perturbation theory is found to give an even better prediction of H m E (within 5.1 per cent at x = 0.5).

Comparison of two hard-sphere reference systems for perturbation theories for mixtures

The Carnahan—Starling equation of state for hard spheres can be extended to mixtures using either a one-fluid theory, or the generalization of scaled-particle (or Percus—Yevick theory) proposed by Boublik and by Mansoori and coworkers. The two reference systems are combined with a perturbation term of the van der Waals form; they are then used to correlate the phase behavior of binary mixtures of nonpolar molecules differing significantly in molecular size. In each case, one adjustable binary parameter ( a 12) is used to correlate vapor—liquid equilibria over the entire composition range. Predicted Henry's constants and liquid densities for the saturated mixture are compared with experiment. The Boublik—Mansoori hard-sphere-mixture equation is superior to the Carnahan—Starling One-Fluid theory, expecially in the dilute region.

Calculation of phase equilibria in nitrogen-ethane mixtures by extended corresponding states

The phase diagram for the nitrogen-ethane mixture is determined via the extended corresponding states one-fluid theory. We support the contention that this mixture is a Type III mixture with a three-phase (liquid-liquid-vapour) line. This line can be calculated extremely well if binary interaction factors are fitted to the three-phase data. Without further adjustment, the liquid-liquid equilibrium (LLE) and vapour-liquid equilibrium (VLE) for the system are predicted satisfactorily. The parameters used, however, are not sufficient to predict satisfactory VLE data near a mixture critical line. This conclusion is in agreement with our previous work.

Resistive ballooning modes in high-beta tokamaks

Resistive ballooning mode stability is examined using one-fluid, two-fluid, and kinetic theories to determine the domain of validity of the resistive-fluid theories in the high-beta Doublet III tokamak. In general, it is found that the requirements for the validity of the resistive-fluid theories in Doublet III are only satisfied on the cold, outermost edge of the plasma with temperatures T ≤ 25 eV. In the domain of validity, the two-fluid and kinetic theories are qualitatively the same and indicate that the dominant effect is parallel resistivity with small corrections from perpendicular resistivity, fluid compression, thermal conduction, and ion collisional viscosity. The generic role of resistive ballooning modes in tokamaks and the implications for anomalous transport are also discussed.

ChemInform Abstract: SPEED OF SOUND, MOLAR VOLUME, AND MOLAR ISOBARIC HEAT CAPACITY FOR BINARY LIQUID MIXTURES: ANALYSIS IN TERMS OF VAN DER WAAL′S ONE‐FLUID THEORY

Chemischer InformationsdienstVolume 16, Issue 17 Article ChemInform Abstract: SPEED OF SOUND, MOLAR VOLUME, AND MOLAR ISOBARIC HEAT CAPACITY FOR BINARY LIQUID MIXTURES: ANALYSIS IN TERMS OF VAN DER WAAL′S ONE-FLUID THEORY M. K. KUMARAN, M. K. KUMARANSearch for more papers by this authorG. C. BENSON, G. C. BENSONSearch for more papers by this authorP. J. D'ARCY, P. J. D'ARCYSearch for more papers by this authorC. J. HALPIN, C. J. HALPINSearch for more papers by this author M. K. KUMARAN, M. K. KUMARANSearch for more papers by this authorG. C. BENSON, G. C. BENSONSearch for more papers by this authorP. J. D'ARCY, P. J. D'ARCYSearch for more papers by this authorC. J. HALPIN, C. J. HALPINSearch for more papers by this author First published: April 30, 1985 https://doi.org/10.1002/chin.198517071AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume16, Issue17April 30, 1985 RelatedInformation

Van der waals one-fluid theory : justification and generalisation

We describe an approach to van der Waals one-fluid theory based on thermodynamic consistency and propose a method for generalising it to non-conformal fluids.

Speed of sound, molar volume, and molar isobaric heat capacity for binary liquid mixtures: analysis in terms of van der Waals's one-fluid theory

The speed of sound and excess molar isobaric heat capacity at 298.15 K, and the excess molar volume at 303.15 K are reported for ( n-dodecane + n-hexane). The results, in combination with the excess molar volume at 298.15 K published previously, are used to obtain the interaction parameters a 12 and b 12 for the mixture treated as a pure fluid obeying a generalized van der Waals's equation of state. Similar analyses, using results from our previous investigations, are presented for (di- n-propylether + n-heptane) and (benzene + cyclohexane).

The Wave Model of Mesothermal Plasma near Wakes and Korteweg-de Vries Equation

The stationary two-dimensional (x, z) near wakes behind a flat-based projectile which moves at a constant mesothermal speed (V∞) along a z-axis in a rarefied, fully ionized, plasma is studied using the wave model previously proposed by one of the authors (VCL). One-fluid theory is used to depict the free expansion of ambient plasma into the vacuum produced behind a fast-moving projectile. This nonstationary, one-dimensional (x, t) flow which is approximated by the K-dV equation can be transformed, through substitution, t=z/V∞, into a stationary two-dimensional (x, z) near wake flow seen by an observer moving with the body velocity (V∞). The initial value problem of the K-dV equation in (x, t) variables is solved by a specially devised numerical method. Comparisons of the present numerical solution for the asymptotically small and large times with available analytical solutions are made and found in satisfactory agreements.

The derivatives along the critical line in a binary mixture near the critical points of pure components in one-fluid theory

Abstract Analytic expressions are obtained for all the first derivatives along the critical line in a binary mixture, near the critical points of pure components, in terms of the one-fluid Van der Waals theory. The conditions for the existence of the gas-gas equilibria of the first kind are shown and discussed for the reference substance represented by the accurate NBS equation of state of argon and by the Van der Waals and Guggenheim equations of state.

On the calculation of critical liquid-vapor lines of binary mixtures

The critical lines of binary mixtures of conformal fluids are calculated on the basis of the one-fluid Van der Waals theory. The conditions for the existence of the gas/gas equilibrium of the first and second type are shown and discussed. The analytical expressions for partial derivatives of Gibbs free energy with respect to concentration, up to the third order, are given in the appendix.

Henry's constants and second virial coefficients from perturbed-hard-chain theory

The perturbed-hard-chain theory for pure fluids is extended to asymmetric mixtures for two limiting regions of composition and density: Henry's constants H and second virial cross coefficients B 12. The extension is made through a modified one-fluid theory approximation which accounts for non-randomness of the mixture. Final equations for H and B 12 require three pure-component parameters but only one binary constant, k 12, characteristic of each molecular pair; k 12 is the same for both H and B 12. The approximate partition function developed here is applicable to multi-component mixtures over the entire fluid density region and appears to be useful for mixtures of nonpolar (or slightly polar) molecules of arbitrary size and shape.

On the derivation and extension of the uniquac equation

Abstract The UNIQUAC equation is derived by phenomenological arguments based on a two-fluid theory. This derivation is free of the inconsistencies which arise when a lattice one-fluid theory is used to derive UNIQUAC or any other local-composition equation. The essential step in the derivation is the adoption of Wilson's assumption that local compositions can be related to overall compositions through Boltzmann factors. In UNIQUAC, the energy terms in the Boltzmann factors are assumed identical to those in the excess energy of mixing. When the assumption of identity is replaced by the much less stringent assumption of proportionality, a three-parameter UNIQUAC equation is derived. This equation often gives a better fit of experimental data whenever all three binary paramters are freely adjusted. Upon assigning a universal value to the third parameter, only marginal improvement is obtained.

Excess Volumes of Mixtures of Acetone, Chloroform, Carbon tetrachloride, 1,4-Dioxane and Tetrahydrofuran with o-Dichlorobenzene

Abstract Excess volumes of mixtures of o-dichlorobenzene with acetone, chloroform, carbon tetrachloride, 1,4-dioxane, and tetrahydrofuran have been measured at 293.15 K as a function of composition. The excess volume data have been used to check the one-fluid theory of mixtures with van der Waals's and Guggenheim's equations of state.

Viscous solutions of the two-fluid solar wind equations

The two-fluid equations describing the ideal, steady, viscous solar wind are examined, and supersonic solutions are sought in which the electron and ion temperatures vary as inverse powers of the radial distance from the Sun. Just two solutions are found, and these are analogous to those found by Whang et al. (1966) and Dahlberg (1970) in one-fluid theory.

On the effects of viscosity in one-fluid solar wind theory

In order to examine the influence of small viscous effects on the in viscid solutions of Parker, Whang & Chang, and Durney the ideal, steady, one-fluid solar wind equations are examined in the limit: Reynolds number → ∞, Prandtl number → 0 (i. e. viscosity → 0, thermal conduction fixed). The method of matched asymptotic expansions is employed, and it is found that the inclusion of viscosity has considerable effect on the solutions far from the Sun. Small viscous terms cause the velocity to drop below the supersonic value of the Parker solution to subsonic values through a diffuse shock, the temperature still following the variation ∝ r -2/7 at large dis­tances r . The result of small viscous effects on the Whang & Chang solution is that the temperature changes from a variation ∝ r -2/5 to follow the r -2/3 law of Whang, Liu & Chang, the velocity remaining supersonic, as r → ∞. The Durney solution is found to be the leading order part of a solution that is uniformly valid as r → ∞ in the limit considered.

On the continuum theory of the two-fluid solar wind for small mass ratio

The continuum theory for the two-fluid solar wind is considered. The fluid is assumed to be a fully ionized neutral plasma of electrons and protons which is compressible, viscous and heat conducting with a constant Prandtl number and a viscosity proportional to (temperature) ω , ω > 1. The gas is under the influence of a gravitational field centred on the Sun. It is assumed that the bulk velocity (at any point) is the same for both electrons and protons, but that an energy transfer can occur between the two species due to binary (Coulomb) collisions. The equations are non-dimensionalized and it is shown that the natural parameter to use in the construction of an asymptotic solution is the mass ratio. The limit mass ratio → zero corresponds to the small Prandtl number limit for the one-fluid theory developed by Johnson (1975). By using the method of matched asymptotic expansions, a solution is constructed that starts from the base of the corona and extends out to a diffuse shock layer. The results obtained exactly parallel the one-fluid theory and many details are identified and absorbed into this analysis. It is shown how the temperatures in the corona eventually become the well-known behaviours: r -2/7 (electrons), r -6/7 (protons) when ω = 5/2 and r is the radial coordinate. However, the continuum theory will probably have failed in the shock layer region - the more so since this occurs at about 100 light years distance - and so further mathematical details are omitted. The numerical estimates given here compare tolerably well with the observed data and very favourably with other work on the same equations.

Effects of Molecular Size and Shape in Solution Thermodynamics

The one-fluid corresponding states theory is used to predict excess thermodynamic quantities of a mixture of spherical molecules of different e and σ. Two prescriptions of ‘van der Waals type’, and a third used by Flory, give the parameters e m and σ m of the solution. Comparison of the results is made with Monte Carlo calculations of Singer and Singer and the Snider–Herrington theory, and also with experimental features of simple and polyatomic spherical molecule mixtures. For each prescription an intuitive discussion is given of contributions to the excess quantities arising from (a) the energetic weakness of (1–2) contacts relative to (1–1) and (2–2) and (b) dissimilarity of free volume between the components. Two free volume contributions are distinguished. One depends on the second derivative with respect to T of the energy, volume, etc. of the reference liquid. The other occurs only in V E where it is of major importance and depends on d V /d T and a dissimilarity of molecular energy/volume parameters of the components. Recent experiments indicate two effects outside current theory. For systems containing anisotropic molecules, there is a third contribution to excess quantities (c), due to short-range orientational order or correlations of molecular orientations in one or both components. Mixing liquids of differing degrees of order usually brings about a net decrease of order, and hence positive contributions in Δ H M and Δ S M . The effect is illustrated by Δ H M values of branched and normal alkane mixtures at 25°, the temperature dependence of Δ H M for such systems, and the widely different. Δ H M of cis and trans dimethylcyclohexanes mixed with the orientationally ordered n -C 16 . The properties of systems containing a nematic liquid crystal (MBBA) and an alkane are sensitive to the alkane shape and indicate that MBBA molecules correlate their orientations with normal, but not with highly branched alkanes. The fourth contribution (d) is seen in systems involving alkanes of the same molecular shape but different degrees of steric hindrance of torsional oscillations. Heats of mixing point to a thermodynamic effect associated with a coupling of the molecular motions of the components.

Equation of state of mixtures of simple fluids at high pressures

Recently Lee and Levesque have extended the Weeks-Chandler-Andersen pure fluid perturbation theory to mixtures and have compared the results to the Leonard-Henderson-Barker mixture theory. The results seem to favour the Leonard-Henderson-Barker theory. This and other previous comparisons of mixture theories have been mostly confined to the study of ‘zero pressure’ thermodynamic properties. In this paper we compare the Lee-Levesque, Leonard-Henderson-Barker and the van der Waals one-fluid theories to high pressure equation of state data for helium-xenon mixtures. This system is modelled by a binary mixture of Lennard-Jones fluids and the hard sphere reference system is characterized by the Grundke-Henderson hard sphere mixture radial distribution function. The Lee-Levesque theory compares favourably with experimental equation of state data up to pressures of 2000 atmospheres. The Leonard-Henderson-Barker and van der Waals one theories are satisfactory. Although the van der Waals one theory yields the poorest results, it does offer the advantage of having the greatest ease of computation. Previous theoretical and Monte Carlo calculations of mixture properties have assumed the geometric mean rule for the mixed interaction energy parameter, ε 12, with consequent disagreement with experimental results. We point out that ε 12 can be determined from mixed second virial coefficient data and use such improved determinations of ε 12. We show that this method yields significantly improved theoretical predictions.

Perturbation theory for mixtures of polar fluids

The thermodynamic perturbation theory of Stell, Rasaiah and Narang is generalized to the case of multi-component Stockmayer fluids. The effects of polarization by the permanent dipoles is included to first order and the perturbation series is summed approximately to all orders in the dipole moments by means of two Pade approximants. The two-body and triplet terms in the expansion have been evaluated by Monte Carlo integration for a specific choice of the reference Lennard-Jones mixture and the results are used to study systematically the effect of dipolar interactions on excess thermodynamic properties. The utility of a one-fluid theory based on the van der Waals model is investigated and it is shown that the approach is useful for obtaining semi-quantitative information on mixtures of weakly polar fluids. The special case of mixtures of hydrogen chloride and xenon is considered and it is shown that the potential model used is inadequate to account for the large deviations from ideality which are observed...

MOLECULAR SHAPE FACTORS FOR AMMONIA AND THEIR APPLICATION TO VAPOR-LIQUID EQUILIBRIUM CALCULATIONS

The empirical molecular shape factors for ammonia relative to methane as a reference were correlated for 0.7≤Tr≤, 1.4 and 0<Pr≤30. They could well represent the compressibility factors and the fugacity coefficients of ammonia. On the basis of the corresponding-states principle, the vapor-liquid equilibria of binary systems containing ammonia were predicted by using pseudo-potential parameters, obtained by the van der Waals one-fluid theory coupled with molecular shape factors. Good results were obtained except in high pressure ranges.