Equation Of State For Fluid Research Articles

High-Accuracy PVT Relationships for Compressed Fluids and Their Application to BET-like Modelling of CO2 and CH4 Adsorption

This paper presents a set of high-accuracy formulae enabling the evaluation of the compression factor, activity and cohesion energy of fluids at near-critical and super-critical temperatures, with reduced molar volumes ranging from 0.4. Such data are necessary in BET-like theoretical modelling of adsorption process. The proposed fluid state equation (PVT relationship) combines a theoretical description of the fluid entropy (based on a hard-sphere model) with cohesion energy relationships obtained via high-accuracy approximations of universal compression factor data and vapour-liquid equilibria. The resultant relationships are incorporated into a BET-like description of adsorption in materials of irregular microporous structure (LBET model). The set of formulae gathered together in this paper allows the possible effective calculation of adsorption isotherms at near- and super-critical temperatures relative to the pore structures. A multi-variant fitting of the LBET model to the empirical data is proposed to detect active constraints for multilayer adsorption and, hence, to obtain information on the structure of the pores. Application of the formulae to the analysis of methane and carbon dioxide adsorption onto an active carbon is discussed.

Equations of State for Fluids: Empirical Temperature Dependence of the Second Virial Coefficients

In this paper, an empirical dependence of the second virial coefficients is derived from equations of state. The second virial coefficient B2 is found to be a linear function of 1/T1+beta, where T is the temperature and beta is a constant and has different value for different substances. Excellent experimental supports to this relationship are reported for nonpolar fluids, polar fluids, heavy globular molecule fluids, and quantum fluid He-4.

A Perturbation Method for the Ornstein−Zernike Equation and the Generic van der Waals Equation of State for a Square Well Potential Model

We calculate the generic van der Waals parameters A and B for a square well model by means of a perturbation theory. To calculate the pair distribution function or the cavity function necessary for the calculation of A and B, we have used the Percus-Yevick integral equation, which is put into an equivalent form by means of the Wiener-Hopf method. This latter method produces a pair of integral equations, which are solved by a perturbation method treating the Mayer function or the well width or the functions in the square well region exterior to the hard core as the perturbation. In the end, the Mayer function times the well width is identified as the perturbation parameter in the present method. In this sense, the present perturbation method is distinct from the existing thermodynamic perturbation theory, which expands the Helmholtz free energy in a perturbation series with the inverse temperature treated as an expansion parameter. The generic van der Waals parameters are explicitly calculated in analytic form as functions of reduced temperature and density. The van der Waals parameters are recovered from them in the limits of vanishing density and high temperature. The equation of state thus obtained is tested against Monte Carlo simulation results and found reliable, provided that the temperature is in the supercritical regime. By scaling the packing fraction with a temperature-dependent hard core, it is suggested to construct an equation of state for fluids with a temperature-dependent hard core that mimicks a soft core repulsive force on the basis of the equation of state derived for the square well model.

Heat of explosion of commercial and brisant high explosives

Methods for determining the heat of explosion of high explosives (HEs) with ideal and nonideal processes of explosive decomposition are considered. It is shown that the heat of explosion is of significance for estimating the efficiency of commercial HEs and is used in the energetic characterization of the working capacity. The heat of explosion of brisant HEs is only part of the blast heat of explosion and is the heat content of gaseous detonation products during their isentropic expansion from the initial state to a certain expansion ratio (determined by experimental conditions). The heat of explosion can be obtained by thermodynamic calculations based on physically justified equations of state for fluids (gaseous detonation products in the chemical-reaction zone of the detonation wave in the supercritical state) and condensed nanocarbon phases (nanographite, nanodiamond, and liquid carbon). Experimental and calculated values of the heat of explosion are given. The thermodynamic calculation is inapplicable to commercial HEs because of the nonideal nature of their detonation. The heat of explosion of commercial HEs can be calculated using the Hess law. The heat of explosion of brisant HEs is not a measure of power. The power of HEs is characterized by the propellant performance. It is shown that even detonation velocity cannot be a measure of the power of HEs. The power and detonation parameters of brisant HEs are determined by the energy release density in unit volume of the chemical-reaction zone of the detonation wave and by the rate of energy release from the shock front rather than by the heat of explosion, which cannot be considered a universal characteristic.

Debye Fluid State Equation

A new form of a fluid state equation, based on a conceptual extrapolation from the Debye equation for the specific heat of solid materials is described. The Debye characteristic temperature, Θ, which is nominally a constant for solids, becomes a function of the fluid density ρ. Further assuming $${\Theta = c_{1}\rho^{2/3}(1 + c_{2} \rho + c_{3} \rho ^{2} + {\cdots})}$$ yields the conventional fluid virial equation in the high-T and low-ρ limits for a monatomic fluid. Additional terms must be added to describe (a) the compressibility of the dense subcooled fluid and (b) properties in the near-critical range. Discussion of the Gruneisen parameter and other factors is included. This Debye fluid theory was used as a state equation for 3He, continuous from 0.005 K to above room temperature.

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.

Gravitational radiation of stellar configurations consisting of incompressible fluid

This article discusses the gravitational radiation of rotating and oscillating stellar configurations with an incompressible fluid equation of state. The method used here makes it possible to determine the frequencies and amplitudes of the gravitational waves for arbitrary values of the central densities. At the densities corresponding to neutron stars, the major parameters of the gravitational radiation are consistent with previous results from more realistic models. Depending on the central density, stellar configurations with an incompressible fluid can emit gravitational waves over a wide range of frequencies, from 10−2 to 104 Hz.

Equation of state of inverse power fluids

A new equation of state for the inverse power, r − n potential, fluid is proposed. It is derived on the basis of the local scaling behaviour of its structural properties, without referring to any perturbative scheme, and therefore recourse to an effective hard sphere diameter. It is shown that the general formula for the compressibility factor can be expressed as the product of three functions. The first represents the hard-sphere equation of state at the same packing fraction, and the other two incorporate the effects of the potential softness, again as functions of density. Using computer simulation results, explicit forms for these soft parts have been established, to give an approximate analytic expression for the r − n fluid equation of state. Two different regions, characterized by positive and negative softness ‘compressibility’ have been found.

Equations of state for fluids containing alternating heteronuclear chain molecules

Statistical associating fluid theory-dimer (SAFT-D) and monomer–dimer mixture theory equations of state of linear homonuclear chain are extended to fluids containing alternating heteronuclear chain molecules separately. The proposed models account for the appropriate site–site correlation functions at contact. The modified equations of state show a good agreement with generalized Flory dimer theory and MD simulation data for small and medium size ratio of hard sphere diameters.

Response to “Comment on ‘Equations of state for fluids: The Dieterici approach revisited’ ” [J. Chem. Phys. 115, 1460 (2001)

A re-evaluation is reported of earlier calculations for vapor–liquid equilibria [R. J. Sadus, J. Chem. Phys. 115, 1460(E) (2001); 116, 5913 (2202)] using the Dieterici–Carnahan–Starling (DCS) equation of state. The results for liquid-phase densities and properties near the critical point are generally consistent with the original work. However, the recalculated vapor-phase densities and coexistence pressures are shifted to substantially higher values. The implications for real fluids are that the DCS equation is likely to yield accurate predictions of both near-critical equilibria and the temperature-density behavior of the liquid phase at the expense of poor agreement with experiment for both vapor densities and pressures.

Two-dimensional fluid equation of state for the entire range of surface densities

A precise equation of state of a monolayer for the entire range of surface densities is derived as the third approximation of the theory of excluded area using a database for the model of hard disks.

Scale invariance without inflation?

We propose a new alternative mechanism to seed a scale invariant spectrum of primordial density perturbations that does not rely on inflation. In our scenario, a perfect fluid dominates the early stages of an expanding, non-inflating universe. Because the speed of sound of the fluid decays, perturbations are left frozen behind the sound horizon, with a spectral index that depends on the fluid equation of state. We explore here a toy model that realizes this idea. Although the model can explain an adiabatic, Gaussian, scale invariant spectrum of primordial perturbations, it turns out that in its simplest form it cannot account for the observed amplitude of the primordial density perturbations.

Analytical Equation of State for Solid-Liquid-Vapor Phases

A simple analytical equation of state has been proposed for describing the phase behavior of three thermodynamic states (solid, liquid, and vapor) of matter. In terms of reduced parameters, it can be written as: $$P_{\text{r}} = \frac{{T_{\text{r}} }}{{V_{\text{R}} - b_{\text{R}} }}\left( {\frac{{V_{\text{R}} - d_{\text{R}} }}{{V_{\text{R}} - c_{\text{R}} }}} \right) - \frac{{a_{\text{R}} }}{{V_{\text{R}}^{\text{2}} }}.$$ Pr and Tr are reduced pressure and temperature with respect to the critical pressure (Pc) and temperature (Tc), respectively, while VR is a reduced molar volume defined as VR=PcV/RTc, where R is the universal gas constant. This may be regarded as an extension of the classical van der Waals's equation of state for fluid (liquid and vapor) only states. The four parameters, aR, bR, cR, and dR in this equation are free adjustable constants, and can be variable with temperature. The basic physical idea underlining the model is presented, and examples applied successfully to actual pure substances and mixtures are demonstrated. Also, applications to the hard-sphere model are examined. Further improvements, limitations, and possible applications of the present model are discussed.

Fluid state equation

A thermodynamic approach based on the analysis of an excluded volume results in a general state equation, including the Planck and van der Waals equations as particular cases, and a new precise state equation.

Pseudo-Pure Fluid Equations of State for the Refrigerant Blends R-410A, R-404A, R-507A, and R-407C

Pseudo-pure fluid equations of state explicit in Helmholtz energy have been developed to permit rapid calculation of the thermodynamic properties of the refrigerant blends R-410A, R-404A, R-507A, and R-407C. The equations were fitted to values calculated from a mixture model developed in previous work for mixtures of R-32, R-125, R-134a, and R-143a. The equations may be used to calculate the single-phase thermodynamic properties of the blends; dew and bubble point properties are calculated with the aid of additional ancillary equations for the saturation pressures. Differences between calculations from the pseudo-pure fluid equations and the full mixture model are on average 0.01%, with all calculations less than 0.1% in density except in the critical region. For the heat capacity and speed of sound, differences are on average 0.1% with maximum differences of 0.5%. Generally, these differences are consistent with the accuracy of available experimental data for the mixtures, and comparisons are given to selected experimental values to verify accuracy estimates. The equations are valid from 200 to 450 K and can be extrapolated to higher temperatures. Computations from the new equations are up to 100 times faster for phase equilibria at a given temperature and 5 times faster for single-phase state points given input conditions of temperature and pressure.

The Dieterici alternative to the van der Waals approach for equations of state: second virial coefficients

Historically, the development of equations of state for fluids has almost invariably followed the lead of the van der Waals equation by simply adding together contributions from intermolecular repulsion and attraction. Recently an alternative approach, first suggested by Dieterici (Ann. Phys. Chem. Wiedemanns Ann.,1899, 69, 685), has been revised (R. J. Sadus, J. Chem. Phys., 2001, 115, 1460) with the benefit of modern developments in equations of state. In contrast to the traditional van der Waals-type equations of state, the Dieterici approach results in an equation of state that is the product of a repulsive term with an exponential attractive term. This formulation significantly enhances the accuracy of the prediction of vapour–liquid equilibria, particularly in the vicinity of the critical point. In this work, the ability of the equation to predict second virial coefficients is investigated. A comparison is also reported with traditional van der Waals-type equations of state. The results indicate that the Dieterici approach yields superior prediction of the second virial coefficients.

Book Review: Equations of State for Fluid and Fluid Mixtures, Parts I and II. J. V. Sengers, R. F. Kayser, and H. J. White, Jr. Elsevier Science B.V., The Netherlands, 2000

Book Review: Equations of State for Fluid and Fluid Mixtures, Parts I and II. J. V. Sengers, R. F. Kayser, and H. J. White, Jr. Elsevier Science B.V., The Netherlands, 2000

On the thermodynamic properties of the Lennard-Jones fluid

An analytical scheme for the evaluation of the compressibility factor of a simple fluid is presented. It is based on the clasical perturbation theory and on a recent (analytical) approximation for the radial distribution function of the hard-sphere fluid. The scheme, which provides, in the case of the Lennard-Jones fluid, explicit expressions for both structural and thermodynamic quantities in a closed form, requires the hard-sphere fluid equation of state as the sole input. Using the Carnahan–Starling equation of state for the hard-sphere reference fluid, the prediction of the critical point as well as the behavior of the pressure of the Lennard-Jones fluid are an improvement in relation to previous work and compare rather well with recent numerical simulations. The same applies to the radial distribution function computed with the present scheme and the Weeks–Chandler–Andersen approach. From a knowledge of the freezing and melting transitions in the hard-sphere system, the liquid and solid branches of the reduced temperature vs. reduced density curve at coexistence for the Lennard-Jones fluid are simply obtained.

Equations of state for fluids: The Dieterici approach revisited

In 1873, van der Waals proposed a simple equation of state that qualitatively described the phase behavior of fluids. Since then, the principles behind the van der Waals equation have been used and refined countless times in the quest for an accurate equation of state. Despite the enormous amount of work reported, the goal of a simple and accurate equation of state for even relatively simple systems, such as monatomic or polyatomic gases, has proved elusive. Therefore, the analysis of phase equilibria with equations of state is more often than not an exercise in data fitting rather than genuine prediction. In this work, we revisit the early work of Dieterici. When coupled with modern developments in equations of state, this little used approach has the potential of generating useful equations of state. To illustrate the usefulness of the Dieterici formula, we use it to derive a simple equation of state based on the Carnahan–Starling hard-sphere term and van der Waals interactions. This simple approach yields more accurate predictions of the phase co-existence of fluids than the traditional additive approach used to develop equations of state.

Chemical potentials of chain solutes in hard body fluids

Abstract Monte Carlo simulations and analytical statistical mechanical expressions are used to predict the free energy required to dissolve hard chains containing up to ten beads in diatomic fluids, over a wide range of solute-solvent sphere diameter ratios and solvent densities. The results are compared with analytical expressions derived from the Bonded Hard Sphere (BHS) and Scaled Particle Theory (SPT) mixed hard body fluid equations of state. Although both theoretical expressions agree very well with simulation results at lower densities, BHS predictions are found to better agree with simulation results at high densities (particularly for small solute particles). Both the simulation and theoretical results imply a strictly linear dependence of solute cavity formation free energy on chain length, in a solvent of a given molecular size and density. The results are used to quantify the influence of both solute and solvent shape on solute cavity formation free energy.