Binary Critical Points

PARAMETER ESTIMATION USING BINARY CRITICAL POINT DATA... 

It is assumed that there are available NCP experimental binary critical point data. These data include values of the pressure, Pc, the temperature, Tc, and the mole fraction, xc, of one of the components at each of the critical points for the binary mixture. The vector k of interaction parameters is determined by fitting the EoS to the critical data. In explicit formulations the interaction parameters are obtained by the minimization of the following least squares objective function ... 

Table 14.8 Interaction Parameter Values from Binary Critical Point Data...

Lattice coordination numbers (2) and the cell volumes (vjj) for both the pure components and mixture lattices are assumed to have the same value. The partition function for this ensemble can be formulated following Equation 2. It is assumed now that the partition function, far from the binary critical point can be approximated by its largest term. Since molecule segments and holes can distribute themselves non-randomly, the partition function must incorporate terms to account for this effect. The nonrandomness correction rjj... 

Hence substituting into (16.95) the values of the various terms given by (16.92), (16.93), (16.94) and (16.96) we find near the binary critical point... 

In (8.4.2) and (8.4.3) the conditions for a binary critical point are given in terms of the change of Gibbs energy on mixing. Those conditions can also be expressed in terms of the fugacity of either component. 

During the 1960s, the classical view of dynamics described above was seen to be incorrect both long-time and critical-point effects were observed in To a good approximation, the sound absorption coefficient in a fluid is determined by the shear and bulk viscosity coefficients. According to the classical theory, the viscosities should contain no critical anomalies at a binary critical point. However, it was observed that sound absorption shows an anomalous increase at a binary critical point, which indicates that the appropriate elements of must also possess a critical anomaly. Critical sound... 

Thus, we have seen how to calculate D and 17 near a binary critical point. The problem of calculating the thermal conductivity and 17 near a liquid-gas critical point is completely isomorphic to the problem discussed. These two problems are the most-studied examples of mode-mode coupling calculations of the critical behavior of transport coefficients. Future work will probably focus on the testing of the many assumptions upon which the results just obtained are based. We feel that Eq. (127) is soundly based, as discussed in Section 2. thus, the validity of Eq. (130), relating i7fc(s) to i7k(s), only depends on the approximations made when solving Eq. (127). 

Fig. 4 shows schematic pTx diagrams (upper row) and the corresponding p T) projections (lower row) for a binary system here p = total pressure, T = temperature, x = mole fraction. Most important for the classification of fluid phase equilibria is the shape of the different critical curves. A critical curve connects all binary critical points in the pTx space here the two coexisting fluid phases become identical, namely at the extreme values of the isothermal p x) or isobaric T x) sections. Details can be found in the earlier publications [2-6,10,12]. 

T-X diagrams were used for an investigation of ternary fluid phase behavior by the method of continuous topological transformation of ternary monovariant ciuves originated in the nonvariant points of binary subsystems with volatile component. In the case of fluid phase diagrams aU these nonvariant points are the binary critical points and file ternary monovariant curves are the critical curves, which join the binary critical points of the same nature or intersect at ternary nonvariant critical point if they start in file binary critical points of different nature. 

Binary critical points Ternary critical points... 

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