Crossover equation of state

Figure A2.5.26. Molar heat capacity C y of a van der Waals fluid as a fimction of temperature from mean-field theory (dotted line) from crossover theory (frill curve). Reproduced from [29] Kostrowicka Wyczalkowska A, Anisimov M A and Sengers J V 1999 Global crossover equation of state of a van der Waals fluid Fluid Phase Equilibria 158-160 532, figure 4, by pennission of Elsevier Science.

Kostrowicka Wyczalkowska A, Anisimov M A and Sengers J V 1999 Global crossover equation of state of a van der Waals fluid Fluid Phase Equilibria 158-160 523-35... 

Kiselev, S.B. Ely, J.F. Lue, L. Elliott, J.R. Computer simulations and crossover equation-of-state of square-well fluids. Fluid Phase Eq. 2002, 200, 121-145. 

Kiselev, S.B. (1998) Cubic crossover equation of state, Fluid Phase Equilibria 147, 7-23. 

The representation of pVTx properties of mixtures by using the cubic EOS is still a subject of active research. Kiselev (1998), Kiselev and Friend (1999), and Kiselev and Ely (2003) developed a cubic crossover equation of state for fluids and fluid mixtures, which incorporates the scaling laws asymptotically close to the critical point and is transformed into the original classical cubic equation of state far away from the critical point. Anderko (2000) and Wei and Sadus (2000) reported comprehensive review of the cubic and generalized van der Waals equations of state and their applicability for modeling of the properties of multicomponent mixtures. 

Parametric crossover equations of state for aqueous solutions in the critical and supercritical regions... 

This crossover equation of state (CREOS) (2.61)-(2.64) has been applied for dilute aqueous NaCl solutions (Belyakov et al, 1997), aqueous toluene (Kiselev et ai, 2002) and n-hexane (Abdulagatov et al., 2005) mixtures, and H2O + NH3 (Kiselev and Rainwater, 1997) solution near flie critical point of pure water and supercritical conditions. The values of the parameters were found from fit of equation... 

The densities of all data points were recalculated from the measured temperatures and pressures with a recently developed equation of state (Tiesinga et al. 1994). This equation consists, for temperatures and densities in the critical region, of a crossover equation of state based on a six-term Landau expansion in parametric form as proposed by Luettmer-Strathmann et al. (1992) and, for outside that region, of a global equation of state proposed by Stewart Jacobsen (1989). The values that were adopted for the critical temperature, pressure and density are... 

The first step in quantitative description of pure polyamorphic fluid is a selection of the model that can qualitatively describe a possible multiplicity of critical points in wide range of temperatures and pressures. A great many of explanations of multicriticality in monocomponent fluids (perturbation theory models semiempirical models lattice models, two-state models, field theoretic models, two-order-parameter models, and parametric crossover model has been disseminated after the pioneering work by Hemmer and Stell Here we test more extensively the modified van der Waals equation of state (MVDW) proposed in work and refine this model by introducing instead of the classical van der Waals repulsive term a very accurate hard sphere equation of state over the entire stable and metastable regions... 

The thermodynamic behavior of fluids near critical points is drastically different from the critical behavior implied by classical equations of state. This difference is caused by long-range fluctuations of the order parameter associated with the critical phase transition. In one-component fluids near the vapor-liquid critical point the order parameter may be identified with the density or in incompressible liquid mixtures near the consolute point with the concentration. To account for the effects of the critical fluctuations in practice, a crossover theory has been developed to bridge the gap between nonclassical critical behavior asymptotically close to the critical point and classical behavior further away from the critical point. We shall demonstrate how this theory can be used to incorporate the effects of critical fluctuations into classical cubic equations of state like the van der Waals equation. Furthermore, we shall show how the crossover theory can be applied to represent the thermodynamic properties of one-component fluids as well as phase-equilibria properties of liquid mixtures including closed solubility loops. We shall also consider crossover critical phenomena in complex fluids, such as solutions of electrolytes and polymer solutions. When the structure of a complex fluid is characterized by a nanoscopic or mesoscopic length scale which is comparable to the size of the critical fluctuations, a specific sharp and even nonmonotonic crossover from classical behavior to asymptotic critical behavior is observed. In polymer solutions the crossover temperature corresponds to a state where the correlation length is equal to the radius of gyration of the polymer molecules. A... 

We shall here elucidate a procedure developed by Kostrowicka Wycza-Ikowska et al. for applying the crossover theorry described in Section 6 to the equation of state of van der Waals [65, 66]. 

We conclude by noting that while it has been shown that crossover versions of classical equations of state, including SAFT-like equations, typically provide accurate predictions for vapour-liquid equilibria, pf/j "2,261 derivative properties " " of both pure fluids and their mixtures close to and far from the critical region, such methods have yet to be applied to the study of liquid-liquid equilibria with the SAFT approach. 

The viscosity of R134a on the saturation line calculated by equation (14.82) is listed in Table 14.23, where subscripts 1 and v indicate values of the saturated liquid and saturated vapor, respectively. The viscosity as a function of temperature and pressure is given in Table 14.24. The KLSS equation uses densities calculated by the noodified BWR equation of state by Huber McLinden (1992) combined with a crossover for the critical region developed by Tang etal. (1991). However, the difference in the calculated viscosity is expected to be small when a different equation of state is used, except in the critical region. 

Llovell, F. Vega, L.F. (2007). Phase equilibria, critical behavior and derivative properties of selected n-alkane/n-alkane and n-alkane/l-alkanol mixtures by the crossover soft-SAFT equation of state. /. Supercrit Fluids 41,204-216. 

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