S. B. Kiselev

Simplified crossover SAFT equation of state for pure fluids and fluid mixtures

A simplified modification of the crossover statistical associating fluid theory (SAFT) EOS is used to describe thermodynamic properties of pure fluids and binary mixtures over a wide range of parameters of state including the nearest vicinity of the critical point. For pure fluids, the simplified crossover (SCR) SAFT model contains only three adjustable parameters but allows an accurate prediction of the critical parameters of pure fluids and yields a better representation of the thermodynamic properties of pure fluids than the original SAFT equation of state. For binary mixtures, simple mixing rules with only one adjustable parameter are used. A comparison is made with experimental data for pure refrigerants R12, R22, R32, R125, R134a, R143a, and mixtures R22CR12, R32CR134a and R125 C R32 in the one- and two-phase regions. The SCR SAFT EOS reproduces the saturated pressure data with an average absolute deviation (AAD) of about 1.1% and the saturated liquid densities with an AAD of about 0.9%. In the one-phase region, the SCR SAFT equation represents the experimental values of pressure with an AAD of about 2.2% in the range of temperatures and density bounded by T T c and 2c.

Generalized corresponding states model for bulk and interfacial properties in pure fluids and fluid mixtures

We have formulated a general approach for transforming an analytical equation of state (EOS) into the crossover form and developed a generalized cubic (GC) EOS for pure fluids, which incorporates nonanalytic scaling laws in the critical region and in the limit ρ→0 is transformed into the ideal gas equation EOS. Using the GC EOS as a reference equation, we have developed a generalized version of the corresponding states (GCS) model, which contains the critical point parameters and accentric factor as input as well as the Ginzburg number Gi. For nonionic fluids we propose a simple correlation between the Ginzburg number Gi and Zc, ω, and molecular weight Mw. In the second step, we develop on the basis of the GCS model and the density functional theory a GCS-density functional theory (DFT) crossover model for the vapor–liquid interface and surface tension. We use the GCS-DFT model for the prediction of the PVT, vapor–liquid equilibrium (VLE) and surface properties of more than 30 pure fluids. In a wide range...

A crossover equation of state for associating fluids

In this work we extend the crossover (CR) modification of the statistical-associating-fluid-theory (SAFT) equation of state (EOS), recently developed and applied for non-associating systems [Ind. Eng. Chem. Res. 38 (1999) 4993] to associating fluids. Unlike the previous crossover EOS that was based on the parametric linear model for the universal crossover function Y, the new CR SAFT EOS is based on Fisher’s recent parametric sine model. This model can be extended into the metastable region and gives analytically connected van der Waals loops in the two-phase region. We show that for associating fluids the new CR SAFT EOS not only yields a better description of the PVT and VLE properties of fluids in the critical region, but also improves the representation of the entire thermodynamic surface. A comparison is made with experimental data for pure normal methanol, ethanol, propanol, butanol, pentanol, and hexanol in the one- and two-phase regions. The CR SAFT EOS reproduces the saturated pressure and liquid density data with an average absolute deviation (AAD) of about 1%. In the one-phase region, the CR SAFT equation represents the experimental values of pressure with an AAD less than 1% in the critical and supercritical region and the liquid densities with an AAD of about 2%.

Kinetic boundary of metastable states in superheated and stretched liquids

A physical boundary of metastable states – kinetic spinodal is introduced as a locus where the mean time of formation of a critical nucleus becomes shorter than a characteristic time governing the decay of fluctuations to local equilibrium. To extend this definition at negative pressures a new thermodynamic relation for the nucleation barrier has been obtained. The kinetic spinodal in this approach is completely determined by the equation of state and by the surface tension of the liquids. Starting from the critical point the kinetic spinodal first traces the limit of stability of superheated liquid, then passes through the negative pressures, thus defining the limit of stability for stretched liquid. For a comparison of the results of calculations with the experimental data in the superheated and stretched fluids the thermodynamic properties of methane and water in the metastable region are considered.

Crossover SAFT Equation of State and Thermodynamic Properties of Propan-1-ol

In this work we have developed a new equation of state (EOS) for propan-1-ol on the basis of the crossover modification (CR) of the statistical-associating-fluid-theory (SAFT) EOS recently developed and applied to n-alkanes. The CR SAFT EOS reproduces the nonanalytical scaling laws in the asymptotic critical region and reduces to the analytical-classical SAFT EOS far away from the critical point. Unlike the previous crossover EOS, the new CR SAFT EOS is based on the parametric sine model for the universal crossover function and is able to represent analytically connected van der Waals loops in the metastable fluid region. The CR SAFT EOS contains 10 system-dependent parameters and allows an accurate representation of the thermodynamic properties of propan-1-ol over a wide range thermodynamic states including the asymptotic singular behavior in the nearest vicinity of the critical point. The EOS was tested against experimental isochoric and isobaric specific heats, speed of sound, PVT, and VLE data in and beyond the critical region. In the one-phase region, the CR SAFT equation represents the experimental values of pressure with an average absolute deviation (AAD) of less than 1% in the critical and supercritical regions and the liquid densities with an AAD of about 1%. A corresponding states principle is used for the extension of the new CR SAFT EOS for propan-1-ol to higher n-alkanols.

Parametric crossover model and physical limit of stability in supercooled water

The two-critical point (TCP) scenario for supercooled water was tested against experimental data with the crossover equation of state (CR EOS) based on the fundamental results of the fluctuation theory of critical phenomena. The CR EOS predicts a second critical point, CP2, in supercooled water with the parameters Tc2=188 K, ρc2=1100 kg⋅m−3, Pc2=230 MPa, and represents the experimental values of the isothermal compressibility in liquid and supercooled water with an average absolute deviation (AAD) of about 1.7% in the pressure range P=0.1–190 MPa, the liquid densities with an AAD of about 0.1%, and the heat capacity with an AAD of about 1.0% in the temperature range 245 K⩽T⩽300 K. The CR EOS also allows calculation of the physical limit of stability in supercooled water—the kinetic spinodal, TKS. At all pressures P<190 MPa, the kinetic spinodal calculated with the CR EOS lies below the homogeneous nucleation temperature, TH, thus satisfying a physically obvious condition TKS⩽TH. We show that the CP2 is al...

Computer simulations and crossover equation of state of square-well fluids

We develop a crossover equation of state (EOS) for square-well fluids with varying well width. This equation yields the exact second and third virial coefficients, and accurately reproduces first-order (high-temperature) perturbation theory results. In addition, this EOS yields the correct scaling exponents near the critical point. We perform extensive new molecular dynamics and Monte Carlo simulations in the one-phase region for varying well widths of λ = 1.5, 2.0, and 3.0. We fit the parameters of our EOS to one-phase and two-phase thermodynamic data from our simulations and those of previous researchers. The resulting EOS is found to represent the thermodynamic properties of these square-well fluids to less than 1% deviation in internal energy and density and 0.1% deviation in vapor pressure.

Curvature effect on the physical boundary of metastable states in liquids

The physical boundary of metastable states, the kinetic spinodal, is introduced as a locus where the lifetime of metastable state becomes shorter than a relaxation time to local equilibrium. The theory does not contain any adjustable parameters. If the surface tension is known, the kinetic spinodal is completely determined by the equation of state only. The curvature effect on the surface tension and nucleation barrier is considered and a general, curvature-corrected, equation for the kinetic spinodal is developed. The theory was tested against experimental data for the homogeneous nucleation limit of superheated, stretched, and supercooled water. In all cases, good agreement between theoretical predictions and experimental data was achieved. We find that in water, the Tolman length is negative and the curvature effect increases the surface tension and the nucleation barrier. The glass transition in supercooled water is also discussed. The high-temperature limit for glassy states is introduced as a second root of the kinetic equation in supercooled fluids.

Molecular dynamic simulations and global equation of state of square-well fluids with the well-widths from λ = 1.1 to 2.1

We present the results of extensive new molecular dynamic (MD) simulations in the one-phase region for square well fluids with well widths λ = 1.10, 1.15, 1.20, 1.25, 1.375, 1.50, 1.75, 1.90, 2.0, and 2.10. These data have been used in developing a crossover equation of state (CR EOS) for square-well fluids with well widths 1.1 ≤ λ ≤ 2.1. The CR EOS incorporates non-analytic scaling laws in the critical region, and in the limit of low densities yields the exact second and third virial coefficients. Also in the high-temperature region, it reproduces first-order perturbation theory results. The CR EOS was tested against our new MD simulations, and earlier MD and Monte-Carlo (MC) simulations reported by other authors as well. Excellent agreement between calculated values and simulation data for all SW fluids is observed. In combination with the density-functional theory, the CR EOS is also capable of reproducing surface tension simulations with high accuracy. Application of the CR EOS for solid–liquid equilibrium calculations in combination with the Lennard–Jones and Devonshire cell model for the solid phase, is also discussed.

Physical Limit of Stability in Supercooled Liquids

The kinetic spinodal (KS) in supercooled liquids, similar to the KS in superheated and stretched liquids, has been introduced as a locus where the mean time of formation of a critical nucleus becomes shorter than a relaxation time to local equilibrium. If the surface tension of the solid–liquid interface is known, the kinetic spinodal is completely determined by the equation of state of the supercooled liquid. The theory was tested against experimental data for the surface tension and the homogeneous nucleation limit for supercooled water. Reasonably good agreement between theoretical predictions and experimental data was observed. A prediction of the high-temperature limit for glass transitions is also discussed.